COMPUTACIÓN SIMBÓLICA - ugr.esanillos/textos/pdf/2016/ComputacionSimbolica.pdf · 2 CAP. I. COLORACIÓN DE GRAFOS 1. Nociones de grafos Antes de continuar deﬁnamos lo que es un

COMPUTACIOacuteN SIMBOacuteLICA

MARIacuteA JOSEacute ZAPATA

Departamento de Aacutelgebra

Universidad de Granada 2016

Director Prof Pascual JaraDepartamento de Aacutelgebra

Trabajo de fin de grado

A mi padre

Agradecimientos

A mi tutor por su inestimable ayuda y paciencia

Introduccioacuten

En los uacuteltimos antildeos las matemaacuteticas discretas han ganado popularidad debido a sus muacuteltiples aplica-ciones dentro de las distintas aacutereas tecnoloacutegicas Una consecuencia directa de este hecho es la intro-duccioacuten de esta disciplina como asignatura propia en la mayoriacutea de ingenieriacuteas En este sentido lateoriacutea de grafos como parte de la matemaacutetica discreta es una de las ramas con mayor aplicabilidadEn este trabajo estudiaremos algoritmos para tratar con grafos la idea es obtener un modelo al-gebraico de los grafos para estudiar sus propiedades y desarrollar nuevos algoritmos de cara a lasmuchas aplicaciones que de los mismos se realizan en la actualidad Aplicaremos los resultados ob-tenidos a un problema de la vida cotidiana la configuracioacuten de semaacuteforos urbanosPara conseguir ver la importancia relativa del uso de un modelo algebraico veremos algunos con-ceptos que se calculaban usando la combinatoria es decir quitando o antildeadiendo elementos y com-probaremos que su dificultad es mucho maacutes alta que usando la modelizacioacuten algebraicaEn una primera instancia las herramientas que vamos a utilizar son la colorabilidad de un grafoel algoritmo de la divisioacuten de polinomios en varias variables las bases de Groebner el polinomiocromaacutetico y las raiacuteces de la unidad para lograr la modelizacioacuten de los semaacuteforosLos contenidos los estructuramos en varios niveles

1 Empezaremos hablando de la k-coloreabilidad de grafos para ello introduciremos brevementeunos conceptos baacutesicos sobre grafos una historia sobre los oriacutegenes de la k-coloreabilidad y algu-nos elementos baacutesicos en dicha teoriacutea asiacute como algunos de los resultados que se han consideradoimportantes para dar una base teoacuterica al proyecto dentro de este campo

2 Posteriormente definiremos y expondremos toda la base teoacuterica sobre anillos de polinomios mo-noideales bases de Groebner etc en los que se basan los resultados de este proyecto

3 Realizaremos un modelo algebraico de la coloreabilidad y los aplicaremos a diversos posiblesmodelos de organizacioacuten del traacutefico en una ciudad

4 El uacuteltimo elemento de este trabajo seraacute la presentacioacuten de diferentes ejemplos en los que sepretende comparar diversas configuraciones en este caso de cruces regulados por semaacuteforosestableciendo la base matemaacutetica para su resolucioacuten y una tabla de conclusiones en cada uno delos casos

Iacutendice general

Agradecimientos IV

Introduccioacuten VI

I COLORACIOacuteN DE GRAFOS 11 Nociones de grafos 22 K-coloreabilidad Nociones baacutesicas 53 Una breve historia de la coloreabilidad 7

II ANILLOS DE POLINOMIOS Y BASES DE GROEBNER 94 Aritmeacutetica de anillos de polinomios Bases de Groebner 105 Bases de Groebner 136 Aplicaciones de las bases de Groebner 15

III NUacuteMERO Y POLINOMIO CROMAacuteTICO 197 Nuacutemero cromaacutetico 228 Polinomio cromaacutetico 23

IV APLICACIONES 339 Introduccioacuten a la aplicacioacuten de la coloracioacuten de grafos en la regulacioacuten de semaacuteforos 33

Bibliografiacutea 75

Bibliografiacutea Referencias Web 75

Iacutendice alfabeacutetico 77

V ENGLISH MEMORY 79

Capiacutetulo I

COLORACIOacuteN DE GRAFOS

Introduccioacuten

Los grafos son objetos que abundan en muchas ramas de la matemaacutetica los podemos usar por ejem-plo para disentildear los diagramas de instalacioacuten de redes eleacutectricas que usan los ingenieros entre otrasmuacuteltiples aplicaciones En general muchos problemas que son de naturaleza combinatoria puedenser pensados como problemas de grafos Hoy en diacutea la teoriacutea de grafos es usada como herramientafundamental en muy diferentes aacutereas ajenas a la matemaacutetica como la investigacioacuten operativa laquiacutemica la fiacutesica la geneacutetica etcEs dentro de este campo el de buscar aplicabilidad a la coloreabilidad de los grafos y a la compu-tacioacuten simboacutelica donde se desarrollaraacute este trabajo

2 CAP I COLORACIOacuteN DE GRAFOS

1 Nociones de grafos

Antes de continuar definamos lo que es un grafo y veamos un ejemplo bastante intuitivo al pensaren un mapa de carreteras podemos considerar dos tipos baacutesicos de elementos ciudades y carreterasNuestro objetivo es modelizar las conexiones entre ciudades por carretera usando un objeto mate-maacutetico abstracto y esto lo conseguiremos mediante el uso de grafos Matemaacuteticamente su definicioacutenesUn grafo es una terna G = (V Aφ) donde V = V (G) es una coleccioacuten finita y no vaciacutea de puntos alos que llamaremos veacutertices de G A= A(G) es una coleccioacuten finita de liacuteneas que llamaremos aristaso lados de G y que unen elementos de V y φ es una aplicacioacuten φ A minusrarr V times V donde para cadaa isin A φ(a) = (v1 v2) siendo v1 v2 isin V Donde a cada elemento de A se le asocia dos elementosv1 y v2 de V de manera que a une los veacutertices v1 y v2 Se dice que v1 y v2 son los extremos de laarista a o lo que es lo mismo que la arista es incidente en v1 y v2 o simplemente que los veacutertices sonadyacentes a la arista Si dos veacutertices o dos lados no son adyacentes se llaman independientes

La manera maacutes habitual de dibujar un grafo es dibujar un punto por cada veacutertice y si existe unaarista entre dichos veacutertices dibujar una liacutenea que los una La representacioacuten de un grafo no es uacutenicaEjemplo

Febrero 2016 Curso 20152016 TRABAJO FIN DE GRADO

SEC 1 NOCIONES DE GRAFOS 3

Se dice que el grafo G es orientado si las aristas soacutelo se pueden recorrer en un sentido En casocontrario diremos que es no orientadoSi un grafo es orientado siendo v1 v2 una arista entonces se dice que v1 es el origen y v2 es el finde la arista En este caso las aristas se llaman flechas del grafo

Una arista de un grafo es un lazo si ϕ(A) = (v v) En un grafo orientado una flecha seraacute un lazo siorigen y fin no coinciden

El grafo G es simple si no tiene ni aristas muacuteltiples ni lazos es decir si no hay maacutes de una flechaentre dos veacutertices y no existe ninguacuten lazo

El grafo G es conexo si para cada dos veacutertices v y w existe una sucesioacuten de lados l1 lt tal que ves adyacente a l1 w es adyacente a lt y cada dos lados li li+1 tienen un veacutertice adyacente en comuacutenEl grafo seraacute disconexo si no es conexo

Definimos tambieacuten una componente conexa de un grafo como un subgrafo conexo maximal esdecir para un veacutertice v la componente conexa de v es el conjunto de veacutertices distintos de v y perte-necientes al grafo para los cuales existe una sucesioacuten de lados de v a cada uno de los veacutertices

A-I Si w estaacute en la componente conexa de v v lo estaacute en la de w Usaremos la notacioacuten K(G) paraindicar las componentes conexas de un grafo

A-II La observacioacuten clave es que si consideramos dos veacutertices distintos de G sus componentesconexas o bien son la misma o bien son disjuntas

A-III Todo grafo es unioacuten disjunta de sus componentes conexas

Un grafo G se llama finito si los conjuntos V y A son conjuntos finitos

Los grafos que vamos a considerar son finitos

TFM Computacioacuten simboacutelica Mariacutea Joseacute Zapata

Definimos el grado de un veacutertice de un grafo finito como el nuacutemero de aristas que inciden en eacutel esdecir como el nuacutemero de lados que lo tienen como adyacente

Diremos que un grafo finito G es regular cuando todos los veacutertices de G tienen el mismo grado

Todo grafo finito se puede representar mediante un graacutefico formado por puntos que representan alos veacutertices y liacuteneas que representan a los lados

SEC 2 K-COLOREABILIDAD NOCIONES BAacuteSICAS 5

2 K-coloreabilidad Nociones baacutesicas

La coloracioacuten de grafos es un caso especial de etiquetado de grafos asignando a cada elemento delgrafo un color Para definir una coloracioacuten de los veacutertices de un grafo haremos que ninguacuten par deveacutertices adyacentes compartan el mismo color Esto se puede extender a aristas del grafo mantenien-do siempre la condicioacuten de que elementos adyacentes no compartan el mismo color simplementesentildealar que este caso puede ser tratados como si de coloracioacuten de veacutertices se tratase considerandoel grafo dual

Sea G un grafo de n veacutertices sea k un entero positivo con k lt n Sea Ck = c1 c2 ck un conjuntode k elementos donde cada ck isin Z+ se denomina color Una kndashcoloracioacuten de los veacutertices de G osimplemente una k-coloracioacuten de G es una aplicacioacuten f V minusrarr Ck verificando que para cada ladoA B se tiene f (A) 6= f (B)De forma intuitiva f asigna colores a cada uno de los veacutertices de G y si dos veacutertices son adyacentesentonces estaacuten coloreados de diferente formaAdemaacutes si si todo par de veacutertices adyacentes recibe colores distintos se dice que es coloracioacuten propia

Dadas dos coloraciones f g de un grafo G se dice que son distinguibles si no se puede obtener unacomo permutacioacuten de los elementos de la otra Esto significa que no existe una permutacioacuten π deCk haciendo conmutativo el siguiente diagrama

f~~~~~~~

Se dice que G es kndashcoloreable si tiene al menos una kndashcoloracioacuten propia y que es uacutenicamentekndashcoloreable si tiene solamente una kndashcoloracioacuten propia distinguible

Si G es un grafo de n veacutertices y uacutenicamente k coloreable entonces tendraacute k coloraciones diferentesno distinguibles entre siacute

La propuesta a realizar en el estudio de semaacuteforos es representar cada cruce por un grafo siendo losveacutertices los semaacuteforos y las aristas las relaciones de incompatibilidad Determinaremos coloracionesaunque no sean uacutenicamente coloreables

SEC 3 UNA BREVE HISTORIA DE LA COLOREABILIDAD 7

3 Una breve historia de la coloreabilidad

Antes de comenzar con la coloreabilidad de los grafos hagamos un breve recorrido por la historia deesta disciplina para entender sus oriacutegenes y evolucioacutenLa coloracioacuten de grafos se introdujo como resultado de intentar colorear un mapa de Inglaterraasociando al mapa un grafo dual para asiacute convertir el problema de la coloracioacuten en un problema degrafosEn 1852 Francis Guthrie que habiacutea sido alumno de Augustus de Morgan postuloacute la conjetura de los4 colores especificando que soacutelo se necesitan 4 colores para colear el mapa de forma que las regionesque comparten un borde comuacuten no reciban el mismo color El teacutermino paiacutes vecino se debe entendercomo paiacuteses adyacentes a lo largo de una liacutenea fronteriza y no por un punto o cantidad finita depuntos si no se hiciese asiacute es faacutecil comprobar que se necesitan maacutes de cuatro colores Para definirpaiacutes tendremos que entenderlo como una regioacuten conexa del plano o tampoco podriacuteamos demostrarla veracidad de esta teoriacuteaEl hermano de Guthrie que en ese momento tambieacuten era alumno de de Morgan le paso este pro-blema a su profesor para saber si existiacutea una prueba matemaacutetica De Morgan fue incapaz de decidirsobre la certeza o veracidad del problema asiacute que se lo comunicoacute a otros matemaacuteticos que empeza-ron a trabajar sobre eacutel En 1860 Charles Peirce trato de probar la conjetura sin resultado positivoTras varios antildeos sin respuesta Arthur Cayley enviacutea el problema a la London Mathematical Societyen 1878 ante su incapacidad de probar la veracidad del mismoAproximadamente un antildeo despueacutes aparece una prueba que permaneceraacute incuestionable durantemaacutes de una deacutecada Desarrollada por Alfred Bray Kempe quieacuten utilizo un meacutetodo conocido comoel Meacutetodo de las cadenas de Kempe Aunque la prueba es incompleta contiene en esencia las ideasbaacutesicas que condujeron un siglo maacutes tarde a la prueba correcta La demostracioacuten de Kempe usaba elconcepto de mapa normal que lo es si ninguna regioacuten incluye a otra y si en cada punto se encuentranexactamente tres regiones En esos mapas no hay regiones con 1 borde Si un mapa no es normalse puede obtener otro normal que para ser coloreado necesite el mismo nuacutemero de colores que eacutelno normal por lo que el estudio se redujo a la demostracioacuten de la veracidad del teorema en mapasnormalesEn realidad Kempe proboacute que cinco colores eran suficientes pero aunque no se habiacutea encontradotodaviacutea un mapa que no fuese 4-coloreable tampoco se habiacutea demostrado que todos teniacutean que serloEn 1890 Heawood descubrioacute que el argumento de Kempe conteniacutea un error y consiguioacute probar elteorema de los 5 colores En el siglo siguiente se fueron introduciendo nuevas teoriacuteas cuyo objetivoera reducir el nuacutemero de colores a 4Fue en 1976 cuando se publica una prueba (asistida por ordenador) que garantiza que todos los ma-pas normales se pueden colorear con a lo sumo cuatro colores Sin embargo esta prueba propuestapor Kenneth Appel y Wolfgang causoacute una gran controversia precisamente porque se ayudaba de unordenadorEn 1997 Neil Robertson Daniel Sanders Paul Seymour y Robin Thomas publicaron una pruebade 42 paacuteginas tambieacuten hecha con la ayuda de un ordenador que siacute fue comuacutenmente aceptadaponiendo fin a un problema que habiacutea ocupado a los matemaacuteticos durante maacutes de un siglo y quede hecho se habiacutea convertido en el problema maacutes estudiado de la teoriacutea de grafos

La coloracioacuten de grafos ha sido estudiada como un problema algoriacutetmico desde 1970 el problemadel nuacutemero cromaacutetico es el problema 21 de Karp NP-completo de 1972 y aproximadamente al mismotiempo varios algoritmos de tiempo exponencial fueron desarrollados basados en back tracking y enla eliminacioacuten y mala contraccioacuten de Zykov (1949)Para ver la importancia actual de la coloracioacutende grafos destacar que una de las mayores aplicaciones de la coloracioacuten de grafos es la asignacioacutende registros en compiladores introducida en 1981El intereacutes en la coloracioacuten de grafos sin embargo es maacutes que histoacuterico teniendo aplicacioacuten directapara la planificacioacuten de toacutepicos encontrados en el mundo real de una gran importancia praacutecticadesde autobuses trenes traacutefico gestioacuten de recursos en las tareas de secuenciacioacuten arquitectura deordenadores y gestioacuten del espacio en las aulas o del traacutefico aeacutereo entre otros En los uacuteltimos antildeos sehan obtenido numerosos avances teoacutericos que extienden los resultados ya conocidos y generalizanla mayoriacutea de las teacutecnicas utilizadasDentro de este campo es donde se desarrolla nuestro trabajo en el que estudiaremos la aplicabilidadde la kndashcoloreabilidad al sistema de semaacuteforos de una ciudad

Capiacutetulo II

ANILLOS DE POLINOMIOS Y BASES DEGROEBNER

Introduccioacuten

Numerosos problemas pueden ser modelados por sistemas de ecuaciones polinomiales N Alon acu-ntildeoacute el teacutermino meacutetodo polinomial para describir el uso de polinomios no lineales para resolver proble-mas combinacionales Usaremos dicho meacutetodo junto con la aplicacioacuten de los conocimientos sobrela teoriacutea algoriacutetmica de ideales polinomiales la cuacuteal permite usar dichos ideales para detectar lak-coloreabilidad Usando entre otras herramientas los algoritmos de la divisioacuten polinomiales losconocimientos sobre bases de Groebner y la programacioacuten en Mathematica conseguiremos desarro-llar un procedimiento de trabajo que nos permita determinar todas las opciones posibles para laregulacioacuten de un sistema de semaacuteforosEn realidad buscamos encontrar soluciones algoriacutetmicas que resuelvan problemas combinacionalesAsociaremos preguntas espciacuteficas a ecuaciones polinomiales las soluciones de dichos sistemas seraacutenlas respuestas a los problemas planteados Esta metodologiacutea es aplicable a numerosos contextosen concreto las soluciones a los sistemas de ecuaciones que plantearemos nos permitiraacute saber lasdistintas combinaciones de los colores de las luces de los semaacuteforos de nuestros cruces tratandoloscomo grafos y explorando su k-coloreabilidad [5]La herramienta fundamental para hacer un desarrollo computacional la proporcionan las bases deGroebner que nos permiten disentildear algoritmos para comparar ideales y dar meacutetodos efectivos parapoder calcular las operaciones aritmeacuteticas elementales con los mismosAntes de comenzar estableceremos las bases teoacutericas sobre anillos de polinomios en los que se basanuestro trabajo

10 CAP II ANILLOS DE POLINOMIOS Y BASES DE GROEBNER

4 Aritmeacutetica de anillos de polinomios Bases de Groebner

41 Introduccioacuten

Vamos a usar la aritmeacutetica de anillos de polinomios en varias indeterminadas con coeficientes enun cuerpo Introduciremos meacutetodos computacionales basados en la divisioacuten con resto en anillos depolinomios en n indeterminadas por lo que necesitaremos introducir relaciones de orden en Nn quesean un buen orden compatible con la suma y con la condicioacuten de que el elemento 0 = (0 middot middot middot 0)sea el elemento miacutenimo Usando las bases de Groebner podremos realizar operaciones aritmeacuteticascon ideales

42 Representacioacuten de polinomios

Se considera un cuerpo K indeterminadas X1 Xn y el anillo K[X1 Xn] de los polinomios enX1 Xn con coeficientes en K Al identificar K[X1 Xn] con K[X1 Xnminus1][Xn] cada elementoF isin K[X1 Xn] se escribe de forma uacutenica como

F =tsum

FiXin con Fi isin K[X1 Xnminus1] (II1)

Cada producto de eacutestas se escribe de forma uacutenica como

X α11 middot middot middotXn

Llamamos monomio a cada una de estas expresiones Por simplicidad al monomio X α11 middot middot middotXn

αn lorepresentaremos por X α siendo α = (α1 αn) isin Nn Entonces el polinomio F se puede escribircomo una combinacioacuten lineal de monomios con coeficientes en K esto es

F =sum

αisinNn

aαX α con aα isin K casi todos nulos

43 Oacuterdenes en Nn

Estamos interesados en la unicidad de esta representacioacuten Buscaremos criterios para asociar a cadapolinomio una expresioacuten uacutenica que nos permita compararlos de forma sencilla y poder desarrollaralgoritmos sobre los mismos

Para poder determinar expresiones uacutenicas para cada polinomio necesitamos utilizar ordenes totalesen Nn (Un orden es un orden total si para cada αβ isin Nn se tiene α β oacute β α)Tambieacuten necesitaremos que sea un buen orden es decir un orden en un conjunto S es un buenorden si cada subconjunto no vaciacuteo tiene un primer elemento

SEC 4 ARITMEacuteTICA DE ANILLOS DE POLINOMIOS BASES DE GROEBNER 11

Es indispensable fijar un buen orden cuando trabajamos con bases de Groebner pues los resultadoscomputacionales dependen del orden fijado Vamos a usar el siguiente ordenOrden lexicograacutefico

αgelex β si para el primer iacutendice i tal que αi 6= βi se tiene αi gt βi

Debido a la biyeccioacuten entre Nn y el conjunto de monomios X α11 middot middot middotX

αnn fijada una ordenacioacuten X1 gt

X2 gt middot middot middotgt Xn de las indeterminadas dada por (α1 middot middot middot αn) 7rarr X α11 middot middot middotX

αnn cada orden o preorden en

Nn define de forma uniacutevoca un orden o preorden en el conjunto de monomios Para poder utilizaresta informacoacuten necesitamos conocer lo siguiente

Lema de Dickson Dado un subconjunto no vaciacuteo S sube Nn existe un subconjunto finito G sube Stal que para cada x isin S existen y isin G y α isin Nn tales que x = y +α

Un subconjunto E sube Nn se llama un monoideal si para cada γ isin E y cada α isin Nn se tieneγ+α isin E esto es E = E +Nn

Cada monoideal tiene un uacutenico sistema de generadores minimal

44 Algoritmo de la divisioacuten

Consideramos el anillo de polinomios K[X1 Xn] Ya conocemos algo de su estructura por ejem-plo es un dominio de factorizacioacuten uacutenica Vamos a profundizar un poco maacutes en su aritmeacuteticaRecordemos que como las indeterminadas se suponen conmutativas cada producto de las mismas sepuede escribir uniacutevocamente en la forma X α1

1 middot middot middotXαnn siendo αi isin N y que abreviadamente podemos

representar este producto por X α siendo α= (α1 αn) isin NnPodemos desarrollar cada polinomio F isin K[X1 Xn] como una combinacioacuten lineal de monomiosen la siguiente forma

F =sum

aαX α

con aα isin K (casi todos nulos) α isin Nn y si α= (α1 αn) entonces X α = X α11 middot middot middotXn

αn Veamos para fijar notacioacuten algunos elementos asociados con el polinomio F cuando tenemos unorden monomial en Nn

(I) El diagrama de Newton de F es N (F) = α isin Nn | aα 6= 0

(II) Si F 6= 0 el exponente de F exp(F) =maxα isin Nn | α isin N (F)

(III) El grado de F grad(F) =maxα1 + middot middot middot+αn | α= (α1 αn) isin N (F)

(IV) El coeficiente liacuteder de F lc(F) = aexp(F)

(V) El teacutermino liacuteder de F lt(F) = aexp(F)Xexp(F)

(VI) El monomio liacuteder de F lm(F) = X exp(F)

Por completitud definimos lc(0) = 0 = lt(0) Como consecuencia para cada F isin K[X1 Xn]tenemos F 6= 0 si y soacutelo si lt(F) 6= 0 si y soacutelo si lc(F) 6= 0

Siguiendo la siguiente notacioacuten Si α1 αt isin Nn es una lista de elementos de Nn definimos∆1 = α1 +Nn

∆2 = (α2 +Nn) ∆1

∆t = (αt +Nn) cupiltt∆

∆= Nn cupilet∆i

Para cada lista de elementos de Nn por ejemplo α1 αt tendremos que ∆1 ∆t ∆ es unaparticioacuten de Nn cuando eliminamos los conjuntos vaciacuteos

Una consecuencia directa de esto es

Algoritmo de la divisioacuten Dado un orden monomial en Nn para cada lista finita de polinomios nonulos

G1 Gt isin K[X1 Xn]

consideramos la particioacuten de Nn determinada por la lista

exp(G1) exp(Gt)

Se verifica que para cada 0 6= F isin K[X1 Xn] existen elementos Q1 Q t y R isin K[X1 Xn]uacutenicos cumpliendo las propiedades siguientes

(1) F =sumt

i=1 Q iGi + R(2) R= 0 oacute N (R) sube∆(3) Para cada iacutendice i se verifica exp(Gi) +N (Q i) sube∆i

Como consecuencia si Q iGi 6= 0 se tiene exp(Q iGi)le exp(F) y si R 6= 0 entonces exp(R)le exp(F)

Llamamos a R el resto de la divisioacuten y lo representamos por R(FG) y a los Q i los cocientes deesta divisioacuten

SEC 5 BASES DE GROEBNER 13

5 Bases de Groebner

Vamos a tratar ahora el caso general de un ideal no nulo del anillo de polinomios y vamos a ver sies posible obtener un sistema de generadores que sea miacutenimo en alguacuten sentidoAntes de establecer el resultado necesitaremos definir Exp(a)Si a un ideal definimos Exp(a) = exp(F) | 0 6= F isin a

Sea a un ideal no nulo de K[X1 Xn] Si A sube Nn es un sistema finito de generadores de Exp(a)para cada conjunto de polinomios Fα | α isin A sube a tales que exp(Fα) = α para cada α isin A se tieneque Fα | α isin A es sistema de generadores de a como ideal

Si a es un ideal de K[X1 Xn] una base de Groebner de a es un conjunto finito de elementos nonulos G= G1 Gt sube a verificando que

Exp(a) = exp(G1) exp(Gt)+Nn = Exp(G) +Nn

De las bases de Groebner sabemos

(1) Cada ideal no nulo de K[X1 Xn] tiene una base de Groebner(2) Toda base de Groebner de un ideal no nulo es un sistema de generadores(3) Teorema de la base de Hilbert Todo ideal de K[X1 Xn] es finitamente generado

Tambieacuten es necesario conocer el teorema de Teorema de Buchberger

Sea a un ideal no nulo del anillo K[X1 Xn] y G un sistema finito de generadores de a Sonequivalentes los siguientes enunciados

(a) G es una base de Groebner de a(b) Para un orden fijado de G y para cada i 6= j se tiene R(S(Gi G j)G) = 0

Siendo S(Gi G j) el sndashpolinomio definido por Gi y G j

Y el algoritmo del mismo nombre que nos permite el caacutelculo de las bases de Groebner

Sea a un ideal no nulo de K[X1 Xn] con un sistema de generadores F1 Ft es posibleconstruir una base de Groebner de a siguiendo los siguientes pasos(1) Se define G0 = F1 Ft(2) Se define Gn+1 =Gn cup R(S(F G)Gn) 6= 0 | F G isinGn

Entonces cuando Gi =Gi+1 tenemos que Gi es una base de Groebner de a

Una base de Groebner G de un a no nulo de K[X1 Xn] se llama minimal si verifica

(1) lc(F) = 1 para cada F isinG(2) exp(F) isin exp(G) | F 6= G isinG+Nn para cada F isinG

Eliminando los elementos que sobran obtenemos

Todo ideal no nulo a de K[X1 Xn] tiene una base de Groebner minimal

Dado un subconjunto G= G1 Gt sube a de un ideal de K[X1 Xn] son equivalentes

(a) G es una base de Groebner minimal(b) exp(G1) exp(Gt) es un sistema miacutenimo de generadores de Exp(a) si imponemos que los

coeficientes liacutederes sean iguales a 1

Como consecuencia los teacuterminos liacutederes de una base de Groebner minimal estaacuten determinados deforma uacutenica y cada dos bases de Groebner minimales tienen el mismo nuacutemero de elementos

Una base de Groebner G de un ideal no nulo a se llama reducida si verifica

(1) lc(F) = 1 para cada F isinG(2) N (F)

exp(G) | F 6= G isinG+Nn= 0 para cada F isinG

Cada ideal no nulo tiene una uacutenica base de Groebner reducida

SEC 6 APLICACIONES DE LAS BASES DE GROEBNER 15

6 Aplicaciones de las bases de Groebner

Vamos a estudiar aplicaciones de la teoriacutea de bases de Groebner hasta ahora desarrollada En primerlugar estudiamos las aplicaciones claacutesicas de las bases de Groebner en orden a calcular con elemen-tos en el anillo K[X1 Xn] La uacuteltima parte la dedicamos al caacutelculo de la dimensioacuten en algunosejemplos de anillos cocientes de anillos de polinomios En esta seccioacuten queremos dejar constanciade los numerosos problemas que pueden resolverse usando bases de Groebner

Problema de pertenencia

ProblemaSea a un ideal izquierda de K[X1 Xn] con un sistema de generadores F1 Fr dado F isinK[X1 Xn] nos planteamos el problema de determinar si F isin a

Esto se hace como sigue Se calcula una base de Groebner G= G1 Gt de a entonces tenemosF isin a si y soacutelo si R(F G) = 0Es posible tambieacuten obtener una expresioacuten de F como combinacioacuten lineal de los generadores origi-nales F1 Fr Para ello uacutenicamente hay que tener en cuenta que por el algoritmo de la divisioacutentenemos una expresioacuten de la forma

F =Q1G1 + middot middot middot+Q t Gt

y como los Gi se obtienen haciendo sndashpolinomios a partir de los F j tenemos que es posible dar laexpresioacuten deseada

Igualdad de ideales

ProblemaSean a1 y a2 ideales de K[X1 Xn] con sistemas de generadores F1

1 F1r1 y F2

1 F2r2 res-

pectivamente El problema es determinar cuando a1 = a2

Conseguimos bases de Groebner reducidas G1 y G2 de a1 y a2 respectivamente Por la unicidad delas bases de Groebner reducidas tenemos a1 = a2 si y soacutelo si G1 =G2

Representantes canoacutenicos

ProblemaDado un ideal a de K[X1 Xn] el problema es dar un criterio y un meacutetodo para determinar unrepresentante canoacutenico en cada clase del cociente K[X1 Xn]a

En primer lugar dado a construimos una base de Groebner G de a Para cada F isin K[X1 Xn]consideramos el resto R(F G) y es claro que se verifica

F + a= R(F G) + a

Ademaacutes R(FG) es uacutenico verificando la igualdad anterior y N (R(F G)) sube ∆ = Nn Exp(a) ver elalgoritmo de la divisioacuten en la paacutegina 12 Este elemento R(F G) lo llamamos la forma normal de laclase de F con respecto a GEl comportamiento de la forma normal es bueno respecto a combinaciones Kndashlineales ya que si a1a2 isin C y F1 F2 isin K[X1 Xn] entonces se verifica R(a1F1+ a2F2G) = a1R(F1G)+ a2R(F2G) Esclaro que por el algoritmo de la divisioacuten tenemos

Fi =Qi1G1 + middot middot middot+Qi

t Gt + R(FiG)

entonces se verificaa1F1 + a2F2 =

a1Q11G1 + middot middot middot+ a1Q

1t Gt + a1R(F1G) + a2Q

21G1 + middot middot middot+ a2Q

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

21)G1 + middot middot middot+ (a1Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

de donde tenemos el resultado ya que

N (a1R(F1G) + a2R(F2G)) sube Nn Exp(a)

y por tanto R(a1F1 + a2F2G) = a1R(F1G) + a2R(F2G) Tenemos entonces para cualesquiera F1F2 isin K[X1 Xn] las equivalencias entre los siguientes enunciados

F1 + a= F2 + aF1 minus F2 isin aR(F1 minus F2G) = 0R(F1G) = R(F2G)

Como consecuencia cada elemento de K[X1 Xn]a estaacute uniacutevocamente determinado y determi-na un elemento R de K[X1 Xn] con N (R) sube Nn Exp(a) Para estos elementos las operacionesen K[X1 Xn]a estaacuten definidas exactamente por estos representantes por la regla

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

Pasamos ahora a estudiar el caso de ideales cofinitos esto es ideales a de K[X1 Xn] tales que elcociente K[X1 Xn]a es de dimensioacuten finita como Kndashespacio vectorial

Kndashbase del cociente

ProblemaSe trata de dar un meacutetodo que permita calcular una base del espacio vectorial K[X1 Xn]a

Para cada clase F + a de K[X1 Xn]a considerando una base de Groebner de a tenemos unrepresentante R de la clase F +a tal queN (R) sube Nn Exp(a) De aquiacute resulta que R se puede escribiren la forma

cαX α

con α isin exp(G) G isinG+Nn = Exp(a) y cα isin K Tenemos entonces que X β | β isin Nn Exp(a) esun sistema de generadores linealmente independiente de K[X1 Xn]a esto resuelve el problema

Operaciones en el cociente

ProblemaDar un criterio que permita calcular las operaciones en el cociente K[X1 Xn]a cuando a es unideal (cofinito) de K[X1 Xn]

Supuesto que a es un ideal cofinito las clases del cociente S = K[X1 Xn]a tienen una Kndashbasefinita y como S es un anillo tenemos un producto interno en S Pero S es una Kndashaacutelgebra finitondashdimensional luego este producto se puede describir completamente en teacuterminos de los productos delos elementos de una Kndashbase El caacutelculo se realiza considerando una base de GroebnerG y calculandolos restos de la divisioacuten por G

Eliminacioacuten de variables

Dado un sistema de ecuaciones polinoacutemicas Fi = 0i=1s siendo cada Fi isin K[X1 Xn] una so-lucioacuten al sistema es un elemento (a1 an) isin Kn tal que Fi(a1 an) = 0 para cada iacutendice iObservar que si llamamos a al ideal generado por F1 Fs entonces para cada sistema de gene-radores G1 Gt de a un elemento (a1 an) es una solucioacuten del sistema Fi = 0i=1s si y soacutelosi es una solucioacuten del sistema G j = 0

Esto significa que los sistemas que tenemos que resolver son aquellos para los que F1 Fs es unabase de Groebner si es necesario reducida de un cierto idealEn el caso en que los Fi son polinomios lineales el sistema Fi = 0i=1s se resuelve por el meacutetodode GaussndashJordan En ese caso se van eliminando variables X1 X2 etc hasta llegar a ecuaciones enlas que cada variable librese expresa en funcioacuten de unas variables dependientes

Este proceso podemos repetirlo si consideramos un sistema de ecuaciones polinoacutemicas no linea-les Fi = 0i=1s Si Fi | i = 1 s es una base de Groebner del ideal correspondiente al quellamaremos a definimos el indasheacutesimo ideal de eliminacioacuten con respecto al orden lexicograacutefico conX1 gt X2 gt gt Xn como ai = a

K[X(i + 1) Xn]

Capiacutetulo III

NUacuteMERO Y POLINOMIO CROMAacuteTICO

Introduccioacuten

El riacuteo Pregolya atraviesa la ciudad de Koumlnisberg En el siglo XVI habiacutea siete puentes que lo cruzabany nunca hubo uno de los habitantes de la ciudad que pudiese hacer una ruta que cruzaraacute cada unode estos puentes una sola vez Leonard Euler trabajo en lo que el llamoacute ldquoEl problema de los puentesde Koumlnigsbergrdquo que es considerado por muchos como el inicio de la teoriacutea de grafosAl principio las ideas sobre grafos de Euler se encontraban centradas uacutenicamente en la resolucioacutende puzles o en el anaacutelisis de juegos Sin embargo a partir del siglo XVII se observoacute que los grafospodiacutean usarse para modelizar un sinfiacuten de cosas diferentes De hecho la teoriacutea sobre coloracioacuten demapas con cuatro colores de De Morgan pareciacutea estar fuera de este campo no obstante el problemapuede ser totalmente modelizado con la teoriacutea de grafos como hemos explicado anteriormente Lateoriacutea de grafos empezoacute a florecer en el siglo XX y su capacidad para modelar matemaacuteticamentedistintas situaciones de la vida empezoacute a ser reconocida su crecimiento auacuten continuaVeamos una explicacioacuten sencilla de coacutemo podemos modelizar por ejemplo el reparto de frecuenciaspara las distintas cadenas de televisioacuten y asiacute entender coacutemo algo tan alejado de veacutertices y aristaspuede ser modelizado mediante ellasEl control de los medios de comunicacioacuten tradicionales (televisioacuten radio y prensa escrita en ordendecreciente de importancia) es fundamental para moldear la opinioacuten puacuteblica Este control se extiendemucho maacutes allaacute y podemos comprobar coacutemo los gobiernos de turno se caracterizan por favorecer deforma descarada a los medios afines a la hora del reparto de frecuencias tanto en las radios comoen las TDT locales Puede que maacutes de uno se pregunte iquestpor queacute hay que repartir las frecuenciasiquestPor queacute cada cual no pone su emisora de radio donde quiera y emite sin maacutes Por las interferenciasclaro Pues por sorprendente que parezca la fiacutesica y las matemaacuteticas juegan un papel fundamentalen esta historia El rol de la fiacutesica es sencillo de vislumbrar estamos hablando de emisioacuten de ondasy por tanto de interferencias Asiacute que voy a tratar de explicar por queacute hemos de tener en cuentatambieacuten a las matemaacuteticas Es faacutecil deducir que si dos emisoras cercanas emiten en una frecuenciatambieacuten cercana se puede producir una interferencia entre ellas por lo tanto habriacutea que evitar laasignacioacuten de frecuencias semejantes a emisoras que no disten mucho entre siacute y no disponemos deun nuacutemero infinito de frecuencias para hacerlo Entonces iquestcoacutemo se puede resolver este problema

20 CAP III NUacuteMERO Y POLINOMIO CROMAacuteTICO

Supongamos que el siguiente graacutefico muestra una determinada zona geograacutefica y que cada puntito(o circulito) sentildeala la ubicacioacuten de nuevas emisoras de radio Hemos unido con una liacutenea de dos endos a aquellas emisoras para las que por la geografiacutea pudieran existir interferencias entre ellas sise les asignan frecuencias cercanas

A continuacioacuten vamos a colorear los circulitos a los que a partir de aquiacute llamaremos veacutertices deforma que dos veacutertices que esteacuten unidos por una liacutenea a las que llamaremos aristas no tengan elmismo color

CAP III NUacuteMERO Y POLINOMIO CROMAacuteTICO 21

Cada color representa una frecuencia y ha bastado con cuatro Hemos usado cuatro colores pararesolver el problema en esta zona geograacutefica Lo que estamos haciendo es representar el problemacon un grafo con veacutertices y aristas y dar una coloracioacuten de veacutertices para el mismoEs claro que el uso de conceptos como polinomio cromaacutetico o nuacutemero cromaacutetico son aplicables adiversas aacutereas de la vida cotidiana lo que viene a reflejar la importancia de esta herramienta en laresolucioacuten de problemas no exclusivamente matemaacuteticos Ver las referencias (1) y (4)

7 Nuacutemero cromaacutetico

El nuacutemero cromaacutetico de un grafo es la menor cantidad de colores necesarios para colorear sus veacuterticessin que dos vertices vecinos tengan el mismo color Claramente se puede colorear cada veacutertice de uncolor diferente pero eso no nos daraacute el nuacutemero cromaacutetico Veremos ahora la definicioacuten y propiedadesde este nuacutemero

El nuacutemero cromaacutetico o iacutendice cromaacutetico de un grafo G es el menor cardinal de los conjuntos Ctales existe una coloracioacuten de G con valores en C es decir el miacutenimo valor k que pertenece a N talque G es kndashcoloreable y se denota por χ(G)

Puesto que todo grafo G con n veacutertices admite siempre una nndashcoloracioacuten se tiene que para cada grafoG existe un valor k que pertenece a N para el cual G es kndashcoloreable pero no es (kminus1)-coloreableA partir de esto podemos definir el nuacutemero cromaacutetico de un grafo Si n= χ(G) se dice que el grafoes nndashcromaacutetico (Es decir cuando el nuacutemero miacutenimo de colores con el que se puede pintar el grafoes igual al nuacutemero de veacutertices del grafo)Algunos grafos especiales tienen iacutendices cromaacuteticos conocidos

1 El grafo K2 (grafo completo de orden 2) con dos veacutertices y un lado tiene iacutendice cromaacutetico 22 El grafo completo Kn (grafo completo de orden n) tiene iacutendice cromaacutetico n3 El iacutendice cromaacutetico de un subgrafo Gprime sube G de un grafo G es menor que el iacutendice cromaacutetico de

G4 Si un grafo es plano entonces su iacutendice cromaacutetico es menor o igual que 45 Si un grafo es un ciclo sabemos que su iacutendice cromaacutetico es 2 si n es par y tres si n es impar

SEC 8 POLINOMIO CROMAacuteTICO 23

8 Polinomio cromaacutetico

Asociado al nuacutemero croacutematico aparece el polinomio cromaacutetico este concepto supone un puenteentre la geometriacutea y el aacutelgebra entre el dibujo y el nuacutemero Comenzaremos a hablar de eacutel con sudefinicioacuten maacutes sencilla

Dado un grafo G y un conjunto de colores k definimos la funcioacuten P(G k) como el nuacutemero de formasdistintas de colorear G usando los k colores

Intentemos dar una explicacioacuten a esta definicioacutenDado un grafo G y una paleta con un nuacutemero determinado k de colores determinar de cuaacutentasmaneras diferentes se puede colorear el grafo G con colores de esa paleta sujetas de nuevo lascoloraciones a la restriccioacuten de que dos extremos de una arista deben llevar colores diferentesAquiacute hay que aclarar queacute significa laquodiferentesraquo aunque la idea corresponde completamente con laintuicioacuten dos coloraciones de un grafo llevadas a cabo con la misma paleta se consideran diferentessi al menos uno de los veacutertices del grafo tiene color diferente en cada una de las dos Asiacute pues lo pri-mero que hay que hacer es modelar este problema de un modo apropiado Para empezar nos damoscuenta de que dada una paleta de colores cualquiera desde el punto de vista de contar coloracionesnos importa poco cuaacuteles sean los colores concretos de la paleta en realidad solo nos va a importarel nuacutemero k de colores que eacutesta contenga Dicho de otro modo si un grafo podemos colorearlo exac-tamente de diez maneras diferentes con los colores rojo amarillo y azul igual podremos colorearlode diez maneras diferentes con los colores verde naranja y rosa o viceversa Solo nos va a importaren cada caso el nuacutemero de colores de la paleta no los colores concretosAhora podemos definir una asignacioacuten (lo que en matemaacuteticas se llama una funcioacuten) del siguientemodo para cada paleta con k colores y para cada grafo G P(G k) seraacute el nuacutemero de coloracionesposibles del grafo G con colores de la paleta A esta asignacioacuten es a lo que se llama polinomiocromaacutetico de GFue Birkhoff quien en 1942 introdujo el polinomio cromaacutetico en su intento de demostrar el teoremade los cuatro colores Al leer la definicioacuten de polinomio cromaacutetico en principio no aparece unpolinomio por ninguacuten sitio solo una asignacioacuten cualquiera Birkhoff demostroacute que dicha funcioacutenera un polinomio y gracias a ella podemos obtener muchiacutesima informacioacuten sobre el grafo Veamosalgunos ejemplos

(1) El grado del polinomio cromaacutetico es siempre el nuacutemero de veacutertices del grafo(2) Si el polinomio cromaacutetico es de grado n el coeficiente de grado nminus 1 cambiado de signo es el

nuacutemero de aristas del grafo(3) Si el polinomio cromaacutetico es de grado n el coeficiente de grado nminus 2 (ligeramente retocado)

cuenta el nuacutemero de triangulitos que se forman en el grafo

(4) Dado un grafo G una componente conexa de G estaacute formada por todos los veacutertices tales queexiste un camino dentro de G entre ellos y las aristas de G que los unen Entonces si el primerteacutermino no nulo del polinomio cromaacutetico es de grado j el grafo tiene j componentes conexas

Otras de las propiedades del polinomio cromaacutetico son

1 P(G 0) = 0

2 P(G k)gt 0 si y soacutelo si G es kndashcoloreable

3 Si un grafo tiene al menos un lado entonces P(G 1) = 0

4 Si el grafo G tiene t componentes conexas G1 Gt entonces P(G n) =prodt

i=1 P(Gi n) Loque reduce el problema a trabajar con grafos conexos

5 Si consideramos K2 entonces un veacutertice se puede colorear de n formas distintas y el segundode nminus1 formas por lo tanto el nuacutemero total de coloraciones P(K2 n) = n(nminus1) y P(Kt n) =n(nminus 1) middot middot middot (nminus t + 1)

Algunas propiedades del polinomio cromaacutetico son

1 Si G no es un grafo nulo es decir tiene alguna arista entonces la suma de los coeficientesde su polinomio cromaacutetico vale siempre 0 Esto es consecuencia de que

j b j = P(G 1) =formas de colorear G con un color= 0

2 Sea G un grafo con r componentes conexas n veacutertices y m aristas Entoncesa) Si G no tiene veacutertices aislados entonces 2r le nb) Si G no tiene veacutertices aislados y ademaacutes mge 4 entonces r le nminus 3

El caacutelculo del polinomio cromaacutetico se puede hacer de diferentes maneras Tradicionalmente se hacalculado usando la combinatoria bien quitando aristas o bien antildeadieacutendolas Veamos algunos ejem-plos

81 CAacuteLCULO DEL POLINOMIO CROMAacuteTICO CON ELIMINACIOacuteN DE UNA ARIS-TA

Contraccioacuten de una arista

Dado un grafo G y sea a = u v arista que une los veacutertices u y v llamaremos contraccioacuten de laarista ldquoardquo del grafo G Ga a la operacioacuten resultante de considerar los veacutertices u y v coacutemo un uacutenicoveacutertice Por tanto Ga tiene un veacutertice menos que G la arista Ga ha desaparecido dos aristas noincidentes que tengan como extremos los veacutertices de a pasan a tener un veacutertice comuacuten y dos aristascualquiera que formen un triaacutengulo con a en G pasan a ser la misma arista en Ga Se realiza dehecho un laquopegadoraquo en el grafo

Usaremos el algoritmo de Eliminacioacuten-contraccioacuten (o algoritmo come aristas) que consiste en aplicarel siguiente teorema

P(G k) = P(G minus a k)minus P(Ga k)

Donde Ga como ya hemos dicho es la contraccioacuten de G y G minus a es un grafo que tiene los mismosveacutertices que G y las mismas aristas que G excepto la arista a que la borramos (los extremos losdejamos)

Graacuteficamente

Ahora expresamos el polinomio cromaacutetico de un grafo con r aristas como diferencia de los polinomioscromaacuteticos de dos grafos tales que cada uno tiene como mucho rminus1 aristas Veamos coacutemo funcionaGa tiene un veacutertice menos que G la arista a ha desaparecido dos aristas no incidentes que tengancomo extremos los veacutertices de a pasan a tener un veacutertice comuacuten y dos aristas cualquiera que formenun triaacutengulo con a en G pasan a ser la misma arista en Ga Se realiza de hecho un nuevo laquopegadoraquoen el grafoPensemos ahora en una coloracioacuten de G minus a Pueden pasar dos cosas que los extremos de la aristaque hemos quitado lleven el mismo color o colores diferentes En el primer caso la coloracioacuten dauna coloracioacuten de Ga (con el veacutertice distinguido de Ga con el color de los extremos de la arista quehemos quitado en G) y en el segundo la coloracioacuten de Gminus a da una coloracioacuten de G Dicho de otromodo habraacute tantas coloraciones de G minus a con k colores como coloraciones de Ga con k colores maacutescoloraciones de G con k colores Escrito resumidamente llegamos al teorema inicial

Lo que hemos conseguido aquiacute es expresar el polinomio cromaacutetico de G en funcioacuten de los polino-mios cromaacuteticos de grafos con al menos una arista menos Ahora si reiteradamente vamos quitandoaristas de esta manera de G minus a y Ga acabaremos escribiendo P(G k) como sumas y restas de po-linomios cromaacuteticos de grafos vaciacuteos De este modo ademaacutes de ver que P(G k) es un polinomiohemos encontrado un meacutetodo para construirlo que no solo puede comprender cualquier personasino lo que es maacutes importante desde el punto de vista del caacutelculo que entiende cualquier ordenadorAsiacute el polinomio cromaacutetico puede calcularse dado un grafo de modo completamente automaacutetico(otra cosa es el tiempo que se tarde)

82 CAacuteLCULO DEL POLINOMIO CROMAacuteTICO CON ADICIOacuteN DE UNA ARISTA

En realidad este no es un algoritmo nuevo sino simplemente otra forma de enfocar el conocido deldquoquitar aristasrdquo Recordamos que en este uacuteltimo obteniacuteamos P(G k) = P(G minus a k) minus P(Ga k) Porlo tanto P(G minus a k) = P(G k) + P(Ga k) Pero esto nos dice que si tenemos un cierto grafo (en lanotacioacuten de arriba P(Gminusa k) su polinomio cromaacutetico se puede escribir como la suma del polinomiocromaacutetico del grafo que obtenemos antildeadieacutendole a P(Gminusa k) una cierta arista a (que por supuestoes una que no estaacute en el grafo) maacutes el del grafo que resulta de identificar los veacutertices de a

iquestCuaacutel es la ventaja de este enfoque sobre el anterior Imaginemos que el grafo del que queremosconocer el polinomio cromaacutetico estaacute muy cerca de ser un grafo completo antildeadiendo unas pocasaristas escribiremos su polinomio como suma de unos cuantos polinomios cromaacuteticos de grafoscompletos cuya expresioacuten conocemos

Sin embargo nosotros usamos un algoritmo definido en Wolfran Mathematica para el caacutelculo de losmismos

ALGOacuteRITMO EN WOLFRAM MATHEMATICA PARA EL CAacuteLCULO DEL POLINOMIO CROMAacuteTICO

Lo primero que se necesita es calcular las distintas opciones de coloreabilidad que tiene el grafo Se define el nuacutemero de veacutertices y las ecuaciones necesarias para determinar cuaacutentas opciones diferentes de coloreabilidad existen

Var=Table[Xii15] Ecu1[n_]=Subscript[X n]5-1

Ecu2[D_]=Subscript[X D[[1]]]4+Subscript[X D[[1]]]3XD[[2]]+Subscript[X D[[1]]]2 Subscript[X D[[2]]]2+XD[[1]] Subscript[X D[[2]]]3+Subscript[X D[[2]]]4

Ecua=Join[Map[Ecu112345]Map[Ecu2121314152324

25343545]] Length[Ecua]

Aux=GroebnerBasis[EcuaVar] Length[Aux]

Aux=Thread[Aux==0] Aux=Solve[AuxVar]

Length[Aux]

Luego procedemos a definir las variables necesarias para poder disentildear nuestra

funcioacuten la que calcularaacute el polinomio cromaacutetico Se definen distintas variables

nuacutemero de veacutertices listas de parejas se define una lista se define el algoritmo para

calcular el primer primo que aparece en esa lista etc

LE=(ListaFlechas=)121314152324 25343545 NV=(NumeroVertices=)5

[ [ ]] [ [ ]]] ] ]

Definimos las diferentes ecuaciones que hay que resolver para la obtencioacuten del

polinomio cromaacutetico

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

Por uacuteltimo definimos la funcioacuten

[ [ ] ]

APLICACIOacuteN CAacuteLCULO POLINOMIO CROMAacuteTICO C4

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Usando estos meacutetodos podriacuteamos faacutecilmente calcular los siguientes polinomios cromaacuteticos

1 P(On k) = kn con On el grafo trivial de n veacutertices

2 P(Kn k) = k(k minus 1)(k minus 2) (k minus n+ 1) es claramente una generalizacioacuten de la propiedadgeneral para todos los grafos

3 P(Ln k) = k(kminus 1)n con Ln el grafo camino de n veacutertices

4 P(Cn k) = k(kminus 1)n+ (minus1)n(kminus 1) con Cn el grafo ciacuteclico de n veacutertices

Hemos visto que todo grafo da lugar a un polinomio cromaacutetico con las siguientes carateriacutesticas

1 El teacutermino independiente a0 del polinomio cromaacutetico es siempre cero

2 Todos los coeficientes del polinomio cromaacutetico son nuacutemeros enteros

3 Los coeficientes del polinomio cromaacutetico se van alternando en signo

4 Todos los coeficientes del polinomio cromaacutetico son distintos de cero a partir de un cierto a j

5 El grado del polinomio cromaacutetico es siempre el nuacutemero de veacutertices del grafo

6 Si el polinomio cromaacutetico es de grado n el coeficiente de grado nminus1 cambiado de signo es elnuacutemero de aristas del grafo

7 Si el polinomio cromaacutetico es de grado n el coeficiente de grado nminus 2 (ligeramente retocado)cuenta el nuacutemero de triangulitos que se forman en el grafo

8 Dado un grafo G una componente de G estaacute formada por todos los veacutertices tales que existe uncamino dentro de G entre ellos y las aristas de G que los unen Entonces si el primer teacuterminono nulo del polinomio cromaacutetico es de grado j el grafo tiene j componentes

9 Sea G un grafo con n veacutertices Si G es kndashcoloreable entonces G tambieacuten es kprimendashcoloreable paratodo kprime pertenece a N tal que k lt kprime A partir de este resultado se deduce que si G no eskndashcoloreable entonces tampoco seraacute kprimendashcoloreable para ninguacuten kprime perteneciente a N tal quek lt kprime

El polinomio cromaacutetico codifica una gran parte de la estructura del grafo Es decir que a partir deun grafo que puede ser un objeto terriblemente enrevesado se puede obtener de modo automaacutetico

un polinomio limpio y claro que inmediatamente nos va a proporcionar un montoacuten de informacioacutenque de otro modo resultariacutea muy difiacutecil de conseguir

Capiacutetulo IV

APLICACIONES

9 Introduccioacuten a la aplicacioacuten de la coloracioacuten de grafos en laregulacioacuten de semaacuteforos

La herramienta fundamental para hacer un desarrollo computacional la proporcionan las bases deGroebner que nos permiten disentildear algoritmos para comparar ideales y dar meacutetodos efectivos parapoder calcular las operaciones aritmeacuteticas elementales con los mismos Tambieacuten vamos a utilizarprincipios de eliminacioacuten de variables es decir encontraremos ecuaciones que soacutelo relacionen lassoluciones de ciertas variables usando los sistemas de generadores proporcionados por las bases deGroebner

Definiremos nuestro sistema de trabajo utilizando para ello una serie de pasos que facilitaraacuten laobtencioacuten de informacioacuten

Inclusioacuten de fotografiacuteas para ilustrar el caso concreto que se estaacute estudiando

Dibujar un esquema del cruce regulado por semaacuteforos que estamos estudiando en cada casopara establecer que regulaciones y restricciones existen en eacutel

Traduciremos ese diagrama en un grafo

Estableceremos el nuacutemero de colores a utilizar

Estableceremos las ecuaciones a resolver

Resolveremos usando el Wolfran Mathematica

Incluiremos una tabla explicativa donde se resumiraacute cada una de las posibles soluciones y latraduciremos al sistema de colores que regulan los semaacuteforos

SEMAacuteFORO CAMINO DE RONDA RONDA MOTOR

34 CAP IV APLICACIONES

SEC 9 INTRODUCCIOacuteN A LA APLICACIOacuteN DE LA COLORACIOacuteN DE GRAFOS EN LA REGULACIOacuteN DE

SEMAacuteFOROS 35

Observando el cruce nos damos cuenta que se puede representar con el siguiente esquema

Situaacutendonos en el punto A los coches pueden ir hacia delante a izquierda o a derecha(en el

cruce un poco maacutes adelante) Y se ven afectados por tres semaacuteforos que no pueden coincidir

exactamente en el mismo color En este cruce los coches tambieacuten pueden venir en una

direccioacuten perpendicular a la situacioacuten del punto A este semaacuteforo marcado con el punto C siacute

puede coincidir con el marcado con el punto B

Traducimos toda esta informacioacuten y usando

httpsmatiestiiwikispacescomfileviewpolinomio+cromaacuteticopdf obtenemos

Para ello tendremos que introducir los datos de la matriz de adyacencia del grafo es decir

poner un 1 o un 0 dependiendo de siacute los lados estaacuten o no relacionados (1 si estaacuten relacionados

0 no) Asiacute es como se transforma nuestro cruce en grafo introduciendo en el programa todos

los datos antes mencionados

Seguacuten lo observado necesitaremos 3 colores para colorear el grafo de cuatro veacutertices Resolveremoslos siguientes algoritmos usando Mathematica y aplicaacutendolo a las parejas de veacutertices unidas porlados (1 2) (13) (1 4) (23) (24)

SEMAacuteFOROS 37

Definimos las siguientes variables atendiendo al nuacutemero de veacutertices que ya sabemos que son 4

Var=Table[Xii14]

Planteamos las siguientes ecuaciones teniendo en cuenta el nuacutemero de colores con el que podemos pintar y los puntos que no pueden estar pintados del mismo color que es lo que determina la lista de parejas

Ecu1[n_]=Xn^3-1

Ecu2[D_]=Subscript[X D[[1]]]2+XD[[1]]XD[[2]]+Subscript[X D[[2]]]2

Ecua=Join[Map[Ecu11234]Map[Ecu21213142324]] Aux=GroebnerBasis[EcuaVar]

Length[Aux] Las ecuaciones a resolver son

minus1+11988313 minus1+11988323 minus1+11988333 minus1+11988343

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

Los caacutelculos se han realizado sobre lo que complica las operaciones y dificulta la interpretacioacuten de las soluciones Si trataraos el problema sobre un cuerpo finito se deberiacutean obtener el mismo nuacutemero de soluciones pero maacutes faacutecilmente entendibles Por ejemplo en nuestro caso estamos trabajando con raiacuteces cuacutebicas de la unidad el lugar adecuado seriacutea un cuerpo p con 3p-1 para asegurar la existencia de raiacuteces cuacutebicas de en p

Las soluciones obtenidas son

Estas soluciones resultan difiacuteciles de interpretar Para poder interpretarlas de un modo maacutes sencillo usaremos que para los elementos de un grupo de orden 3 sabemos que 3=p -1 donde p es un nuacutemero primo(principio de DrsquoAlembert) por lo que se cumple que p = 3k + 1 daacutendole a k distintos valores vamos obteniendo los valores de p Si k = 0 ⟹ p = 1 Si k = 1 ⟹ p = 4 Si k = 2 ⟹ p = 7 es el primer primo que nos aparece por lo que necesitaremos hacer las operaciones moacutedulo 7

SEMAacuteFOROS 39

En Mathematica el algoritmo que se usa para la resolucioacuten de las ecuaciones usando moacutedulo 7 es praacutecticamente el mismo

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Aux=Solve[AuxVar Modulusrarr7] Length[Aux]

Las soluciones son

1198831rarr1 1198832rarr2 1198833rarr4 1198834rarr4 1198831rarr1 1198832rarr4 1198833rarr2 1198834rarr2 1198831rarr2 1198832rarr1 1198833rarr4 1198834rarr4 1198831rarr2 1198832rarr4 1198833rarr1 1198834rarr1 1198831rarr4 1198832rarr1 1198833rarr2 1198834rarr2 1198831rarr4 1198832rarr2 1198833rarr1 1198834rarr1

Maacutes faacuteciles de interpretar y mucho maacutes raacutepido su caacutelculo usando el ordenador

Estas soluciones resultan difiacuteciles de interpretar Para poder interpretarlas de un modo maacutes sencillovamos a trabajar con los elementos de un grupo de orden 3 sabemos que 3p minus 1 donde p es unnuacutemero primo (principio de DrsquoAlembert) por lo que se cumple que p = 3k+1 daacutendole a k distintosvalores vamos obteniendo los valores de p k = 0 =rArr p = 1 k = 1 =rArr p = 4 k = 2 =rArr p = 7 es elprimer primo que nos aparece por lo que necesitaremos hacer las operaciones moacutedulo 7

Nos salen 6 soluciones diferentes si observamos atentamente la tabla de representacioacuten de colorespodemos observar que en realidad solo hay tres coloroaciones diferentes las demaacutes se obtienen comopermutaciones de las mismas Para verlo maacutes intuitivamente observaremos los resultados nuacutemericosde cada una de las soluciones

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

Claramente se puede ver que unos resultados son permutaciones de otros El hecho de colorearun grafo de n veacutertices con k colores es lo mismo que formar listas con repeticiones permitidas delongitud n con los colores de manera que se respeten las restricciones que imponen los veacutertices queno pueden ser coloreados igual

Este mismo significado tendraacuten todas las demaacutes tablas expuestas en este trabajo es decir todas lasopciones de coloreabilidad no son propias unas se obtienen como permutaciones de las otras

Una coloracioacuten de cualquier grafo G con n colores consiste en asignar a cada veacutertice un color deforma que los extremos de cada arista tengan un color diferente Lo importante es que se ldquorespeterdquola restriccioacuten de no permitir que veacutertices adyacentes tengan el mismo color es por ello que aparecenvarias soluciones pero no son todas ldquototalmenterdquo diferentes

Ahora seraacute maacutes sencillo interpretar la tabla de soluciones

SEMAacuteFOROS 41

Su interpretacioacuten seguacuten el siguiente coacutedigo de colores

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

Los coches pueden ir hacia delante o a la derecha en una esquina e igual en la otra ninguno de

los cuatro puede coincidir con el mismo color en el mismo momento

Seguacuten lo observado necesitaremos 4 colores para colorear el grafo de cuatro veacutertices Resolveremoslos siguientes algoritmos usando Mathematica y aplicaacutendolo a las parejas de veacutertices unidas porlados (1 2) (13) (1 4) (2 3) (24) (3 4)

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Ecu2[D_]=Subscript[X D[[1]]]3+XD[[1]]2XD[[2]]+ XD[[1]]2XD[[2]]2+Subscript[X D[[2]]]3

Ecua=Join[Map[Ecu11234]Map[Ecu2121314232434]]

Aux=GroebnerBasis[EcuaVar] Aux=Thread[Aux==0]

Aux=Solve[AuxVar] Length[Aux]

Las ecuaciones a resolver son

Los caacutelculos se han realizado sobre las soluciones no son difiacuteciles de interpretar por lo que no es necesario recurrir a trabajar sobre un cuerpo finito nos dariacutea el mismo resultado pero con nuacutemeros enteros

Las soluciones son

1198831 rarr 1 1198832 rarr ⅈ 1198833 rarr minusⅈ 1198834 rarr minus1 1198831 rarr ⅈ 1198832 rarr 1 1198833 rarr minusⅈ 1198834 rarr minus1 1198831 rarr 1 1198832 rarr minusⅈ 1198833 rarr ⅈ 1198834 rarr minus1 1198831 rarr minusⅈ 1198832 rarr 1 1198833 rarr ⅈ 1198834 rarr minus1 1198831 rarr ⅈ 1198832 rarr minusⅈ 1198833 rarr 1 1198834 rarr minus1 1198831 rarr minusⅈ 1198832 rarr ⅈ 1198833 rarr 1 1198834 rarr minus1 1198831 rarr 1 1198832 rarr ⅈ 1198833 rarr minus1 1198834 rarr minusⅈ 1198831 rarr ⅈ 1198832 rarr 1 1198833 rarr minus1 1198834 rarr minusⅈ 1198831 rarr 1 1198832 rarr minus1 1198833 rarr ⅈ 1198834 rarr minusⅈ 1198831 rarr minus1 1198832 rarr 1 1198833 rarr ⅈ 1198834 rarr minusⅈ 1198831 rarr ⅈ 1198832 rarr minus1 1198833 rarr 1 1198834 rarr minusⅈ 1198831 rarr minus1 1198832 rarr ⅈ 1198833 rarr 1 1198834 rarr minusⅈ 1198831 rarr 1 1198832 rarr minusⅈ 1198833 rarr minus1 1198834 rarr ⅈ 1198831 rarr minusⅈ 1198832 rarr 1 1198833 rarr minus1 1198834 rarr ⅈ 1198831 rarr 1 1198832 rarr minus1 1198833 rarr minusⅈ 1198834 rarr ⅈ 1198831 rarr minus1 1198832 rarr 1 1198833 rarr minusⅈ 1198834 rarr ⅈ 1198831 rarr minusⅈ 1198832 rarr minus1 1198833 rarr 1 1198834 rarr ⅈ 1198831 rarr minus1 1198832 rarr minusⅈ 1198833 rarr 1 1198834 rarr ⅈ 1198831 rarr ⅈ 1198832 rarr minusⅈ 1198833 rarr minus1 1198834 rarr 1 1198831 rarr minusⅈ 1198832 rarr ⅈ 1198833 rarr minus1 1198834 rarr 1 1198831 rarr ⅈ 1198832 rarr minus1 1198833 rarr minusⅈ 1198834 rarr 1 1198831 rarr minus1 1198832 rarr ⅈ 1198833 rarr minusⅈ 1198834 rarr 1 1198831 rarr minusⅈ 1198832 rarr minus1 1198833 rarr ⅈ 1198834 rarr 1 1198831 rarr minus1 1198832 rarr minusⅈ 1198833 rarr ⅈ 1198834 rarr 1

SEMAacuteFOROS 47

SEMAacuteFORO FUENTES

SEMAacuteFOROS 49

El esquema del cruce es

Usando httpsmatiestiiwikispacescomfileviewpolinomio+cromaacuteticopdf obtenemos

Seguacuten lo observado necesitaremos 4 colores para colorear el grafo de cuatro veacutertices Resolveremoslos siguientes algoritmos usando Mathematica y aplicaacutendolo a las parejas de veacutertices unidas porlados (1 2) (13) (1 4) (16) (23) (2 4) (26) (4 5)

SEMAacuteFOROS 51

Var=Table[Xii16] Planteamos las siguientes ecuaciones teniendo en cuenta el nuacutemero de colores con el que podemos pintar y los puntos que no pueden estar pintados del mismo color que es lo que nos determina la lista de parejas definidas en el algoritmo

Ecu1[n_]=Xn^4-1 Ecu2[D_]=Subscript[X D[[1]]]3+Subscript[X D[[1]]]2XD[[2]]+XD[[1]] Subscript[X

D[[2]]]2+Subscript[X D[[2]]]3

Los caacutelculos se han realizado sobre las soluciones no son difiacuteciles de interpretar por lo que no es necesario que recurramos a trabajar sobre un cuerpo finito 5 nos dariacutean el mismo nuacutemero de resultados y las soluciones seriacutean nuacutemeros enteros

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

Ahora es el momento de representar las soluciones asignamos a cada solucioacuten un color en

total obtenemos 288 soluciones aunque lo maacutes importante es saber que no son todas

coloraciones propias unas son permutaciones de otras (la justificacioacuten se puede encontrar en

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 i X3 i X3 i X3 i X3 i X3 i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 i i i X2 i X2 i X2 i X2 i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

[1] PASCUAL JARA NOTAS DE TRABAJO ANILLOS DE POLINOMIOS AacuteLGEBRA CONMUTATIVABAacuteSICA UGR 2016

[2] MARIacuteA ROSA MURGA DIacuteAZ COLORACIOacuteN EN GRAFOS UNIVERSIDAD DE CANTABRIA2013

[3] ANA ISABEL PEREZ MARTIacuteN TFG MEacuteTODOS POLINOMIALES PARA TRABAJAR CON GRAFOSUNIVERSIDAD DE VALLADOLID 2014

[4] ANTONIO GARVIacuteN COLOREANDO MAPAS UNIVERSIDAD DE MAacuteLAGA

[5] JA DE LOREA C J HILLAR PN MALKIN M OMAR RECOGNIZING GRAPH THEORETICPROPERTIES WITH POLYNOMIAL IDEALS ELECTRONIC J COMB 17 2010 26pp

[6] NICHOLE SCHIMANSKI REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE INMATHEMATICS PORLAND STATE UNIVERSITY 2011

[7] JM HARRIS JL HIRST MJ MOSSINGHOFF S AXTER KA RIBET COMBINATORICS ANDGRAPH THEORY SPRINGER 2000

Refencias Web

Un tipo de referencias

1 httpwwwjotdownes20141entusiasmo-por-el-polinomio-cromatico

2 httpwwwjotdownes201310clara-grima-los-colores-de-la-radio

3 httpsmatiestiiwikispacescomfileviewpolinomio+cromaacuteticopdf

4 httpseswikipediaorgwikiColoraciC3B3n_de_grafos

Iacutendice alfabeacutetico

Exp(a) 13iacutendice cromaacutetico 22

algoritmode Buchberger 13de la divisioacuten 12

arista 2incidente 2

basede Groebner 13

base de Groebnerminimal 14reducida 14

cociente 12coeficiente

liacuteder 12color 5coloracioacuten 5

distinguible 5propia 5

diagramade Newton 11

exponente 12

flecha 3

grado 12grafo 2

kndashcoloreable 5nndashcromaacutetico 22uacutenicamente kndashcoloreable 5componente conexa 3conexo 3disconexo 3

finito 3no orientado 3orientado 3regular 4simple 3

lado 2lazo 3lema

Dickson 11

monoideal 11monomio 10

liacuteder 12

nuacutemero cromaacutetico 22

ordenbuen orden 10total 10

particioacuten 12polinomio

cromaacutetico 23

resto 12

sndashpolinomio 13

teacuterminoliacuteder 12

teoremabase de Hilbert 13de Buchberger 13

veacutertice 2fin 3grado 4

78 IacuteNDICE ALFABEacuteTICO

origen 3veacutertices

adyacentes 2independientes 2

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

With this essay we want to introduce algebraic equations as a way to solve historical problemsproblems that have been already solved but of which demonstration involve too much time and thatcan be easily replace with a modern way of problem solving One example can be the computationof the chromatic polynomial first it was solved using combinatorial techniques now it solved usingalgebraical procedures

We also shall establish a way of working using algebra to solve problems of our quotidian life as theregulation of a traffic light cross

We shall list what is needed during the process that allows us to get our final equations Thoseequations will be solved by Wolfram Mathematic program

We shall start listing the importance of Discrete Mathematics and the different number of applicationsthat can be found for them

In the last few years Discrete Mathematics has won a great popularity just because it can be used inmany different technological areas A direct result of this fact is the introduction of this discipline asa main subject in the major part of engineering degrees Graph theory is one of the branches withmost applicability inside sciences field

There are a lot of different applications for graphs Nowadays graph theory is used as a basic tool inseveral fields as important as Operative Researching Chemistry Physics Genetic etc or can be usedfor designing installation diagrams of electric nets Generally those problems have been resolvedusing Combinatorial Mathematics the introduction of Graph theory has supposed a really greatimprovement that makes things be determined more easily

Before continuing letrsquos define superficially what a graph is we will use a simple and intuitive exam-ple to do it We will think in a road map on it we can distinguish two type of objects cities and roadswe will modelize these connections between cities by roads using a mathematical abstract objectWe will do that using graphs The usual way of drawing a Graphs is drawing a point for each vertexIf there exists an edge between two vertices we will draw a line connecting them The representationof a graph is not unique

80 CAP V ENGLISH MEMORY

Colourability of graphs is an special case of labelling graphs We will assign to each item of thegraph a colour To define a colourability of the vertices of the graphs we will need to oblige to eachcontiguous vertices not to share same colour We can extend that condition to edges and faces so wewill keep as condition that contiguous items will not share same colours Each of these cases will betreating as if they were verticesThe problem of efficiently colouring the vertices of a graph is a problem nearly as old as graph theoryitself Indeed one of the most celebrated theorems of modern mathematics is the ldquofourndashcolour Theo-remrdquo which states that any planar graph can be properly coloured with four colours This famousresult was conjectured in 1852 by Francis Guthrie and yet defied proof until 1976 when it was finallyconfirmed by Kenneth Appel and Wolfgang Haken Their proof made essential use of a computer togenerate and verify many subcases of the argument The interest in graph colouring however ismore than historical With direct applications to scheduling the topic finds many realndashworld usesof great practical importance In recent years there have been several theoretical advances in thesubject that extend familiar results and generalize many of the techniquesIn our essay we will show two different ways of computing the chromatic polynomial of a graphThe first one is combinatorial it is hard and difficult The second one uses a Mathematica algorithmand will make things really easyA great range of problems can be modelled for systems of polynomial equations We will mentionterms that N Alon coined and that are described in Recognizing graph theoretic properties withpolynomial ideals This term is Polynomial Method and with it he describes the use of non-linealpolynomials for solving combinatorial problemsContinuing with the inspection of this method and showing how the algorithmic theory of polynomialideals can be applied to detect kndashcolourability We shall use between others thing division algorithmGroebner basis and Wolfrang Mathematic software and programmingWe shall explore k-colourability using commutative algebra technics and using algebraic geometryIn this report we also will use arithmetic of polynomials rings in several indeterminates with coef-ficient in a field We will introduce computational methods based on division with remainder in apolynomial ring with n indeterminates To achieve that we will need to introduce order relations inn An indispensable condition for this order relation is that it needs to be a good order compatiblewith addition and with zero element that means that (0 0) should be the minimum element forthis specific order In this dissertation we will use Groebner basis for getting a way to do arithmeticoperations with ideals Some of the things we are going to use are(1) Cyclotomic polynomial φn(ω) its definition will allow us to use the nndashth primitive roots of the

unit as a way to solve colourability problems We will define and solve those equations(2) The relationship between the division algorithm and Groebner basis will be an important tool for

making our operations due to the special characteristic that tell us that every division with res-pect to a Groebner basis get always the same remainder and that it will be zero if the polynomialbelong to the ideal generated by the Groebner basis

(3) Using Wolfrang Mathematica we will design an algorithm that will calculate the different solu-tions of colourability of every graph we want to get coloured for that we only need to tell to theprogramme how many vertices and colours we will be used

(4) Using ldquohttpporcomputadorcomgrafoscromaticohtmlrdquo we will able to know how many co-lours we need to use in order to colour our graph

CAP V ENGLISH MEMORY 81

(5) So the problem is quickly solved only indicating which points are related and the number ofcolours that we shall use This way we obtain all the range of different solutions

The last part of our work is centred in the application of the theory to a practical use We shall applythose data to traffic lights

The first thing is to represent our traffic lights cross with a graph We shall define which point canbe related to other that means that we shall establish which of each traffic lights can be colouredwith the same colour at the same time That way we will obtain which pairs are related

Then we shall get the graph draw and the number of colours that we need to color the graphKnowing how many colours we need allow us to translate that information in the world of algebraWe will use the numbers of colours needed to define which primitive roots of the unit we will needto solve equations It is basic information because that knowledge will be the origin of the equationswe will resolve

When we get that ready we will use Wolfram Mathematic program to resolve the equations thatallow us to know the different solutions for colouring our graph

Sometimes the solutions will be difficult to be interpreted in those cases we will introduce a newidea Using DrsquoAlembert principle we will find a prime that will allow us to resolve those equationsusing module this prime the solutions obtain with this procedure will be really easy to be interpreted

Last part of the essay will be tables where in an intuitive way we can see all the different ways thatour traffic lights can get A small example is listed now in order to get understood what we will doduring the whole work

In a street cross there is three traffic lights one to allow cars on the right side to go other to allowcars continue going to the front and the last one that allow cars going to the left Our cross will besomething like that

Clearly when traffic light number 1 the one which allow cars keep going straight is green trafficLight 2 will be red so number 1 and 2 canrsquot be coloured the same way so they need to be coloureddifferently For traffic light number 3 and number 2 happen the same so 3 and 2 canrsquot be at the samecolor at the same time For traffic light 1 and traffic light 3 they can be same coloured at the sametime but also can be coloured differently

We shall need to use (12) (13) (2 3) pairs and we shall need only three colours to coloured this

graphs So we shall need to use the equations defined by third roots of the unit We shall obtainfollowing equations

Var= Table [X i i 1 3]Ecu1[n_]=Xn

3 minus 1Ecu2[D_]=XD[[1]]

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

When we resolve that we obtain our solutions that will be translate into a table So summarizingwe have used algebraic equations to solve a problem that traditionally has been solved using com-binatorial The use of this tool together with the use of modern software allows us to obtain resultquicker and more efficiently than before Modern mathematics are a faithful reflect of modern worldUsing what science brings us to make our life easy it is an intelligent way of using our resources

Agradecimientos

Introduccioacuten

I COLORACIOacuteN DE GRAFOS




II ANILLOS DE POLINOMIOS Y BASES DE GROEBNER


5 Bases de Groebner


III NUacuteMERO Y POLINOMIO CROMAacuteTICO



IV APLICACIONES

9 Introduccioacuten a la aplicacioacuten de la coloracioacuten de grafos en la regulacioacuten de semaacuteforos

Bibliografiacutea

Bibliografiacutea Referencias Web


V ENGLISH MEMORY

Director Prof Pascual JaraDepartamento de Aacutelgebra

Trabajo de fin de grado

A mi padre

Agradecimientos

Introduccioacuten

Iacutendice general

Agradecimientos IV

V ENGLISH MEMORY 79

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

A mi padre

Agradecimientos

Introduccioacuten

Iacutendice general

Agradecimientos IV

V ENGLISH MEMORY 79

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Agradecimientos

Introduccioacuten

Iacutendice general

Agradecimientos IV

V ENGLISH MEMORY 79

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Introduccioacuten

Iacutendice general

Agradecimientos IV

V ENGLISH MEMORY 79

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Iacutendice general

Agradecimientos IV

V ENGLISH MEMORY 79

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo I

Introduccioacuten

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

f~~~~~~~

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo II

Introduccioacuten

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

F =tsum

F =sum

αisinNn

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

F =sum

aαX α

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

∆2 = (α2 +Nn) ∆1

∆= Nn cupilet∆i

G1 Gt isin K[X1 Xn]

exp(G1) exp(Gt)

(1) F =sumt

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

5 Bases de Groebner

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Igualdad de ideales

1 F1r1 y F2

1 F2r2 res-

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

F + a= R(F G) + a

t Gt + R(FiG)

2t Gt + a2R(F2G) =

(a1Q11 + a2Q

1t + a2Q

2t )Gt + a1R(F1G) + a2R(F2G)

a1(R1 + a) + a2(R2 + a) = (a1R1 + a2R2) + a

Ideales cofinitos

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

cαX α

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

K[X(i + 1) Xn]

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo III

Introduccioacuten

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

1 P(G 0) = 0

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Graacuteficamente

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Length[Aux]

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

[ [ ]] [ [ ]]] ] ]

] sum ]] ]]

[ ] ]]

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

[ ] [ ]]

[ ] [ ] sum [[ ]]

[ [ ] [ ]]

[ ] [ ]]

[ [ ] ]

Funcion2[42Z]

1+(15+(25+10 (-3+Z)) (-2+Z)) (-1+Z)

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo IV

APLICACIONES

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 35

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 37

Var=Table[Xii14]

Ecu1[n_]=Xn^3-1

11988312+11988311198832+11988322 11988312+11988311198833+11988332 11988312+11988311198834+11988342 11988322+11988321198833+11988332 11988322+11988321198834+11988342

minus1+11988343 1198833minus1198834

11988322+11988321198834+11988342 1198831+1198832+1198834 minus1+11988343=0 1198833minus1198834=0

11988322+11988321198834+11988342=0 1198831+1198832+1198834=0 1198831+1198832+1198834=0

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 39

Ecu1[n_]=Xn^3-1

Aux=Thread[Aux==0]

Las soluciones son

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

(1 23 4) (1 42 2) (1 24 4) (2 41 1) (4 12 2) (1 23 4)

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 41

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFORO BEIRO

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 43

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 45

Var=Table[Xii14]

Ecu1[n_]=Xn^4-1

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Las soluciones son

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 47

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 49

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 51

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 53

Las soluciones son

X11 X2-i X3-1 X4i X5-1 X6-1

X11 X2-i X3i X4i X5-1 X6-1

X1i X2-i X3-1 X41 X5-1 X6-1

X1i X2-i X31 X41 X5-1 X6-1

X11 X2i X3-1 X4-i X5-1 X6-1

X11 X2i X3-i X4-i X5-1 X6-1

X1-i X2i X3-1 X41 X5-1 X6-1

X1-i X2i X31 X41 X5-1 X6-1

X1i X21 X3-1 X4-i X5-1 X6-1

X1i X21 X3-i X4-i X5-1 X6-1

X1-i X21 X3-1 X4i X5-1 X6-1

X1-i X21 X3i X4i X5-1 X6-1

X1i X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3-1 X4-1 X5-i X6-1

X11 X2-i X3i X4-1 X5-i X6-1

X1i X2-i X31 X4-1 X5-i X6-1

X11 X2-i X3-1 X4i X5-i X6-1

X11 X2-i X3i X4i X5-i X6-1

X1i X2-i X3-1 X41 X5-i X6-1

X1i X2-i X31 X41 X5-i X6-1

X1-i X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-1 X4-1 X5-i X6-1

X11 X2i X3-i X4-1 X5-i X6-1

X1-i X2i X31 X4-1 X5-i X6-1

X1-i X2i X3-1 X41 X5-i X6-1

X1-i X2i X31 X41 X5-i X6-1

X1-i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-1 X4-1 X5-i X6-1

X1i X21 X3-i X4-1 X5-i X6-1

X1-i X21 X3i X4-1 X5-i X6-1

X1-i X21 X3-1 X4i X5-i X6-1

X1-i X21 X3i X4i X5-i X6-1

X1i X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X11 X2-i X3-1 X4-1 X5i X6-1

X11 X2-i X3i X4-1 X5i X6-1

X1i X2-i X31 X4-1 X5i X6-1

X1i X2-i X3-1 X41 X5i X6-1

X1i X2-i X31 X41 X5i X6-1

X1-i X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-1 X4-1 X5i X6-1

X11 X2i X3-i X4-1 X5i X6-1

X1-i X2i X31 X4-1 X5i X6-1

X11 X2i X3-1 X4-i X5i X6-1

X11 X2i X3-i X4-i X5i X6-1

X1-i X2 i X3-1 X41 X5 i X6-1

X1- i X2 i X31 X41 X5 i X6-1

X1- i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3-1 X4-1 X5 i X6-1

X1 i X21 X3- i X4-1 X5 i X6-1

X1- i X21 X3 i X4-1 X5 i X6-1

X1 i X21 X3-1 X4- i X5 i X6-1

X1 i X21 X3- i X4- i X5 i X6-1

X1 i X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3-1 X4-1 X51 X6-1

X11 X2- i X3 i X4-1 X51 X6-1

X1 i X2- i X31 X4-1 X51 X6-1

X11 X2- i X3-1 X4 i X51 X6-1

X11 X2- i X3 i X4 i X51 X6-1

X1- i X2 X3-1 X4-1 X51 X6-1

X11 X2 i X3-1 X4-1 X51 X6-1

X11 X2 i X3- i X4-1 X51 X6-1

X1- i X2 i X31 X4-1 X51 X6-1

X11 X2 i X3-1 X4- i X51 X6-1

X11 X2 i X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3-1 X4-1 X51 X6-1

X1 i X21 X3- i X4-1 X51 X6-1

X1- i X21 X3 i X4-1 X51 X6-1

X1 i X21 X3-1 X4- i X51 X6-1

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 55

X1 i X21 X3- i X4- i X51 X6-1

X1- i X21 X3-1 X4 i X51 X6-1

X1- i X21 X3 i X4 i X51 X6-1

X1 i X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3- i X4- i X5-1 X6- i

X11 X2-1 X3 i X4- i X5-1 X6- i

X1 i X2-1 X31 X4- i X5-1 X6- i

X11 X2-1 X3- i X4 i X5-1 X6- i

X11 X2-1 X3 i X4 i X5-1 X6- i

X1 i X2-1 X3- i X41 X5-1 X6- i

X1 i X2-1 X31 X41 X5-1 X6- i

X1-1 X2 i X3- i X4- i X5-1 X6- i

X11 X2 i X3- X4- i X5-1 X6- i

X11 X2 i X3-1 X4- i X5-1 X6- i

X1-1 X2 i X31 X4- i X5-1 X6- i

X1-1 X2 i X3- i X41 X5-1 X6- i

X1-1 X2 i X31 X41 X5-1 X6- i

X1-1 X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3- i X4- i X5-1 X6- i

X1 i X21 X3-1 X4- i X5-1 X6- i

X1-1 X21 X3 i X4- i X5-1 X6- i

X1-1 X21 X3- i X4 i X5-1 X6- i

X1-1 X21 X3 i X4 i X5-1 X6- i

X11 X2-1 X3- i X4 i X5- i X6- i

X11 X2-1 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X41 X5- i X6- i

X1 i X2-1 X31 X41 X5- i X6- i

X11 X2 i X3-1 X4-1 X5- i X6- i

X11 X2 i X3- i X4-1 X5- i X6- i

X1-1 X2 i X3- i X41 X5- i X6- i

X1-1 X2 i X31 X41 X5- i X6- i

X1 i X21 X3-1 X4-1 X5- i X6- i

X1 i X21 X3- i X4-1 X5- i X6- i

X1-1 X21 X3- i X4 i X5- i X6- i

X1-1 X21 X3 i X4 i X5- i X6- i

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 i X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3- i X4- i X5 i X6- i

X11 X2-1 X3 i X4- i X5 i X6- i

X1 i X2-1 X31 X4- i X5 i X6- i

X1 i X2-1 X3- i X41 X5 i X6- i

X1 i X2-1 X31 X41 X5 i X6- i

X11 X2 i X3-1 X4-1 X5 i X6- i

X11 X2 i X3- i X4-1 X5 i X6- i

X1-1 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3- i X4- i X5 i X6- i

X11 X2 i X3-1 X4- i X5 i X6- i

X1-1 X2 i X31 X4- i X5 i X6- i

X1-1 X2 i X3- i X41 X5 i X6- i

X1-1 X2 i X31 X41 X5 i X6- i

X1 i X21 X3-1 X4-1 X5 i X6- i

X1 i X21 X3- i X4-1 X5 i X6- i

X1-1 X21 X3- i X4- i X5 i X6- i

X1 i X21 X3- i X4- i X5 i X6- i

X1 i X21 X3-1 X4- i X5 i X6- i

X1-1 X21 X3 i X4- i X5 i X6- i

X1 i X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3- i X4- i X51 X6- i

X11 X2-1 X3 i X4- i X51 X6- i

X1 i X2-1 X31 X4- i X51 X6- i

X11 X2-1 X3- i X4 i X51 X6- i

X11 X2-1 X3 i X4 i X51 X6- i

X11 X2 i X3-1 X4-1 X51 X6- i

X11 X2 i X3- i X4-1 X51 X6- i

X1-1 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3- i X4- i X51 X6- i

X11 X2 i X3-1 X4- i X51 X6- i

X1-1 X2 i X31 X4- i X51 X6- i

X1 i X21 X3-1 X4-1 X51 X6- i

X1 i X21 X3- i X4-1 X51 X6- i

X1-1 X21 X3- i X4- i X51 X6- i

X1 i X21 X3- i X4- i X51 X6- i

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 57

X1 i X21 X3-1 X4- i X51 X6- i

X1-1 X21 X3 i X4- i X51 X6- i

X1-1 X21 X3- i X4 i X51 X6- i

X1-1 X21 X3 i X4 i X51 X6- i

X11 X2-1 X3- i X4- i X5-1 X6 i

X11 X2-1 X3 i X4- i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3 i X4 i X5-1 X6 i

X11 X2-1 X3- i X4 i X5-1 X6 i

X1- i X2-1 X31 X4 i X5-1 X6 i

X1- i X2-1 X3 i X41 X5-1 X6 i

X1- i X2-1 X31 X41 X5-1 X6 i

X1-1 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3 i X4 i X5-1 X6 i

X11 X2- i X3-1 X4 i X5-1 X6 i

X1-1 X2- i X31 X4 i X5-1 X6 i

X1-1 X2- i X3 i X41 X5-1 X6 i

X1-1 X2- i X31 X41 X5-1 X6 i

X1-1 X21 X3- i X4- i X5-1 X6 i

X1-1 X21 X3 i X4- i X5-1 X6 i

X1-1 X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3 i X4 i X5-1 X6 i

X1- i X21 X3-1 X4 i X5-1 X6 i

X1-1 X21 X3- i X4 i X5-1 X6 i

X1- i X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3 i X4 i X5- i X6 i

X11 X2-1 X3- i X4 i X5- i X6 i

X1- i X2-1 X31 X4 i X5- i X6 i

X1- i X2-1 X3 i X41 X5- i X6 i

X1- i X2-1 X31 X41 X5- i X6 i

X11 X2- i X3-1 X4-1 X5- i X6 i

X11 X2- i X3 i X4-1 X5- i X6 i

X1-1 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3 i X4 i X5- i X6 i

X11 X2- i X3-1 X4 i X5- i X6 i

X1-1 X2- i X31 X4 i X5- i X6 i

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1-1 X2- i X3 i X41 X5- i X6 i

X1-1 X2- i X31 X41 X5- i X6 i

X1- i X21 X3-1 X4-1 X5- i X6 i

X1- i X21 X3 i X4-1 X5- i X6 i

X1-1 X21 X3 i X4 i X5- i X6 i

X1- i X21 X3 i X4 i X5- i X6 i

X1- i X21 X3-1 X4 i X5- i X6 i

X1-1 X21 X3- i X4 i X5- i X6 i

X11 X2-1 X3- i X4- i X5 i X6 i

X11 X2-1 X3 i X4- i X5 i X6 i

X1- i X2-1 X3 i X41 X5 i X6 i

X1- i X2-1 X31 X41 X5 i X6 i

X11 X2- i X3-1 X4-1 X5 i X6 i

X11 X2- i X3 i X4-1 X5 i X6 i

X1-1 X2- i X3 i X41 X5 i X6 i

X1-1 X2- i X31 X41 X5 i X6 i

X1- i X21 X3-1 X4-1 X5 i X6 i

X1- i X21 X3 i X4-1 X5 i X6 i

X1-1 X21 X3- i X4- i X5 i X6 i

X1-1 X21 X3 i X4- i X5 i X6 i

X11 X2-1 X3- i X4- i X51 X6 i

X11 X2-1 X3 i X4- i X51 X6 i

X1- i X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3 i X4 i X51 X6 i

X11 X2-1 X3- i X4 i X51 X6 i

X1- i X2-1 X31 X4 i X51 X6 i

X11 X2- i X3-1 X4-1 X51 X6 i

X11 X2- i X3 i X4-1 X51 X6 i

X1-1 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3 i X4 i X51 X6 i

X11 X2- i X3-1 X4 i X51 X6 i

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 59

X1-1 X2- i X31 X4 i X51 X6 i

X1- i X21 X3-1 X4-1 X51 X6 i

X1- i X21 X3 i X4-1 X51 X6 i

X1-1 X21 X3- i X4- i X51 X6 i

X1-1 X21 X3 i X4- i X51 X6 i

X1-1 X21 X3 i X4 i X51 X6 i

X1- i X21 X3 i X4 i X51 X6 i

X1- i X21 X3-1 X4 i X51 X6 i

X1-1 X21 X3- i X4 i X51 X6 i

X1 i X2-1 X3- i X4- i X5-1 X61

X1 i X2-1 X31 X4- i X5-1 X61

X1- i X2-1 X3 i X4 i X5-1 X61

X1- i X2-1 X31 X4 i X5-1 X61

X1- i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X31 X41 X5-1 X61

X1 i X2-1 X3- i X41 X5-1 X61

X1- i X2-1 X3 i X41 X5-1 X61

X1-1 X2-i X3 i X4 i X5-1 X61

X1-1 X2- i X31 X4 i X5-1 X61

X1-1 X2- i X31 X41 X5-1 X61

X1 i X2- i X31 X41 X5-1 X61

X1 i X2- i X3-1 X41 X5-1 X61

X1-1 X2- i X3 i X41 X5-1 X61

X1-1 X2 i X3- i X4- i X5-1 X61

X1-1 X2i X31 X4-i X5-1 X61

X1-1 X2i X31 X41 X5-1 X61

X1-i X2i X31 X41 X5-1 X61

X1-i X2i X3-1 X41 X5-1 X61

X1-1 X2i X3-i X41 X5-1 X61

X1-i X2-1 X3i X4i X5-i X61

X1-i X2-1 X31 X4i X5-i X61

X1-i X2-1 X31 X41 X5-i X61

X1i X2-1 X31 X41 X5-i X61

X1i X2-1 X3-i X41 X5-i X61

X1-i X2-1 X3i X41 X5-i X61

X1i X2-i X3-1 X4-1 X5-i X61

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1i X2-i X31 X4-1 X5-i X61

X1-1 X2-i X3i X4i X5-i X61

X1-1 X2- i X31 X4 i X5- i X61

X1-1 X2-i X31 X41 X5-i X61

X1i X2-i X31 X41 X5-i X61

X1i X2-i X3-1 X41 X5-i X61

X1-1 X2-i X3i X41 X5-i X61

X1- i X2 i X3-1 X4-1 X5- i X61

X1-i X2i X31 X4-1 X5-i X61

X1-1 X2i X31 X41 X5-i X61

X1-i X2i X31 X41 X5-i X61

X1-i X2i X3-1 X41 X5-i X61

X1-1 X2i X3-i X41 X5-i X61

X1i X2-1 X3-i X4-i X5i X61

X1 i X2-1 X31 X4- i X5 i X61

X1-i X2-1 X31 X41 X5i X61

X1i X2-1 X31 X41 X5i X61

X1i X2-1 X3-i X41 X5i X61

X1-i X2-1 X3i X41 X5i X61

X1i X2-i X3-1 X4-1 X5i X61

X1i X2-i X31 X4-1 X5i X61

X1-1 X2-i X31 X41 X5i X61

X1i X2-i X31 X41 X5i X61

X1i X2-i X3-1 X41 X5i X61

X1-1 X2-i X3i X41 X5i X61

X1-i X2i X3-1 X4-1 X5i X61

X1-i X2i X31 X4-1 X5i X61

X1-1 X2i X3-i X4-i X5i X61

X1-1 X2i X31 X4-i X5i X61

X1-1 X2 i X31 X41 X5 i X61

X1-i X2i X31 X41 X5i X61

X1-i X2i X3-1 X41 X5i X61

X1-1 X2i X3-i X41 X5i X61

X1i X2-1 X3-i X4-i X51 X61

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 61

X1i X2-1 X31 X4-i X51 X61

X1-i X2-1 X3i X4i X51 X61

X1-i X2-1 X31 X4i X51 X61

X1i X2-i X3-1 X4-1 X51 X61

X1i X2-i X31 X4-1 X51 X61

X1-1 X2-i X3i X4i X51 X61

X1-1 X2-i X31 X4i X51 X61

X1-i X2i X3-1 X4-1 X51 X61

X1-i X2i X31 X4-1 X51 X61

X1-1 X2i X3-i X4-i X51 X61

X1-1 X2i X31 X4-i X51 X61

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

el primer ejemplo)

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 63

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 i X4 -1 X4 i X4 i X4 i X4 i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 65

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 1 X5 1 X5 -1 X5 -i X5 -i

X6 -1 X6 -1 X6 -i X6 -i X6 -1 X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 1 X5 1 X5 i X5 i X5 -i X5 -i

X6 i X6 -i X6 i X6 -i X6 i X6 -i

X1 1 X1 1 X1 1 X1 1 X1 1 X1 1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 -1 X5 1 X5 -1 X5 1 X5 i X5 i

X6 -1 X6 -1 X6 i X6 i X6 -1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X5 -1 X5 -1 X5 -i X5 -i X5 i X5 i

X6 i X6 -i X6 1 X6 i X6 -i X6 i

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 67

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -i X6 1 X6 -i X6 1 X6 -i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

X1 -1 X1 -1 X1 -1 X1 -1 X1 -1 X1 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 -1 X5 1 X5 -1 X5 i X5 i

X6 1 X6 1 X6 i X6 i X6 1 X6 i

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 69

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 -i X2 -i X2 -i X2 -i X2 -i X2 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 i X5 i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 71

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 -i X6 1 X6 1 X6 i X6 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -i X3 -i X3 -i X3 -i X3 -i X3 -i

X4 -i X4 -i X4 -i X4 -i X4 -i X4 -i

X5 -1 X5 -1 X5 i X5 -i X5 -i X5 i

X6 -1 X6 i X6 -1 X6 -1 X6 i X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 -1 X5 -1 X5 -i X5 -i

X6 1 X6 -1 X6 1 X6 -1 X6 1 X6 -1

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

SEMAacuteFOROS 73

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X4 -1 X4 -1 X4 -1 X4 -1 X4 -1 X4 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 1 X2 1 X2 1 X2 1 X2 1 X2 1

X3 -1 X3 -1 X3 -1 X3 -1 X3 -1 X3 -1

X5 -1 X5 -1 X5 i X5 i X5 -i X5 -i

X6 -1 X6 i X6 -1 X6 i X6 -1 X6 -i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X3 1 X3 1 X3 1 X3 1 X3 1 X3 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X4 1 X4 1 X4 1 X4 1 X4 1 X4 1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

X1 -i X1 -i X1 -i X1 -i X1 -i X1 -i

X2 -1 X2 -1 X2 -1 X2 -1 X2 -1 X2 -1

X5 1 X5 1 X5 i X5 -i X5 -i X5 i

X6 1 X6 i X6 1 X6 1 X6 i X6 i

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Bibliografiacutea

Refencias Web

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

arista 2incidente 2

basede Groebner 13

exponente 12

flecha 3

grado 12grafo 2

lado 2lazo 3lema

Dickson 11

liacuteder 12

cromaacutetico 23

resto 12

sndashpolinomio 13

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Capiacutetulo V

ENGLISH MEMORY

ENGLISH REPORT

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

2 + XD[[1]] lowast XD[[2]] + XD[[2]]2

Agradecimientos

Introduccioacuten






5 Bases de Groebner





IV APLICACIONES


Bibliografiacutea



V ENGLISH MEMORY

Documents

COMPUTACIÓN SIMBÓLICA - ugr.esanillos/textos/pdf/2016/ComputacionSimbolica.pdf · 2 CAP. I. COLORACIÓN DE GRAFOS 1. Nociones de grafos Antes de continuar deﬁnamos lo que es un