% aboutgap.tex
% 1
\indexentry{About GAP}{57}
% 2
\indexentry{About Conventions}{58}
% 2
\indexentry{About Starting and Leaving GAP}{58}
% 2
\indexentry{About First Steps}{59}
% 2
\indexentry{About Help}{60}
% 2
\indexentry{About Syntax Errors}{60}
% 2
\indexentry{About Constants and Operators}{60}
% 2
\indexentry{About Variables and Assignments}{62}
% 2
\indexentry{About Functions}{64}
% 2
\indexentry{About Lists}{65}
% 2
\indexentry{About Identical Lists}{67}
% 2
\indexentry{About Sets}{69}
% 2
\indexentry{About Vectors and Matrices}{70}
% 2
\indexentry{About Records}{72}
% 2
\indexentry{About Ranges}{73}
% 2
\indexentry{About Loops}{74}
% 2
\indexentry{About Further List Operations}{76}
% 2
\indexentry{About Writing Functions}{77}
% 2
\indexentry{About Groups}{81}
% 2
\indexentry{About Operations of Groups}{89}
% 2
\indexentry{About Finitely Presented Groups and Presentations}{97}
% 2
\indexentry{About Fields}{102}
% 2
\indexentry{About Matrix Groups}{106}
% 2
\indexentry{About Domains and Categories}{107}
% 2
\indexentry{About Mappings and Homomorphisms}{115}
% 2
\indexentry{About Character Tables}{120}
% 2
\indexentry{About Group Libraries}{135}
% 2
\indexentry{About the Implementation of Domains}{141}
% 2
\indexentry{About Defining New Domains}{150}
% 2
\indexentry{About Defining New Parametrized Domains}{158}
% 2
\indexentry{About Defining New Group Elements}{162}
% language.tex
% 1
\indexentry{The Programming Language}{179}
% 2
\indexentry{Lexical Structure}{180}
% 2
\indexentry{Symbols}{180}
% 2
\indexentry{Whitespaces}{181}
\indexentry{space}{181}
\indexentry{blank}{181}
\indexentry{tabulator}{181}
\indexentry{newline}{181}
\indexentry{comments}{181}
% 2
\indexentry{Keywords}{182}
% 2
\indexentry{Identifiers}{182}
% 2
\indexentry{Expressions}{182}
\indexentry{evaluation}{182}
% 2
\indexentry{Variables}{183}
\indexentry{scope}{183}
\indexentry{bound}{183}
% 2
\indexentry{Function Calls}{184}
% 2
\indexentry{Comparisons}{185}
% 2
\indexentry{Operations}{186}
\indexentry{precedence}{186}
\indexentry{associativity}{186}
% 2
\indexentry{Statements}{186}
\indexentry{execution}{186}
% 2
\indexentry{Assignments}{187}
\indexentry{assignment!variable}{187}
% 2
\indexentry{Procedure Calls}{188}
% 2
\indexentry{If}{188}
\indexentry{if}{188}
\indexentry{if statement}{188}
\indexentry{fi}{188}
\indexentry{then}{188}
\indexentry{else}{188}
\indexentry{elif}{188}
% 2
\indexentry{While}{189}
\indexentry{while}{189}
\indexentry{while loop}{189}
\indexentry{loop!while}{189}
% 2
\indexentry{Repeat}{189}
\indexentry{repeat}{189}
\indexentry{repeat loop}{189}
\indexentry{loop!repeat}{189}
\indexentry{until}{189}
% 2
\indexentry{For}{190}
\indexentry{for}{190}
\indexentry{for loop}{190}
\indexentry{loop!for}{190}
\indexentry{do}{190}
\indexentry{od}{190}
% 2
\indexentry{Functions}{191}
\indexentry{function}{191}
\indexentry{end}{191}
\indexentry{local}{191}
\indexentry{recursion}{191}
\indexentry{recursive functions}{191}
\indexentry{environment}{191}
\indexentry{body}{191}
% 2
\indexentry{Return}{193}
\indexentry{return}{193}
% 2
\indexentry{The Syntax in BNF}{193}
\indexentry{BNF}{193}
% environm.tex
% 1
\indexentry{Environment}{197}
% 2
\indexentry{Main Loop}{197}
\indexentry{read eval print loop}{197}
\indexentry{loop!read eval print}{197}
\indexentry{prompt}{197}
\indexentry{prompt!partial}{197}
\indexentry{syntax errors}{197}
\indexentry{errors!syntax}{197}
\indexentry{output!suppressing}{197}
\indexentry{last}{197}
\indexentry{previous result}{197}
% 2
\indexentry{Break Loops}{199}
% 2
\indexentry{Error}{199}
% 2
\indexentry{Line Editing}{199}
% 2
\indexentry{Help}{201}
% 2
\indexentry{Reading Sections}{201}
\indexentry{help!scrolling}{201}
% 2
\indexentry{Format of Sections}{201}
\indexentry{help!format}{201}
% 2
\indexentry{Browsing through the Sections}{202}
\indexentry{help!browsing}{202}
% 2
\indexentry{Redisplaying a Section}{203}
\indexentry{help!redisplaying}{203}
% 2
\indexentry{Abbreviating Section Names}{203}
\indexentry{help!abbreviating}{203}
% 2
\indexentry{Help Index}{203}
\indexentry{help!index}{203}
% 2
\indexentry{Read}{204}
\indexentry{read!a file}{204}
\indexentry{load!a file}{204}
\indexentry{file!read a}{204}
\indexentry{file!load a}{204}
% 2
\indexentry{ReadLib}{205}
\indexentry{read!a library file}{205}
\indexentry{load!a library file}{205}
\indexentry{file!read a library}{205}
\indexentry{file!load a library}{205}
% 2
\indexentry{Print}{205}
% 2
\indexentry{PrintTo}{205}
\indexentry{print!to a file}{205}
\indexentry{file!print to a}{205}
% 2
\indexentry{AppendTo}{206}
\indexentry{append!to a file}{206}
\indexentry{file!append to a}{206}
% 2
\indexentry{LogTo}{206}
\indexentry{log!to a file}{206}
\indexentry{file!log to a}{206}
% 2
\indexentry{LogInputTo}{206}
\indexentry{log input!to a file}{206}
\indexentry{file!log input to a}{206}
% 2
\indexentry{SizeScreen}{206}
% 2
\indexentry{Runtime}{206}
% 2
\indexentry{Profile}{207}
% 2
\indexentry{Exec}{208}
% 2
\indexentry{Edit}{208}
% domain.tex
% 1
\indexentry{Domains}{209}
% 2
\indexentry{Domain Records}{210}
% 2
\indexentry{Dispatchers}{210}
\indexentry{operations record}{210}
\indexentry{record!operations}{210}
\indexentry{dispatcher functions}{210}
\indexentry{default functions}{210}
% 2
\indexentry{More about Dispatchers}{211}
% 2
\indexentry{An Example of a Computation in a Domain}{212}
% 2
\indexentry{Domain}{213}
% 2
\indexentry{Elements}{214}
\indexentry{elements!of a domain}{214}
% 2
\indexentry{Comparisons of Domains}{214}
% 2
\indexentry{Membership Test for Domains}{216}
\indexentry{in!for domains}{216}
\indexentry{membership test!for domains}{216}
% 2
\indexentry{IsFinite}{216}
\indexentry{finiteness test!for domains}{216}
% 2
\indexentry{Size}{217}
\indexentry{size!of a domain}{217}
% 2
\indexentry{IsSubset}{217}
\indexentry{subset test!for domains}{217}
% 2
\indexentry{Intersection}{217}
\indexentry{intersection!of domains}{217}
% 2
\indexentry{Union}{218}
\indexentry{union!of domains}{218}
% 2
\indexentry{Difference}{219}
\indexentry{set difference!of domains}{219}
% 2
\indexentry{Representative}{220}
\indexentry{representative!of a domain}{220}
% 2
\indexentry{Random}{220}
\indexentry{random element!of a domain}{220}
% ring.tex
% 1
\indexentry{Rings}{223}
% 2
\indexentry{IsRing}{223}
% 2
\indexentry{Ring}{224}
% 2
\indexentry{DefaultRing}{224}
% 2
\indexentry{Comparisons of Ring Elements}{225}
% 2
\indexentry{Operations for Ring Elements}{225}
% 2
\indexentry{Quotient}{226}
% 2
\indexentry{IsCommutativeRing}{226}
% 2
\indexentry{IsIntegralRing}{226}
% 2
\indexentry{IsUniqueFactorizationRing}{227}
% 2
\indexentry{IsEuclideanRing}{227}
% 2
\indexentry{IsUnit}{228}
% 2
\indexentry{Units}{228}
% 2
\indexentry{IsAssociated}{228}
% 2
\indexentry{StandardAssociate}{229}
% 2
\indexentry{Associates}{229}
% 2
\indexentry{IsIrreducible}{230}
% 2
\indexentry{IsPrime}{230}
% 2
\indexentry{Factors}{230}
% 2
\indexentry{EuclideanDegree}{231}
% 2
\indexentry{EuclideanRemainder}{231}
% 2
\indexentry{EuclideanQuotient}{232}
% 2
\indexentry{QuotientRemainder}{232}
% 2
\indexentry{Mod}{233}
% 2
\indexentry{QuotientMod}{233}
% 2
\indexentry{PowerMod}{234}
% 2
\indexentry{Gcd}{234}
% 2
\indexentry{GcdRepresentation}{235}
% 2
\indexentry{Lcm}{235}
% 2
\indexentry{Ring Records}{236}
% field.tex
% 1
\indexentry{Fields}{239}
% 2
\indexentry{IsField}{239}
% 2
\indexentry{Field}{240}
% 2
\indexentry{DefaultField}{240}
% 2
\indexentry{Fields over Subfields}{241}
% 2
\indexentry{Comparisons of Field Elements}{241}
% 2
\indexentry{Operations for Field Elements}{242}
% 2
\indexentry{GaloisGroup}{242}
\indexentry{Galois group!of a field}{242}
\indexentry{automorphism group!of a field}{242}
% 2
\indexentry{MinPol}{243}
\indexentry{minimal polynom!of a field element}{243}
% 2
\indexentry{CharPol}{243}
\indexentry{characteristic polynom!of a field element}{243}
% 2
\indexentry{Norm}{244}
\indexentry{norm!of a field element}{244}
% 2
\indexentry{Trace}{245}
\indexentry{trace!of a field element}{245}
% 2
\indexentry{Conjugates}{245}
\indexentry{Galois conjugates!of a field element}{245}
\indexentry{conjugates!of a field element, Galois}{245}
% 2
\indexentry{Field Homomorphisms}{246}
\indexentry{homomorphisms!of fields}{246}
% 2
\indexentry{IsFieldHomomorphism}{246}
\indexentry{IsHomomorphism!for fields}{246}
% 2
\indexentry{KernelFieldHomomorphism}{247}
\indexentry{Kernel!for fields}{247}
% 2
\indexentry{Mapping Functions for Field Homomorphisms}{247}
\indexentry{IsInjective!for field homomorphisms}{247}
\indexentry{IsSurjective!for field homomorphisms}{247}
\indexentry{equality!for field homomorphisms}{247}
\indexentry{Image!for field homomorphisms}{247}
\indexentry{Images!for field homomorphisms}{247}
\indexentry{PreImage!for field homomorphisms}{247}
\indexentry{PreImages!for field homomorphisms}{247}
% 2
\indexentry{Field Records}{248}
% group.tex
% 1
\indexentry{Groups}{249}
% 2
\indexentry{Group Elements}{250}
% 2
\indexentry{Comparisons of Group Elements}{250}
\indexentry{equality!of group elements}{250}
\indexentry{ordering!of group elements}{250}
% 2
\indexentry{Operations for Group Elements}{250}
\indexentry{product!of group elements}{250}
\indexentry{quotient!of group elements}{250}
\indexentry{conjugate!of a group element}{250}
\indexentry{power!of group elements}{250}
\indexentry{product!of list and group element}{251}
\indexentry{quotient!of list and group element}{251}
\indexentry{Comm!for group elements}{251}
\indexentry{LeftNormedComm!for group elements}{251}
\indexentry{RightNormedComm!for group elements}{251}
\indexentry{LeftQuotient!for group elements}{251}
% 2
\indexentry{IsGroupElement}{251}
\indexentry{test!for group element}{251}
% 2
\indexentry{Order}{252}
\indexentry{order!of a group element}{252}
% 2
\indexentry{More about Groups and Subgroups}{252}
% 2
\indexentry{IsParent}{253}
% 2
\indexentry{Parent}{253}
% 2
\indexentry{Group}{254}
% 2
\indexentry{AsGroup}{255}
% 2
\indexentry{IsGroup}{255}
% 2
\indexentry{Subgroup}{255}
% 2
\indexentry{AsSubgroup}{256}
% 2
\indexentry{Subgroups}{256}
% 2
\indexentry{Agemo}{256}
% 2
\indexentry{Centralizer}{257}
% 2
\indexentry{Centre}{257}
% 2
\indexentry{Closure}{258}
% 2
\indexentry{CommutatorSubgroup}{259}
% 2
\indexentry{ConjugateSubgroup}{259}
% 2
\indexentry{Core}{259}
% 2
\indexentry{DerivedSubgroup}{260}
% 2
\indexentry{FittingSubgroup}{260}
% 2
\indexentry{FrattiniSubgroup}{261}
% 2
\indexentry{NormalClosure}{261}
% 2
\indexentry{NormalIntersection}{261}
% 2
\indexentry{Normalizer}{261}
% 2
\indexentry{PCore}{262}
% 2
\indexentry{PrefrattiniSubgroup}{262}
% 2
\indexentry{Radical}{263}
% 2
\indexentry{SylowSubgroup}{263}
% 2
\indexentry{TrivialSubgroup}{263}
% 2
\indexentry{FactorGroup}{263}
% 2
\indexentry{FactorGroupElement}{264}
% 2
\indexentry{CommutatorFactorGroup}{265}
% 2
\indexentry{Series of Subgroups}{265}
% 2
\indexentry{DerivedSeries}{265}
% 2
\indexentry{CompositionSeries}{266}
% 2
\indexentry{ElementaryAbelianSeries}{266}
% 2
\indexentry{JenningsSeries}{266}
% 2
\indexentry{LowerCentralSeries}{267}
% 2
\indexentry{PCentralSeries}{267}
% 2
\indexentry{SubnormalSeries}{267}
% 2
\indexentry{UpperCentralSeries}{268}
% 2
\indexentry{Properties and Property Tests}{268}
% 2
\indexentry{AbelianInvariants}{269}
% 2
\indexentry{DimensionsLoewyFactors}{269}
% 2
\indexentry{EulerianFunction}{270}
% 2
\indexentry{Exponent}{270}
% 2
\indexentry{Factorization}{270}
% 2
\indexentry{Index}{271}
% 2
\indexentry{IsAbelian}{271}
% 2
\indexentry{IsCentral}{271}
% 2
\indexentry{IsConjugate}{272}
% 2
\indexentry{IsCyclic}{272}
% 2
\indexentry{IsElementaryAbelian}{272}
% 2
\indexentry{IsNilpotent}{273}
% 2
\indexentry{IsNormal}{273}
% 2
\indexentry{IsPerfect}{274}
% 2
\indexentry{IsSimple}{274}
% 2
\indexentry{IsSolvable}{274}
% 2
\indexentry{IsSubgroup}{275}
% 2
\indexentry{IsSubnormal}{275}
% 2
\indexentry{IsTrivial for Groups}{276}
\indexentry{IsTrivial!for groups}{276}
% 2
\indexentry{GroupId}{276}
% 2
\indexentry{PermutationCharacter}{279}
\indexentry{character!permutation}{279}
% 2
\indexentry{Conjugacy Classes}{279}
% 2
\indexentry{ConjugacyClasses}{279}
% 2
\indexentry{ConjugacyClass}{280}
% 2
\indexentry{IsConjugacyClass}{280}
% 2
\indexentry{Set Functions for Conjugacy Classes}{281}
\indexentry{Elements!for Conjugacy Classes}{281}
\indexentry{Size!for Conjugacy Classes}{281}
\indexentry{in!for Conjugacy Classes}{281}
\indexentry{Random!for Conjugacy Classes}{281}
% 2
\indexentry{Conjugacy Class Records}{281}
% 2
\indexentry{ConjugacyClassesSubgroups}{282}
% 2
\indexentry{Lattice}{283}
\indexentry{SetPrintLevel}{285}
\indexentry{PrintClassSubgroupLattice}{287}
\indexentry{InfoLattice1}{288}
\indexentry{PrintClassSubgroupLattice}{288}
\indexentry{SetPrintLevel}{288}
% 2
\indexentry{ConjugacyClassSubgroups}{288}
% 2
\indexentry{IsConjugacyClassSubgroups}{289}
% 2
\indexentry{Set Functions for Subgroup Conjugacy Classes}{289}
\indexentry{Elements!for conjugacy classes of subgroups}{289}
\indexentry{in!for conjugacy classes of subgroups}{289}
\indexentry{Size!for conjugacy classes of subgroups}{290}
% 2
\indexentry{Subgroup Conjugacy Class Records}{290}
% 2
\indexentry{ConjugacyClassesMaximalSubgroups}{290}
% 2
\indexentry{MaximalSubgroups}{291}
% 2
\indexentry{NormalSubgroups}{291}
% 2
\indexentry{ConjugateSubgroups}{292}
% 2
\indexentry{Cosets of Subgroups}{292}
% 2
\indexentry{RightCosets}{292}
\indexentry{cosets!right}{292}
% 2
\indexentry{RightCoset}{293}
\indexentry{Coset}{293}
\indexentry{coset!right}{293}
% 2
\indexentry{IsRightCoset}{293}
\indexentry{IsCoset}{293}
\indexentry{coset!right}{293}
% 2
\indexentry{Set Functions for Right Cosets}{294}
\indexentry{RightCosetGroupOps}{294}
\indexentry{Elements!for right cosets}{294}
\indexentry{IsFinite!for right cosets}{294}
\indexentry{Size!for right cosets}{294}
\indexentry{comparison!of right cosets}{294}
\indexentry{Intersection!for right cosets}{294}
\indexentry{Random!for right cosets}{294}
\indexentry{Print!for right cosets}{294}
\indexentry{product!for right cosets}{295}
% 2
\indexentry{Right Cosets Records}{295}
\indexentry{domain record!for right cosets}{295}
% 2
\indexentry{LeftCosets}{295}
\indexentry{cosets!left}{295}
% 2
\indexentry{LeftCoset}{296}
\indexentry{coset!left}{296}
% 2
\indexentry{IsLeftCoset}{296}
\indexentry{coset!left}{296}
% 2
\indexentry{DoubleCosets}{297}
\indexentry{cosets!double}{297}
% 2
\indexentry{DoubleCoset}{297}
\indexentry{coset!double}{297}
% 2
\indexentry{IsDoubleCoset}{298}
\indexentry{coset!double}{298}
% 2
\indexentry{Set Functions for Double Cosets}{298}
\indexentry{DoubleCosetGroupOps}{298}
\indexentry{Elements!for double cosets}{298}
\indexentry{IsFinite!for double cosets}{298}
\indexentry{Size!for double cosets}{298}
\indexentry{comparison!of double cosets}{298}
\indexentry{Intersection!for double cosets}{299}
\indexentry{Random!for double cosets}{299}
\indexentry{Print!for double cosets}{299}
\indexentry{product!for double cosets}{299}
% 2
\indexentry{Double Coset Records}{299}
% 2
\indexentry{Group Constructions}{300}
% 2
\indexentry{DirectProduct}{300}
\indexentry{Embedding!into direct products}{300}
\indexentry{Projection!onto component of direct products}{300}
% 2
\indexentry{DirectProduct for Groups}{301}
\indexentry{DirectProduct!for groups}{301}
% 2
\indexentry{SemidirectProduct}{301}
\indexentry{Embedding!into semidirect products}{301}
\indexentry{Projection!onto component of semidirect products}{301}
% 2
\indexentry{SemidirectProduct for Groups}{302}
\indexentry{SemidirectProduct!for groups}{302}
% 2
\indexentry{SubdirectProduct}{302}
\indexentry{Projection!for subdirect products}{303}
% 2
\indexentry{WreathProduct}{303}
% 2
\indexentry{WreathProduct for Groups}{304}
% 2
\indexentry{Group Homomorphisms}{304}
\indexentry{homomorphisms!of groups}{304}
% 2
\indexentry{IsGroupHomomorphism}{305}
\indexentry{IsHomomorphism!for groups}{305}
% 2
\indexentry{KernelGroupHomomorphism}{305}
\indexentry{Kernel!for groups}{305}
% 2
\indexentry{Mapping Functions for Group Homomorphisms}{306}
\indexentry{IsInjective!for group homomorphisms}{306}
\indexentry{IsSurjective!for group homomorphisms}{306}
\indexentry{equality!of group homomorphisms}{306}
\indexentry{ordering!of group homomorphisms}{306}
\indexentry{Image!for group homomorphisms}{307}
\indexentry{Images!for group homomorphisms}{307}
\indexentry{PreImages!for group homomorphisms}{307}
\indexentry{PreImage!for group homomorphisms}{307}
% 2
\indexentry{NaturalHomomorphism}{307}
\indexentry{group homomorphisms!natural}{307}
\indexentry{homomorphisms!natural, group}{307}
% 2
\indexentry{ConjugationGroupHomomorphism}{308}
\indexentry{group homomorphisms!conjugation}{308}
\indexentry{homomorphisms!conjugation, group}{308}
% 2
\indexentry{InnerAutomorphism}{309}
\indexentry{group homomorphisms!inner}{309}
\indexentry{homomorphisms!inner, group}{309}
% 2
\indexentry{GroupHomomorphismByImages}{309}
\indexentry{group homomorphisms!by images}{309}
\indexentry{homomorphisms!by images, group}{309}
\indexentry{IsMapping!for GroupHomomorphismByImages}{310}
\indexentry{Image!for GroupHomomorphismByImages}{310}
\indexentry{ImagesRepresentative!for GroupHomomorphismByImages}{310}
\indexentry{InverseMapping!for GroupHomomorphismByImages}{311}
\indexentry{CompositionMapping!for GroupHomomorphismByImages}{311}
% 2
\indexentry{Set Functions for Groups}{311}
\indexentry{Elements!for groups}{311}
\indexentry{IsSubset!for groups}{311}
\indexentry{Intersection!for groups}{311}
% 2
\indexentry{Elements for Groups}{311}
% 2
\indexentry{Intersection for Groups}{312}
% 2
\indexentry{Operations for Groups}{312}
\indexentry{operations!for groups}{312}
\indexentry{conjugate!of a group}{312}
\indexentry{membershiptest!for groups}{312}
\indexentry{product!of a group and a group element}{312}
\indexentry{quotient!of groups}{313}
% 2
\indexentry{Group Records}{313}
% operatio.tex
% 1
\indexentry{Operations of Groups}{317}
% 2
\indexentry{Other Operations}{318}
\indexentry{OnPoints}{318}
\indexentry{OnPairs}{318}
\indexentry{OnTuples}{318}
\indexentry{OnSets}{318}
\indexentry{OnRight}{318}
\indexentry{OnLeft}{318}
\indexentry{OnRightCosets}{318}
\indexentry{OnLeftCosets}{318}
\indexentry{OnLines}{318}
% 2
\indexentry{Cycle}{319}
% 2
\indexentry{CycleLength}{319}
% 2
\indexentry{Cycles}{320}
% 2
\indexentry{CycleLengths}{320}
% 2
\indexentry{Permutation}{321}
% 2
\indexentry{IsFixpoint}{322}
% 2
\indexentry{IsFixpointFree}{322}
% 2
\indexentry{DegreeOperation}{323}
% 2
\indexentry{IsTransitive}{323}
% 2
\indexentry{Transitivity}{324}
% 2
\indexentry{IsRegular}{325}
% 2
\indexentry{IsSemiRegular}{326}
% 2
\indexentry{Orbit}{326}
% 2
\indexentry{OrbitLength}{327}
% 2
\indexentry{Orbits}{328}
% 2
\indexentry{OrbitLengths}{329}
% 2
\indexentry{Operation}{329}
% 2
\indexentry{OperationHomomorphism}{330}
\indexentry{group homomorphisms!operation}{330}
\indexentry{homomorphisms!operation, group}{330}
\indexentry{Image!for OperationHomomorphism}{330}
\indexentry{PreImage!for OperationHomomorphism}{330}
\indexentry{Kernel!for OperationHomomorphism}{330}
% 2
\indexentry{Blocks}{331}
% 2
\indexentry{IsPrimitive}{332}
% 2
\indexentry{Stabilizer}{332}
% 2
\indexentry{RepresentativeOperation}{333}
% 2
\indexentry{RepresentativesOperation}{334}
% 2
\indexentry{IsEquivalentOperation}{335}
% vecspace.tex
% 1
\indexentry{Vector Spaces}{337}
% 2
\indexentry{VectorSpace}{337}
% 2
\indexentry{IsVectorSpace}{338}
% 2
\indexentry{Vector Space Records}{338}
% 2
\indexentry{Set Functions for Vector Spaces}{339}
\indexentry{Elements!for vector spaces}{339}
\indexentry{Size!of vector spaces}{339}
\indexentry{IsFinite!for vector spaces}{339}
\indexentry{Intersection!of vector spaces}{339}
% 2
\indexentry{IsSubspace}{339}
% 2
\indexentry{Base}{339}
\indexentry{Base!of vector space}{339}
% 2
\indexentry{AddBase}{340}
\indexentry{AddBase!for vector space}{340}
% 2
\indexentry{Dimension}{341}
\indexentry{Dimension!of vector space}{341}
% 2
\indexentry{LinearCombination}{341}
\indexentry{LinearCombination!in vector space}{341}
% 2
\indexentry{Coefficients}{342}
\indexentry{Coefficients!in vector space}{342}
% integer.tex
% 1
\indexentry{Integers}{343}
\indexentry{type!integer}{343}
% 2
\indexentry{Comparisons of Integers}{344}
\indexentry{comparisons!of integers}{344}
% 2
\indexentry{Operations for Integers}{344}
\indexentry{operations!for integers}{344}
% 2
\indexentry{QuoInt}{345}
\indexentry{integer part of a quotient}{345}
% 2
\indexentry{RemInt}{345}
\indexentry{remainder of a quotient}{345}
% 2
\indexentry{IsInt}{346}
\indexentry{test!for an integer}{346}
% 2
\indexentry{Int}{346}
\indexentry{convert!to an integer}{346}
% 2
\indexentry{AbsInt}{346}
\indexentry{absolute value of an integer}{346}
% 2
\indexentry{SignInt}{346}
\indexentry{sign!of an integer}{346}
% 2
\indexentry{ChineseRem}{347}
\indexentry{chinese remainder}{347}
% 2
\indexentry{LogInt}{347}
\indexentry{logarithm of an integer}{347}
% 2
\indexentry{RootInt}{347}
\indexentry{root!of an integer}{347}
\indexentry{square root!of an integer}{347}
% 2
\indexentry{SmallestRootInt}{348}
\indexentry{root!of an integer, smallest}{348}
% 2
\indexentry{Set Functions for Integers}{348}
% 2
\indexentry{Ring Functions for Integers}{349}
% 2
\indexentry{Primes}{350}
\indexentry{list!of primes}{350}
% 2
\indexentry{IsPrimeInt}{350}
\indexentry{test!for a prime}{350}
% 2
\indexentry{IsPrimePowerInt}{351}
\indexentry{test!for a power of a prime}{351}
% 2
\indexentry{NextPrimeInt}{351}
\indexentry{larger prime}{351}
% 2
\indexentry{PrevPrimeInt}{352}
\indexentry{smaller prime}{352}
% 2
\indexentry{FactorsInt}{352}
\indexentry{factorization!of an integer}{352}
% 2
\indexentry{DivisorsInt}{352}
\indexentry{divisors!of an integer}{352}
% 2
\indexentry{Sigma}{353}
\indexentry{sum!of divisors of an integer}{353}
\indexentry{mersenne primes}{353}
\indexentry{primes!mersenne}{353}
% 2
\indexentry{Tau}{353}
\indexentry{number!of divisors of an integer}{353}
% 2
\indexentry{MoebiusMu}{354}
\indexentry{Moebius inversion function}{354}
% numtheor.tex
% 1
\indexentry{Number Theory}{355}
\indexentry{prime residue group}{355}
% 2
\indexentry{PrimeResidues}{355}
\indexentry{prime residue group}{355}
% 2
\indexentry{Phi}{356}
\indexentry{Eulers totient function}{356}
\indexentry{prime residue group!order}{356}
\indexentry{order!of the prime residue group}{356}
% 2
\indexentry{Lambda}{356}
\indexentry{Carmichaels lambda function}{356}
\indexentry{prime residue group!exponent}{356}
\indexentry{exponent!of the prime residue group}{356}
% 2
\indexentry{OrderMod}{357}
\indexentry{multiplicative order of an integer}{357}
% 2
\indexentry{IsPrimitiveRootMod}{357}
\indexentry{test!for a primitive root}{357}
\indexentry{prime residue group!generator}{357}
\indexentry{generator!of the prime residue group}{357}
% 2
\indexentry{PrimitiveRootMod}{358}
\indexentry{primitive root modulo an integer}{358}
\indexentry{prime residue group!generator}{358}
\indexentry{generator!of the prime residue group}{358}
% 2
\indexentry{Jacobi}{358}
\indexentry{quadratic residue}{358}
\indexentry{residue!quadratic}{358}
% 2
\indexentry{Legendre}{358}
\indexentry{quadratic residue}{358}
\indexentry{residue!quadratic}{358}
% 2
\indexentry{RootMod}{359}
\indexentry{quadratic residue}{359}
\indexentry{residue!quadratic}{359}
\indexentry{root!of an integer modulo another}{359}
% 2
\indexentry{RootsUnityMod}{359}
\indexentry{modular roots}{359}
\indexentry{root!of 1 modulo an integer}{359}
% rational.tex
% 1
\indexentry{Rationals}{361}
\indexentry{type!rationals}{361}
% 2
\indexentry{IsRat}{361}
\indexentry{test!for a rational}{361}
% 2
\indexentry{Numerator}{362}
\indexentry{numerator!of a rational}{362}
% 2
\indexentry{Denominator}{362}
\indexentry{denominator!of a rational}{362}
% 2
\indexentry{Comparisons of Rationals}{363}
\indexentry{comparisons!of rationals}{363}
% 2
\indexentry{Operations for Rationals}{363}
\indexentry{operations!for rationals}{363}
% 2
\indexentry{Set Functions for Rationals}{364}
% 2
\indexentry{Field Functions for Rationals}{364}
% cyclotom.tex
% 1
\indexentry{Cyclotomics}{365}
\indexentry{type!cyclotomic}{365}
\indexentry{irrationalities}{365}
% 2
\indexentry{More about Cyclotomics}{365}
\indexentry{cyclotomic field elements}{365}
\indexentry{E}{365}
\indexentry{roots of unity}{365}
% 2
\indexentry{Cyclotomic Integers}{366}
% 2
\indexentry{IntCyc}{367}
% 2
\indexentry{RoundCyc}{367}
% 2
\indexentry{IsCyc}{367}
\indexentry{test!for a cyclotomic}{367}
% 2
\indexentry{IsCycInt}{367}
\indexentry{test!for a cyclotomic integer}{367}
% 2
\indexentry{NofCyc}{368}
% 2
\indexentry{CoeffsCyc}{368}
\indexentry{coefficients!for cyclotomics}{368}
% 2
\indexentry{Comparisons of Cyclotomics}{368}
\indexentry{operators!for cyclotomics}{368}
% 2
\indexentry{Operations for Cyclotomics}{369}
\indexentry{operators!for cyclotomics}{369}
% 2
\indexentry{GaloisCyc}{369}
\indexentry{galois conjugation}{369}
\indexentry{galois automorphism}{369}
% 2
\indexentry{ATLAS irrationalities}{370}
\indexentry{$b_N$}{370}
\indexentry{$c_N$}{370}
\indexentry{$d_N$}{370}
\indexentry{$e_N$}{370}
\indexentry{$f_N$}{370}
\indexentry{$g_N$}{370}
\indexentry{$h_N$}{370}
\indexentry{$i_N$}{370}
\indexentry{$j_N$}{370}
\indexentry{$k_N$}{370}
\indexentry{$l_N$}{370}
\indexentry{$m_N$}{370}
\indexentry{$r_N$}{370}
\indexentry{$s_N$}{370}
\indexentry{$t_N$}{370}
\indexentry{$u_N$}{370}
\indexentry{$v_N$}{370}
\indexentry{$w_N$}{370}
\indexentry{$x_N$}{370}
\indexentry{$y_N$}{370}
\indexentry{$n_k$}{370}
\indexentry{atomic irrationalities}{370}
\indexentry{EB}{370}
\indexentry{EC}{370}
\indexentry{ED}{370}
\indexentry{EE}{370}
\indexentry{EF}{370}
\indexentry{EG}{370}
\indexentry{EH}{370}
\indexentry{EI}{370}
\indexentry{EJ}{370}
\indexentry{EK}{370}
\indexentry{EL}{370}
\indexentry{EM}{370}
\indexentry{ER}{370}
\indexentry{ES}{370}
\indexentry{ET}{370}
\indexentry{EU}{370}
\indexentry{EV}{370}
\indexentry{EW}{370}
\indexentry{EX}{370}
\indexentry{EY}{370}
\indexentry{NK}{370}
% 2
\indexentry{StarCyc}{371}
\indexentry{galois conjugate!unique}{371}
% 2
\indexentry{Quadratic}{371}
\indexentry{quadratic irrationalities}{371}
\indexentry{quadratic number fields}{371}
% 2
\indexentry{GaloisMat}{372}
\indexentry{galois conjugate characters}{372}
% 2
\indexentry{RationalizedMat}{373}
\indexentry{rational characters}{373}
% gaussian.tex
% 1
\indexentry{Gaussians}{375}
\indexentry{type!gaussian rationals}{375}
\indexentry{type!gaussian integers}{375}
% 2
\indexentry{Comparisons of Gaussians}{375}
\indexentry{equality!of gaussians}{375}
\indexentry{ordering!of gaussians}{375}
% 2
\indexentry{Operations for Gaussians}{376}
\indexentry{sum!of gaussians}{376}
\indexentry{difference!of gaussians}{376}
\indexentry{product!of gaussians}{376}
\indexentry{quotient!of gaussians}{376}
\indexentry{power!of gaussians}{376}
% 2
\indexentry{IsGaussRat}{377}
\indexentry{test!for gaussian rational}{377}
% 2
\indexentry{IsGaussInt}{377}
\indexentry{test!for gaussian integer}{377}
% 2
\indexentry{Set Functions for Gaussians}{377}
\indexentry{membership test!for gaussians}{377}
\indexentry{in!for gaussians}{377}
\indexentry{Random!for gaussians}{377}
% 2
\indexentry{Field Functions for Gaussian Rationals}{378}
\indexentry{Conjugates!for gaussians}{378}
\indexentry{Norm!for gaussians}{378}
\indexentry{Trace!for gaussians}{378}
% 2
\indexentry{Ring Functions for Gaussian Integers}{378}
\indexentry{IsUnit!for gaussians}{378}
\indexentry{Units!for gaussians}{378}
\indexentry{IsAssociated!for gaussians}{378}
\indexentry{Associates!for gaussians}{378}
\indexentry{StandardAssociate!for gaussians}{378}
\indexentry{EuclideanDegree!for gaussians}{378}
\indexentry{EuclideanRemainder!for gaussians}{378}
\indexentry{EuclideanQuotient!for gaussians}{378}
\indexentry{QuotientRemainder!for gaussians}{378}
\indexentry{IsPrime!for gaussians}{378}
\indexentry{IsIrreducible!for gaussians}{378}
\indexentry{Factors!for gaussians}{378}
% 2
\indexentry{TwoSquares}{379}
\indexentry{representation!as a sum of two squares}{379}
% numfield.tex
% 1
\indexentry{Subfields of Cyclotomic Fields}{381}
% 2
\indexentry{IsNumberField}{382}
\indexentry{test!for number field}{382}
% 2
\indexentry{IsCyclotomicField}{382}
\indexentry{test!for a cyclotomic field}{382}
% 2
\indexentry{Number Field Records}{382}
\indexentry{field!number}{382}
\indexentry{NF}{382}
% 2
\indexentry{Cyclotomic Field Records}{383}
\indexentry{field!cyclotomic}{383}
\indexentry{CF}{383}
% 2
\indexentry{DefaultField and Field for Cyclotomics}{384}
\indexentry{conductor}{384}
\indexentry{default field!for cyclotomics}{384}
\indexentry{field!for cyclotomics}{384}
% 2
\indexentry{DefaultRing and Ring for Cyclotomic Integers}{385}
\indexentry{default ring!for cyclotomic integers}{385}
\indexentry{ring!for cyclotomic integers}{385}
% 2
\indexentry{GeneratorsPrimeResidues}{385}
\indexentry{generators!of Galois group}{385}
% 2
\indexentry{GaloisGroup for Number Fields}{386}
\indexentry{number fields!Galois group}{386}
\indexentry{automorphism group!of number fields}{386}
% 2
\indexentry{ZumbroichBase}{386}
% 2
\indexentry{Integral Bases for Number Fields}{387}
\indexentry{LenstraBase}{387}
% 2
\indexentry{NormalBaseNumberField}{388}
\indexentry{base!of a number field}{388}
% 2
\indexentry{Coefficients for Number Fields}{388}
% 2
\indexentry{Domain Functions for Number Fields}{389}
% algext.tex
% 1
\indexentry{Algebraic extensions of fields}{391}
\indexentry{Field Extensions}{391}
% 2
\indexentry{AlgebraicExtension}{391}
% 2
\indexentry{IsAlgebraicExtension}{392}
\indexentry{test!for algebraic extension}{392}
% 2
\indexentry{RootOf}{392}
\indexentry{primitive element}{392}
% 2
\indexentry{Algebraic Extension Elements}{392}
\indexentry{type!algebraic elements}{392}
\indexentry{Operations for algebraic elements}{392}
% 2
\indexentry{Set functions for Algebraic Extensions}{392}
\indexentry{membership test!for algebraic extensions}{392}
\indexentry{in!for algebraic Elements}{392}
\indexentry{Random!for algebraic Extensions}{392}
% 2
\indexentry{IsNormalExtension}{393}
\indexentry{test!for normal extension}{393}
% 2
\indexentry{MinpolFactors}{393}
% 2
\indexentry{GaloisGroup for Extension Fields}{393}
\indexentry{Galois group!of an extension field}{393}
\indexentry{automorphism group!of an extension field}{393}
% 2
\indexentry{ExtensionAutomorphism}{394}
\indexentry{field homomorphisms!of algebraic extensions}{394}
% 2
\indexentry{Field functions for Algebraic Extensions}{394}
\indexentry{Norm!for algebraic extensions}{394}
\indexentry{Trace!for algebraic extensions}{394}
\indexentry{DefaultField!for algebraic extensions}{394}
\indexentry{Field!for algebraic extensions}{394}
% 2
\indexentry{Algebraic Extension Records}{395}
\indexentry{record fields!for algebraic extension fields}{395}
% 2
\indexentry{Extension Element Records}{395}
\indexentry{record fields!for extension elements}{395}
% 2
\indexentry{IsAlgebraicElement}{395}
\indexentry{test!for algebraic element}{395}
% 2
\indexentry{Algebraic extensions of the Rationals}{395}
% 2
\indexentry{DefectApproximation}{396}
\indexentry{defect}{396}
% 2
\indexentry{GaloisType}{396}
\indexentry{Galois}{396}
% 2
\indexentry{ProbabilityShapes}{396}
% 2
\indexentry{DecomPoly}{396}
\indexentry{decomposition!of polynomials}{396}
\indexentry{ideal decomposition}{396}
% unknown.tex
% 1
\indexentry{Unknowns}{399}
\indexentry{data type!unknown}{399}
% 2
\indexentry{Unknown}{400}
% 2
\indexentry{IsUnknown}{400}
% 2
\indexentry{Comparisons of Unknowns}{401}
% 2
\indexentry{Operations for Unknowns}{401}
% finfield.tex
% 1
\indexentry{Finite Fields}{403}
\indexentry{field!finite}{403}
\indexentry{galois field}{403}
\indexentry{field!galois}{403}
% 2
\indexentry{Finite Field Elements}{403}
\indexentry{Z}{403}
% 2
\indexentry{Comparisons of Finite Field Elements}{404}
\indexentry{comparisons!of finite field elements}{404}
% 2
\indexentry{Operations for Finite Field Elements}{405}
% 2
\indexentry{IsFFE}{406}
\indexentry{test!for a finite field element}{406}
% 2
\indexentry{CharFFE}{406}
\indexentry{characteristic!of a finite field element}{406}
% 2
\indexentry{DegreeFFE}{407}
\indexentry{degree!of a finite field element}{407}
% 2
\indexentry{OrderFFE}{407}
\indexentry{order!of a finite field element}{407}
% 2
\indexentry{IntFFE}{407}
\indexentry{convert!a finite field element to an integer}{407}
% 2
\indexentry{LogFFE}{408}
\indexentry{logarithm!of a finite field element, discrete}{408}
\indexentry{discrete logarithm!of a finite field element}{408}
% 2
\indexentry{GaloisField}{408}
\indexentry{GF}{408}
% 2
\indexentry{FrobeniusAutomorphism}{409}
\indexentry{homomorphisms!Frobenius, field}{409}
\indexentry{field homomorphisms!Frobenius}{409}
\indexentry{Image!for Frobenius automorphisms}{409}
\indexentry{CompositionMapping!for Frobenius automorphisms}{409}
% 2
\indexentry{Set Functions for Finite Fields}{409}
\indexentry{Elements!for finite fields}{409}
\indexentry{in!for finite fields}{409}
\indexentry{membership test!for finite fields}{409}
\indexentry{Random!for finite fields}{409}
\indexentry{Intersection!for finite fields}{409}
% 2
\indexentry{Field Functions for Finite Fields}{410}
\indexentry{GaloisGroup!for finite fields}{410}
\indexentry{Conjugates!for finite fields}{410}
\indexentry{Norm!for finite fields}{410}
% polynom.tex
% 1
\indexentry{Polynomials}{411}
% 2
\indexentry{Multivariate Polynomials}{413}
% 2
\indexentry{Indeterminate}{413}
\indexentry{X}{413}
% 2
\indexentry{Polynomial}{414}
% 2
\indexentry{IsPolynomial}{414}
% 2
\indexentry{Comparisons of Polynomials}{414}
\indexentry{comparisons!of polynomials}{414}
% 2
\indexentry{Operations for Polynomials}{415}
\indexentry{operations!for polynomials}{415}
% 2
\indexentry{Degree}{417}
% 2
\indexentry{LeadingCoefficient}{418}
% 2
\indexentry{Value}{418}
% 2
\indexentry{Derivative}{418}
% 2
\indexentry{InterpolatedPolynomial}{419}
% 2
\indexentry{ConwayPolynomial}{419}
% 2
\indexentry{CyclotomicPolynomial}{419}
% 2
\indexentry{PolynomialRing}{420}
% 2
\indexentry{IsPolynomialRing}{420}
% 2
\indexentry{LaurentPolynomialRing}{420}
% 2
\indexentry{IsLaurentPolynomialRing}{421}
% 2
\indexentry{Ring Functions for Polynomial Rings}{421}
\indexentry{EuclideanDegree!for polynomials}{421}
\indexentry{EuclideanRemainder!for polynomials}{421}
\indexentry{EuclideanQuotient!for polynomials}{421}
\indexentry{QuotientRemainder!for polynomials}{421}
\indexentry{Gcd!for polynomials}{422}
\indexentry{Factors!for polynomials}{422}
\indexentry{StandardAssociate!for polynomials}{423}
% 2
\indexentry{Ring Functions for Laurent Polynomial Rings}{423}
\indexentry{EuclideanDegree!for polynomials}{423}
\indexentry{Gcd!for polynomials}{423}
\indexentry{Factors!for polynomials}{424}
\indexentry{StandardAssociate!for polynomials}{424}
% permutat.tex
% 1
\indexentry{Permutations}{425}
% 2
\indexentry{Comparisons of Permutations}{426}
% 2
\indexentry{Operations for Permutations}{426}
% 2
\indexentry{IsPerm}{427}
% 2
\indexentry{LargestMovedPointPerm}{427}
% 2
\indexentry{SmallestMovedPointPerm}{428}
% 2
\indexentry{SignPerm}{428}
% 2
\indexentry{SmallestGeneratorPerm}{428}
% 2
\indexentry{ListPerm}{428}
% 2
\indexentry{PermList}{429}
% 2
\indexentry{RestrictedPerm}{429}
% 2
\indexentry{MappingPermListList}{429}
% permgrp.tex
% 1
\indexentry{Permutation Groups}{431}
% 2
\indexentry{IsPermGroup}{431}
% 2
\indexentry{PermGroupOps.MovedPoints}{432}
% 2
\indexentry{PermGroupOps.SmallestMovedPoint}{432}
% 2
\indexentry{PermGroupOps.LargestMovedPoint}{432}
% 2
\indexentry{PermGroupOps.NrMovedPoints}{432}
% 2
\indexentry{Stabilizer Chains}{433}
% 2
\indexentry{StabChain}{434}
% 2
\indexentry{MakeStabChain}{435}
% 2
\indexentry{ExtendStabChain}{436}
% 2
\indexentry{ReduceStabChain}{436}
% 2
\indexentry{MakeStabChainStrongGenerators}{436}
% 2
\indexentry{Base for Permutation Groups}{437}
% 2
\indexentry{PermGroupOps.Indices}{437}
% 2
\indexentry{PermGroupOps.StrongGenerators}{437}
% 2
\indexentry{ListStabChain}{438}
% 2
\indexentry{PermGroupOps.ElementProperty}{438}
% 2
\indexentry{PermGroupOps.SubgroupProperty}{439}
% 2
\indexentry{CentralCompositionSeriesPPermGroup}{440}
% 2
\indexentry{PermGroupOps.PgGroup}{440}
% 2
\indexentry{Set Functions for Permutation Groups}{440}
\indexentry{Random!for Permutation Groups}{440}
\indexentry{Size!for Permutation Groups}{441}
\indexentry{Elements!for Permutation Groups}{441}
\indexentry{Intersection!for Permutation Groups}{441}
% 2
\indexentry{Group Functions for Permutation Groups}{441}
\indexentry{Conjugate Subgroup!of Permutation Group}{441}
\indexentry{Centralizer!for Permutation Groups}{441}
\indexentry{Normalizer!for Permutation Groups}{441}
\indexentry{SylowSubgroup!for Permutation Groups}{441}
\indexentry{Coset!for Permutation Groups}{442}
\indexentry{Cosets!for Permutation Groups}{442}
\indexentry{PermutationCharacter}{442}
\indexentry{ElementaryAbelianSeries!for Permutation Groups}{443}
\indexentry{IsSolvable!for Permutation Groups}{443}
\indexentry{CompositionSeries!for Permutation Groups}{443}
\indexentry{ExponentsPermSolvablePermGroup}{444}
\indexentry{AgGroup!for Permutation Groups}{444}
% 2
\indexentry{Operations of Permutation Groups}{445}
\indexentry{IsSemiRegular!for Permutation Groups}{445}
\indexentry{RepresentativeOperation!for Permutation Groups}{445}
\indexentry{Stabilizer!for Permutation Groups}{445}
\indexentry{Blocks!for Permutation Groups}{446}
% 2
\indexentry{Homomorphisms for Permutation Groups}{446}
\indexentry{GroupHomomorphismsByImages!for permutation groups}{446}
\indexentry{IsMapping!for GroupHomomorphismByImages for permutation groups}{446}
\indexentry{Image!for GroupHomomorphismByImages for permutation groups}{446}
\indexentry{CompositionMapping!for GroupHomomorphismByImages for permutation groups}{446}
\indexentry{OperationHomomorphism!for transitive constituents}{446}
\indexentry{Image!for transitive constituent homomorphisms}{447}
\indexentry{PreImages!for transitive constituent homomorphisms}{447}
\indexentry{OperationHomomorphism!for blocks}{447}
\indexentry{Image!for blocks homomorphisms}{447}
\indexentry{PreImage!for blocks homomorphisms}{447}
\indexentry{Kernel!for blocks homomorphisms}{447}
% 2
\indexentry{Random Methods for Permutation Groups}{448}
\indexentry{Random! Methods for Permutation Groups}{448}
\indexentry{Schreier-Sims!Random}{448}
\indexentry{StabChainOptions}{448}
% 2
\indexentry{Permutation Group Records}{449}
% word.tex
% 1
\indexentry{Words in Abstract Generators}{451}
\indexentry{words}{451}
\indexentry{type!words}{451}
\indexentry{IdWord}{451}
% 2
\indexentry{AbstractGenerator}{452}
% 2
\indexentry{AbstractGenerators}{452}
% 2
\indexentry{Comparisons of Words}{453}
% 2
\indexentry{Operations for Words}{453}
\indexentry{product!of words}{453}
\indexentry{product!of list and group element}{453}
\indexentry{quotient!of words}{453}
\indexentry{quotient!of list and word}{453}
\indexentry{power!of words}{453}
\indexentry{conjugate!of a word}{453}
\indexentry{Comm!for words}{453}
\indexentry{LeftQuotient!for words}{453}
% 2
\indexentry{IsWord}{454}
% 2
\indexentry{LengthWord}{455}
\indexentry{length!of a word}{455}
% 2
\indexentry{ExponentSumWord}{455}
% 2
\indexentry{Subword}{455}
% 2
\indexentry{PositionWord}{456}
% 2
\indexentry{SubstitutedWord}{456}
% 2
\indexentry{EliminatedWord}{456}
% 2
\indexentry{MappedWord}{457}
% fpgrp.tex
% 1
\indexentry{Finitely Presented Groups}{459}
% 2
\indexentry{FreeGroup}{460}
% 2
\indexentry{Set Functions for Finitely Presented Groups}{460}
\indexentry{Size!for finitely presented groups}{461}
\indexentry{in!for finitely presented groups}{461}
\indexentry{Elements!for finitely presented groups}{461}
\indexentry{Intersection!for finitely presented groups}{461}
% 2
\indexentry{Group Functions for Finitely Presented Groups}{461}
\indexentry{Order!for finitely presented groups}{462}
\indexentry{Index!for finitely presented groups}{462}
\indexentry{Normalizer!for finitely presented groups}{462}
\indexentry{CommutatorFactorGroup!for finitely presented groups}{462}
\indexentry{AbelianInvariants!for finitely presented groups}{462}
\indexentry{AbelianInvariantsSubgroupFpGroup}{462}
\indexentry{AbelianInvariantsSubgroupFpGroupRrs}{462}
\indexentry{AbelianInvariantsSubgroupFpGroupMtc}{463}
\indexentry{AbelianInvariantsNormalClosureFpGroup}{463}
\indexentry{AbelianInvariantsNormalClosureFpGroupRrs}{463}
% 2
\indexentry{CosetTableFpGroup}{464}
% 2
\indexentry{OperationCosetsFpGroup}{465}
% 2
\indexentry{IsIdenticalPresentationFpGroup}{465}
% 2
\indexentry{LowIndexSubgroupsFpGroup}{466}
% 2
\indexentry{Presentation Records}{466}
\indexentry{Tietze record}{466}
\indexentry{PresentationFpGroup}{466}
\indexentry{FpGroupPresentation}{467}
\indexentry{TzPrintStatus}{467}
\indexentry{TzPrintGenerators}{467}
\indexentry{TzPrintRelators}{467}
\indexentry{TzPrintPresentation}{468}
\indexentry{TzPrint}{468}
\indexentry{Save!for presentation records}{469}
% 2
\indexentry{Changing Presentations}{469}
\indexentry{AddGenerator}{470}
\indexentry{AddRelator}{470}
\indexentry{RemoveRelator}{470}
% 2
\indexentry{Subgroup Presentations}{470}
\indexentry{PresentationSubgroupRrs}{470}
\indexentry{Reduced Reidemeister-Schreier}{470}
\indexentry{primary subgroup generators}{471}
\indexentry{secondary subgroup generators}{471}
\indexentry{augmented coset table}{471}
\indexentry{PresentationSubgroupMtc}{471}
\indexentry{Modified Todd-Coxeter}{471}
\indexentry{augmented coset table}{472}
\indexentry{primary subgroup generators}{472}
\indexentry{secondary subgroup generators}{472}
\indexentry{PresentationSubgroup}{473}
\indexentry{PresentationNormalClosureRrs}{473}
\indexentry{PresentationNormalClosure}{473}
% 2
\indexentry{SimplifiedFpGroup}{474}
% 2
\indexentry{Tietze Transformations}{474}
\indexentry{total length of a presentation}{474}
\indexentry{SimplifyPresentation}{475}
\indexentry{TzGo}{475}
\indexentry{TzGoGo}{476}
\indexentry{TzEliminate}{476}
\indexentry{TzSearch}{477}
\indexentry{TzSearchEqual}{478}
\indexentry{TzFindCyclicJoins}{478}
\indexentry{TzSubstitute}{478}
\indexentry{TzSubstituteCyclicJoins}{482}
\indexentry{TzPrintLengths}{482}
\indexentry{TzPrintPairs}{482}
\indexentry{TzPrintOptions}{482}
\indexentry{Tietze options}{482}
% 2
\indexentry{DecodeTree}{485}
\indexentry{tree decoding}{485}
\indexentry{secondary subgroup generators}{485}
\indexentry{primary subgroup generators}{485}
\indexentry{subgroup generators tree}{485}
% agwords.tex
% 1
\indexentry{Words in Finite Polycyclic Groups}{489}
\indexentry{Ag Words}{489}
% 2
\indexentry{More about Ag Words}{489}
% 2
\indexentry{Ag Word Comparisons}{490}
\indexentry{equality!of ag words}{490}
\indexentry{ordering!of ag words}{490}
% 2
\indexentry{CentralWeight}{491}
% 2
\indexentry{CompositionLength}{491}
% 2
\indexentry{Depth}{491}
% 2
\indexentry{IsAgWord}{492}
% 2
\indexentry{LeadingExponent}{492}
% 2
\indexentry{RelativeOrder}{492}
% 2
\indexentry{CanonicalAgWord}{493}
% 2
\indexentry{DifferenceAgWord}{493}
% 2
\indexentry{ReducedAgWord}{494}
% 2
\indexentry{SiftedAgWord}{494}
% 2
\indexentry{SumAgWord}{494}
% 2
\indexentry{ExponentAgWord}{495}
% 2
\indexentry{ExponentsAgWord}{495}
% aggroup.tex
% 1
\indexentry{Finite Polycyclic Groups}{497}
\indexentry{Ag Groups}{497}
% 2
\indexentry{More about Ag Groups}{497}
% 2
\indexentry{Construction of Ag Groups}{498}
% 2
\indexentry{Ag Group Operations}{498}
% 2
\indexentry{Ag Group Records}{499}
% 2
\indexentry{Set Functions for Ag Groups}{499}
\indexentry{Elements!for ag groups}{499}
\indexentry{in!for ag groups}{499}
\indexentry{membership test!for ag groups}{499}
\indexentry{IsSubset!for ag groups}{499}
\indexentry{Intersection!for ag groups}{500}
\indexentry{Size!for ag groups}{500}
% 2
\indexentry{Elements for Ag Groups}{500}
% 2
\indexentry{Intersection for Ag Groups}{500}
% 2
\indexentry{Size for Ag Groups}{500}
% 2
\indexentry{Group Functions for Ag Groups}{501}
\indexentry{Group!for ag groups}{501}
\indexentry{Centralizer!for ag groups}{501}
\indexentry{ConjugateSubgroup!for ag groups}{501}
\indexentry{CommutatorSubgroup!for ag groups}{501}
\indexentry{ElementaryAbelianSeries!for ag groups}{502}
\indexentry{NormalIntersection!for ag groups}{502}
\indexentry{Normalizer!for ag groups}{502}
\indexentry{SylowSubgroup!for ag groups}{502}
\indexentry{DerivedSeries!for ag groups}{502}
\indexentry{LowerCentralSeries!for ag groups}{502}
\indexentry{AbelianInvariants!for ag groups}{503}
\indexentry{Random!for ag groups}{503}
\indexentry{IsCyclic!for ag groups}{503}
\indexentry{IsFinite!for ag groups}{503}
\indexentry{IsNilpotent!for ag group}{503}
\indexentry{IsNormal!for ag groups}{503}
\indexentry{IsPerfect!for ag group}{503}
\indexentry{IsSubgroup!for ag groups}{503}
\indexentry{ConjugacyClasses!for ag groups}{503}
\indexentry{Orbit!for ag groups}{503}
\indexentry{Stabilizer!for ag groups}{504}
\indexentry{AsGroup!for ag groups}{504}
\indexentry{FpGroup!for ag groups}{504}
\indexentry{RightCoset!for ag groups}{504}
\indexentry{AbelianGroup!for ag groups}{504}
\indexentry{CyclicGroup!for ag groups}{504}
\indexentry{ElementaryAbelianGroup!for ag groups}{504}
\indexentry{DirectProduct!for ag groups}{504}
\indexentry{WreathProduct!for ag groups}{504}
% 2
\indexentry{AsGroup for Ag Groups}{504}
% 2
\indexentry{Group for Ag Groups}{505}
% 2
\indexentry{CommutatorSubgroup for Ag Groups}{505}
% 2
\indexentry{Normalizer for Ag Groups}{505}
% 2
\indexentry{AbelianInvariants for Ag Groups}{505}
% 2
\indexentry{IsCyclic for Ag Groups}{506}
% 2
\indexentry{IsNormal for Ag Groups}{506}
% 2
\indexentry{IsSubgroup for Ag Groups}{506}
% 2
\indexentry{Stabilizer for Ag Groups}{506}
% 2
\indexentry{CyclicGroup for Ag Groups}{506}
% 2
\indexentry{ElementaryAbelianGroup for Ag Groups}{507}
% 2
\indexentry{DirectProduct for Ag Groups}{507}
% 2
\indexentry{WreathProduct for Ag Groups}{508}
% 2
\indexentry{RightCoset for Ag Groups}{508}
% 2
\indexentry{FpGroup for Ag Groups}{509}
% 2
\indexentry{Ag Group Functions}{509}
% 2
\indexentry{AgGroup}{509}
% 2
\indexentry{IsAgGroup}{510}
% 2
\indexentry{AgGroupFpGroup}{510}
% 2
\indexentry{IsConsistent}{510}
% 2
\indexentry{IsElementaryAbelianAgSeries}{511}
% 2
\indexentry{MatGroupAgGroup}{511}
% 2
\indexentry{PermGroupAgGroup}{512}
% 2
\indexentry{RefinedAgSeries}{512}
% 2
\indexentry{ChangeCollector}{512}
% 2
\indexentry{The Prime Quotient Algorithm}{513}
% 2
\indexentry{PQuotient}{513}
% 2
\indexentry{Save}{515}
% 2
\indexentry{PQp}{516}
% 2
\indexentry{InitPQp}{516}
% 2
\indexentry{FirstClassPQp}{516}
% 2
\indexentry{NextClassPQp}{516}
% 2
\indexentry{Weight}{517}
% 2
\indexentry{Factorization for PQp}{517}
% 2
\indexentry{The Solvable Quotient Algorithm}{517}
% 2
\indexentry{SolvableQuotient}{517}
% 2
\indexentry{InitSQ}{519}
% 2
\indexentry{ModulesSQ}{519}
% 2
\indexentry{NextModuleSQ}{520}
% 2
\indexentry{Generating Systems of Ag Groups}{520}
% 2
\indexentry{AgSubgroup}{521}
% 2
\indexentry{Cgs}{521}
% 2
\indexentry{Igs}{522}
% 2
\indexentry{IsNormalized}{522}
% 2
\indexentry{Normalize}{522}
% 2
\indexentry{Normalized}{522}
% 2
\indexentry{MergedCgs}{522}
% 2
\indexentry{MergedIgs}{523}
% 2
\indexentry{Factor Groups of Ag Groups}{523}
% 2
\indexentry{FactorGroup for AgGroups}{524}
\indexentry{FactorGroup!for ag groups}{524}
% 2
\indexentry{CollectorlessFactorGroup}{524}
% 2
\indexentry{FactorArg}{524}
% 2
\indexentry{Subgroups and Properties of Ag Groups}{525}
% 2
\indexentry{CompositionSubgroup}{525}
% 2
\indexentry{HallSubgroup}{526}
% 2
\indexentry{PRump}{526}
% 2
\indexentry{RefinedSubnormalSeries}{526}
% 2
\indexentry{SylowComplements}{527}
% 2
\indexentry{SylowSystem}{527}
% 2
\indexentry{SystemNormalizer}{528}
% 2
\indexentry{MinimalGeneratingSet}{529}
% 2
\indexentry{IsElementAgSeries}{529}
% 2
\indexentry{IsPNilpotent}{529}
% 2
\indexentry{NumberConjugacyClasses}{529}
% 2
\indexentry{Exponents}{530}
% 2
\indexentry{FactorsAgGroup}{530}
% 2
\indexentry{MaximalElement}{531}
% 2
\indexentry{Orbitalgorithms of Ag Groups}{531}
% 2
\indexentry{AffineOperation}{531}
% 2
\indexentry{AgOrbitStabilizer}{532}
% 2
\indexentry{LinearOperation}{532}
% 2
\indexentry{Intersections of Ag Groups}{533}
% 2
\indexentry{ExtendedIntersectionSumAgGroup}{533}
% 2
\indexentry{IntersectionSumAgGroup}{534}
% 2
\indexentry{SumAgGroup}{535}
% 2
\indexentry{SumFactorizationFunctionAgGroup}{535}
% 2
\indexentry{One Cohomology Group}{536}
% 2
\indexentry{OneCoboundaries}{536}
% 2
\indexentry{OneCocycles}{537}
% 2
\indexentry{Complements}{539}
% 2
\indexentry{Complement}{539}
% 2
\indexentry{Complementclasses}{539}
% 2
\indexentry{CoprimeComplement}{540}
% 2
\indexentry{ComplementConjugatingAgWord}{540}
% 2
\indexentry{HallConjugatingWordAgGroup}{541}
% 2
\indexentry{Example, normal closure}{541}
% saggroup.tex
% 1
\indexentry{Special Ag Groups}{545}
% 2
\indexentry{More about Special Ag Groups}{545}
% 2
\indexentry{Construction of Special Ag Groups}{547}
% 2
\indexentry{Restricted Special Ag Groups}{547}
% 2
\indexentry{Special Ag Group Records}{548}
% 2
\indexentry{MatGroupSagGroup}{550}
% 2
\indexentry{DualMatGroupSagGroup}{550}
% 2
\indexentry{Ag Group Functions for Special Ag Groups}{551}
% list.tex
% 1
\indexentry{Lists}{553}
\indexentry{type!list}{553}
% 2
\indexentry{IsList}{554}
\indexentry{test!for a list}{554}
% 2
\indexentry{List}{554}
\indexentry{convert!to a list}{554}
\indexentry{map}{554}
% 2
\indexentry{List Elements}{555}
\indexentry{accessing!list elements}{555}
% 2
\indexentry{Length}{556}
\indexentry{length!of a list}{556}
% 2
\indexentry{List Assignment}{556}
\indexentry{assignment!to a list}{556}
% 2
\indexentry{Add}{558}
\indexentry{add!an element to a list}{558}
% 2
\indexentry{Append}{558}
\indexentry{add!elements to a list}{558}
\indexentry{append!elements to a list}{558}
% 2
\indexentry{Identical Lists}{559}
% 2
\indexentry{IsIdentical}{560}
% 2
\indexentry{Enlarging Lists}{561}
% 2
\indexentry{Comparisons of Lists}{562}
\indexentry{comparisons!of lists}{562}
% 2
\indexentry{Operations for Lists}{562}
\indexentry{operations!for lists}{562}
% 2
\indexentry{In}{563}
\indexentry{test!for membership}{563}
% 2
\indexentry{Position}{563}
\indexentry{find!an element in a list}{563}
% 2
\indexentry{PositionSorted}{564}
\indexentry{find!an element in a sorted list}{564}
% 2
\indexentry{PositionProperty}{565}
% 2
\indexentry{Concatenation}{565}
\indexentry{concatenation!of lists}{565}
% 2
\indexentry{Flat}{565}
% 2
\indexentry{Reversed}{566}
\indexentry{reverse the elements of a list}{566}
% 2
\indexentry{Sublist}{566}
% 2
\indexentry{Cartesian}{566}
\indexentry{cross product of lists}{566}
% 2
\indexentry{Number}{567}
\indexentry{number!of elements in a list}{567}
% 2
\indexentry{Collected}{567}
% 2
\indexentry{Filtered}{568}
% 2
\indexentry{ForAll}{568}
% 2
\indexentry{ForAny}{569}
% 2
\indexentry{First}{569}
% 2
\indexentry{Sort}{569}
\indexentry{sort a list}{569}
% 2
\indexentry{SortParallel}{570}
% 2
\indexentry{Sortex}{570}
% 2
\indexentry{Permuted}{570}
% 2
\indexentry{Product}{571}
\indexentry{multiply!the elements of a list}{571}
% 2
\indexentry{Sum}{571}
\indexentry{add!the elements of a list}{571}
% 2
\indexentry{Maximum}{571}
\indexentry{maximum!of integers}{571}
\indexentry{maximum!of a list}{571}
% 2
\indexentry{Minimum}{572}
\indexentry{minimum!of integers}{572}
\indexentry{minimum!of a list}{572}
% 2
\indexentry{Iterated}{572}
\indexentry{iterate a function over a list}{572}
% 2
\indexentry{RandomList}{572}
\indexentry{RandomSeed}{573}
% set.tex
% 1
\indexentry{Sets}{575}
\indexentry{multisets}{575}
% 2
\indexentry{IsSet}{576}
\indexentry{test!for a set}{576}
% 2
\indexentry{Set}{576}
\indexentry{convert!to a set}{576}
% 2
\indexentry{IsEqualSet}{576}
\indexentry{test!for set equality}{576}
% 2
\indexentry{AddSet}{577}
\indexentry{add!an element to a set}{577}
% 2
\indexentry{RemoveSet}{577}
\indexentry{remove!an element from a set}{577}
% 2
\indexentry{UniteSet}{577}
\indexentry{union!of sets}{577}
% 2
\indexentry{IntersectSet}{578}
\indexentry{intersection!of sets}{578}
% 2
\indexentry{SubtractSet}{578}
\indexentry{subtract!a set from another}{578}
% 2
\indexentry{Set Functions for Sets}{578}
\indexentry{test!for subsets}{578}
\indexentry{IsSubset!for sets}{578}
\indexentry{union!of sets}{579}
\indexentry{intersection!of sets}{579}
% 2
\indexentry{More about Sets}{579}
% blister.tex
% 1
\indexentry{Boolean Lists}{581}
\indexentry{lists!boolean}{581}
\indexentry{subsets}{581}
\indexentry{blist}{581}
% 2
\indexentry{BlistList}{581}
% 2
\indexentry{ListBlist}{582}
% 2
\indexentry{IsBlist}{582}
% 2
\indexentry{SizeBlist}{582}
% 2
\indexentry{IsSubsetBlist}{583}
% 2
\indexentry{UnionBlist}{583}
\indexentry{union!of boolean lists}{583}
% 2
\indexentry{IntersectionBlist}{583}
\indexentry{intersection!of boolean lists}{583}
% 2
\indexentry{DifferenceBlist}{584}
\indexentry{difference!of boolean lists}{584}
% 2
\indexentry{UniteBlist}{584}
\indexentry{union!of boolean lists}{584}
% 2
\indexentry{IntersectBlist}{584}
\indexentry{intersection!of boolean lists}{584}
% 2
\indexentry{SubtractBlist}{584}
\indexentry{subtract!a boolean list from another}{584}
% 2
\indexentry{More about Boolean Lists}{585}
% string.tex
% 1
\indexentry{Strings and Characters}{587}
\indexentry{type!strings}{587}
\indexentry{doublequotes}{587}
\indexentry{backslash}{587}
\indexentry{special character sequences}{587}
% 2
\indexentry{String}{589}
\indexentry{convert!to a string}{589}
% 2
\indexentry{ConcatenationString}{589}
\indexentry{concatenation!of strings}{589}
\indexentry{append!one string to another}{589}
% 2
\indexentry{SubString}{590}
\indexentry{substring!of a string}{590}
\indexentry{part!of a string}{590}
% 2
\indexentry{Comparisons of Strings}{590}
\indexentry{comparisons!of strings}{590}
% 2
\indexentry{IsString}{591}
\indexentry{test!for a string}{591}
% 2
\indexentry{LengthString}{591}
\indexentry{length!of a string}{591}
% range.tex
% 1
\indexentry{Ranges}{593}
% 2
\indexentry{IsRange}{594}
\indexentry{test!for a range}{594}
% 2
\indexentry{More about Ranges}{594}
% vector.tex
% 1
\indexentry{Vectors}{597}
\indexentry{scalars}{597}
\indexentry{base!of vector space}{597}
\indexentry{dimension!of vector space}{597}
% 2
\indexentry{Operations for Vectors}{598}
\indexentry{operations!for vectors}{598}
% 2
\indexentry{IsVector}{599}
\indexentry{test!for a vector}{599}
% 2
\indexentry{NormedVector}{599}
% 2
\indexentry{More about Vectors}{599}
% rowspace.tex
% 1
\indexentry{Row Spaces}{601}
% 2
\indexentry{More about Row Spaces}{601}
% 2
\indexentry{Row Space Bases}{602}
% 2
\indexentry{Row Space Cosets}{602}
% 2
\indexentry{Quotient Spaces}{603}
% 2
\indexentry{Subspaces and Parent Spaces}{603}
% 2
\indexentry{RowSpace}{604}
% 2
\indexentry{Operations for Row Spaces}{604}
% 2
\indexentry{Functions for Row Spaces}{605}
% 2
\indexentry{IsRowSpace}{606}
% 2
\indexentry{Subspace}{606}
% 2
\indexentry{AsSubspace}{606}
% 2
\indexentry{AsSpace}{607}
% 2
\indexentry{NormedVectors}{607}
% 2
\indexentry{Coefficients for Row Space Bases}{607}
% 2
\indexentry{SiftedVector}{607}
% 2
\indexentry{Basis}{608}
% 2
\indexentry{CanonicalBasis}{608}
% 2
\indexentry{SemiEchelonBasis}{609}
% 2
\indexentry{IsSemiEchelonBasis}{609}
% 2
\indexentry{NumberVector}{610}
% 2
\indexentry{ElementRowSpace}{610}
% 2
\indexentry{Operations for Row Space Cosets}{610}
% 2
\indexentry{Functions for Row Space Cosets}{611}
% 2
\indexentry{IsSpaceCoset}{611}
% 2
\indexentry{Operations for Quotient Spaces}{612}
% 2
\indexentry{Functions for Quotient Spaces}{612}
% 2
\indexentry{Row Space Records}{612}
% 2
\indexentry{Row Space Basis Records}{613}
% 2
\indexentry{Row Space Coset Records}{613}
% 2
\indexentry{Quotient Space Records}{614}
% matrix.tex
% 1
\indexentry{Matrices}{615}
\indexentry{matrix}{615}
\indexentry{type!matrices}{615}
% 2
\indexentry{Operations for Matrices}{615}
% 2
\indexentry{IsMat}{617}
% 2
\indexentry{IdentityMat}{618}
% 2
\indexentry{NullMat}{618}
% 2
\indexentry{TransposedMat}{618}
% 2
\indexentry{KroneckerProduct}{619}
% 2
\indexentry{DimensionsMat}{619}
% 2
\indexentry{TraceMat}{619}
% 2
\indexentry{DeterminantMat}{619}
% 2
\indexentry{RankMat}{620}
% 2
\indexentry{OrderMat}{620}
% 2
\indexentry{TriangulizeMat}{620}
% 2
\indexentry{BaseMat}{621}
% 2
\indexentry{NullspaceMat}{621}
% 2
\indexentry{SolutionMat}{621}
% 2
\indexentry{DiagonalizeMat}{622}
% 2
\indexentry{ElementaryDivisorsMat}{622}
% 2
\indexentry{PrintArray}{622}
% matring.tex
% 1
\indexentry{Matrix Rings}{623}
% 2
\indexentry{Set Functions for Matrix Rings}{623}
% 2
\indexentry{Ring Functions for Matrix Rings}{624}
\indexentry{IsUnit!for matrix rings}{624}
% matgrp.tex
% 1
\indexentry{Matrix Groups}{625}
% 2
\indexentry{Set Functions for Matrix Groups}{625}
\indexentry{in!for matrix groups}{625}
\indexentry{Size!for matrix groups}{625}
\indexentry{Intersection!for matrix groups}{625}
\indexentry{Random!for matrix groups}{625}
% 2
\indexentry{Group Functions for Matrix Groups}{626}
\indexentry{Centralizer!for matrix groups}{626}
\indexentry{Normalizer!for matrix groups}{626}
\indexentry{SylowSubgroup!for matrix groups}{626}
\indexentry{ConjugacyClasses!for matrix groups}{626}
\indexentry{PermGroup!for matrix groups}{626}
\indexentry{Stabilizer!for matrix groups}{626}
\indexentry{RepresentativeOperation!for matrix groups}{626}
% 2
\indexentry{Matrix Group Records}{627}
% grplib.tex
% 1
\indexentry{Group Libraries}{629}
% 2
\indexentry{The Basic Groups Library}{629}
\indexentry{CyclicGroup}{629}
\indexentry{AbelianGroup}{630}
\indexentry{ElementaryAbelianGroup}{630}
\indexentry{DihedralGroup}{630}
\indexentry{PolyhedralGroup}{631}
\indexentry{SymmetricGroup}{631}
\indexentry{AlternatingGroup}{631}
\indexentry{GeneralLinearGroup}{631}
\indexentry{SpecialLinearGroup}{632}
\indexentry{SymplecticGroup}{632}
\indexentry{GeneralUnitaryGroup}{632}
\indexentry{SpecialUnitaryGroup}{632}
% 2
\indexentry{Selection Functions}{632}
% 2
\indexentry{Example Functions}{633}
% 2
\indexentry{Extraction Functions}{634}
% 2
\indexentry{The Primitive Groups Library}{636}
\indexentry{AllPrimitiveGroups}{636}
\indexentry{OnePrimitiveGroup}{636}
\indexentry{PrimitiveGroup}{636}
\indexentry{Frobenius group}{637}
% 2
\indexentry{The Transitive Groups Library}{638}
\indexentry{AllTransitiveGroups}{638}
\indexentry{TransitiveGroup}{638}
\indexentry{TransitiveIdentification}{638}
% 2
\indexentry{The Solvable Groups Library}{640}
\indexentry{AllSolvableGroups}{640}
\indexentry{OneSolvableGroup}{640}
\indexentry{SolvableGroup}{640}
% 2
\indexentry{The 2-Groups Library}{641}
\indexentry{2-groups}{641}
\indexentry{AllTwoGroups}{641}
\indexentry{OneTwoGroup}{641}
\indexentry{TwoGroup}{641}
% 2
\indexentry{The 3-Groups Library}{643}
\indexentry{3-groups}{643}
\indexentry{AllThreeGroups}{643}
\indexentry{OneThreeGroup}{643}
\indexentry{ThreeGroup}{643}
% 2
\indexentry{The Irreducible Solvable Linear Groups Library}{645}
\indexentry{AllIrreducibleSolvableGroups}{645}
\indexentry{OneIrreducibleSolvableGroup}{645}
\indexentry{IrreducibleSolvableGroup}{646}
% 2
\indexentry{The Crystallographic Groups Library}{647}
\indexentry{crystallographic groups}{647}
\indexentry{NrCrystalFamilies}{648}
\indexentry{DisplayCrystalFamily}{648}
\indexentry{NrCrystalSystems}{649}
\indexentry{DisplayCrystalSystem}{649}
\indexentry{NrQClassesCrystalSystem}{649}
\indexentry{Hermann-Mauguin  symbol}{650}
\indexentry{DisplayQClass}{650}
\indexentry{FpGroupQClass}{651}
\indexentry{AgGroupQClass}{651}
\indexentry{CharTableQClass}{652}
\indexentry{NrZClassesQClass}{653}
\indexentry{DisplayZClass}{653}
\indexentry{MatGroupZClass}{654}
\indexentry{NormalizerZClass}{654}
\indexentry{NrSpaceGroupTypesZClass}{656}
\indexentry{NrDadeGroups}{656}
\indexentry{DadeGroup}{656}
\indexentry{DadeGroupNumbersZClass}{656}
\indexentry{ZClassRepsDadeGroup}{656}
\indexentry{DisplaySpaceGroupType}{657}
\indexentry{DisplaySpaceGroupGenerators}{658}
\indexentry{SpaceGroup}{658}
% algebra.tex
% 1
\indexentry{Algebras}{661}
% 2
\indexentry{More about Algebras}{662}
% 2
\indexentry{Algebras and Unital Algebras}{662}
% 2
\indexentry{Parent Algebras and Subalgebras}{663}
% 2
\indexentry{Algebra}{664}
% 2
\indexentry{UnitalAlgebra}{664}
% 2
\indexentry{IsAlgebra}{665}
% 2
\indexentry{IsUnitalAlgebra}{665}
% 2
\indexentry{Subalgebra}{665}
% 2
\indexentry{UnitalSubalgebra}{666}
% 2
\indexentry{IsSubalgebra}{666}
% 2
\indexentry{AsAlgebra}{667}
% 2
\indexentry{AsUnitalAlgebra}{667}
% 2
\indexentry{AsSubalgebra}{667}
% 2
\indexentry{AsUnitalSubalgebra}{668}
% 2
\indexentry{Operations for Algebras}{668}
% 2
\indexentry{Zero and One for Algebras}{669}
% 2
\indexentry{Set Theoretic Functions for Algebras}{669}
% 2
\indexentry{Property Tests for Algebras}{670}
% 2
\indexentry{Vector Space Functions for Algebras}{670}
% 2
\indexentry{Algebra Functions for Algebras}{671}
% 2
\indexentry{TrivialSubalgebra}{672}
% 2
\indexentry{Operation for Algebras}{672}
% 2
\indexentry{OperationHomomorphism for Algebras}{673}
% 2
\indexentry{Algebra Homomorphisms}{673}
\indexentry{homomorphisms!of algebras}{673}
% 2
\indexentry{Mapping Functions for Algebra Homomorphisms}{673}
% 2
\indexentry{Algebra Elements}{674}
\indexentry{equality!of algebra elements}{674}
\indexentry{ordering!of algebra elements}{674}
\indexentry{product!of algebra elements}{674}
\indexentry{product!of list and algebra element}{674}
\indexentry{sum!of algebra elements}{674}
\indexentry{sum!of list and algebra element}{674}
\indexentry{difference!of algebra elements}{674}
\indexentry{difference!of list and algebra element}{674}
\indexentry{power!of algebra elements}{674}
\indexentry{test!for algebra element}{674}
% 2
\indexentry{IsAlgebraElement}{675}
% 2
\indexentry{Algebra Records}{675}
% 2
\indexentry{FFList}{676}
% algfp.tex
% 1
\indexentry{Finitely Presented Algebras}{677}
% 2
\indexentry{More about Finitely Presented Algebras}{677}
% 2
\indexentry{FreeAlgebra}{678}
% 2
\indexentry{FpAlgebra}{679}
% 2
\indexentry{IsFpAlgebra}{679}
% 2
\indexentry{Operators for Finitely Presented Algebras}{680}
% 2
\indexentry{Functions for Finitely Presented Algebras}{680}
% 2
\indexentry{PrintDefinitionFpAlgebra}{681}
% 2
\indexentry{MappedExpression}{681}
% 2
\indexentry{Elements of Finitely Presented Algebras}{681}
\indexentry{IsFpAlgebraElement}{681}
% 2
\indexentry{ElementAlgebra}{683}
% 2
\indexentry{NumberAlgebraElement}{683}
% algmat.tex
% 1
\indexentry{Matrix Algebras}{685}
% 2
\indexentry{More about Matrix Algebras}{685}
% 2
\indexentry{Bases for Matrix Algebras}{686}
% 2
\indexentry{IsMatAlgebra}{686}
% 2
\indexentry{Zero and One for Matrix Algebras}{686}
% 2
\indexentry{Functions for Matrix Algebras}{686}
% 2
\indexentry{Algebra Functions for Matrix Algebras}{687}
% 2
\indexentry{RepresentativeOperation for Matrix Algebras}{687}
% 2
\indexentry{MatAlgebra}{687}
% 2
\indexentry{NullAlgebra}{688}
% 2
\indexentry{Fingerprint}{688}
% 2
\indexentry{NaturalModule}{689}
% module.tex
% 1
\indexentry{Modules}{691}
% 2
\indexentry{More about Modules}{691}
% 2
\indexentry{Row Modules}{692}
% 2
\indexentry{Free Modules}{692}
% 2
\indexentry{Module}{693}
% 2
\indexentry{Submodule}{693}
% 2
\indexentry{AsModule}{694}
% 2
\indexentry{AsSubmodule}{694}
% 2
\indexentry{AsSpace for Modules}{694}
% 2
\indexentry{IsModule}{694}
% 2
\indexentry{IsFreeModule}{695}
% 2
\indexentry{Operations for Row Modules}{695}
% 2
\indexentry{Functions for Row Modules}{696}
% 2
\indexentry{StandardBasis for Row Modules}{696}
% 2
\indexentry{IsEquivalent for Row Modules}{696}
% 2
\indexentry{IsIrreducible for Row Modules}{697}
% 2
\indexentry{FixedSubmodule}{697}
% 2
\indexentry{Module Homomorphisms}{697}
\indexentry{OperationHomomorphism for Modules}{697}
\indexentry{OperationModule}{697}
% 2
\indexentry{Row Module Records}{698}
% 2
\indexentry{Module Homomorphism Records}{699}
% mapping.tex
% 1
\indexentry{Mappings}{701}
% 2
\indexentry{IsGeneralMapping}{702}
% 2
\indexentry{IsMapping}{702}
% 2
\indexentry{IsInjective}{703}
% 2
\indexentry{IsSurjective}{703}
% 2
\indexentry{IsBijection}{704}
% 2
\indexentry{Comparisons of Mappings}{705}
% 2
\indexentry{Operations for Mappings}{706}
% 2
\indexentry{Image}{708}
% 2
\indexentry{Images}{710}
% 2
\indexentry{ImagesRepresentative}{711}
% 2
\indexentry{PreImage}{711}
% 2
\indexentry{PreImages}{713}
% 2
\indexentry{PreImagesRepresentative}{714}
% 2
\indexentry{CompositionMapping}{714}
% 2
\indexentry{PowerMapping}{715}
% 2
\indexentry{InverseMapping}{716}
% 2
\indexentry{IdentityMapping}{716}
% 2
\indexentry{MappingByFunction}{717}
% 2
\indexentry{Mapping Records}{717}
% homomorp.tex
% 1
\indexentry{Homomorphisms}{719}
% 2
\indexentry{IsHomomorphism}{719}
% 2
\indexentry{IsMonomorphism}{720}
% 2
\indexentry{IsEpimorphism}{721}
% 2
\indexentry{IsIsomorphism}{721}
% 2
\indexentry{IsEndomorphism}{722}
% 2
\indexentry{IsAutomorphism}{722}
% 2
\indexentry{Kernel}{723}
% boolean.tex
% 1
\indexentry{Booleans}{725}
\indexentry{type!boolean}{725}
\indexentry{logical}{725}
% 2
\indexentry{Comparisons of Booleans}{725}
\indexentry{comparisons!of booleans}{725}
% 2
\indexentry{Operations for Booleans}{726}
\indexentry{operations!for booleans}{726}
\indexentry{logical operations}{726}
\indexentry{or}{726}
\indexentry{and}{726}
\indexentry{not}{726}
% 2
\indexentry{IsBool}{727}
\indexentry{test!for a boolean}{727}
% record.tex
% 1
\indexentry{Records}{729}
\indexentry{type!records}{729}
% 2
\indexentry{Accessing Record Elements}{730}
\indexentry{accessing!record elements}{730}
% 2
\indexentry{Record Assignment}{730}
\indexentry{assignment!to a record}{730}
% 2
\indexentry{Identical Records}{731}
% 2
\indexentry{Comparisons of Records}{733}
\indexentry{equality!of records}{733}
\indexentry{ordering!of records}{733}
% 2
\indexentry{Operations for Records}{735}
\indexentry{sum!of records}{735}
\indexentry{difference!of records}{735}
\indexentry{product!of records}{735}
\indexentry{quotient!of records}{735}
\indexentry{power!of records}{735}
% 2
\indexentry{In for Records}{736}
\indexentry{in!for records}{736}
\indexentry{membership test!for records}{736}
% 2
\indexentry{Printing of Records}{737}
% 2
\indexentry{IsRec}{738}
\indexentry{test!for records}{738}
% 2
\indexentry{IsBound}{738}
\indexentry{test!for record elements}{738}
\indexentry{test!for list elements}{738}
% 2
\indexentry{Unbind}{739}
% 2
\indexentry{Copy}{739}
\indexentry{copy!an object}{739}
\indexentry{clone!an object}{739}
% 2
\indexentry{ShallowCopy}{740}
\indexentry{copy!an object}{740}
\indexentry{clone!an object}{740}
% 2
\indexentry{RecFields}{741}
% combinat.tex
% 1
\indexentry{Combinatorics}{743}
\indexentry{selections}{743}
\indexentry{partitions}{743}
% 2
\indexentry{Factorial}{743}
% 2
\indexentry{Binomial}{744}
\indexentry{coefficient!binomial}{744}
\indexentry{number!binomial}{744}
% 2
\indexentry{Bell}{744}
\indexentry{number!Bell}{744}
% 2
\indexentry{Stirling1}{745}
\indexentry{Stirling number of the first kind}{745}
\indexentry{number!Stirling, of the first kind}{745}
% 2
\indexentry{Stirling2}{745}
\indexentry{Stirling number of the second kind}{745}
\indexentry{number!Stirling, of the second kind}{745}
% 2
\indexentry{Combinations}{746}
\indexentry{NrCombinations}{746}
\indexentry{powerset}{746}
\indexentry{subsets}{746}
% 2
\indexentry{Arrangements}{746}
% 2
\indexentry{UnorderedTuples}{747}
\indexentry{NrUnorderedTuples}{747}
% 2
\indexentry{Tuples}{748}
\indexentry{NrTuples}{748}
% 2
\indexentry{PermutationsList}{748}
\indexentry{NrPermutationsList}{748}
\indexentry{permutations!list}{748}
% 2
\indexentry{Derangements}{749}
\indexentry{NrDerangements}{749}
\indexentry{permutations!fixpointfree}{749}
% 2
\indexentry{Permanent}{749}
% 2
\indexentry{PartitionsSet}{750}
\indexentry{NrPartitionsSet}{750}
\indexentry{partitions!of a set}{750}
% 2
\indexentry{Partitions}{750}
\indexentry{NrPartitions}{750}
\indexentry{partitions!of an integer}{750}
% 2
\indexentry{OrderedPartitions}{751}
\indexentry{NrOrderedPartitions}{751}
\indexentry{partitions!ordered, of an integer}{751}
\indexentry{partitions!improper, of an integer}{751}
% 2
\indexentry{RestrictedPartitions}{752}
\indexentry{NrRestrictedPartitions}{752}
\indexentry{partitions!restricted, of an integer}{752}
% 2
\indexentry{SignPartition}{753}
% 2
\indexentry{AssociatedPartition}{753}
% 2
\indexentry{PowerPartition}{753}
\indexentry{symmetric group!powermap}{753}
% 2
\indexentry{PartitionTuples}{753}
% 2
\indexentry{Fibonacci}{754}
\indexentry{sequence!fibonacci}{754}
% 2
\indexentry{Lucas}{754}
\indexentry{sequence!lucas}{754}
% 2
\indexentry{Bernoulli}{755}
\indexentry{sequence!bernoulli}{755}
% tom.tex
% 1
\indexentry{Tables of Marks}{757}
% 2
\indexentry{More about Tables of Marks}{757}
% 2
\indexentry{Table of Marks Records}{758}
% 2
\indexentry{The Library of Tables of Marks}{758}
% 2
\indexentry{TableOfMarks}{759}
\indexentry{TableOfMarks}{759}
% 2
\indexentry{Marks}{760}
% 2
\indexentry{NrSubs}{760}
% 2
\indexentry{WeightsTom}{760}
% 2
\indexentry{MatTom}{761}
% 2
\indexentry{TomMat}{761}
% 2
\indexentry{DecomposedFixedPointVector}{761}
% 2
\indexentry{TestTom}{762}
% 2
\indexentry{DisplayTom}{762}
% 2
\indexentry{NormalizerTom}{763}
% 2
\indexentry{IntersectionsTom}{763}
% 2
\indexentry{IsCyclicTom}{764}
% 2
\indexentry{FusionCharTableTom}{764}
% 2
\indexentry{PermCharsTom}{764}
% 2
\indexentry{MoebiusTom}{764}
% 2
\indexentry{CyclicExtensionsTom}{765}
% 2
\indexentry{IdempotentsTom}{765}
% 2
\indexentry{ClassTypesTom}{765}
% 2
\indexentry{ClassNamesTom}{765}
% 2
\indexentry{TomCyclic}{766}
% 2
\indexentry{TomDihedral}{766}
% 2
\indexentry{TomFrobenius}{767}
% chartabl.tex
% 1
\indexentry{Character Tables}{769}
\indexentry{tables}{769}
% 2
\indexentry{Some Notes on Character Theory in GAP}{769}
% 2
\indexentry{Character Table Records}{771}
\indexentry{character tables!format}{771}
\indexentry{tables!format}{771}
% 2
\indexentry{Brauer Table Records}{775}
\indexentry{Brauer tables!format}{775}
\indexentry{tables!format}{775}
% 2
\indexentry{IsCharTable}{777}
% 2
\indexentry{PrintCharTable}{777}
% 2
\indexentry{TestCharTable}{777}
% 2
\indexentry{Operations Records for Character Tables}{778}
\indexentry{CharTableOps}{778}
\indexentry{BrauerTableOps}{778}
% 2
\indexentry{Functions for Character Tables}{778}
\indexentry{AbelianInvariants!for character tables}{778}
\indexentry{Agemo!for character tables}{778}
\indexentry{Automorphisms!for character tables}{778}
\indexentry{Centre!for character tables}{778}
\indexentry{CharacterDegrees!for character tables}{778}
\indexentry{DerivedSubgroup!for character tables}{778}
\indexentry{Display!for character tables}{778}
\indexentry{ElementaryAbelianSeries!for character tables}{778}
\indexentry{Exponent!for character tables}{778}
\indexentry{FittingSubgroup!for character tables}{778}
\indexentry{FrattiniSubgroup!for character tables}{778}
\indexentry{FusionConjugacyClasses!for character tables}{778}
\indexentry{Induced!for character tables}{778}
\indexentry{IsAbelian!for character tables}{778}
\indexentry{IsCyclic!for character tables}{778}
\indexentry{IsNilpotent!for character tables}{779}
\indexentry{IsSimple!for character tables}{779}
\indexentry{IsSolvable!for character tables}{779}
\indexentry{IsSupersolvable!for character tables}{779}
\indexentry{LowerCentralSeries!for character tables}{779}
\indexentry{MaximalNormalSubgroups!for character tables}{779}
\indexentry{NoMessageScalarProduct!for character tables}{779}
\indexentry{NormalClosure!for character tables}{779}
\indexentry{NormalSubgroups!for character tables}{779}
\indexentry{Print!for character tables}{779}
\indexentry{Restricted!for character tables}{779}
\indexentry{ScalarProduct!for character tables}{779}
\indexentry{Size!for character tables}{779}
\indexentry{SizesConjugacyClasses!for character tables}{779}
\indexentry{SupersolvableResiduum!for character tables}{779}
\indexentry{UpperCentralSeries!for character tables}{779}
% 2
\indexentry{Operators for Character Tables}{779}
\indexentry{mod for character tables}{779}
\indexentry{{\tt  /} for character tables}{779}
% 2
\indexentry{Conventions for Character Tables}{779}
\indexentry{character tables!conventions}{779}
% 2
\indexentry{Getting Character Tables}{780}
\indexentry{tables}{780}
\indexentry{character tables}{780}
\indexentry{library tables}{780}
\indexentry{generic character tables}{780}
% 2
\indexentry{CharTable}{780}
\indexentry{character tables!access to}{780}
\indexentry{character tables!calculate}{780}
\indexentry{Dixon Schneider}{780}
\indexentry{character tables!of groups}{780}
% 2
\indexentry{Advanced Methods for Dixon Schneider Calculations}{784}
\indexentry{character tables!computation}{784}
\indexentry{DixonInit}{784}
\indexentry{DixontinI}{784}
\indexentry{DixonSplit}{784}
\indexentry{CombinatoricSplit}{784}
\indexentry{IncludeIrreducibles}{785}
\indexentry{SplitCharacters}{785}
% 2
\indexentry{An Example of Advanced Dixon Schneider Calculations}{785}
% 2
\indexentry{CharTableFactorGroup}{787}
\indexentry{table of factor group}{787}
\indexentry{factor group!table of}{787}
% 2
\indexentry{CharTableNormalSubgroup}{788}
\indexentry{table of normal subgroup}{788}
\indexentry{normal subgroup!table of}{788}
% 2
\indexentry{CharTableDirectProduct}{788}
\indexentry{Cartesian product}{788}
\indexentry{direct product}{788}
\indexentry{Kronecker product}{788}
\indexentry{tensor product}{788}
% 2
\indexentry{CharTableWreathSymmetric}{789}
\indexentry{wreath product!character table}{789}
% 2
\indexentry{CharTableRegular}{791}
\indexentry{p-regular table}{791}
\indexentry{regular classes}{791}
% 2
\indexentry{CharTableIsoclinic}{791}
\indexentry{isoclinic table}{791}
% 2
\indexentry{CharTableSplitClasses}{792}
\indexentry{split classes}{792}
% 2
\indexentry{CharTableCollapsedClasses}{793}
\indexentry{fusion of classes}{793}
% 2
\indexentry{CharDegAgGroup}{794}
% 2
\indexentry{CharTableSSGroup}{794}
% 2
\indexentry{MatRepresentationsPGroup}{795}
\indexentry{Matrix Representations of Finite Polycyclic Groups}{795}
\indexentry{Monomial Representations of Finite Polycyclic Groups}{795}
% 2
\indexentry{CharTablePGroup}{796}
\indexentry{Characters of Finite Polycyclic Groups}{796}
% 2
\indexentry{InitClassesCharTable}{796}
\indexentry{initialize classlengths}{796}
% 2
\indexentry{InverseClassesCharTable}{797}
% 2
\indexentry{ClassNamesCharTable}{797}
\indexentry{class names}{797}
% 2
\indexentry{ClassMultCoeffCharTable}{797}
\indexentry{class multiplication coefficient}{797}
\indexentry{structure constant}{797}
% 2
\indexentry{MatClassMultCoeffsCharTable}{798}
\indexentry{structure constant}{798}
\indexentry{class multiplication coefficient}{798}
% 2
\indexentry{ClassStructureCharTable}{798}
\indexentry{class multiplication coefficient}{798}
\indexentry{structure constant}{798}
% 2
\indexentry{RealClassesCharTable}{799}
\indexentry{classes!real}{799}
% 2
\indexentry{ClassOrbitCharTable}{799}
\indexentry{classes!of cyclic subgroup}{799}
% 2
\indexentry{ClassRootsCharTable}{799}
\indexentry{classes!roots of}{799}
% 2
\indexentry{NrPolyhedralSubgroups}{799}
\indexentry{subgroups!polyhedral}{799}
% 2
\indexentry{DisplayCharTable}{800}
\indexentry{character table!display}{800}
% 2
\indexentry{SortCharactersCharTable}{801}
\indexentry{character tables!sort}{801}
\indexentry{characters!sort}{801}
\indexentry{tables!sort}{801}
% 2
\indexentry{SortClassesCharTable}{803}
\indexentry{character tables!sort}{803}
\indexentry{tables!sort}{803}
% 2
\indexentry{SortCharTable}{804}
\indexentry{character tables!sort}{804}
\indexentry{tables!sort}{804}
% 2
\indexentry{MatAutomorphisms}{805}
\indexentry{automorphism group!of a matrix}{805}
% 2
\indexentry{TableAutomorphisms}{806}
\indexentry{automorphism group!of a character table}{806}
% 2
\indexentry{TransformingPermutations}{806}
% 2
\indexentry{TransformingPermutationsCharTables}{806}
% 2
\indexentry{GetFusionMap}{807}
\indexentry{fusion map!get}{807}
\indexentry{subgroup fusions}{807}
% 2
\indexentry{StoreFusion}{808}
\indexentry{fusion!store}{808}
\indexentry{subgroup fusions}{808}
% 2
\indexentry{FusionConjugacyClasses}{808}
% 2
\indexentry{MAKElb11}{809}
\indexentry{MOC!interface to}{809}
% 2
\indexentry{ScanMOC}{809}
\indexentry{MOC!interface to}{809}
% 2
\indexentry{MOCChars}{809}
\indexentry{MOC!interface to}{809}
% 2
\indexentry{GAPChars}{809}
\indexentry{MOC!interface to}{809}
% 2
\indexentry{MOCTable}{809}
\indexentry{MOC!interface to}{809}
% 2
\indexentry{PrintToMOC}{811}
\indexentry{MOC!interface to}{811}
% 2
\indexentry{PrintToCAS}{811}
\indexentry{CAS tables,CAS format,CAS}{811}
% gentable.tex
% 1
\indexentry{Generic Character Tables}{813}
\indexentry{character tables!generic}{813}
\indexentry{tables!generic}{813}
\indexentry{library tables!generic}{813}
% 2
\indexentry{More about Generic Character Tables}{813}
% 2
\indexentry{Examples of Generic Character Tables}{814}
\indexentry{tables!generic}{814}
\indexentry{character tables!generic}{814}
% 2
\indexentry{CharTableSpecialized}{816}
\indexentry{character tables!generic}{816}
\indexentry{tables!generic}{816}
% characte.tex
% 1
\indexentry{Characters}{817}
% 2
\indexentry{ScalarProduct}{817}
\indexentry{characters!scalar product of}{817}
% 2
\indexentry{MatScalarProducts}{818}
\indexentry{characters!scalar product of}{818}
% 2
\indexentry{Decomposition}{818}
\indexentry{decomposition matrix}{818}
\indexentry{DEC}{818}
% 2
\indexentry{Subroutines of Decomposition}{819}
\indexentry{LinearIndependentColumns}{819}
\indexentry{InverseMatMod}{820}
\indexentry{PadicCoefficients}{820}
\indexentry{IntegralizedMat}{820}
\indexentry{DecompositionInt}{820}
% 2
\indexentry{KernelChar}{820}
% 2
\indexentry{PrimeBlocks}{820}
% 2
\indexentry{Indicator}{821}
\indexentry{Frobenius Schur indicator}{821}
% 2
\indexentry{Eigenvalues}{821}
% 2
\indexentry{MolienSeries}{822}
\indexentry{ValueMolienSeries}{822}
% 2
\indexentry{Reduced}{822}
\indexentry{characters!reduced}{822}
% 2
\indexentry{ReducedOrdinary}{823}
\indexentry{characters!reduced}{823}
% 2
\indexentry{Tensored}{823}
\indexentry{characters!tensor products of}{823}
% 2
\indexentry{Symmetrisations}{824}
\indexentry{characters!symmetrisations of}{824}
% 2
\indexentry{SymmetricParts}{824}
\indexentry{characters!symmetrisations of}{824}
% 2
\indexentry{AntiSymmetricParts}{825}
\indexentry{characters!symmetrisations of}{825}
% 2
\indexentry{MinusCharacter}{825}
\indexentry{characters!symmetrisations of}{825}
% 2
\indexentry{OrthogonalComponents}{825}
\indexentry{symmetrizations!orthogonal}{825}
\indexentry{Frame}{825}
\indexentry{Murnaghan components}{825}
% 2
\indexentry{SymplecticComponents}{826}
\indexentry{symmetrizations!symplectic}{826}
\indexentry{Murnaghan components}{826}
% 2
\indexentry{IrreducibleDifferences}{826}
\indexentry{characters!irreducible differences of}{826}
% 2
\indexentry{Restricted}{827}
\indexentry{characters!restricted}{827}
% 2
\indexentry{Inflated}{827}
\indexentry{characters!inflated}{827}
% 2
\indexentry{Induced}{828}
\indexentry{characters!induced}{828}
% 2
\indexentry{InducedCyclic}{828}
\indexentry{characters!induce from cyclic subgroups}{828}
% 2
\indexentry{CollapsedMat}{829}
\indexentry{classes!collapse}{829}
% 2
\indexentry{Power}{829}
% 2
\indexentry{Permutation Character Candidates}{830}
\indexentry{characters!permutation}{830}
\indexentry{candidates!for permutation characters}{830}
\indexentry{permutation characters!candidates for}{830}
% 2
\indexentry{IsPermChar}{830}
\indexentry{characters!permutation}{830}
\indexentry{candidates!for permutation characters}{830}
\indexentry{permutation characters!candidates for}{830}
% 2
\indexentry{PermCharInfo}{830}
\indexentry{subgroup and permutation character}{830}
% 2
\indexentry{Inequalities}{831}
% 2
\indexentry{PermBounds}{832}
% 2
\indexentry{PermChars}{832}
\indexentry{permutation characters}{832}
% 2
\indexentry{Faithful Permutation Characters}{833}
\indexentry{permutation characters!faithful candidates for}{833}
% 2
\indexentry{LLLReducedBasis}{834}
\indexentry{LLL algorithm!for vectors}{834}
\indexentry{short vectors spanning a lattice}{834}
\indexentry{lattice base reduction}{834}
% 2
\indexentry{LLLReducedGramMat}{835}
\indexentry{LLL algorithm!for Gram matrices}{835}
\indexentry{lattice base reduction}{835}
% 2
\indexentry{LLL}{836}
\indexentry{LLL algorithm!for characters}{836}
\indexentry{short vectors spanning a lattice}{836}
\indexentry{lattice base reduction}{836}
% 2
\indexentry{OrthogonalEmbeddings}{836}
\indexentry{embeddings of lattices}{836}
\indexentry{OrthogonalEmbeddingsSpecialDimension}{837}
% 2
\indexentry{ShortestVectors}{838}
% 2
\indexentry{Extract}{838}
% 2
\indexentry{Decreased}{839}
% 2
\indexentry{DnLattice}{840}
\indexentry{$D_n$ lattices}{840}
\indexentry{DnLatticeIterative}{840}
% 2
\indexentry{ContainedDecomposables}{841}
% 2
\indexentry{ContainedCharacters}{842}
% 2
\indexentry{ContainedSpecialVectors}{842}
% 2
\indexentry{ContainedPossibleCharacters}{843}
% 2
\indexentry{ContainedPossibleVirtualCharacters}{843}
% paramaps.tex
% 1
\indexentry{Maps and Parametrized Maps}{845}
\indexentry{maps}{845}
\indexentry{parametrized maps}{845}
% 2
\indexentry{More about Maps and Parametrized Maps}{845}
\indexentry{map!parametrized}{845}
\indexentry{paramap}{845}
\indexentry{class functions}{845}
% 2
\indexentry{CompositionMaps}{846}
\indexentry{map!composition}{846}
% 2
\indexentry{InverseMap}{846}
\indexentry{map!inverse of a}{846}
% 2
\indexentry{ProjectionMap}{847}
% 2
\indexentry{Parametrized}{847}
\indexentry{map!parametrize}{847}
% 2
\indexentry{ContainedMaps}{847}
% 2
\indexentry{UpdateMap}{848}
% 2
\indexentry{CommutativeDiagram}{848}
% 2
\indexentry{TransferDiagram}{849}
% 2
\indexentry{Indeterminateness}{850}
\indexentry{map!indeterminateness}{850}
% 2
\indexentry{PrintAmbiguity}{850}
% 2
\indexentry{Powermap}{851}
\indexentry{powermaps}{851}
% 2
\indexentry{SubgroupFusions}{851}
\indexentry{fusions}{851}
\indexentry{subgroup fusions}{851}
% 2
\indexentry{InitPowermap}{852}
\indexentry{powermaps}{852}
% 2
\indexentry{Congruences}{853}
\indexentry{powermaps}{853}
% 2
\indexentry{ConsiderKernels}{854}
\indexentry{powermaps}{854}
% 2
\indexentry{ConsiderSmallerPowermaps}{854}
\indexentry{powermaps}{854}
% 2
\indexentry{InitFusion}{855}
\indexentry{subgroup fusions}{855}
% 2
\indexentry{CheckPermChar}{855}
\indexentry{subgroup fusions}{855}
\indexentry{permutation character}{855}
% 2
\indexentry{CheckFixedPoints}{856}
\indexentry{subgroup fusions}{856}
% 2
\indexentry{TestConsistencyMaps}{856}
\indexentry{subgroup fusions}{856}
% 2
\indexentry{ConsiderTableAutomorphisms}{857}
\indexentry{subgroup fusions}{857}
\indexentry{table automorphisms}{857}
% 2
\indexentry{PowermapsAllowedBySymmetrisations}{857}
\indexentry{powermaps}{857}
% 2
\indexentry{FusionsAllowedByRestrictions}{858}
\indexentry{subgroup fusions}{858}
% 2
\indexentry{OrbitFusions}{859}
\indexentry{subgroup fusions}{859}
\indexentry{table automorphisms}{859}
% 2
\indexentry{OrbitPowermaps}{860}
\indexentry{powermaps}{860}
\indexentry{matrix automorphisms}{860}
% 2
\indexentry{RepresentativesFusions}{860}
\indexentry{subgroup fusions}{860}
\indexentry{table automorphisms}{860}
% 2
\indexentry{RepresentativesPowermaps}{861}
\indexentry{powermaps}{861}
\indexentry{matrix automorphisms}{861}
% 2
\indexentry{Indirected}{861}
\indexentry{map!indirection by a}{861}
% 2
\indexentry{Powmap}{862}
% 2
\indexentry{ElementOrdersPowermap}{862}
% gettable.tex
% 1
\indexentry{Character Table Libraries}{865}
\indexentry{character tables}{865}
\indexentry{tables}{865}
\indexentry{library tables}{865}
\indexentry{generic character tables}{865}
% 2
\indexentry{Contents of the Table Libraries}{865}
\indexentry{character tables!libraries of}{865}
\indexentry{tables!libraries of}{865}
\indexentry{libraries of character tables}{865}
% 2
\indexentry{Selecting Library Tables}{867}
% 2
\indexentry{ATLAS Tables}{868}
\indexentry{character tables!ATLAS}{868}
\indexentry{tables!library}{868}
\indexentry{library of character tables}{868}
% 2
\indexentry{Examples of the ATLAS format for GAP tables}{871}
\indexentry{character tables!CAS}{871}
\indexentry{tables!library}{871}
\indexentry{library of character tables}{871}
% 2
\indexentry{CAS Tables}{875}
\indexentry{character tables!CAS}{875}
\indexentry{tables!library}{875}
\indexentry{library of character tables}{875}
% 2
\indexentry{Organization of the Table Libraries}{875}
% 2
\indexentry{How to Extend a Table Library}{877}
\indexentry{library tables!add}{877}
\indexentry{tables!add to a library}{877}
\indexentry{NotifyCharTable}{877}
\indexentry{PrintToLib}{877}
% 2
\indexentry{FirstNameCharTable}{878}
% 2
\indexentry{FileNameCharTable}{878}
% classfun.tex
% 1
\indexentry{Class Functions}{879}
% 2
\indexentry{Why Group Characters}{879}
% 2
\indexentry{More about Class Functions}{881}
% 2
\indexentry{Operators for Class Functions}{882}
% 2
\indexentry{Functions for Class Functions}{883}
\indexentry{Centre for class functions}{883}
\indexentry{Degree for class functions}{883}
\indexentry{Determinant for characters}{883}
\indexentry{Kernel for class functions}{883}
\indexentry{Norm for class functions}{883}
\indexentry{Omega for characters}{883}
% 2
\indexentry{ClassFunction}{884}
% 2
\indexentry{VirtualCharacter}{885}
% 2
\indexentry{Character}{885}
% 2
\indexentry{IsClassFunction}{886}
% 2
\indexentry{IsVirtualCharacter}{886}
% 2
\indexentry{IsCharacter}{886}
% 2
\indexentry{Irr}{887}
% 2
\indexentry{InertiaSubgroup}{887}
% 2
\indexentry{OrbitsCharacters}{887}
% 2
\indexentry{Storing Subgroup Information}{888}
% 2
\indexentry{NormalSubgroupClasses}{889}
% 2
\indexentry{ClassesNormalSubgroup}{890}
% 2
\indexentry{FactorGroupNormalSubgroupClasses}{890}
% 2
\indexentry{Class Function Records}{890}
% monomial.tex
% 1
\indexentry{Monomiality Questions}{891}
% 2
\indexentry{More about Monomiality Questions}{891}
% 2
\indexentry{Alpha}{892}
% 2
\indexentry{Delta}{893}
% 2
\indexentry{BergerCondition}{893}
% 2
\indexentry{TestHomogeneous}{893}
% 2
\indexentry{TestQuasiPrimitive}{894}
\indexentry{IsQuasiPrimitive}{894}
% 2
\indexentry{IsPrimitive for Characters}{895}
% 2
\indexentry{TestInducedFromNormalSubgroup}{895}
% 2
\indexentry{TestSubnormallyMonomial}{896}
\indexentry{IsSubnormallyMonomial}{896}
% 2
\indexentry{TestMonomialQuick}{897}
% 2
\indexentry{TestMonomial}{897}
\indexentry{IsMonomial for groups}{897}
\indexentry{IsMonomial for characters}{897}
% 2
\indexentry{TestRelativelySM}{898}
% 2
\indexentry{IsMinimalNonmonomial}{899}
% 2
\indexentry{MinimalNonmonomialGroup}{899}
% install.tex
% 1
\indexentry{Getting and Installing GAP}{901}
\indexentry{installation}{901}
\indexentry{options}{901}
% 2
\indexentry{Getting GAP}{901}
\indexentry{ftp}{901}
% 2
\indexentry{Upgrading GAP}{903}
% 2
\indexentry{GAP for UNIX}{907}
\indexentry{BSD}{907}
\indexentry{4.2BSD}{907}
\indexentry{4.3BSD}{907}
\indexentry{ULTRIX}{907}
\indexentry{System V}{907}
\indexentry{SysV}{907}
\indexentry{HP-UX}{907}
\indexentry{SunOS}{907}
% 2
\indexentry{Installation of GAP for UNIX}{908}
\indexentry{installation!under UNIX}{908}
\indexentry{UNIX!installation}{908}
% 2
\indexentry{Features of GAP for UNIX}{912}
\indexentry{features!under UNIX}{912}
\indexentry{UNIX!features}{912}
\indexentry{options!under UNIX}{912}
\indexentry{UNIX!options}{912}
\indexentry{.gaprc}{912}
% 2
\indexentry{GAP for MS-DOS}{914}
\indexentry{GAP for MS-DOS}{914}
\indexentry{MSDOS}{914}
\indexentry{Windows}{914}
% 2
\indexentry{Copyright of GAP for MS-DOS}{915}
% 2
\indexentry{Installation of GAP for MS-DOS}{916}
\indexentry{installation!under MS-DOS}{916}
\indexentry{MS-DOS!installation}{916}
\indexentry{installation!under Windows}{916}
\indexentry{Windows!installation}{916}
% 2
\indexentry{Features of GAP for MS-DOS}{920}
\indexentry{features!under MS-DOS}{920}
\indexentry{MS-DOS!features}{920}
\indexentry{options!under MS-DOS}{920}
\indexentry{MS-DOS!options}{920}
\indexentry{gap.rc}{920}
\indexentry{.gaprc}{920}
% 2
\indexentry{GAP for TOS}{922}
\indexentry{TOS}{922}
\indexentry{Atari ST}{922}
% 2
\indexentry{Copyright of GAP for TOS}{923}
% 2
\indexentry{Installation of GAP for TOS}{923}
\indexentry{installation!under TOS}{923}
\indexentry{TOS!installation}{923}
% 2
\indexentry{Features of GAP for TOS}{927}
\indexentry{features!under TOS}{927}
\indexentry{TOS!features}{927}
\indexentry{options!under TOS}{927}
\indexentry{TOS!options}{927}
\indexentry{gap.rc}{927}
\indexentry{.gaprc}{927}
% 2
\indexentry{Porting GAP}{930}
% share.tex
% 1
\indexentry{Share Libraries}{933}
% 2
\indexentry{RequirePackage}{934}
% 2
\indexentry{ANU pq Package}{935}
% 2
\indexentry{Installing the ANU pq Package}{935}
% 2
\indexentry{ANU Sq Package}{942}
\indexentry{Sq}{942}
% 2
\indexentry{Installing the ANU Sq Package}{943}
% 2
\indexentry{GRAPE Package}{946}
% 2
\indexentry{Installing the GRAPE Package}{947}
% 2
\indexentry{MeatAxe Package}{950}
% 2
\indexentry{Installing the MeatAxe Package}{950}
% 2
\indexentry{NQ Package}{952}
\indexentry{NilpotentQuotient}{952}
% 2
\indexentry{Installing the NQ Package}{952}
% 2
\indexentry{SISYPHOS Package}{954}
% 2
\indexentry{Installing the SISYPHOS Package}{955}
% 2
\indexentry{Smash Package}{957}
% 2
\indexentry{Installing the Smash Package}{957}
% 2
\indexentry{Vector Enumeration Package}{958}
% 2
\indexentry{Installing the Vector Enumeration Package}{958}
% 2
\indexentry{Weyl Package}{960}
% 2
\indexentry{Installing the Weyl Package}{960}
% 2
\indexentry{The XGap Package}{962}
% 2
\indexentry{Installing the XGap Package}{962}
% anupq.tex
% 1
\indexentry{ANU Pq}{965}
% 2
\indexentry{Pq}{965}
% 2
\indexentry{PqHomomorphism}{966}
% 2
\indexentry{PqDescendants}{966}
% 2
\indexentry{PqList}{969}
% 2
\indexentry{SavePqList}{970}
% 2
\indexentry{StandardPresentation}{970}
\indexentry{automorphisms!of p groups}{970}
% 2
\indexentry{IsIsomorphicPGroup}{972}
% cohomolo.tex
% 1
\indexentry{Cohomology}{973}
% 2
\indexentry{CHR}{974}
% 2
\indexentry{SchurMultiplier}{974}
% 2
\indexentry{CoveringGroup}{974}
% 2
\indexentry{FirstCohomologyDimension}{974}
% 2
\indexentry{SecondCohomologyDimension}{974}
% 2
\indexentry{SplitExtension}{975}
% 2
\indexentry{NonsplitExtension}{975}
% 2
\indexentry{CalcPres}{975}
% 2
\indexentry{PermRep}{976}
% 2
\indexentry{Further Information}{976}
% grape.tex
% 1
\indexentry{Grape}{979}
% 2
\indexentry{Functions to construct and modify graphs}{980}
% 2
\indexentry{Graph}{980}
% 2
\indexentry{EdgeOrbitsGraph}{981}
% 2
\indexentry{NullGraph}{982}
% 2
\indexentry{CompleteGraph}{982}
% 2
\indexentry{JohnsonGraph}{983}
% 2
\indexentry{AddEdgeOrbit}{983}
% 2
\indexentry{RemoveEdgeOrbit}{984}
% 2
\indexentry{AssignVertexNames}{984}
% 2
\indexentry{Functions to inspect graphs, vertices and edges}{985}
% 2
\indexentry{IsGraph}{985}
% 2
\indexentry{OrderGraph}{985}
% 2
\indexentry{IsVertex}{985}
% 2
\indexentry{VertexName}{986}
% 2
\indexentry{Vertices}{986}
% 2
\indexentry{VertexDegree}{986}
% 2
\indexentry{VertexDegrees}{986}
% 2
\indexentry{IsLoopy}{986}
% 2
\indexentry{IsSimpleGraph}{987}
% 2
\indexentry{Adjacency}{987}
% 2
\indexentry{IsEdge}{987}
% 2
\indexentry{DirectedEdges}{987}
% 2
\indexentry{UndirectedEdges}{988}
% 2
\indexentry{Distance}{988}
% 2
\indexentry{Diameter}{988}
% 2
\indexentry{Girth}{989}
% 2
\indexentry{IsConnectedGraph}{989}
% 2
\indexentry{IsBipartite}{989}
% 2
\indexentry{IsNullGraph}{990}
% 2
\indexentry{IsCompleteGraph}{990}
% 2
\indexentry{Functions to determine regularity properties of graphs}{990}
% 2
\indexentry{IsRegularGraph}{991}
% 2
\indexentry{LocalParameters}{991}
% 2
\indexentry{GlobalParameters}{991}
% 2
\indexentry{IsDistanceRegular}{991}
% 2
\indexentry{CollapsedAdjacencyMat}{992}
% 2
\indexentry{OrbitalGraphIntersectionMatrices}{992}
% 2
\indexentry{Some special vertex subsets of a graph}{992}
% 2
\indexentry{ConnectedComponent}{992}
% 2
\indexentry{ConnectedComponents}{993}
% 2
\indexentry{Bicomponents}{993}
% 2
\indexentry{DistanceSet}{993}
% 2
\indexentry{Layers}{993}
% 2
\indexentry{IndependentSet}{994}
% 2
\indexentry{Functions to construct new graphs from old}{994}
% 2
\indexentry{InducedSubgraph}{994}
% 2
\indexentry{DistanceSetInduced}{994}
% 2
\indexentry{DistanceGraph}{995}
% 2
\indexentry{ComplementGraph}{995}
% 2
\indexentry{PointGraph}{996}
% 2
\indexentry{EdgeGraph}{996}
% 2
\indexentry{UnderlyingGraph}{997}
% 2
\indexentry{QuotientGraph}{997}
% 2
\indexentry{BipartiteDouble}{998}
% 2
\indexentry{GeodesicsGraph}{998}
% 2
\indexentry{CollapsedIndependentOrbitsGraph}{999}
% 2
\indexentry{CollapsedCompleteOrbitsGraph}{999}
% 2
\indexentry{NewGroupGraph}{1000}
% 2
\indexentry{Vertex-Colouring and Complete Subgraphs}{1000}
% 2
\indexentry{VertexColouring}{1001}
% 2
\indexentry{CompleteSubgraphs}{1001}
% 2
\indexentry{CompleteSubgraphsOfGivenSize}{1001}
% 2
\indexentry{Functions depending on nauty}{1002}
% 2
\indexentry{AutGroupGraph}{1002}
% 2
\indexentry{IsIsomorphicGraph}{1002}
% 2
\indexentry{An example}{1003}
% guava.tex
% 1
\indexentry{GUAVA}{1005}
% 2
\indexentry{Codewords}{1006}
% 2
\indexentry{Codeword}{1006}
% 2
\indexentry{IsCodeword}{1007}
% 2
\indexentry{Comparisons of Codewords}{1008}
% 2
\indexentry{Operations for Codewords}{1008}
% 2
\indexentry{VectorCodeword}{1009}
% 2
\indexentry{PolyCodeword}{1009}
% 2
\indexentry{TreatAsVector}{1009}
% 2
\indexentry{TreatAsPoly}{1010}
% 2
\indexentry{NullWord}{1010}
% 2
\indexentry{DistanceCodeword}{1011}
% 2
\indexentry{Support}{1011}
% 2
\indexentry{WeightCodeword}{1011}
% 2
\indexentry{Codes}{1012}
% 2
\indexentry{IsCode}{1014}
% 2
\indexentry{IsLinearCode}{1014}
% 2
\indexentry{IsCyclicCode}{1014}
% 2
\indexentry{Comparisons of Codes}{1015}
% 2
\indexentry{Operations for Codes}{1015}
% 2
\indexentry{Generating Unrestricted Codes}{1016}
% 2
\indexentry{ElementsCode}{1017}
% 2
\indexentry{HadamardCode}{1017}
% 2
\indexentry{ConferenceCode}{1018}
% 2
\indexentry{MOLSCode}{1018}
% 2
\indexentry{RandomCode}{1019}
% 2
\indexentry{NordstromRobinsonCode}{1019}
% 2
\indexentry{GreedyCode}{1019}
% 2
\indexentry{LexiCode}{1020}
% 2
\indexentry{Generating Linear Codes}{1020}
% 2
\indexentry{GeneratorMatCode}{1021}
% 2
\indexentry{CheckMatCode}{1021}
% 2
\indexentry{HammingCode}{1022}
% 2
\indexentry{ReedMullerCode}{1022}
% 2
\indexentry{ExtendedBinaryGolayCode}{1022}
% 2
\indexentry{ExtendedTernaryGolayCode}{1023}
% 2
\indexentry{AlternantCode}{1023}
% 2
\indexentry{GoppaCode}{1023}
% 2
\indexentry{GeneralizedSrivastavaCode}{1024}
% 2
\indexentry{SrivastavaCode}{1024}
% 2
\indexentry{CordaroWagnerCode}{1024}
% 2
\indexentry{RandomLinearCode}{1025}
% 2
\indexentry{BestKnownLinearCode}{1025}
% 2
\indexentry{Generating Cyclic Codes}{1026}
% 2
\indexentry{GeneratorPolCode}{1026}
% 2
\indexentry{CheckPolCode}{1027}
% 2
\indexentry{BinaryGolayCode}{1027}
% 2
\indexentry{TernaryGolayCode}{1027}
% 2
\indexentry{RootsCode}{1028}
% 2
\indexentry{BCHCode}{1028}
% 2
\indexentry{ReedSolomonCode}{1029}
% 2
\indexentry{QRCode}{1029}
% 2
\indexentry{FireCode}{1030}
% 2
\indexentry{WholeSpaceCode}{1030}
% 2
\indexentry{NullCode}{1030}
% 2
\indexentry{RepetitionCode}{1031}
% 2
\indexentry{CyclicCodes}{1031}
% 2
\indexentry{Manipulating Codes}{1031}
% 2
\indexentry{ExtendedCode}{1032}
\indexentry{Parity check}{1032}
% 2
\indexentry{PuncturedCode}{1032}
% 2
\indexentry{EvenWeightSubcode}{1033}
% 2
\indexentry{PermutedCode}{1033}
% 2
\indexentry{ExpurgatedCode}{1034}
% 2
\indexentry{AugmentedCode}{1034}
% 2
\indexentry{RemovedElementsCode}{1035}
% 2
\indexentry{AddedElementsCode}{1035}
% 2
\indexentry{ShortenedCode}{1036}
% 2
\indexentry{LengthenedCode}{1037}
% 2
\indexentry{ResidueCode}{1037}
% 2
\indexentry{ConstructionBCode}{1037}
% 2
\indexentry{DualCode}{1038}
% 2
\indexentry{ConversionFieldCode}{1038}
% 2
\indexentry{CosetCode}{1038}
% 2
\indexentry{ConstantWeightSubcode}{1039}
% 2
\indexentry{StandardFormCode}{1039}
% 2
\indexentry{DirectSumCode}{1040}
% 2
\indexentry{UUVCode}{1041}
% 2
\indexentry{DirectProductCode}{1041}
% 2
\indexentry{IntersectionCode}{1041}
% 2
\indexentry{UnionCode}{1042}
% 2
\indexentry{Basic Functions for Codes}{1042}
% 2
\indexentry{Domain Functions for Codes}{1043}
% 2
\indexentry{Printing and Saving Codes}{1044}
% 2
\indexentry{GeneratorMat}{1045}
% 2
\indexentry{CheckMat}{1045}
% 2
\indexentry{GeneratorPol}{1046}
% 2
\indexentry{CheckPol}{1046}
% 2
\indexentry{RootsOfCode}{1046}
% 2
\indexentry{WordLength}{1047}
% 2
\indexentry{Redundancy}{1047}
% 2
\indexentry{MinimumDistance}{1047}
% 2
\indexentry{CoveringRadius}{1048}
% 2
\indexentry{WeightDistribution}{1049}
% 2
\indexentry{InnerDistribution}{1049}
% 2
\indexentry{OuterDistribution}{1049}
% 2
\indexentry{DistancesDistribution}{1050}
% 2
\indexentry{IsPerfectCode}{1050}
% 2
\indexentry{IsMDSCode}{1050}
% 2
\indexentry{IsSelfDualCode}{1051}
% 2
\indexentry{IsSelfOrthogonalCode}{1051}
% 2
\indexentry{IsEquivalent}{1052}
% 2
\indexentry{CodeIsomorphism}{1052}
% 2
\indexentry{AutomorphismGroup}{1052}
% 2
\indexentry{Decode}{1053}
% 2
\indexentry{Syndrome}{1053}
% 2
\indexentry{SyndromeTable}{1054}
% 2
\indexentry{StandardArray}{1054}
% 2
\indexentry{Display}{1055}
% 2
\indexentry{CodewordNr}{1056}
% 2
\indexentry{Code Records}{1056}
% 2
\indexentry{Bounds on codes}{1058}
% 2
\indexentry{UpperBoundSingleton}{1059}
\indexentry{Bounds!Singleton}{1059}
% 2
\indexentry{UpperBoundHamming}{1059}
\indexentry{Bounds!Hamming}{1059}
\indexentry{Bounds!Sphere packing bound}{1059}
% 2
\indexentry{UpperBoundJohnson}{1060}
\indexentry{Bounds!Johnson}{1060}
% 2
\indexentry{UpperBoundPlotkin}{1060}
\indexentry{Bounds!Plotkin}{1060}
% 2
\indexentry{UpperBoundElias}{1060}
\indexentry{Bounds!Elias}{1060}
% 2
\indexentry{UpperBoundGriesmer}{1061}
\indexentry{Bounds!Griesmer}{1061}
% 2
\indexentry{UpperBound}{1061}
\indexentry{Bounds!UpperBound}{1061}
% 2
\indexentry{OptimalityCode}{1061}
% 2
\indexentry{OptimalityLinearCode}{1062}
% 2
\indexentry{LowerBoundMinimumDistance}{1062}
% 2
\indexentry{UpperBoundMinimumDistance}{1062}
% 2
\indexentry{BoundsMinimumDistance}{1063}
% 2
\indexentry{Matrices for Codes}{1063}
% 2
\indexentry{KrawtchoukMat}{1064}
% 2
\indexentry{GrayMat}{1064}
% 2
\indexentry{SylvesterMat}{1064}
% 2
\indexentry{HadamardMat}{1065}
% 2
\indexentry{MOLS}{1065}
% 2
\indexentry{PutStandardForm}{1066}
% 2
\indexentry{IsInStandardForm}{1067}
% 2
\indexentry{PermutedCols}{1067}
% 2
\indexentry{VerticalConversionFieldMat}{1067}
% 2
\indexentry{HorizontalConversionFieldMat}{1068}
% 2
\indexentry{IsLatinSquare}{1068}
% 2
\indexentry{AreMOLS}{1068}
% 2
\indexentry{Miscellaneous functions}{1069}
% 2
\indexentry{SphereContent}{1069}
% 2
\indexentry{Krawtchouk}{1069}
% 2
\indexentry{PrimitiveUnityRoot}{1069}
% 2
\indexentry{ReciprocalPolynomial}{1070}
% 2
\indexentry{CyclotomicCosets}{1070}
% 2
\indexentry{WeightHistogram}{1071}
% mtx.tex
% 1
\indexentry{The MeatAxe}{1073}
% 2
\indexentry{More about the MeatAxe in GAP}{1074}
% 2
\indexentry{GapObject}{1074}
% 2
\indexentry{Using the MeatAxe in GAP. An Example}{1075}
% 2
\indexentry{MeatAxe Matrices}{1077}
\indexentry{IsMeatAxeMat}{1077}
% 2
\indexentry{MeatAxeMat}{1077}
% 2
\indexentry{Operations for MeatAxe Matrices}{1078}
% 2
\indexentry{Functions for MeatAxe Matrices}{1079}
\indexentry{Algebra for MeatAxe Matrices}{1079}
\indexentry{CharacteristicPolynomial for MeatAxe matrices}{1079}
\indexentry{Display for MeatAxe matrices}{1079}
\indexentry{Dimensions for MeatAxe matrices}{1079}
\indexentry{Group for MeatAxe Matrices}{1079}
\indexentry{KroneckerProduct for MeatAxe matrices}{1079}
\indexentry{Order for MeatAxe matrices}{1079}
\indexentry{Rank for MeatAxe matrices}{1079}
\indexentry{SumIntersectionSpaces for MeatAxe matrices}{1079}
\indexentry{Trace for MeatAxe matrices}{1079}
\indexentry{Transposed for MeatAxe matrices}{1079}
% 2
\indexentry{BrauerCharacterValue}{1080}
% 2
\indexentry{MeatAxe Permutations}{1080}
\indexentry{IsMeatAxePerm}{1080}
% 2
\indexentry{MeatAxePerm}{1080}
% 2
\indexentry{Operations for MeatAxe Permutations}{1081}
% 2
\indexentry{Functions for MeatAxe Permutations}{1081}
\indexentry{Display for MeatAxe Permutations}{1081}
\indexentry{Order for MeatAxe Permutations}{1081}
% 2
\indexentry{MeatAxe Matrix Groups}{1081}
% 2
\indexentry{Functions for MeatAxe Matrix Groups}{1081}
\indexentry{Operation for MeatAxe Matrix Groups}{1081}
\indexentry{RandomOrders for MeatAxe Matrix Groups}{1081}
% 2
\indexentry{MeatAxe Matrix Algebras}{1082}
% 2
\indexentry{Functions for MeatAxe Matrix Algebras}{1082}
\indexentry{Fingerprint for MeatAxe Matrix Algebras}{1082}
\indexentry{Module for MeatAxe Matrix Algebras}{1082}
\indexentry{NaturalModule for MeatAxe Matrix Algebras}{1082}
\indexentry{RandomOrders for MeatAxe Matrix Algebras}{1082}
% 2
\indexentry{MeatAxe Modules}{1083}
% 2
\indexentry{Set Theoretic Functions for MeatAxe Modules}{1083}
\indexentry{Size for MeatAxe Modules}{1083}
\indexentry{Intersection for MeatAxe Modules}{1083}
% 2
\indexentry{Vector Space Functions for MeatAxe Modules}{1083}
\indexentry{Base for MeatAxe Modules}{1083}
\indexentry{Dimension for MeatAxe Modules}{1083}
% 2
\indexentry{Module Functions for MeatAxe Modules}{1083}
\indexentry{CompositionFactors for MeatAxe Modules}{1083}
\indexentry{KroneckerProduct for MeatAxe Modules}{1083}
\indexentry{IsIrreducible for MeatAxe Modules}{1083}
\indexentry{IsAbsolutelyIrreducible for MeatAxe Modules}{1083}
\indexentry{IsEquivalent for MeatAxe Modules}{1083}
\indexentry{SplittingField for MeatAxe Modules}{1083}
\indexentry{Lattice for MeatAxe Modules}{1083}
% 2
\indexentry{MeatAxe.Unbind}{1085}
% 2
\indexentry{MeatAxe Object Records}{1085}
% sisyphos.tex
% 1
\indexentry{Sisyphos}{1089}
% 2
\indexentry{PrintSISYPHOSWord}{1089}
% 2
\indexentry{PrintSisyphosInputPGroup}{1090}
% 2
\indexentry{IsCompatiblePCentralSeries}{1091}
% 2
\indexentry{Automorphisms}{1091}
\indexentry{Automorphisms of $p$-groups}{1091}
\indexentry{OuterAutomorphisms}{1091}
\indexentry{NormalizedAutomorphisms}{1091}
\indexentry{NormalizedOuterAutomorphisms}{1091}
% 2
\indexentry{AgNormalizedAutomorphisms}{1092}
% 2
\indexentry{AgNormalizedOuterAutomorphisms}{1092}
% 2
\indexentry{IsIsomorphic}{1092}
% 2
\indexentry{Isomorphisms}{1093}
% 2
\indexentry{CorrespondingAutomorphism}{1094}
% 2
\indexentry{AutomorphismGroupElements}{1094}
% 2
\indexentry{NormalizedUnitsGroupRing}{1094}
% smash.tex
% 1
\indexentry{Smash, Matrix Groups and $G$-Modules}{1097}
% 2
\indexentry{GModule}{1097}
% 2
\indexentry{IsGModule}{1097}
% 2
\indexentry{DualGMod}{1098}
% 2
\indexentry{InducedGMod}{1098}
% 2
\indexentry{PermGMod}{1098}
% 2
\indexentry{TensorProductGMod}{1098}
% 2
\indexentry{WedgeGMod}{1098}
% 2
\indexentry{WreathProd}{1098}
% 2
\indexentry{WreathPower}{1099}
% 2
\indexentry{IsIrredGMod}{1099}
% 2
\indexentry{SubQuotGMod}{1099}
% 2
\indexentry{SpinBasis}{1100}
% 2
\indexentry{IsAbsIrredGMod}{1100}
% 2
\indexentry{FieldGenCentMat}{1100}
% 2
\indexentry{IsomGMod}{1100}
% 2
\indexentry{HomGMod}{1101}
% 2
\indexentry{MinSubGMods}{1101}
% 2
\indexentry{ChopGMod}{1101}
% 2
\indexentry{SmashGMod}{1101}
% 2
\indexentry{SemiLinearDecomp}{1102}
% 2
\indexentry{TensorProductDecomp}{1102}
% 2
\indexentry{SymTensorProductDecomp}{1103}
% 2
\indexentry{ExtraSpecialDecomp}{1103}
% 2
\indexentry{IsPrimitiveGMod}{1104}
% 2
\indexentry{MinBlocks}{1104}
% 2
\indexentry{BlockSystemFlag}{1104}
% 2
\indexentry{InitialiseSeed}{1104}
% 2
\indexentry{RandomElement}{1105}
% 2
\indexentry{ChooseRandomElements}{1105}
% 2
\indexentry{ElementOfOrder}{1105}
% 2
\indexentry{ElementWithCharPol}{1105}
% 2
\indexentry{LargestPrimeOrderElement}{1105}
% 2
\indexentry{LargestPrimePowerOrderElement}{1106}
% 2
\indexentry{MatrixOrder}{1106}
% 2
\indexentry{Other matrix functions}{1106}
% 2
\indexentry{Components of a $G$-module record}{1106}
% 2
\indexentry{Examples}{1108}
% ve.tex
% 1
\indexentry{Vector Enumeration}{1115}
% 2
\indexentry{Operation for Finitely Presented Algebras}{1115}
% 2
\indexentry{More about Vector Enumeration}{1116}
\indexentry{VEInput}{1116}
\indexentry{CallVE}{1116}
\indexentry{VEOutput}{1116}
\indexentry{FpAlgebraOps.OperationQuotientModule}{1116}
% 2
\indexentry{Examples of Vector Enumeration}{1118}
% 2
\indexentry{Using Vector Enumeration with the MeatAxe}{1121}
% weyl.tex
% 1
\indexentry{Weyl Groups and Hecke Algebras}{1123}
% 2
\indexentry{CartanMat}{1131}
\indexentry{Cartan matrices}{1131}
% 2
\indexentry{DirectSumCartanMat}{1131}
\indexentry{Cartan matrices!direct sum of}{1131}
% 2
\indexentry{SimpleReflectionMatrices}{1132}
% 2
\indexentry{Rootsystem}{1132}
% 2
\indexentry{PermRepresentationRoots}{1132}
% 2
\indexentry{Weyl}{1133}
% 2
\indexentry{PermWeylWord}{1134}
% 2
\indexentry{WeylWordPerm}{1134}
% 2
\indexentry{WeylLengthPerm}{1134}
% 2
\indexentry{ReducedWeylWord}{1135}
% 2
\indexentry{LongestWeylWord}{1135}
% 2
\indexentry{WeylReflections}{1135}
% 2
\indexentry{WeylRightCosetRepresentatives}{1135}
% 2
\indexentry{WeylCosetPermRepresentation}{1136}
% 2
\indexentry{WeylElements}{1136}
% 2
\indexentry{WeylConjugacyClasses}{1136}
% 2
\indexentry{ParametersCentralizers}{1137}
% 2
\indexentry{Bruhat}{1137}
% 2
\indexentry{KazhdanLusztigPolynomial}{1138}
% 2
\indexentry{KLCoefficient}{1138}
% 2
\indexentry{WeylMueMat}{1138}
% 2
\indexentry{DecomposedLeftCells}{1139}
% 2
\indexentry{LeftCells}{1139}
% 2
\indexentry{LeftCellRepresentation}{1140}
% 2
\indexentry{Hecke}{1140}
% 2
\indexentry{WeylClassPolynomials}{1140}
% 2
\indexentry{HeckeReflectionRepresentation}{1141}
% 2
\indexentry{CheckHeckeDefiningRelations}{1141}
% 2
\indexentry{CharHeckeRepresentation}{1141}
% 2
\indexentry{HeckeCharTable}{1142}