Index

* 4.13
    for character tables 71.7
+ 4.13
- 4.13
-A 3.1
-a 3.1
-B 3.1
-b 3.1
-C 3.1
-D 3.1
-e 3.1
-E 3.1
-f 3.1
-g 3.1
-g -g 3.1
-h 3.1
-i 3.1
-infinity 18.2-1
-K 3.1
-l 3.1
-L 3.1
-M 3.1
-m 3.1
-n 3.1
-O 3.1
-o 3.1
-P 3.1
-p 3.1
-q 3.1
-R 3.1
-r 3.1
-s 3.1
-T 3.1
-U 3.1
-W 3.1
-x 3.1
-X 3.1
-y 3.1
-z 3.1
/ 4.13
    for character tables 71.7
\" 27.2
\' 27.2
\\ 27.2
\b 27.2
\c 27.2
\r 27.2
\XYZ 27.2
^, for class functions 72.4
\< 31.11-1
    for associative words 37.3-2
    for nonassociative words 36.2-2
    for pcwords 46.2-1
    for permutations 42.2-1
    for two elements in a f.p. group 47.3-2
    for two strings 27.6-2
\* 31.12-1
    for pcwords 46.2-2
\*, for transformations 53.4
\+ 31.12-1
\. 29.7-3
\.\:\= 29.7-3
\/ 31.12-1
    for a free group and a list of elements 47.2-1
    for a free monoid and a list of pairs of elements 52.5-1
    for a free semigroup and a list of pairs of elements 52.2-1
\/, for a transformation and a permutation 53.4
\<, for transformations 53.4
\= 31.11-1
    for associative words 37.3-1
    for nonassociative words 36.2-1
    for pcwords 46.2-1
    for permutations 42.2-1
\=, for transformations 53.4
\=, for two elements in a f.p. group 47.3-1
    for two elements in a f.p. semigroup 52.3-1
    for two strings 27.6-1
\[\] 21.2-1
\[\]\:\= 21.2-1
\^ 31.12-1
    for a field and a pair of integers 61.9-5
    for a field and an integer 61.9-4
\^, for a positive integer and a transformation 53.4
    for a transformation and a permutation 53.4
\in, element test for lists 21.8-1
    for a collection 30.6-1
    for strictly sorted lists 21.19-1
\mod 31.12-1
    for residue class rings 14.5-1
    for two pcgs 45.9-5
\{\} 21.3-1
\{\}\:\= 21.4-1
^ 4.13
abelian number field 60.2-3
abelian number fields, CanonicalBasis 60.3
    Galois group 60.4
AbelianGroup 50.1-3
AbelianInvariants 39.16-1
    for a character table 71.8-5
AbelianInvariants, for groups 39.16-1
AbelianInvariantsMultiplier 39.24-3
AbelianInvariantsNormalClosureFpGroup 47.15-4
AbelianInvariantsNormalClosureFpGroupRrs 47.15-5
AbelianInvariantsOfList 25.2-10
AbelianInvariantsSubgroupFpGroup 47.15-1
AbelianInvariantsSubgroupFpGroupMtc 47.15-2
AbelianInvariantsSubgroupFpGroupRrs, for a group and a coset table 47.15-3
    for two groups 47.15-3
AbelianNumberField 60.1-2
AbelianSubfactorAction 41.8-3
About GAP manual 1.
AbsInt 14.2-6
absolute value of an integer 14.2-6
AbsoluteDiameter 19.2-4
AbsoluteIrreducibleModules 71.15-2
AbsolutelyIrreducibleModules 71.15-2
AbsoluteValue 18.1-8
AbsolutIrreducibleModules 71.15-2
abstract word 36.1-1
AbstractWordTietzeWord 48.3-2
accessing, list elements 21.3
    record elements 29.2
AClosestVectorCombinationsMatFFEVecFFE 23.6-5
AClosestVectorCombinationsMatFFEVecFFECoords 23.6-5
Acos 19.2-1
Acosh 19.2-1
ActingAlgebra 62.11-13
ActingDomain 41.12-3
action, by conjugation 41.2-1
Action, for a group, an action domain, etc. 41.7-2
    for an external set 41.7-2
action, on blocks 41.2-4
    on sets 41.2-4
ActionHomomorphism, for a group, an action domain, etc. 41.7-1
    for an action image 41.7-1
    for an external set 41.7-1
actions 41.2
ActivateProfileColour 7.7-18
ActorOfExternalSet 41.12-15
Add 21.4-2
add, an element to a set 21.19-4
AddCoeffs 23.4-2
AddDictionary 28.3-4
AddGenerator 48.5-1
AddGeneratorsExtendSchreierTree 43.11-10
addition 4.13
    list and non-list 21.13-3
    matrices 24.3
    matrix and scalar 24.3
    operation 31.12-1
    rational functions 66.2
    scalar and matrix 24.3
    scalar and matrix list 24.3 24.3
    vector and scalar 23.2
    vectors 23.2
AdditiveInverse 31.10-9
AdditiveInverseAttr 31.10-9
AdditiveInverseImmutable 31.10-9
AdditiveInverseMutable 31.10-9
AdditiveInverseOp 31.10-9
AdditiveInverseSameMutability 31.10-9
AdditiveInverseSM 31.10-9
AdditiveNeutralElement 55.3-5
AddRelator 48.5-3
AddRowVector 23.4-1
AddRule 38.1-9
AddRuleReduced 38.1-10
AddSet 21.19-4
AdjointAssociativeAlgebra 64.9-2
AdjointBasis 62.9-5
AdjointMatrix 64.9-1
AdjointModule 62.11-19
AffineAction 45.14-4
AffineActionLayer 45.14-5
Agemo 39.14-2
Algebra 62.2-1
AlgebraByStructureConstants 62.4-1
AlgebraGeneralMappingByImages 62.10-1
AlgebraHomomorphismByImages 62.10-2
AlgebraHomomorphismByImagesNC 62.10-3
AlgebraicExtension 67.1-1
AlgebraWithOne 62.2-2
AlgebraWithOneGeneralMappingByImages 62.10-4
AlgebraWithOneHomomorphismByImages 62.10-5
AlgebraWithOneHomomorphismByImagesNC 62.10-6
AllAutomorphisms 40.9-3
AllBlocks 41.11-4
AllEndomorphisms 40.9-3
AllHomomorphismClasses 40.9-2
AllHomomorphisms 40.9-3
AllIrreducibleSolvableGroups 50.11-3
AllLibraryGroups 50.5
AllPrimitiveGroups 50.5
AllSmallGroups 50.7-2
AllSmallNonabelianSimpleGroups 39.15-16
AllSubgroups 39.19-5
AllTransitiveGroups 50.5
Alpha 75.2-1
AlternatingGroup, for a degree 50.1-9
    for a domain 50.1-9
and 20.4-2
    for filters 13.2 20.4-2
ANFAutomorphism 60.4-2
AntiIsomorphismTransformationSemigroup 53.7-6
antisymmetric relation 33.2-4
AntiSymmetricParts 72.11-3
Append 21.4-5
AppendTo 9.7-3
    for streams 10.4-4
ApplicableMethod 7.2-1
ApplicableMethodTypes 7.2-1
Apply 21.20-10
ApplySimpleReflection 64.7-4
ApproximateSuborbitsStabilizerPermGroup 43.10-15
ARCH_IS_MAC_OS_X 3.4-2
ARCH_IS_UNIX 3.4-1
ARCH_IS_WINDOWS 3.4-3
arg, special function argument 4.23
    special function argument, calling with 4.11-1
Argument, for complex numbers 19.2-1
arithmetic operators, precedence 4.13
ArithmeticElementCreator 80.9-1
Arrangements 16.2-4
arrow notation for functions 4.23
AsAlgebra 62.9-7
AsAlgebraWithOne 62.9-8
AsBinaryRelationOnPoints, for a binary relation 33.3-3
    for a permutation 33.3-3
    for a transformation 33.3-3
AsBlockMatrix 24.17-1
AscendingChain 39.17-16
AsDivisionRing 58.1-9
AsDuplicateFreeList 21.20-5
AsField 58.1-9
AsGroup 39.2-5
AsGroupGeneralMappingByImages 40.1-5
Asin 19.2-1
Asinh 19.2-1
AsInternalFFE 59.2-6
AsLeftIdeal 56.2-11
AsLeftModule 57.1-5
AsList 30.3-8
AsMagma 35.2-10
AsMonoid 51.2-5
AsPartialPerm, for a permutation 54.4-1
    for a permutation and a positive integer 54.4-1
    for a permutation and a set of positive integers 54.4-1
    for a transformation 54.4-2
    for a transformation and a positive integer 54.4-2
    for a transformation and a set of positive integer 54.4-2
AsPermutation 42.5-5
AsPolynomial 66.4-5
AsRightIdeal 56.2-11
AsSemigroup 51.1-6
Assert 7.5-3
AssertionLevel 7.5-2
AsSet 30.3-10
AssignGeneratorVariables 37.2-3
assignment, to a list 21.4
    to a record 29.3
    variable 4.15
AssignNiceMonomorphismAutomorphismGroup 40.8-1
AssociatedPartition 16.2-28
AssociatedReesMatrixSemigroupOfDClass 51.9-11
Associates 56.5-4
associativity 4.13
AssocWordByLetterRep 37.6-9
AsSortedList 30.3-9
AsSSortedList 30.3-10
AsStruct 31.4
AsSubalgebra 62.9-9
AsSubalgebraWithOne 62.9-10
AsSubgroup 39.3-4
AsSubgroupOfWholeGroupByQuotient 47.13-3
AsSubmagma 35.2-11
AsSubmonoid 51.2-6
AsSubsemigroup 51.1-7
AsSubspace 61.2-4
AsSubstruct 31.8
AsTransformation 53.3-1
AsTwoSidedIdeal 56.2-11
AsVectorSpace 61.2-3
at exit functions 6.7
Atan 19.2-1
Atan2 19.2-1
Atanh 19.2-1
AtlasIrrationality 18.4-6
atomic irrationalities 18.4
AttributeValueNotSet 13.6-3
AugmentationIdeal 65.1-7
AugmentedCosetTableInWholeGroup 47.9-1
AugmentedCosetTableMtc 47.9-2
AugmentedCosetTableRrs 47.9-3
automatic loading of GAP packages 76.2
automorphism group, of number fields 60.4
AutomorphismDomain 40.7-3
AutomorphismGroup 40.7-1
AutomorphismGroup, for groups with pcgs 45.16
AutomorphismsOfTable 71.9-4
\(b_N\) (irrational value) 18.4-1
backslash character 27.2
backspace character 27.2
Backtrace, GAP3 name for Where 6.4-5
BANNER 77.4
BaseFixedSpace 24.7-8
BaseIntersectionIntMats 25.1-5
BaseIntMat 25.1-4
BaseMat 24.11-1
BaseMatDestructive 24.11-2
BaseOfGroup 43.10-2
BaseOrthogonalSpaceMat 24.11-3
BaseStabChain 43.10-1
BaseSteinitzVectors 24.11-5
BasicSpinRepresentationOfSymmetricGroup 39.24-9
BasicWreathProductOrdering 34.4-11
Basis 61.5-2
BasisNC 61.5-2
BasisVectors 61.6-1
Bell 16.1-3
Bernoulli 16.1-4
BestQuoInt 14.3-2
BestSplittingMatrix 71.17-5
BiAlgebraModule 62.11-6
BiAlgebraModuleByGenerators 62.11-3
BibEntry 76.3-15
BilinearFormMat 64.6-13
binary relation 33.
BinaryRelationByElements 33.1-2
BinaryRelationOnPoints 33.3-1
BinaryRelationOnPointsNC 33.3-1
BindGlobal 4.9-7
Binomial 16.1-2
BisectInterval 19.2-4
blank 4.4
BlistList 22.2-1
BlockMatrix 24.17-2
Blocks, for a group, an action domain, etc. 41.11-1
    for an external set 41.11-1
BlocksInfo 71.11-3
BlownUpMat 24.13-3
BlownUpVector 24.13-4
BlowupInterval 19.2-4
BlowUpIsomorphism 44.3-3
body 4.23
BombieriNorm 66.12-1
bound 4.8
Brauer character 72.8-1
BrauerCharacterValue 72.15-2
BrauerTable, for a character table, and a prime integer 71.3-2
    for a group, and a prime integer 71.3-2
BrauerTableOp 71.3-2
BravaisGroup 44.6-11
BravaisSubgroups 44.6-12
BravaisSupergroups 44.6-13
Break loop message 6.4-4
break statement 4.21
browsing backwards 2.2
browsing backwards one chapter 2.2
browsing forward 2.2
browsing forward one chapter 2.2
browsing the next section browsed 2.2
browsing the previous section browsed 2.2
\(c_N\) (irrational value) 18.4-1
CallFuncList 5.2-1
CallWithTimeout 5.3-1
CallWithTimeoutList 5.3-1
CanComputeIndex 39.25-5
CanComputeIsSubset 39.25-6
CanComputeSize 39.25-3
CanComputeSizeAnySubgroup 39.25-4
candidates, for permutation characters 72.13
CanEasilyCompareElements 31.11-2
CanEasilyCompareElementsFamily 31.11-2
CanEasilyComputePcgs 45.2-3
CanEasilyComputeWithIndependentGensAbelianGroup 39.25-2
CanEasilySortElements 31.11-2
CanEasilySortElementsFamily 31.11-2
CanEasilyTestMembership 39.25-1
canonical basis, for matrix spaces 61.9-10
    for row spaces 61.9-9
CanonicalBasis 61.5-3
CanonicalGenerators 64.6-14
CanonicalPcElement 45.5-9
CanonicalPcgs 45.8-2
CanonicalPcgsByGeneratorsWithImages 45.9-7
CanonicalRepresentativeDeterminatorOfExternalSet 41.12-14
CanonicalRepresentativeOfExternalSet 41.12-13
CanonicalRightCosetElement 39.7-3
Carmichael's lambda function 15.2-3
carriage return character 27.2
CartanMatrix 64.6-12
CartanSubalgebra 64.3-7
Cartesian, for a list 21.20-16
    for various objects 21.20-16
CategoriesOfObject 13.3-1
CategoryCollections 30.2-4
CategoryFamily 79.1-2
Ceil 19.2-1
center 35.4-4
Center 35.4-5
central character 72.8-17
CentralCharacter 72.8-17
CentralIdempotentsOfAlgebra 62.9-17
centraliser 35.4-4
Centralizer, for a class of objects in a magma 35.4-4
    for a magma and a submagma 35.4-4
    for a magma and an element 35.4-4
Centralizer, for groups with pcgs 45.16
CentralizerInGLnZ 44.6-8
CentralizerModulo 39.18-7
CentralizerSizeLimitConsiderFunction 45.17-2
CentralNormalSeriesByPcgs 45.11-8
Centre 35.4-5
Centre, for groups with pcgs 45.16
centre, of a character 72.8-11
CentreOfCharacter 72.8-11
CF, for (subfield and) conductor 60.1-1
    for (subfield and) generators 60.1-1
ChangeStabChain 43.11-3
Character, for a character table and a list 72.6-3
    for a group and a list 72.6-3
character tables 71.3
    access to 71.3
    calculate 71.3
    infix operators 71.7
    of groups 71.3
character value, of group element using powering operator 72.4
CharacterDegrees, for a character table 71.8-1
    for a group 71.8-1
Characteristic 31.10-1
    for a class function 72.4-1
characteristic polynomial, for field elements 58.3-3
CharacteristicPolynomial 24.13-1
CharacterNames 71.9-6
CharacterParameters 71.9-7
characters 72.
    permutation 72.13
    symmetrizations of 72.11-1
CharacterTable, for a group 71.3-1
    for a string 71.3-1
    for an ordinary character table 71.3-1
CharacterTableDirectProduct 71.20-1
CharacterTableFactorGroup 71.20-3
CharacterTableIsoclinic 71.20-4
CharacterTableRegular 71.3-3
CharacterTableWithSortedCharacters 71.21-1
CharacterTableWithSortedClasses 71.21-3
CharacterTableWithStoredGroup 71.6-4
CharacterTableWreathSymmetric 71.20-5
CharInt 27.8-2
CharsFamily 27.4-6
CharSInt 27.8-4
CheckDigitISBN 14.6-1
CheckDigitISBN13 14.6-1
CheckDigitPostalMoneyOrder 14.6-1
CheckDigitTestFunction 14.6-2
CheckDigitUPC 14.6-1
CheckFixedPoints 73.5-10
CheckForHandlingByNiceBasis 61.12-3
CheckPermChar 73.7-2
ChevalleyBasis 64.6-2
ChiefNormalSeriesByPcgs 45.11-16
ChiefSeries 39.17-1
ChiefSeriesThrough 39.17-2
ChiefSeriesUnderAction 39.17-3
Chinese remainder 14.3-9
ChineseRem 14.3-9
Chomp 27.7-18
Cite 76.3-16
CIUnivPols 66.1-5
class function 72.1-1
class function objects 72.1-1
class functions 73.5
    as ring elements 72.4
class multiplication coefficient 71.12-7 71.12-8 71.12-9
ClassElementLattice 39.20-2
classes, real 71.9-11
ClassesSolvableGroup 45.17-1
ClassFunction, for a character table and a list 72.6-1
    for a group and a list 72.6-1
ClassFunctionSameType 72.6-4
ClassMultiplicationCoefficient, for character tables 71.12-7
ClassMultiplicationCoefficient, for character tables 71.12-7
ClassNames 71.9-6
ClassNamesTom 70.7-5
ClassOrbit 71.9-12
ClassParameters 71.9-7
ClassPermutation 71.21-5
ClassPositionsOfAgemo 71.10-2
ClassPositionsOfCenter, for a character table 71.10-3
ClassPositionsOfCentre, for a character 72.8-12
    for a character table 71.10-3
ClassPositionsOfDerivedSubgroup 71.10-5
ClassPositionsOfDirectProductDecompositions 71.10-4
ClassPositionsOfElementaryAbelianSeries 71.10-6
ClassPositionsOfFittingSubgroup 71.10-7
ClassPositionsOfKernel 72.8-10
ClassPositionsOfLowerCentralSeries 71.10-8
ClassPositionsOfMaximalNormalSubgroups 71.10-1
ClassPositionsOfMinimalNormalSubgroups 71.10-1
ClassPositionsOfNormalClosure 71.10-12
ClassPositionsOfNormalSubgroup 71.23-2
ClassPositionsOfNormalSubgroups 71.10-1
ClassPositionsOfPCore 71.10-11
ClassPositionsOfSupersolvableResiduum 71.10-10
ClassPositionsOfUpperCentralSeries 71.10-9
ClassRoots 71.9-13
ClassStructureCharTable 71.12-8
ClassTypesTom 70.7-4
CleanedTailPcElement 45.5-11
ClearCacheStats 7.7-21
ClearProfile 7.7-10
clone, an object 12.7
CloseMutableBasis 61.8-6
CloseStream 10.2-1
ClosureGroup 39.4-1
ClosureGroupAddElm 39.4-2
ClosureGroupCompare 39.4-2
ClosureGroupDefault 39.4-3
ClosureGroupIntest 39.4-2
ClosureLeftModule 57.2-3
ClosureNearAdditiveGroup, for a near-additive group and an element 55.4-1
    for two near-additive groups 55.4-1
ClosureRing, for a ring and a ring element 56.1-8
    for two rings 56.1-8
ClosureStruct 31.3
ClosureSubgroup 39.4-4
ClosureSubgroupNC 39.4-4
Coboundaries 64.12-7
Cochain 64.12-2
CochainSpace 64.12-3
cocycles 39.23
Cocycles, for Lie algebra module 64.12-6
CodegreeOfPartialPerm 54.3-2
CodegreeOfPartialPermCollection 54.3-2
CodegreeOfPartialPermSemigroup 54.7-2
CodePcGroup 46.9-2
CodePcgs 46.9-1
coefficient, binomial 16.1-2
Coefficients 61.6-3
coefficients, for cyclotomics 18.1-10
CoefficientsAndMagmaElements 65.2-4
CoefficientsFamily 66.19-3
CoefficientsMultiadic 14.3-8
CoefficientsOfLaurentPolynomial 66.13-2
CoefficientsOfUnivariatePolynomial 66.4-9
CoefficientsOfUnivariateRationalFunction 66.4-7
CoefficientsQadic 14.3-7
CoefficientsRing 66.15-3
CoeffsCyc 18.1-10
CoeffsMod 23.4-4
cohomology 39.23
COHORTS_PRIMITIVE_GROUPS 50.9-4
CoKernelOfAdditiveGeneralMapping 32.10-6
CoKernelOfMultiplicativeGeneralMapping 32.9-6
CollapsedMat 73.5-16
Collected 21.20-3
CollectionsFamily 30.2-1
ColorPrompt 3.6-1
Columns 51.9-9
Combinations 16.2-1
CombinatorialCollector 46.4-2
Comm 31.12-3
Comm, for words 37.4
comments 4.4
CommutativeDiagram 73.5-9
CommutatorFactorGroup 39.18-3
CommutatorLength 39.12-4
    for a character table 71.8-5
CommutatorSubgroup 39.12-2
Compacted 21.20-2
CompanionMat 24.13-5
CompareVersionNumbers 76.3-7
comparison, fp semigroup elements 52.3-1
    operation 31.11-1
    rational functions 66.3
comparisons, of booleans 20.3
    of lists 21.10
CompatibleConjugacyClasses 71.6-5
CompatiblePairs 46.8-8
ComplementClassesRepresentatives 39.11-6
ComplementClassesRepresentativesEA 39.23-4
ComplementIntMat 25.1-6
ComplementSystem 39.13-5
ComplexConjugate 18.5-2
    for a class function 72.4-2
ComplexI 19.2-1
ComplexificationQuat, for a matrix 62.5-2
    for a vector 62.5-2
ComponentPartialPermInt 54.5-3
ComponentRepsOfPartialPerm 54.3-20
ComponentRepsOfTransformation 53.5-19
ComponentsOfPartialPerm 54.3-18
ComponentsOfTransformation 53.5-17
ComponentTransformationInt 53.4-3
CompositionMapping 32.2-4
CompositionMapping, for Frobenius automorphisms 59.4-1
CompositionMapping2 32.2-5
CompositionMapping2General 32.2-5
CompositionMaps 73.5-1
CompositionOfStraightLinePrograms 37.8-7
CompositionSeries 39.17-5
CompositionSeries, for groups with pcgs 45.16
ComputedBrauerTables 71.3-2
ComputedClassFusions 73.3-2
ComputedIndicators 71.12-5
ComputedIsPSolubleCharacterTables 71.12-3
ComputedIsPSolvableCharacterTables 71.12-3
ComputedPowerMaps 73.1-1
ComputedPrimeBlockss 71.11-1
Concatenation, for a list of lists 21.20-1
    for several lists 21.20-1
concatenation, of lists 21.20
Conductor, for a collection of cyclotomics 18.1-7
    for a cyclotomic 18.1-7
ConfluentRws 38.1-6
Congruences, for character tables 73.6-2
ConjugacyClass 39.10-1
ConjugacyClasses, attribute 39.10-2
    for character tables 71.6-2
ConjugacyClasses, for groups with pcgs 45.16
    for linear groups 50.3
ConjugacyClassesByOrbits 39.10-4
ConjugacyClassesByRandomSearch 39.10-3
ConjugacyClassesMaximalSubgroups 39.19-4
ConjugacyClassesPerfectSubgroups 39.20-7
ConjugacyClassesSubgroups 39.19-3
ConjugacyClassSubgroups 39.19-1
conjugate, matrix 24.3
    of a word 37.4
ConjugateDominantWeight 64.7-6
ConjugateDominantWeightWithWord 64.7-6
ConjugateGroup 39.2-6
Conjugates 58.3-6
ConjugateSubgroup 39.3-8
ConjugateSubgroups 39.3-9
conjugation 41.2-1
ConjugatorAutomorphism 40.6-2
ConjugatorAutomorphismNC 40.6-2
ConjugatorIsomorphism 40.6-1
ConjugatorOfConjugatorIsomorphism 40.6-5
ConsiderKernels 73.6-3
ConsiderSmallerPowerMaps 73.6-4
ConsiderStructureConstants 73.3-7
ConsiderTableAutomorphisms 73.7-3
ConstantTimeAccessList 21.17-6
ConstantTransformation 53.2-9
constituent, of a group character 72.8-5
ConstituentsCompositionMapping 32.2-7
ConstituentsOfCharacter 72.8-8
ContainedCharacters 73.5-17
ContainedDecomposables 73.5-17
ContainedMaps 73.5-6
ContainedPossibleCharacters 73.5-15
ContainedPossibleVirtualCharacters 73.5-15
ContainedSpecialVectors 73.5-15
ContainedTom 70.9-5
ContainingTom 70.9-6
continue statement 4.22
ContinuedFractionApproximationOfRoot 15.6-2
ContinuedFractionExpansionOfRoot 15.6-1
convert, to a string 27.4
ConvertToBlistRep 22.5-1
ConvertToCharacterTable 71.3-5
ConvertToCharacterTableNC 71.3-5
ConvertToMatrixRep, for a list (and a field) 24.14-2
    for a list (and a prime power) 24.14-2
ConvertToMatrixRepNC, for a list (and a field) 24.14-2
    for a list (and a prime power) 24.14-2
ConvertToRangeRep 21.22-2
ConvertToStringRep 27.4-2
ConvertToTableOfMarks 70.6-5
ConvertToVectorRep, for a list (and a field) 23.3-1
    for a list (and a prime power) 23.3-1
ConvertToVectorRepNC, for a list (and a field) 23.3-1
    for a list (and a prime power) 23.3-1
ConwayPolynomial 59.5-1
coprime 4.13
Copy 12.7
copy, an object 12.7
CopyListEntries 21.4-4
CopyOptionsDefaults 43.11-2
CopyStabChain 43.11-1
CopyToStringRep 27.4-3
Core 39.11-2
CorrespondingGeneratorsByModuloPcgs 45.9-6
Cos 19.2-1
coset 39.7
CosetDecomposition 39.7-5
CosetLeadersMatFFE 23.6-6
CosetTable 47.6-1
CosetTableBySubgroup 47.6-4
CosetTableDefaultLimit 47.6-7
CosetTableDefaultMaxLimit 47.6-6
CosetTableFromGensAndRels 47.6-5
CosetTableInWholeGroup 47.8-1
CosetTableOfFpSemigroup 52.7-1
CosetTableStandard 47.7-1
Cosh 19.2-1
Cot 19.2-1
Coth 19.2-1
CoverageLineByLine 7.7-15
CrcFile 9.7-7
CrcString 27.9-4
CrystGroupDefaultAction 44.7-1
Csc 19.2-1
Csch 19.2-1
CubeRoot 19.2-1
Cycle 41.9-3
CycleIndex, for a permutation and an action domain 41.9-7
    for a permutation group and an action domain 41.9-7
CycleLength 41.9-4
CycleLengths 41.9-6
Cycles 41.9-5
CyclesOfTransformation 53.5-20
CycleStructureClass 72.8-14
CycleStructurePerm 42.4-2
CycleTransformationInt 53.5-21
CyclicExtensionsTom, for a list of primes 70.9-7
    for a prime 70.9-7
CyclicGroup 50.1-2
cyclotomic field elements 18.
cyclotomic fields, CanonicalBasis 60.3
CyclotomicField, for (subfield and) conductor 60.1-1
    for (subfield and) generators 60.1-1
CyclotomicPolynomial 66.9-1
Cyclotomics 18.1-2
CyclotomicsFamily 18.1-3
\(d_N\) (irrational value) 18.4-1
Darstellungsgruppe, see EpimorphismSchurCover 39.24
data type, unknown 74.
DataType 13.9-2
DayDMY 27.10-4
DaysInMonth 27.10-2
DaysInYear 27.10-1
DEC 25.4
DeclareAttribute 79.18-3
DeclareAttribute, example 80.5
DeclareAttribute!example 80.8-3
DeclareAutoPackage 77.2
DeclareAutoreadableVariables 76.3-9
DeclareCategory 79.18-1
DeclareFilter 79.18-5
DeclareGlobalFunction 79.18-7
DeclareGlobalVariable 79.18-8
DeclareHandlingByNiceBasis 61.12-1
DeclareInfoClass 7.4-2
DeclareOperation 79.18-6
DeclarePackage 77.2
DeclarePackageAutoDocumentation 77.2
DeclarePackageDocumentation 77.2
DeclareProperty 79.18-4
DeclareRepresentation 79.18-2
DeclareRepresentation, belongs to implementation part 79.19
    example 80.6
DeclareSynonym 79.18-10
DeclareSynonymAttr 79.18-10
DeclareUserPreference 3.2-4
DecodeTree 48.10-1
decompose, a group character 72.8-5
DecomposedFixedPointVector 70.9-8
DecomposeTensorProduct 64.13-3
Decomposition 25.4-1
decomposition matrix 25.4
DecompositionInt 25.4-5
DecompositionMatrix 71.11-4
Decreased 72.10-7
DEFAULTDISPLAYSTRING 27.7-2
DefaultField, for a list of generators 58.1-4
    for cyclotomics 18.1-16
    for finite field elements 59.3-1
    for several generators 58.1-4
DefaultFieldByGenerators 58.1-5
DefaultFieldOfMatrix 24.4-2
DefaultFieldOfMatrixGroup 44.2-2
DefaultInfoHandler 7.4-6
DefaultRing, for a collection 56.1-3
    for finite field elements 59.3-1
    for ring elements 56.1-3
DefaultRingByGenerators 56.1-5
DefaultStabChainOptions 43.8-3
DEFAULTVIEWSTRING 27.7-4
DefiningPolynomial 58.2-7
DefiningQuotientHomomorphism 47.13-4
DegreeFFE, for a FFE 59.2-1
    for a matrix of FFEs 59.2-1
    for a vector of FFEs 59.2-1
DegreeIndeterminate 66.6-1
DegreeOfBinaryRelation 33.2-10
DegreeOfCharacter 72.8-4
DegreeOfLaurentPolynomial 66.5-3
DegreeOfPartialPerm 54.3-1
DegreeOfPartialPermCollection 54.3-1
DegreeOfPartialPermSemigroup 54.7-2
DegreeOfTransformation 53.5-1
DegreeOfTransformationCollection 53.5-1
DegreeOfTransformationSemigroup 53.7-2
DegreeOverPrimeField 58.2-6
Delta 75.2-2
denominator, of a rational 17.2-5
DenominatorCyc 18.1-11
DenominatorOfModuloPcgs 45.9-4
DenominatorOfRationalFunction 66.4-3
DenominatorRat 17.2-5
DenseHashTable 28.6-1
DenseIntKey 28.5-1
deprecated 77.
DepthOfPcElement 45.5-4
DepthOfUpperTriangularMatrix 24.12-3
Derangements 16.2-14
Derivations 64.2-6
Derivative 66.6-5
DerivedLength 39.17-8
DerivedSeriesOfGroup 39.17-7
DerivedSubgroup 39.12-3
DerivedSubgroupsTom 70.9-2
DerivedSubgroupsTomPossible 70.9-3
DerivedSubgroupsTomUnique 70.9-3
DerivedSubgroupTom 70.9-2
DescriptionOfRootOfUnity 18.1-13
Determinant 24.4-4
determinant, integer matrix 25.3-1
determinant character 72.8-18
DeterminantIntMat 25.3-1
DeterminantMat 24.4-4
DeterminantMatDestructive 24.4-5
DeterminantMatDivFree 24.4-6
DeterminantOfCharacter 72.8-18
DiagonalizeIntMat 25.2-8
DiagonalizeMat 24.9-3
DiagonalMat 24.5-4
DiagonalOfMat 24.12-1
DictionaryByPosition 28.3-1
DicyclicGroup 50.1-7
Difference 30.5-4
DifferenceBlist 22.3-3
DihedralGroup 50.1-6
Dimension 57.3-3
DimensionOfHighestWeightModule 64.13-4
DimensionOfMatrixGroup 44.2-1
DimensionOfVectors 61.9-6
DimensionsLoewyFactors 39.17-15
DimensionsMat 24.4-1
DirectoriesLibrary 9.3-5
DirectoriesPackageLibrary 76.3-5
DirectoriesPackagePrograms 76.3-6
DirectoriesSystemPrograms 9.3-6
Directory 9.3-2
DirectoryContents 9.3-7
DirectoryCurrent 9.3-4
DirectoryDesktop 9.3-8
DirectoryHome 9.3-9
DirectoryTemporary 9.3-3
DirectProduct 49.1-1
DirectProductOp 49.1-1
DirectSum 56.9-5
DirectSumDecomposition, for Lie algebras 62.9-18
DirectSumOfAlgebraModules, for a list of Lie algebra modules 62.11-23
    for two Lie algebra modules 62.11-23
DirectSumOfAlgebras, for a list of algebras 62.9-14
    for two algebras 62.9-14
DirectSumOp 56.9-5
disable automatic loading 76.2
DisableAttributeValueStoring 13.6-5
Discriminant 66.6-6
Display 6.3-6
    for a character table 71.13-3
    for a ffe 59.6-1
    for a table of marks 70.4-3
    for class functions 72.5-3
DisplayCacheStats 7.7-20
DisplayCompositionSeries 39.17-6
DisplayEggBoxOfDClass 51.8-7
DisplayImfInvariants 50.12-2
DisplayInformationPerfectGroups, for a pair [ order, index ] 50.8-7
    for group order (and index) 50.8-7
DisplayOptions 71.13-4
DisplayOptionsStack 8.1-6
DisplayPackageLoadingLog 76.2-4
DisplayProfile 7.7-9
DisplayString 27.7-1
DistancePerms 42.2-2
DistancesDistributionMatFFEVecFFE 23.6-4
DistancesDistributionVecFFEsVecFFE 23.6-3
DistanceVecFFE 23.6-2
division 4.13
    operation 31.12-1
division rings 58.
DivisionRingByGenerators 58.1-8
divisors, of an integer 14.4-12
DivisorsInt 14.4-12
Dixon-Schneider algorithm 71.16
DixonInit 71.17-2
DixonRecord 71.17-1
DixonSplit 71.17-4
DixontinI 71.17-3
DMYDay 27.10-3
DMYhmsSeconds 27.10-11
DnLattice 72.10-8
DnLatticeIterative 72.10-9
do 4.20
document formats (text, dvi, ps, pdf, HTML) 2.3
document formats!for help books 84.3
Domain 31.9-3
DomainByGenerators 31.9-3
DomainOfPartialPerm 54.3-4
DomainOfPartialPermCollection 54.3-4
DominantCharacter, for a root system and a highest weight 64.13-2
    for a semisimple Lie algebra and a highest weight 64.13-2
DominantWeights 64.13-1
dot-file 39.20-3
DotFileLatticeSubgroups 39.20-3
DoubleCoset 39.9-1
DoubleCosetRepsAndSizes 39.9-5
DoubleCosets 39.9-3
DoubleCosetsNC 39.9-3
DoubleCoverOfAlternatingGroup 39.24-11
DoubleHashArraySize 28.7-2
doublequote character 27.2
doublequotes 27.1
DownEnv 6.5-1
duplicate free 21.17-2
DuplicateFreeList 21.20-4
DxIncludeIrreducibles 71.17-6
E 18.1-1
\(e_N\) (irrational value) 18.4-1
EANormalSeriesByPcgs 45.11-4
Earns, for a group, an action domain, etc. 41.10-6
    for an external set 41.10-6
EB 18.4-1
EC 18.4-1
ED 18.4-1
Edit 6.10-1
EE 18.4-1
EF 18.4-1
EG 18.4-1
EggBoxOfDClass 51.8-6
EH 18.4-1
EI 18.4-2
Eigenspaces 24.8-4
Eigenvalues 24.8-3
EigenvaluesChar 72.8-19
Eigenvectors 24.8-5
EJ 18.4-4
EK 18.4-4
EL 18.4-4
element test, for lists 21.8-1
ElementaryAbelianGroup 50.1-4
ElementaryAbelianSeries, for a group 39.17-9
    for a list 39.17-9
ElementaryAbelianSeriesLargeSteps 39.17-9
ElementaryDivisorsMat 24.9-1
ElementaryDivisorsMatDestructive 24.9-1
ElementaryDivisorsTransformationsMat 24.9-2
ElementaryDivisorsTransformationsMatDestructive 24.9-2
ElementOfFpGroup 47.4-5
ElementOfFpSemigroup 52.4-2
ElementOfMagmaRing 65.2-6
ElementOrdersPowerMap 73.1-3
ElementProperty 43.12-2
Elements 30.3-11
elements, definition 12.2
    of a list or collection 30.3-10
ElementsFamily 30.2-3
ElementsStabChain 43.10-9
elif 4.17
EliminatedWord 37.4-6
EliminationOrdering 66.17-10
ElmWPObj 86.2
ElmWPObj 86.2-1
else 4.17
EM 18.4-4
emacs 6.11
email addresses 1.5
Embedding, example for direct products 49.1-1
    example for semidirect products 49.2-1
    example for wreath products 49.4-1
Embedding, for a domain and a positive integer 32.2-10
    for group products 49.6-1
Embedding, for Lie algebras 64.1-3
    for magma rings 65.3
Embedding, for two domains 32.2-10
embeddings, find all 40.9-5
EmptyBinaryRelation, for a degree 33.1-4
    for a domain 33.1-4
EmptyMatrix 24.5-3
EmptyPartialPerm 54.2-6
EmptyPlist 21.9-1
EmptySCTable 62.4-3
EmptyStabChain 43.11-7
EmptyString 27.4-5
EnableAttributeValueStoring 13.6-6
end 4.23
End 61.10-6
EndlineFunc 5.1-5
EndsWith 27.7-19
Enumerator 30.3-2
EnumeratorByBasis 61.6-5
EnumeratorByFunctions, for a domain and a record 30.3-4
    for a family and a record 30.3-4
EnumeratorOfCombinations 16.2-2
EnumeratorOfTuples 16.2-9
EnumeratorSorted 30.3-3
environment 4.23
Epicentre 39.24-4
EpimorphismFromFreeGroup 39.5-1
EpimorphismNilpotentQuotient 47.14-4
EpimorphismNonabelianExteriorSquare 39.24-6
EpimorphismPGroup 47.14-3
EpimorphismQuotientSystem 47.14-2
epimorphisms, find all 40.9-4
EpimorphismSchurCover 39.24-1
EpimorphismSolvableQuotient 47.14-6
EqFloat 19.2-2
equality, associative words 37.3-1
    elements of finitely presented groups 47.3-1
    for pcwords 46.2-1
    for transformations 53.4
    nonassociative words 36.2-1
    of booleans 20.3-1
    of records 29.5
    operation 31.11-1
equality test 4.12
    for permutations 42.2-1
equivalence class 33.7-1
equivalence relation 33.2-8 33.5
EquivalenceClasses, attribute 33.7-3
EquivalenceClassOfElement 33.7-4
EquivalenceClassOfElementNC 33.7-4
EquivalenceClassRelation 33.7-2
EquivalenceRelationByPairs 33.5-3
EquivalenceRelationByPairsNC 33.5-3
EquivalenceRelationByPartition 33.5-1
EquivalenceRelationByPartitionNC 33.5-1
EquivalenceRelationByProperty 33.5-4
EquivalenceRelationByRelation 33.5-2
EquivalenceRelationPartition 33.6-1
ER 18.4-2
Erf 19.2-1
Error 6.6-1
ErrorCount 6.6-3
ErrorNoReturn 6.6-2
ErrorNoTraceBack 6.4-3
errors, syntax 6.1
ES 18.4-3
escaped characters 27.2
escaping non-special characters 27.2
ET 18.4-3
EU 18.4-3
EuclideanDegree 56.6-2
EuclideanQuotient 56.6-3
EuclideanRemainder 56.6-4
Euler's totient function 15.2-2
EulerianFunction 39.16-3
EulerianFunctionByTom 70.9-9
EV 18.4-3
EvalStraightLineProgElm 37.9-4
EvalString 27.9-3
evaluation 4.7
    strings 27.9-1
EW 18.4-3
EX 18.4-3
ExactSizeConsiderFunction 39.21-5
Excel 10.11
Exec 11.1-2
execution 4.14
exit 6.7
Exp 19.2-1
Exp10 19.2-1
Exp2 19.2-1
Expanded form of monomials 66.21
Expm1 19.2-1
Exponent 39.16-2
    for a character table 71.8-5
exponent, of the prime residue group 15.2-3
exponentiation, operation 31.12-1
ExponentOfPcElement 45.5-2
ExponentsConjugateLayer 45.6-1
ExponentsOfCommutator 45.6-4
ExponentsOfConjugate 45.6-3
ExponentsOfPcElement 45.5-3
ExponentsOfRelativePower 45.6-2
ExponentSumWord 37.4-2
ExponentSyllable 37.5-2
ExtendedPcgs 45.7-8
ExtendRootDirectories 76.2-3
ExtendStabChain 43.11-4
Extension 46.8-5
ExtensionNC 46.8-5
ExtensionRepresentatives 46.8-9
Extensions 46.8-4
exterior power 72.11-3
ExteriorCentre 39.24-4
ExteriorPowerOfAlgebraModule 64.15-2
External representation of polynomials 66.21
ExternalOrbit 41.12-9
ExternalOrbits, for a group, an action domain, etc. 41.12-11
    for an external set 41.12-11
ExternalOrbitsStabilizers, for a group, an action domain, etc. 41.12-12
    for an external set 41.12-12
ExternalSet 41.12-2
ExternalSet, computing orbits 85.3
ExternalSubset 41.12-7
Extract 72.10-5
ExtraspecialGroup 50.1-8
ExtRepDenominatorRatFun 66.21-3
ExtRepNumeratorRatFun 66.21-2
ExtRepOfObj 79.16-1
    for a cyclotomic 18.1-12
ExtRepPolynomialRatFun 66.21-6
EY 18.4-3
\(f_N\) (irrational value) 18.4-1
FactorCosetAction 41.8-1
    for fp groups 47.6-3
FactorFreeSemigroupByRelations 52.2-2
FactorGroup 39.18-2
FactorGroupFpGroupByRels 47.2-2
FactorGroupNC 39.18-2
FactorGroupNormalSubgroupClasses 71.23-4
FactorGroupTom 70.9-11
Factorial 16.1-1
factorization 39.5
Factorization 39.5-2
Factors 56.5-9
    for polynomials over abelian number fields 60.2-1
    of polynomial 66.10-1
FactorsInt 14.4-7
    using Pollard's Rho 14.4-7
FactorsOfDirectProduct 71.20-2
FactorsSquarefree 66.10-2
fail 20.2-1
FaithfulModule, for Lie algebras 62.11-20
FamiliesOfGeneralMappingsAndRanges 32.14-5
FamiliesOfRows 71.22-5
FamilyForOrdering 34.3-4
FamilyObj 13.1-1
FamilyPcgs 46.1-1
FamilyRange 32.14-3
FamilySource 32.14-4
features, under UNIX 3.1
fi 4.17
Fibonacci 16.3-1
Field, for (a field and) a list of generators 58.1-3
    for several generators 58.1-3
field homomorphisms, Frobenius 59.4-1
FieldByGenerators 58.1-8
FieldExtension 58.2-9
FieldOfMatrixGroup 44.2-3
FieldOverItselfByGenerators 58.2-2
fields 58.
FileDescriptorOfStream 10.2-2
Filename, for a directory and a string 9.4-1
    for a list of directories and a string 9.4-1
FilenameFunc 5.1-4
Filtered 21.20-20
FindSl2 64.9-7
finiteness test, for a list or collection 30.4-2
First 21.20-22
FittingSubgroup 39.12-5
FixedPointsOfPartialPerm, for a partial perm 54.3-8
    for a partial perm coll 54.3-8
Flat 21.20-6
FlatKernelOfTransformation 53.5-11
Float 19.2-7
FLOAT, constants 19.2-6
Floor 19.2-1
flush character 27.2
FlushCaches 79.18-11
FOA triples 85.
for loop 4.20
ForAll 21.20-23
ForAny 21.20-24
FORCE_QUIT_GAP 6.7-4
FpElmComparisonMethod 47.3-3
FpGroupPresentation 48.1-4
FpGrpMonSmgOfFpGrpMonSmgElement 52.1-7
FpLieAlgebraByCartanMatrix 64.11-1
Frac 19.2-1
Frame 72.11-4
FrattiniSubgroup 39.12-6
FrattiniSubgroup, for groups with pcgs 45.16
FreeAbelianGroup 50.1-5
FreeAlgebra, for ring and several names 62.3-1
    for ring, rank (and name) 62.3-1
FreeAlgebraWithOne, for ring and several names 62.3-2
    for ring, rank (and name) 62.3-2
FreeAssociativeAlgebra, for ring and several names 62.3-3
    for ring, rank (and name) 62.3-3
FreeAssociativeAlgebraWithOne, for ring and several names 62.3-4
    for ring, rank (and name) 62.3-4
FreeGeneratorsOfFpGroup 47.4-2
FreeGeneratorsOfFpSemigroup 52.4-4
FreeGeneratorsOfWholeGroup 47.4-2
FreeGroup, for a list of names 37.2-1
    for given rank 37.2-1
    for infinitely many generators 37.2-1
    for various names 37.2-1
FreeGroupOfFpGroup 47.4-1
FreeLeftModule 57.3-2
FreeLieAlgebra, for ring and several names 64.2-4
    for ring, rank (and name) 64.2-4
FreeMagma, for a list of names 36.4-1
    for given rank 36.4-1
    for infinitely many generators 36.4-1
    for various names 36.4-1
FreeMagmaRing 65.1-1
FreeMagmaWithOne, for a list of names 36.4-2
    for given rank 36.4-2
    for infinitely many generators 36.4-2
    for various names 36.4-2
FreeMonoid, for a list of names 51.2-9
    for given rank 51.2-9
    for infinitely many generators 51.2-9
    for various names 51.2-9
FreeMonoidOfRewritingSystem 52.6-7
FreeProduct, for a list 49.5-1
    for several groups 49.5-1
FreeSemigroup, for a list of names 51.1-10
    for given rank 51.1-10
    for infinitely many generators 51.1-10
    for various names 51.1-10
FreeSemigroupOfFpSemigroup 52.4-3
FreeSemigroupOfRewritingSystem 52.6-6
Frobenius automorphism 59.4-1
FrobeniusAutomorphism 59.4-1
FrobeniusCharacterValue 72.15-1
FullMatrixAlgebra 62.5-4
FullMatrixAlgebraCentralizer 62.9-15
FullMatrixLieAlgebra 64.2-5
FullMatrixModule 57.3-11
FullMatrixSpace 61.9-5
FullRowModule 57.3-9
FullRowSpace 61.9-4
FullTransformationMonoid 53.7-3
FullTransformationSemigroup 53.7-3
FunctionAction 41.12-4
FunctionField, for an integral ring and a list of indeterminate numbers 66.15-8
    for an integral ring and a list of indeterminates 66.15-8
    for an integral ring and a list of names (and an exclusion list) 66.15-8
    for an integral ring and a rank (and an exclusion list) 66.15-8
FunctionOperation 77.1
functions, as in mathematics 32.
    as in programming language 5.
    definition by arrow notation 4.23
    definition of 4.23
    recursive 4.23
    with a variable number of arguments 4.23
    with a variable number of arguments, calling 4.11-1
FunctionsFamily 5.5-3
FusionCharTableTom 70.11-1
FusionConjugacyClasses, for a homomorphism 73.3-1
    for two character tables 73.3-1
    for two groups 73.3-1
FusionConjugacyClassesOp, for a homomorphism 73.3-1
    for two character tables 73.3-1
fusions 73.3
FusionsAllowedByRestrictions 73.7-4
FusionsTom 70.7-6
\(G\)-sets 41.12
    computing orbits 85.3
\(g_N\) (irrational value) 18.4-1
gac 76.3-10
GaloisCyc, for a class function 72.4-2
    for a cyclotomic 18.5-1
    for a list of cyclotomics 18.5-1
GaloisField, for characteristic and degree 59.3-2
    for characteristic and polynomial 59.3-2
    for field size 59.3-2
    for subfield and degree 59.3-2
    for subfield and polynomial 59.3-2
GaloisGroup, for abelian number fields 60.4-1
    of field 58.3-1
    of rational class of a group 39.10-8
GaloisMat 18.5-5
GaloisStabilizer 60.2-5
GaloisType 66.11-3
Gamma 19.2-1
GammaL 50.2-9
gap.ini 3.2-1
Gap3CatalogueIdGroup 50.7-7
GAP_EXIT_CODE 6.7-2
GAPInfo 3.5-1
GAPInfo.Architecture 76.3-6
GAPInfo.CommandLineOptions 3.1
GAPInfo.Keywords 4.5
GAPInfo.ProfileThreshold 7.7-9
GAPInfo.RootPaths 9.2
GAPInfo.TimeoutsSupported 5.3-2
GAPInfo.UserGapRoot 9.2
GAPInfo.Version 7.8
GapInputPcGroup 46.6-1
GapInputSCTable 62.4-5
GAPKB_REW 52.6-2
GAPTCENUM 47.6-5
GasmanLimits 7.11-3
GasmanMessageStatus 7.11-2
GasmanStatistics 7.11-1
Gaussian algorithm 24.7
GaussianIntegers 60.5-1
GaussianRationals 60.1-3
Gcd, for (a ring and) a list of elements 56.7-1
    for (a ring and) several elements 56.7-1
Gcdex 14.3-5
GcdInt 14.3-4
GcdOp 56.7-2
GcdRepresentation, for (a ring and) a list of elements 56.7-3
    for (a ring and) several elements 56.7-3
GcdRepresentationOp 56.7-4
GeneralisedEigenspaces 24.8-2
GeneralisedEigenvalues 24.8-1
generalized characters 72.
generalized conjugation technique 87.1
GeneralizedEigenspaces 24.8-2
GeneralizedEigenvalues 24.8-1
GeneralLinearGroup, for dimension and a ring 50.2-1
    for dimension and field size 50.2-1
GeneralMappingByElements 32.2-1
GeneralMappingsFamily 32.14-6
GeneralOrthogonalGroup 50.2-6
GeneralSemilinearGroup 50.2-9
GeneralUnitaryGroup 50.2-3
generator, of the prime residue group 15.3-3 15.3-4
GeneratorsOfAdditiveGroup 55.3-4
GeneratorsOfAdditiveMagma 55.3-2
GeneratorsOfAdditiveMagmaWithZero 55.3-3
GeneratorsOfAlgebra 62.9-1
GeneratorsOfAlgebraModule 62.11-7
GeneratorsOfAlgebraWithOne 62.9-2
GeneratorsOfDivisionRing 58.1-6
GeneratorsOfDomain 31.9-2
GeneratorsOfEquivalenceRelationPartition 33.6-2
GeneratorsOfField 58.1-7
GeneratorsOfGroup 39.2-4
GeneratorsOfIdeal 56.2-7
GeneratorsOfInverseMonoid 51.3-4
GeneratorsOfInverseSemigroup 51.3-3
GeneratorsOfLeftIdeal 56.2-8
GeneratorsOfLeftModule 57.1-4
GeneratorsOfLeftOperatorAdditiveGroup 57.1-3
GeneratorsOfLeftVectorSpace 61.3-1
GeneratorsOfMagma 35.4-1
GeneratorsOfMagmaWithInverses 35.4-3
GeneratorsOfMagmaWithOne 35.4-2
GeneratorsOfMonoid 51.2-7
GeneratorsOfNearAdditiveGroup 55.3-4
GeneratorsOfNearAdditiveMagma 55.3-2
GeneratorsOfNearAdditiveMagmaWithZero 55.3-3
GeneratorsOfPresentation 48.1-3
GeneratorsOfRightIdeal 56.2-9
GeneratorsOfRightModule 57.1-9
GeneratorsOfRightOperatorAdditiveGroup 57.1-8
GeneratorsOfRing 56.1-6
GeneratorsOfRingWithOne 56.3-4
GeneratorsOfRws 38.1-12
GeneratorsOfSemigroup 51.1-8
GeneratorsOfStruct 31.3
GeneratorsOfTwoSidedIdeal 56.2-7
GeneratorsOfVectorSpace 61.3-1
GeneratorsPrimeResidues 15.2-4
GeneratorsSmallest 39.22-1
GeneratorsSubgroupsTom 70.10-1
GeneratorSyllable 37.5-3
GetCyclotomicsLimit 18.6-1
GetFusionMap 73.3-3
getting help 2.1
GF, for characteristic and degree 59.3-2
    for characteristic and polynomial 59.3-2
    for field size 59.3-2
    for subfield and degree 59.3-2
    for subfield and polynomial 59.3-2
GL, for dimension and a ring 50.2-1
    for dimension and field size 50.2-1
GlobalMersenneTwister 14.7-4
GlobalRandomSource 14.7-4
GModuleByMats, for empty list, the dimension, and a field 69.1-1
    for generators and a field 69.1-1
GO 50.2-6
GQuotients 40.9-4
Grading 62.9-20
graphviz 39.20-3
GreensDClasses 51.8-9
GreensDClassOfElement 51.8-8
GreensDRelation 51.8-1
GreensHClasses 51.8-9
GreensHClassOfElement 51.8-8
GreensHRelation 51.8-1
GreensJClasses 51.8-9
GreensJClassOfElement 51.8-8
GreensJRelation 51.8-1
GreensLClasses 51.8-9
GreensLClassOfElement 51.8-8
GreensLRelation 51.8-1
GreensRClasses 51.8-9
GreensRClassOfElement 51.8-8
GreensRRelation 51.8-1
GroebnerBasis, for a list and a monomial ordering 66.18-1
    for an ideal and a monomial ordering 66.18-1
GroebnerBasisNC 66.18-1
Group, for a list of generators (and an identity element) 39.2-1
    for several generators 39.2-1
group actions 41. 41.2
    operations syntax 41.1
group algebra 65.
group characters 72.
group operations 41.2 77.1
group ring 65.
GroupByGenerators 39.2-2
    with explicitly specified identity element 39.2-2
GroupByRws 46.4-6
GroupByRwsNC 46.4-6
GroupGeneralMappingByImages 40.1-3
    from group to itself 40.1-3
GroupGeneralMappingByImagesNC 40.1-3
    from group to itself 40.1-3
GroupHClassOfGreensDClass 51.8-10
GroupHomomorphismByFunction, by function (and inverse function) between two domains 40.1-4
    by function and function that computes one preimage 40.1-4
GroupHomomorphismByImages 40.1-1
GroupHomomorphismByImagesNC 40.1-2
GroupOfPcgs 45.4-5
GroupRing 65.1-2
GroupStabChain 43.10-5
GroupWithGenerators 39.2-3
GrowthFunctionOfGroup 39.5-3
    with word length limit 39.5-3
GU 50.2-3
\(h_N\) (irrational value) 18.4-1
HallSubgroup 39.13-3
HallSystem 39.13-6
HallSystem, for groups with pcgs 45.16
HasAbelianFactorGroup 39.18-5
HasElementaryAbelianFactorGroup 39.18-6
HasIndeterminateName 66.1-4
HasParent 31.7-1
HasseDiagramBinaryRelation 33.4-4
HeadPcElementByNumber 45.5-12
HELP_ADD_BOOK 84.1-1
HELP_REMOVE_BOOK 84.1-2
HELP_VIEWER_INFO 84.4-1
HenselBound 66.12-3
Hermite normal form 77.3
HermiteNormalFormIntegerMat 25.2-4
HermiteNormalFormIntegerMatTransform 25.2-5
HeuristicCancelPolynomialsExtRep 66.24-3
HexStringInt 27.7-8
HighestWeightModule 64.14-5
HMSMSec 27.10-7
Hom 61.10-5
HomeEnumerator 41.12-5
HomomorphismQuotientSemigroup 51.7-2
homomorphisms, find all 40.9
    Frobenius, field 59.4-1
Hypothenuse 19.2-1
\(i_N\) (irrational value) 18.4-2
Ideal 56.2-1
IdealByGenerators 56.2-4
IdealNC 56.2-2
Ideals 56.9-4
Idempotent 53.2-4
Idempotents 35.4-6
IdempotentsTom 70.7-8
IdempotentsTomInfo 70.7-8
IdentificationOfConjugacyClasses 71.6-3
Identifier, for character tables 71.9-8
    for tables of marks 70.7-9
Identity 31.10-2
IdentityBinaryRelation, for a degree 33.1-3
    for a domain 33.1-3
IdentityFromSCTable 62.4-7
IdentityMapping 32.2-9
IdentityMat 24.5-1
IdentityTransformation 53.2-8
IdFunc 5.4-6
IdGap3SolvableGroup 50.7-7
IdGroup 50.7-5
IdSmallGroup 50.7-5
IdsOfAllSmallGroups 50.7-6
if statement 4.17
Image, for Frobenius automorphisms 59.4-1
Image, set of images of a collection under a mapping 32.4-6
    set of images of the source of a general mapping 32.4-6
    unique image of an element under a mapping 32.4-6
image, vector under matrix 24.3
ImageElm 32.4-5
ImageListOfPartialPerm 54.3-6
ImageListOfTransformation 53.5-2
ImageOfPartialPermCollection 54.3-5
Images, set of images of a collection under a mapping 32.4-7
    set of images of an element under a mapping 32.4-7
    set of images of the source of a general mapping 32.4-7
ImagesElm 32.4-3
ImageSetOfPartialPerm 54.3-7
ImageSetOfTransformation 53.5-3
ImagesRepresentative 32.4-2
ImagesSet 32.4-4
ImagesSmallestGenerators 40.3-5
ImagesSource 32.4-1
ImaginaryPart 18.5-2
ImfInvariants 50.12-3
ImfMatrixGroup 50.12-4
ImfNumberQClasses 50.12-1
ImfNumberQQClasses 50.12-1
ImfNumberZClasses 50.12-1
Immutable 12.6-3
ImmutableBasis 61.8-4
ImmutableMatrix 24.14-1
in, for lists 21.8-1
    operation for 30.6
\in, operation for testing membership 30.6
IncreaseInterval 19.2-4
IndependentGeneratorExponents 39.22-6
IndependentGeneratorsOfAbelianGroup 39.22-5
Indeterminate, for a family and a number 66.1-1
    for a ring (and a name, and an exclusion list) 66.1-1
    for a ring (and a number) 66.1-1
IndeterminateName 66.1-4
Indeterminateness 73.5-13
IndeterminateNumberOfLaurentPolynomial 66.13-3
IndeterminateNumberOfUnivariateRationalFunction 66.1-2
IndeterminateOfUnivariateRationalFunction 66.1-3
IndeterminatesOfFunctionField 66.15-2
IndeterminatesOfPolynomialRing 66.15-2
Index, for a group and its subgroup 39.3-2
    for two character tables 71.12-1
IndexInWholeGroup 39.3-3
IndexNC, for a group and its subgroup 39.3-2
IndexPeriodOfPartialPerm 54.3-16
IndexPeriodOfTransformation 53.5-15
Indicator 71.12-5
IndicatorOp 71.12-5
IndicesCentralNormalSteps 45.11-7
IndicesChiefNormalSteps 45.11-15
IndicesEANormalSteps 45.11-3
IndicesInvolutaryGenerators 47.6-9
IndicesNormalSteps 45.11-17
IndicesOfAdjointBasis 62.9-6
IndicesPCentralNormalStepsPGroup 45.11-11
IndicesStabChain 43.10-7
Indirected 73.5-4
InducedAutomorphism 40.7-6
InducedClassFunction, for a given monomorphism 72.9-3
    for a supergroup 72.9-3
    for the character table of a supergroup 72.9-3
InducedClassFunctions 72.9-4
InducedClassFunctionsByFusionMap 72.9-5
InducedCyclic 72.9-6
InducedPcgs 45.7-4
InducedPcgsByGenerators 45.7-5
InducedPcgsByGeneratorsNC 45.7-5
InducedPcgsByPcSequence 45.7-2
InducedPcgsByPcSequenceAndGenerators 45.7-6
InducedPcgsByPcSequenceNC 45.7-2
InducedPcgsWrtFamilyPcgs 46.1-3
InducedPcgsWrtSpecialPcgs 45.13-8
Inequalities 72.14-5
inequality, of booleans 20.3-1
    of records 29.5
inequality test 4.12
InertiaSubgroup 72.8-13
Inf 19.2-4
infinity 18.2-1
inflated class functions 72.9
Info 7.4-5
InfoAlgebra 62.1-1
InfoAttributes 13.6-4
InfoBckt 43.12-4
InfoCharacterTable 71.4-2
InfoCoh 39.23-5
InfoComplement 39.11-7
InfoCoset 39.9-6
InfoFpGroup 47.1-3
InfoGroebner 66.18-4
InfoGroup 39.2-8
InfoLattice 39.20-9
InfoLevel 7.4-4
InfoMatrix 24.1-1
InfoMonomial 75.1-1
InfoNumtheor 15.1-1
InfoObsolete 77.4-1
InfoOptions 8.1-7
InfoPackageLoading 76.2-4
InfoPcSubgroup 39.21-6
InfoPoly 66.5-8
InfoText 12.8-3
InfoText, (for Conway polynomials) 59.5-1
InfoText, for character tables 71.9-9
InfoTom 70.6-1
InfoWarning 7.4-7
Init 14.7-3
InitFusion 73.7-1
InitPowerMap 73.6-1
InjectionZeroMagma 35.2-13
inner product, of group characters 72.8-5
InnerAutomorphism 40.6-3
InnerAutomorphismNC 40.6-3
InnerAutomorphismsAutomorphismGroup 40.7-5
InParentFOA 85.2-1
InputFromUser 10.6-3
InputLogTo, for a filename 9.7-5
    for streams 10.4-6
    stop logging input 9.7-5
InputOutputLocalProcess 10.8-2
InputTextFile 10.5-1
InputTextNone 10.9-1
InputTextString 10.7-1
InputTextUser 10.6-1
InsertTrivialStabilizer 43.11-8
InstallAtExit 6.7-5
InstallCharReadHookFunc 10.10-1
InstalledPackageVersion 76.3-4
InstallFactorMaintenance 31.13-5
InstallFlushableValue 79.18-9
InstallFlushableValueFromFunction 79.18-9
InstallGlobalFunction 79.18-7
InstallHandlingByNiceBasis 61.12-1
InstallImmediateMethod 78.6-1
InstallIsomorphismMaintenance 31.13-6
InstallMethod 78.2-1
InstallOtherMethod 78.2-2
InstallReadlineMacro 6.9-4
InstallSubsetMaintenance 31.13-4
InstallTrueMethod 78.7-1
InstallValue 79.18-9
Int 14.2-3
    for a cyclotomic 18.1-5
    for a FFE 59.2-3
    for strings 27.9-1
IntChar 27.8-1
integer part of a quotient 14.3-1
Integers, global variable 14.1-1
IntegralizedMat 25.4-4
IntegratedStraightLineProgram 37.8-8
IntermediateGroup 39.17-17
IntermediateResultOfSLP 37.8-10
IntermediateResultOfSLPWithoutOverwrite 37.8-11
IntermediateResultsOfSLPWithoutOverwrite 37.8-12
IntermediateSubgroups 39.17-18
InterpolatedPolynomial 56.7-10
IntersectBlist 22.4-3
Intersection, for a list 30.5-2
Intersection, for groups with pcgs 45.16
Intersection, for various collections 30.5-2
intersection, of collections 30.5-2
    of sets 21.19-7
Intersection2 30.5-2
IntersectionBlist, for a list 22.3-2
    for various boolean lists 22.3-2
IntersectionsTom 70.9-10
IntersectSet 21.19-7
IntFFE 59.2-3
IntFFESymm, for a FFE 59.2-4
    for a vector of FFEs 59.2-4
IntHexString 27.9-1
IntScalarProducts 73.5-15
IntVecFFE 59.2-5
InvariantBilinearForm 44.5-1
InvariantElementaryAbelianSeries 39.17-10
InvariantLattice 44.6-6
InvariantQuadraticForm 44.5-5
InvariantSesquilinearForm 44.5-3
InvariantSubgroupsElementaryAbelianGroup 39.21-2
Inverse 31.10-8
    for a pcword 46.2-2
    for a transformation 53.5-14
Inverse, group homomorphism 40.2
inverse, matrix 24.3
    of class function 72.4
InverseAttr 31.10-8
InverseClasses 71.9-10
InverseGeneralMapping 32.2-3
InverseImmutable 31.10-8
InverseMap 73.5-2
InverseMatMod 24.15-1
InverseMonoid 51.3-2
InverseMutable 31.10-8
InverseOfTransformation 53.5-13
InverseOp 31.10-8
InverseRepresentative 43.10-11
InverseSameMutability 31.10-8
InverseSemigroup 51.3-1
InverseSM 31.10-8
InversesOfSemigroupElement 51.4-3
InvocationReadlineMacro 6.9-4
Irr, for a character table 71.8-2
    for a group 71.8-2
irrationalities 18.
IrrBaumClausen 71.14-3
IrrConlon 71.14-2
IrrDixonSchneider 71.14-1
irreducible character 72.8-3
irreducible characters, computation 71.17
IrreducibleDifferences 72.10-3
IrreducibleModules 71.15-1
IrreducibleModules, for groups with pcgs 45.16
IrreducibleRepresentations 71.14-4
IrreducibleRepresentationsDixon 71.14-5
IrreducibleSolvableGroup 50.11-6
IrreducibleSolvableGroupMS 50.11-1
Is16BitsFamily 37.6-7
Is32BitsFamily 37.6-7
IsAbelian 35.4-9
    for a character table 71.8-5
IsAbelianNumberField 60.2-3
IsAbelianNumberFieldPolynomialRing 66.15-6
IsAbelianTom 70.8-1
IsAdditiveElement 31.14-3
IsAdditiveElementWithInverse 31.14-7
IsAdditiveElementWithZero 31.14-5
IsAdditiveGroup 55.1-6
IsAdditiveGroupGeneralMapping 32.10-4
IsAdditiveGroupHomomorphism 32.10-4
IsAdditivelyCommutative 55.3-1
IsAdditivelyCommutativeElement 31.15-2
IsAdditivelyCommutativeElementCollColl 31.15-2
IsAdditivelyCommutativeElementCollection 31.15-2
IsAdditivelyCommutativeElementFamily 31.15-2
IsAdditiveMagma 55.1-4
IsAdditiveMagmaWithInverses 55.1-6
IsAdditiveMagmaWithZero 55.1-5
IsAlgebra 62.8-3
IsAlgebraGeneralMapping 32.12-3
IsAlgebraHomomorphism 32.12-3
IsAlgebraicElement 67.2-1
IsAlgebraicExtension 67.1-2
IsAlgebraModuleElement 62.11-8
IsAlgebraModuleElementCollection 62.11-8
IsAlgebraModuleElementFamily 62.11-8
IsAlgebraWithOne 62.8-4
IsAlgebraWithOneGeneralMapping 32.12-4
IsAlgebraWithOneHomomorphism 32.12-4
IsAlmostSimple, for a character table 71.8-5
IsAlmostSimpleGroup 39.15-11
IsAlphaChar 27.5-4
IsAlternatingGroup 43.4-3
IsAnticommutative 56.4-6
IsAntisymmetricBinaryRelation 33.2-4
IsAssociated 56.5-3
IsAssociative 35.4-7
IsAssociativeElement 31.15-1
IsAssociativeElementCollColl 31.15-1
IsAssociativeElementCollection 31.15-1
IsAssocWord 37.1-1
IsAssocWordWithInverse 37.1-1
IsAssocWordWithOne 37.1-1
IsAttributeStoringRep 80.5 80.6
IsAutomorphismGroup 40.7-4
IsBasicWreathLessThanOrEqual 37.3-4
IsBasicWreathProductOrdering 34.4-12
IsBasis 61.5-1
IsBasisByNiceBasis 61.11-5
IsBasisOfAlgebraModuleElementSpace 62.11-14
IsBergerCondition, for a character 75.2-3
    for a group 75.2-3
IsBijective 32.3-6
IsBinaryRelation 33.1-1
IsBinaryRelation, same as IsEndoGeneralMapping 33.
IsBLetterAssocWordRep 37.6-3
IsBLetterWordsFamily 37.6-4
IsBlist 22.1-1
IsBlistRep 22.5-1
IsBlockMatrixRep 24.17
IsBool 20.1-1
IsBound, for a global variable 4.8-1
    for a list index 21.5-1
    for a record component 29.6-1
    for multiple indices 21.5-1
IsBound\. 29.7-3
IsBound\[\] 21.2-1
IsBoundElmWPObj 86.2-1
IsBoundGlobal 4.9-5
IsBrauerTable 71.4-1
IsBravaisGroup 44.6-10
IsBuiltFromAdditiveMagmaWithInverses 38.3-1
IsBuiltFromGroup 38.3-1
IsBuiltFromMagma 38.3-1
IsBuiltFromMagmaWithInverses 38.3-1
IsBuiltFromMagmaWithOne 38.3-1
IsBuiltFromSemigroup 38.3-1
IsCanonicalBasis 61.7-1
IsCanonicalBasisFullMatrixModule 61.9-10
IsCanonicalBasisFullRowModule 61.9-9
IsCanonicalNiceMonomorphism 40.5-4
IsCanonicalPcgs 45.8-1
IsCentral 35.4-8
IsCentralFactor 39.24-7
IsChar 27.1-1
IsCharacter 72.8-1
IsCharacteristicSubgroup 39.3-7
IsCharacterTable 71.4-1
IsCharacterTableInProgress 71.4-1
IsCharCollection 27.1-1
IsCheapConwayPolynomial 59.5-2
IsClassFunction 72.1-1
IsClassFusionOfNormalSubgroup 71.12-4
IsClosedStream 10.1-2
IsCochain 64.12-1
IsCochainCollection 64.12-1
IsCollection 30.1-1
IsCollectionFamily 30.2-2
IsCommutative 35.4-9
IsCommutativeElement 31.15-3
IsCommutativeElementCollColl 31.15-3
IsCommutativeElementCollection 31.15-3
IsComponentObjectRep 80.6
IsCompositionMappingRep 32.2-6
IsConfluent, for a rewriting system 38.1-5
    for an algebra with canonical rewriting system 38.1-5
    for pc groups 46.4-7
IsConjugacyClassSubgroupsByStabilizerRep 39.19-2
IsConjugacyClassSubgroupsRep 39.19-2
IsConjugate, for a group and two elements 39.10-9
    for a group and two groups 39.10-9
IsConjugatorAutomorphism 40.6-4
IsConjugatorIsomorphism 40.6-4
IsConstantRationalFunction 66.4-11
IsConstantTimeAccessGeneralMapping 32.13-2
IsConstantTimeAccessList 21.1-6
IsContainedInSpan 61.8-5
IsCopyable 12.6-1
IsCyc 18.1-3
IsCyclic 39.15-1
    for a character table 71.8-5
IsCyclicTom 70.8-1
IsCyclotomic 18.1-3
IsCyclotomicField 60.2-4
IsCyclotomicMatrixGroup 44.6-1
IsDenseList 21.1-2
IsDiagonalMat 24.4-8
IsDictionary 28.3-2
IsDigitChar 27.5-1
IsDirectory 9.3-1
IsDirectoryPath 9.6-5
IsDirectProductElement 32.1-1
IsDisjoint 19.2-4
IsDistributive 56.4-5
IsDivisionRing 58.1-1
IsDomain 31.9-1
IsDoneIterator 30.8-4
IsDoubleCoset, operation 39.9-4
IsDuplicateFree 21.17-2
IsDuplicateFreeList 21.17-2
IsDxLargeGroup 71.17-8
IsElementaryAbelian 39.15-2
    for a character table 71.8-5
IsElementOfFpMonoid 52.1-6
IsElementOfFpSemigroup 52.1-5
IsElementOfFreeMagmaRing 65.2-2
IsElementOfFreeMagmaRingCollection 65.2-2
IsElementOfFreeMagmaRingFamily 65.2-3
IsElementOfMagmaRingModuloRelations 65.4-1
IsElementOfMagmaRingModuloRelationsCollection 65.4-1
IsElementOfMagmaRingModuloRelationsFamily 65.4-2
IsElementOfMagmaRingModuloSpanOfZeroFamily 65.5-1
IsEmpty 30.4-1
IsEmptyString 27.4-4
IsEndOfStream 10.3-6
IsEndoGeneralMapping 32.13-3
IsEndoGeneralMapping, same as IsBinaryRelation 33.
IsEqualSet 21.19-2
IsEquivalenceClass 33.7-1
IsEquivalenceRelation 33.2-8
IsEuclideanRing 56.6-1
IsEvenInt 14.2-4
IsExecutableFile 9.6-4
IsExistingFile 9.6-1
IsExtAElement 31.14-1
IsExternalOrbit 41.12-8
IsExternalSet 41.12-1
IsExternalSubset 41.12-6
IsExtLElement 31.14-8
IsExtRElement 31.14-9
IsFamilyPcgs 46.1-2
IsFFE 59.1-1
IsFFECollColl 59.1-1
IsFFECollCollColl 59.1-1
IsFFECollection 59.1-1
IsFFEMatrixGroup 44.2-5
IsField 58.1-2
IsFieldControlledByGaloisGroup 58.3
IsFieldHomomorphism 32.12-5
IsFinite 30.4-2
    float 19.2-5
    for a character table 71.8-5
IsFiniteDimensional 57.3-4
    for matrix algebras 62.8-7
IsFiniteFieldPolynomialRing 66.15-5
IsFinitelyGeneratedGroup 39.15-17
IsFiniteOrderElement 31.15-4
IsFiniteOrderElementCollColl 31.15-4
IsFiniteOrderElementCollection 31.15-4
IsFiniteOrdersPcgs 45.4-2
IsFixedStabilizer 43.11-9
IsFLMLOR 62.8-1
IsFLMLORWithOne 62.8-2
IsFpGroup 47.1-2
IsFpMonoid 52.1-4
IsFpSemigroup 52.1-3
IsFreeGroup 37.2-2
IsFreeLeftModule 57.3-1
IsFreeMagmaRing 65.1-3
IsFreeMagmaRingWithOne 65.1-4
IsFromFpGroupGeneralMappingByImages 40.10-10
IsFromFpGroupHomomorphismByImages 40.10-10
IsFromFpGroupStdGensGeneralMappingByImages 40.10-11
IsFromFpGroupStdGensHomomorphismByImages 40.10-11
IsFullHomModule 61.10-7
IsFullMatrixModule 57.3-10
IsFullRowModule 57.3-8
IsFullSubgroupGLorSLRespectingBilinearForm 44.5-2
IsFullSubgroupGLorSLRespectingQuadraticForm 44.5-6
IsFullSubgroupGLorSLRespectingSesquilinearForm 44.5-4
IsFullTransformationMonoid 53.7-4
IsFullTransformationSemigroup 53.7-4
IsFunction 5.5-1
IsFunctionField 66.15-9
IsGAPRandomSource 14.7-4
IsGaussianIntegers 60.5-2
IsGaussianRationals 60.1-3
IsGaussianSpace 61.9-3
IsGaussInt 18.1-14
IsGaussRat 18.1-15
IsGeneralizedDomain 31.9-1
IsGeneralizedRowVector 21.12-1
IsGeneralLinearGroup 44.4-1
IsGeneralMapping 32.13-1
IsGeneralMappingFamily 32.14-2
IsGeneratorsOfSemigroup 51.1-9
IsGeneratorsOfStruct 31.3
IsGL 44.4-1
IsGlobalRandomSource 14.7-4
IsGreensClass 51.8-3
IsGreensDClass 51.8-3
IsGreensDRelation 51.8-2
IsGreensHClass 51.8-3
IsGreensHRelation 51.8-2
IsGreensJClass 51.8-3
IsGreensJRelation 51.8-2
IsGreensLClass 51.8-3
IsGreensLessThanOrEqual 51.8-4
IsGreensLRelation 51.8-2
IsGreensRClass 51.8-3
IsGreensRelation 51.8-2
IsGreensRRelation 51.8-2
IsGroup 39.2-7
IsGroupGeneralMapping 32.9-4
IsGroupGeneralMappingByAsGroupGeneralMappingByImages 40.10-3
IsGroupGeneralMappingByImages 40.10-1
IsGroupGeneralMappingByPcgs 40.10-7
IsGroupHClass 51.8-11
IsGroupHomomorphism 32.9-4
IsGroupOfAutomorphisms 40.7-2
IsGroupRing 65.1-5
IsHandledByNiceBasis 61.11-6
IsHandledByNiceMonomorphism 40.5-1
IsHasseDiagram 33.2-7
IsHomogeneousList 21.1-3
IsIdempotent 31.10-7
IsIdenticalObj 12.5-1
IsIncomparableUnder 34.3-3
IsInducedFromNormalSubgroup 75.3-4
IsInducedPcgs 45.7-1
IsInducedPcgsWrtSpecialPcgs 45.13-7
IsInfBitsFamily 37.6-7
IsInfiniteAbelianizationGroup 47.16-1
IsInfiniteAbelianizationGroup, for groups 47.16-1
IsInfinity 18.2-1
IsInjective 32.3-4
IsInjectiveListTrans 53.4-2
IsInnerAutomorphism 40.6-4
IsInputOutputStream 10.8-1
IsInputStream 10.1-3
IsInputTextNone 10.1-5
IsInputTextStream 10.1-4
IsInt 14.2-1
IsIntegerMatrixGroup 44.6-3
IsIntegers 14.1-2
IsIntegralBasis 61.7-2
IsIntegralCyclotomic 18.1-4
IsIntegralRing 56.4-1
IsInternallyConsistent 12.8-4
    for character tables 71.12-2
    for tables of marks 70.9-1
IsInverseMonoid 51.4-8
IsInverseSemigroup 51.4-8
IsInverseSubsemigroup 51.3-5
IsIrreducibleCharacter 72.8-3
IsIrreducibleRingElement 56.5-7
IsIterator 30.8-3
IsJacobianElement 31.15-5
IsJacobianElementCollColl 31.15-5
IsJacobianElementCollection 31.15-5
IsJacobianRing 56.4-8
IsLaurentPolynomial 66.4-10
IsLaurentPolynomialDefaultRep 66.21-7
IsLDistributive 56.4-3
IsLeftAlgebraModuleElement 62.11-9
IsLeftAlgebraModuleElementCollection 62.11-9
IsLeftIdeal 56.2-3
IsLeftIdealInParent 56.2-3
IsLeftModule 57.1-2
IsLeftModuleGeneralMapping 32.11-2
IsLeftModuleHomomorphism 32.11-2
IsLeftOperatorAdditiveGroup 57.1-1
IsLeftSemigroupIdeal 51.5-3
IsLeftVectorSpace 61.1-1
IsLessThanOrEqualUnder 34.3-8
IsLessThanUnder 34.3-7
IsLetterAssocWordRep 37.6-1
IsLetterWordsFamily 37.6-2
IsLexicographicallyLess 21.20-9
IsLexOrderedFFE 59.1-3
IsLieAbelian 64.5-1
IsLieAlgebra 62.8-5
IsLieMatrix 24.2-3
IsLieNilpotent 64.5-2
IsLieObject 64.1-2
IsLieObjectCollection 64.1-2
IsLieSolvable 64.5-3
IsLinearMapping 32.11-3
IsLinearMappingsModule 61.10-9
IsLineByLineProfileActive 7.7-19
IsList 21.1-1
IsListDefault 21.12-3
IsListOrCollection 30.3-1
IsLogOrderedFFE 59.1-3
IsLookupDictionary 28.3-3
IsLowerAlphaChar 27.5-2
IsLowerTriangularMat 24.4-10
IsMagma 35.1-1
IsMagmaHomomorphism 32.8-1
IsMagmaRingModuloRelations 65.4-4
IsMagmaRingModuloSpanOfZero 65.5-2
IsMagmaRingObjDefaultRep 65.2-1
IsMagmaWithInverses 35.1-4
IsMagmaWithInversesIfNonzero 35.1-3
IsMagmaWithOne 35.1-2
IsMagmaWithZeroAdjoined 35.2-12
IsMapping 32.3-3
IsMatchingSublist 21.17-1
IsMatrix 24.2-1
IsMatrixGroup 44.1-1
IsMatrixModule 57.3-7
IsMatrixSpace 61.9-2
IsMersenneTwister 14.7-4
IsMinimalNonmonomial 75.5-1
IsModuloPcgs 45.9-2
IsMonoid 51.2-1
IsMonomial, for a character table 71.8-5
IsMonomial, for positive integers 75.4-3
IsMonomialGroup 39.15-9
IsMonomialMatrix 24.4-7
IsMonomialNumber 75.4-3
IsMonomialOrdering 66.17-1
IsMultiplicativeElement 31.14-10
IsMultiplicativeElementWithInverse 31.14-13
IsMultiplicativeElementWithOne 31.14-11
IsMultiplicativeElementWithZero 31.14-12
IsMultiplicativeGeneralizedRowVector 21.12-2
IsMultiplicativeZero 35.4-11
IsMutable 12.6-2
IsMutableBasis 61.8-1
IsNaN 19.2-5
IsNaturalAlternatingGroup 43.4-1
IsNaturalGL 44.4-2
IsNaturalGLnZ 44.6-4
IsNaturalSL 44.4-4
IsNaturalSLnZ 44.6-5
IsNaturalSymmetricGroup 43.4-1
IsNearAdditiveElement 31.14-2
IsNearAdditiveElementWithInverse 31.14-6
IsNearAdditiveElementWithZero 31.14-4
IsNearAdditiveGroup 55.1-3
IsNearAdditiveMagma 55.1-1
IsNearAdditiveMagmaWithInverses 55.1-3
IsNearAdditiveMagmaWithZero 55.1-2
IsNearlyCharacterTable 71.4-1
IsNearRingElement 31.14-15
IsNearRingElementWithInverse 31.14-19
IsNearRingElementWithOne 31.14-17
IsNegInfinity 18.2-1
IsNegRat 17.2-3
IsNilpotent, for a character table 71.8-5
IsNilpotent, for groups with pcgs 45.16
IsNilpotentElement 64.9-5
IsNilpotentGroup 39.15-3
IsNilpotentTom 70.8-1
IsNInfinity 19.2-5
IsNonassocWord 36.1-3
IsNonassocWordCollection 36.1-4
IsNonassocWordWithOne 36.1-3
IsNonassocWordWithOneCollection 36.1-4
IsNonnegativeIntegers 14.1-2
IsNonSPGeneralMapping 32.14-1
IsNonTrivial 30.4-4
IsNormal 39.3-6
IsNormalBasis 61.7-3
IsNotIdenticalObj 12.5-2
IsNumberField 60.2-2
IsObject 12.1-1
IsOddInt 14.2-5
isomorphic, pc group 46.4-8 46.5-2
IsomorphicSubgroups 40.9-5
IsomorphismFpAlgebra 62.10-10
IsomorphismFpGroup 47.11-1
IsomorphismFpGroup, for subgroups of fp groups 47.12
IsomorphismFpGroupByGenerators 47.11-2
IsomorphismFpGroupByGeneratorsNC 47.11-2
IsomorphismFpGroupByPcgs 46.3-2
IsomorphismFpSemigroup 52.2-3
IsomorphismGroups 40.9-1
IsomorphismMatrixAlgebra 62.10-11
IsomorphismPartialPermMonoid 54.7-6
IsomorphismPartialPermSemigroup 54.7-6
IsomorphismPcGroup 46.5-2
IsomorphismPermGroup 43.3-1
    for Imf matrix groups 50.12-5
IsomorphismPermGroupImfGroup 50.12-6
IsomorphismReesMatrixSemigroup 51.9-3
IsomorphismReesZeroMatrixSemigroup 51.9-3
IsomorphismRefinedPcGroup 46.4-8
IsomorphismRepStruct 31.5
isomorphisms, find all 40.9-1
IsomorphismSCAlgebra, for an algebra 62.10-12
    w.r.t. a given basis 62.10-12
IsomorphismSimplifiedFpGroup 47.12-1
IsomorphismSpecialPcGroup 46.5-3
IsomorphismTransformationMonoid 53.7-5
IsomorphismTransformationSemigroup 53.7-5
IsomorphismTypeInfoFiniteSimpleGroup, for a character table 71.8-5
    for a group 39.15-12
    for a group order 39.15-12
IsOne 31.10-5
IsOperation 5.5-2
IsOrdering 34.1-1
IsOrderingOnFamilyOfAssocWords 34.4-1
IsOrdinaryMatrix 24.2-2
IsOrdinaryTable 71.4-1
IsOutputStream 10.1-6
IsOutputTextNone 10.1-8
IsOutputTextStream 10.1-7
IsPackageMarkedForLoading 76.3-8
IsPadicExtensionNumber 68.2-3
IsPadicExtensionNumberFamily 68.2-4
IsParentPcgsFamilyPcgs 46.1-4
IsPartialOrderBinaryRelation 33.2-6
IsPartialPerm 54.1-1
IsPartialPermCollection 54.1-2
IsPartialPermMonoid 54.7-1
IsPartialPermSemigroup 54.7-1
IsPcGroup 46.3-1
IsPcGroupGeneralMappingByImages 40.10-8
IsPcGroupHomomorphismByImages 40.10-8
IsPcgs 45.2-2
IsPcgsCentralSeries 45.11-5
IsPcgsChiefSeries 45.11-13
IsPcgsElementaryAbelianSeries 45.11-1
IsPcgsPCentralSeriesPGroup 45.11-9
IsPerfect, for a character table 71.8-5
IsPerfectGroup 39.15-5
IsPerfectTom 70.8-1
IsPerm 42.1-1
IsPermCollColl 42.1-2
IsPermCollection 42.1-2
IsPermGroup 43.1-1
IsPermGroupGeneralMapping 40.10-5
IsPermGroupGeneralMappingByImages 40.10-5
IsPermGroupHomomorphism 40.10-5
IsPermGroupHomomorphismByImages 40.10-5
IsPGroup 39.15-19
IsPInfinity 19.2-5
IsPNilpotent 39.15-24
IsPolycyclicGroup 39.15-7
IsPolynomial 66.4-4
IsPolynomialDefaultRep 66.21-5
IsPolynomialFunction 66.4-1
IsPolynomialFunctionsFamily 66.19-2
IsPolynomialRing 66.15-4
IsPosInt 14.2-2
IsPositiveIntegers 14.1-2
IsPosRat 17.2-2
IsPreimagesByAsGroupGeneralMappingByImages 40.10-4
IsPreOrderBinaryRelation 33.2-5
IsPrime 56.5-8
IsPrimeField 58.2-5
IsPrimeInt 14.4-2
IsPrimeOrdersPcgs 45.4-3
IsPrimePowerInt 14.4-4
IsPrimitive, for a group, an action domain, etc. 41.10-7
    for an external set 41.10-7
IsPrimitiveCharacter 75.3-2
IsPrimitivePolynomial 66.4-12
IsPrimitiveRootMod 15.3-4
IsProbablyPrimeInt 14.4-2
IsPseudoCanonicalBasisFullHomModule 61.10-8
IsPSolubleCharacterTable 71.12-3
IsPSolubleCharacterTableOp 71.12-3
IsPSolvable 39.15-23
IsPSolvableCharacterTable 71.12-3
IsPSolvableCharacterTableOp 71.12-3
IsPurePadicNumber 68.1-5
IsPurePadicNumberFamily 68.1-6
IsQuasiPrimitive 75.3-3
IsQuaternion 62.8-8
IsQuaternionCollColl 62.8-8
IsQuaternionCollection 62.8-8
IsQuickPositionList 21.23-1
IsQuotientSemigroup 51.7-1
IsRandomSource 14.7-1
IsRange 21.22-1
IsRat 17.2-1
IsRationalFunction 66.4-1
IsRationalFunctionDefaultRep 66.21-1
IsRationalFunctionsFamily 66.19-2
IsRationalMatrixGroup 44.6-2
IsRationals 17.1-1
IsRationalsPolynomialRing 66.15-7
IsRDistributive 56.4-4
IsReadableFile 9.6-2
IsReadOnlyGlobal 4.9-1
IsRecord 29.1-1
IsRecordCollColl 29.1-1
IsRecordCollection 29.1-1
IsRectangularTable 21.1-5
IsReduced 38.1-7
IsReductionOrdering 34.4-3
IsReesCongruence 51.6-2
IsReesCongruenceSemigroup 51.4-7
IsReesMatrixSemigroup 51.9-7
IsReesMatrixSemigroupElement 51.9-4
IsReesMatrixSubsemigroup 51.9-6
IsReesZeroMatrixSemigroup 51.9-7
IsReesZeroMatrixSemigroupElement 51.9-4
IsReesZeroMatrixSubsemigroup 51.9-6
IsReflexiveBinaryRelation 33.2-1
IsRegular, for a group, an action domain, etc. 41.10-5
    for an external set 41.10-5
IsRegularDClass 51.8-12
IsRegularSemigroup 51.4-1
IsRegularSemigroupElement 51.4-2
IsRelativelySM, for a character 75.4-6
    for a group 75.4-6
IsRestrictedJacobianElement 31.15-5
IsRestrictedJacobianElementCollColl 31.15-5
IsRestrictedJacobianElementCollection 31.15-5
IsRestrictedLieAlgebra 64.8-1
IsRestrictedLieObject 64.1-2
IsRestrictedLieObjectCollection 64.1-2
IsRewritingSystem 38.1-1
IsRightAlgebraModuleElement 62.11-10
IsRightAlgebraModuleElementCollection 62.11-10
IsRightCoset 39.7-4
IsRightIdeal 56.2-3
IsRightIdealInParent 56.2-3
IsRightModule 57.1-7
IsRightOperatorAdditiveGroup 57.1-6
IsRightSemigroupIdeal 51.5-3
IsRing 56.1-1
IsRingElement 31.14-16
IsRingElementWithInverse 31.14-20
IsRingElementWithOne 31.14-18
IsRingGeneralMapping 32.12-1
IsRingHomomorphism 32.12-1
IsRingWithOne 56.3-1
IsRingWithOneGeneralMapping 32.12-2
IsRingWithOneHomomorphism 32.12-2
IsRootSystem 64.6-3
IsRootSystemFromLieAlgebra 64.6-4
IsRowModule 57.3-6
IsRowSpace 61.9-1
IsRowVector 23.1-1
IsScalar 31.14-20
IsSemiEchelonized 61.9-7
IsSemigroup 51.1-1
IsSemigroupCongruence 51.6-1
IsSemigroupIdeal 51.5-3
IsSemilatticeAsSemigroup 77.6-1
IsSemiRegular, for a group, an action domain, etc. 41.10-4
    for an external set 41.10-4
IsSet 21.17-4
IsShortLexLessThanOrEqual 37.3-3
IsShortLexOrdering 34.4-7
IsSimple, for a character table 71.8-5
IsSimpleAlgebra 62.8-6
IsSimpleGroup 39.15-10
IsSimpleSemigroup 51.4-4
IsSingleValued 32.3-2
IsSL 44.4-3
IsSolvable, for a character table 71.8-5
IsSolvableGroup 39.15-6
IsSolvableTom 70.8-1
IsSortedList 21.17-3
IsSpecialLinearGroup 44.4-3
IsSpecialPcgs 45.13-1
IsSPGeneralMapping 32.14-1
IsSporadicSimple, for a character table 71.8-5
IsSSortedList 21.17-4
IsStandardIterator 30.8-1
IsStraightLineProgElm 37.9-1
IsStraightLineProgram 37.8-1
IsStream 10.1-1
IsString 27.1-2
IsStringRep 27.4-1
IsStruct 31.6
IsSubgroup 39.3-5
IsSubgroupFpGroup 47.1-1
IsSubgroupOfWholeGroupByQuotientRep 47.13-2
IsSubgroupSL 44.4-5
IsSubmonoidFpMonoid 52.1-2
IsSubnormal 39.3-10
IsSubnormallyMonomial, for a character 75.4-5
    for a group 75.4-5
IsSubsemigroup 51.1-4
IsSubsemigroupFpSemigroup 52.1-1
IsSubset 30.5-1
IsSubsetBlist 22.2-4
IsSubsetLocallyFiniteGroup 39.15-18
IsSubsetSet 21.19-3
IsSubspacesVectorSpace 61.4-2
IsSubstruct 31.8
IsSupersolvable, for a character table 71.8-5
IsSupersolvable, for groups with pcgs 45.16
IsSupersolvableGroup 39.15-8
IsSurjective 32.3-5
IsSyllableAssocWordRep 37.6-5
IsSyllableWordsFamily 37.6-6
IsSymmetricBinaryRelation 33.2-2
IsSymmetricGroup 43.4-2
IsSymmetricInverseMonoid 54.7-4
IsSymmetricInverseSemigroup 54.7-4
IsTable 21.1-4
IsTableOfMarks 70.6-2
IsTableOfMarksWithGens 70.10-3
IsToPcGroupGeneralMappingByImages 40.10-9
IsToPcGroupHomomorphismByImages 40.10-9
IsToPermGroupGeneralMappingByImages 40.10-6
IsToPermGroupHomomorphismByImages 40.10-6
IsTotal 32.3-1
IsTotalOrdering 34.3-2
IsTransformation 53.1-1
IsTransformationCollection 53.1-2
IsTransformationMonoid 53.7-1
IsTransformationSemigroup 53.7-1
IsTransitive, for a character 72.8-15
    for a group, an action domain, etc. 41.10-1
    for a permutation group 41.10-1
    for an external set 41.10-1
IsTransitiveBinaryRelation 33.2-3
IsTranslationInvariantOrdering 34.4-2
IsTrivial 30.4-3
IsTwoSidedIdeal 56.2-3
IsTwoSidedIdealInParent 56.2-3
IsUEALatticeElement 64.14-1
IsUEALatticeElementCollection 64.14-1
IsUEALatticeElementFamily 64.14-1
IsUniqueFactorizationRing 56.4-2
IsUnit 56.5-1
IsUnivariatePolynomial 66.4-8
IsUnivariatePolynomialRing 66.16-2
IsUnivariateRationalFunction 66.4-6
IsUnknown 74.1-3
IsUpperAlphaChar 27.5-3
IsUpperTriangularMat 24.4-9
IsValidIdentifier 4.6-1
IsVector 31.14-14
IsVectorSpace 61.1-1
IsVirtualCharacter 72.8-2
IsWeightLexOrdering 34.4-9
IsWeightRepElement 64.14-4
IsWeightRepElementCollection 64.14-4
IsWeightRepElementFamily 64.14-4
IsWellFoundedOrdering 34.3-1
IsWeylGroup 64.7-1
IsWholeFamily 30.4-5
IsWLetterAssocWordRep 37.6-3
IsWLetterWordsFamily 37.6-4
IsWord 36.1-1
IsWordCollection 36.1-2
IsWordWithInverse 36.1-1
IsWordWithOne 36.1-1
IsWreathProductOrdering 34.4-14
IsWritableFile 9.6-3
IsXInfinity 19.2-5
IsZero 31.10-6
IsZeroGroup 51.4-6
IsZeroSimpleSemigroup 51.4-5
IsZeroSquaredElement 31.15-6
IsZeroSquaredElementCollColl 31.15-6
IsZeroSquaredElementCollection 31.15-6
IsZeroSquaredRing 56.4-7
IsZmodnZObj 14.5-4
IsZmodnZObjNonprime 14.5-4
IsZmodpZObj 14.5-4
IsZmodpZObjLarge 14.5-4
IsZmodpZObjSmall 14.5-4
Iterated 21.20-27
Iterator 30.8-1
iterator, for low index subgroups 47.10-1
IteratorByBasis 61.6-6
IteratorByFunctions 30.8-8
IteratorList 30.8-6
IteratorOfCartesianProduct, for a list of lists 21.20-17
    for several lists 21.20-17
IteratorOfCombinations 16.2-2
IteratorOfPartitions 16.2-19
IteratorOfTuples 16.2-10
IteratorSorted 30.8-2
IteratorStabChain 43.10-10
\(j_N\) (irrational value) 18.4-4
Jacobi 15.4-1
JenningsLieAlgebra 64.8-4
JenningsSeries 39.17-14
JoinEquivalenceRelations 33.6-3
JoinOfIdempotentPartialPermsNC 54.2-4
JoinOfPartialPerms 54.2-4
JoinStringsWithSeparator 27.7-17
JordanDecomposition 24.13-2
\(k_N\) (irrational value) 18.4-4
KappaPerp 64.9-4
KB_REW 52.6-2
kernel, group homomorphism 40.2
    of a matrix 24.7-4
KernelOfAdditiveGeneralMapping 32.10-5
KernelOfCharacter 72.8-9
KernelOfMultiplicativeGeneralMapping 32.9-5
KernelOfTransformation 53.5-12
KeyDependentOperation 85.1-1
KillingMatrix 64.9-3
KnownAttributesOfObject 13.5-1
KnownPropertiesOfObject 13.7-1
KnownTruePropertiesOfObject 13.7-2
KnowsDictionary 28.3-5
KnowsHowToDecompose 39.25-7
KnuthBendixRewritingSystem, for a monoid and a reduction ordering 52.6-3
    for a semigroup and a reduction ordering 52.6-3
Krasner-Kaloujnine theorem 49.4-4
KroneckerProduct 24.5-8
KuKGenerators 49.4-4
\(l_N\) (irrational value) 18.4-4
Lambda 15.2-3
larger or equal 4.12
larger test 4.12
LargerQuotientBySubgroupAbelianization 47.14-7
LargestElementGroup 39.22-2
LargestElementStabChain 43.10-14
LargestImageOfMovedPoint, for a partial permutation 54.3-15
    for a partial permutation coll 54.3-15
    for a transformation 53.5-10
    for a transformation coll 53.5-10
LargestMovedPoint, for a list or collection of permutations 42.3-2
    for a partial perm 54.3-13
    for a partial perm coll 54.3-13
    for a permutation 42.3-2
    for a transformation 53.5-8
    for a transformation coll 53.5-8
LargestUnknown 74.1-2
last 6.1
last2 6.1
last3 6.1
LastSystemError 9.1-1
LaTeX, for a decomposition matrix 71.11-4
    for GAP objects 27.11
    for permutation characters 72.13
    for the result of a straight line program 37.8-5
LaTeXStringDecompositionMatrix 71.11-5
lattice base reduction 25.5-1 25.5-2
lattice basis reduction, for virtual characters 72.10-4
LatticeByCyclicExtension 39.21-1
LatticeGeneratorsInUEA 64.14-2
LatticeSubgroups 39.20-1
LatticeSubgroupsByTom 70.3-3
LaurentPolynomialByCoefficients 66.13-1
LaurentPolynomialByExtRep 66.22-3
LaurentPolynomialByExtRepNC 66.22-3
LClassOfHClass 51.8-5
Lcm, for (a ring and) a list of elements 56.7-6
    for (a ring and) several elements 56.7-6
LcmInt 14.3-6
LcmOp 56.7-7
LeadCoeffsIGS 45.7-7
LeadingCoefficient 66.6-3
LeadingCoefficientOfPolynomial 66.17-4
LeadingExponentOfPcElement 45.5-5
LeadingMonomial 66.6-4
LeadingMonomialOfPolynomial 66.17-2
LeadingTermOfPolynomial 66.17-3
left cosets 39.7-4
LeftActingAlgebra 62.11-11
LeftActingDomain 57.1-11
LeftActingRingOfIdeal 56.2-10
LeftAlgebraModule 62.11-4
LeftAlgebraModuleByGenerators 62.11-1
LeftDerivations 64.2-6
LeftIdeal 56.2-1
LeftIdealByGenerators 56.2-5
LeftIdealNC 56.2-2
LeftModuleByGenerators 57.1-10
LeftModuleByHomomorphismToMatAlg 62.11-17
LeftModuleGeneralMappingByImages 61.10-1
LeftModuleHomomorphismByImages 61.10-2
LeftModuleHomomorphismByImagesNC 61.10-2
LeftModuleHomomorphismByMatrix 61.10-3
LeftOne, for a partial perm 54.3-21
    for a transformation 53.5-22
LeftQuotient 31.12-2
LeftQuotient, for words 37.4
LeftShiftRowVector 23.5-1
legacy 77.
Legendre 15.4-2
Length 21.17-5
    for a associative word 37.4-1
length, of a word 37.4-1
LengthsTom 70.7-3
LengthWPObj 86.2-1
LenstraBase 60.3-2
LessThanFunction 34.3-5
LessThanOrEqualFunction 34.3-6
LetterRepAssocWord 37.6-8
LevelsOfGenerators 34.4-15
LeviMalcevDecomposition, for Lie algebras 62.9-19
LexicographicOrdering 34.4-5
LGFirst 45.13-5
LGLayers 45.13-4
LGLength 45.13-6
LGWeights 45.13-3
library tables 71.3
LieAlgebra, for an associative algebra 64.2-3
    for field and generators 64.2-3
LieAlgebraByStructureConstants 64.2-1
LieBracket 31.12-4
LieCenter 64.3-1
LieCentralizer 64.3-2
LieCentre 64.3-1
LieCoboundaryOperator 64.12-5
LieDerivedSeries 64.4-1
LieDerivedSubalgebra 64.3-4
LieFamily 64.1-3
LieLowerCentralSeries 64.4-2
LieNilRadical 64.3-5
LieNormalizer 64.3-3
LieObject 64.1-1
LieSolvableRadical 64.3-6
LieUpperCentralSeries 64.4-3
LiftedInducedPcgs 45.10-4
LiftedPcElement 45.10-3
LinearAction 45.14-2
LinearActionLayer 45.14-3
LinearCharacters, for a character table 71.8-3
    for a group 71.8-3
LinearCombination 61.6-4
LinearCombinationPcgs 45.5-7
LinearIndependentColumns 25.4-2
LinearOperation 45.14-2
LinearOperationLayer 45.14-3
LinesOfStraightLineProgram 37.8-3
List, for a collection 30.3-5
    for a list (and a function) 21.20-19
list, sorted 21.17-3
list and non-list, difference 21.13-4
    left quotient 21.14-6
    mod 21.14-5
    product 21.14-3
    quotient 21.14-4
list assignment, operation 21.2
list boundedness test, operation 21.2
list element, access 21.3
    assignment 21.4
    operation 21.2
list equal, comparison 21.10
list of available books 2.2
list smaller, comparison 21.10
list unbind, operation 21.2
ListBlist 22.2-2
ListN 21.20-28
ListOfDigits 14.2-11
ListPerm 42.5-1
ListStabChain 43.10-8
ListTransformation 53.5-2
ListWithIdenticalEntries 21.15-1
ListX 21.21-1
LLL 72.10-4
LLL algorithm, for Gram matrices 25.5-2
    for vectors 25.5-1
    for virtual characters 72.10-4
LLLReducedBasis 25.5-1
LLLReducedGramMat 25.5-2
LoadDynamicModule 76.3-11
LoadPackage 76.2-1
local 4.23
Log 19.2-1
Log10 19.2-1
Log1p 19.2-1
Log2 19.2-1
logarithm, discrete 15.3-2
    of a root of unity 18.1-13
LogFFE 59.2-2
logical 20.
Logical conjunction 20.4-2
Logical disjunction 20.4-1
Logical negation 20.4-3
logical operations 20.4
LogInt 14.2-8
LogMod 15.3-2
LogModShanks 15.3-2
LogPackageLoadingMessage 76.2-4
LogTo, for a filename 9.7-4
    for streams 10.4-5
    stop logging 9.7-4
LongestWeylWordPerm 64.7-5
LookupDictionary 28.3-6
loop, for 4.20
    read eval print 6.1
    repeat 4.19
    while 4.18
loop over iterator 4.20
loop over object 4.20
loop over range 4.20
loops, leaving 4.21
    restarting 4.22
LowercaseString 27.7-11
LowerCentralSeriesOfGroup 39.17-11
LowIndexSubgroupsFpGroup 47.10-1
LowIndexSubgroupsFpGroupIterator 47.10-1
LQUO, for a permutation and transformation 53.4
    for a permutation or partial permutation and partial permutation 54.5
Lucas 16.3-2
\(m_N\) (irrational value) 18.4-4
Magma 35.2-1
MagmaByGenerators 35.2-4
MagmaByMultiplicationTable 35.3-1
MagmaElement 35.3-4
MagmaHomomorphismByFunctionNC 32.8-2
MagmaRingModuloSpanOfZero 65.5-3
MagmaWithInverses 35.2-3
MagmaWithInversesByGenerators 35.2-6
MagmaWithInversesByMultiplicationTable 35.3-3
MagmaWithOne 35.2-2
MagmaWithOneByGenerators 35.2-5
MagmaWithOneByMultiplicationTable 35.3-2
MagmaWithZeroAdjoined 35.2-13
MakeConfluent 38.1-11
MakeFloat 19.2-7
MakeImmutable 12.6-4
MakeReadOnlyGlobal 4.9-2
MakeReadWriteGlobal 4.9-3
map, parametrized 73.5
MappedWord 36.3-1
MappingByFunction, by function (and inverse function) between two domains 32.2-2
    by function and function that computes one preimage 32.2-2
MappingGeneratorsImages 40.10-2
MappingPermListList 42.5-3
maps 73.
MarksTom 70.7-1
MatAlgebra 62.5-4
MatClassMultCoeffsCharTable 71.12-9
MathieuGroup 50.1-11
MatLieAlgebra 64.2-5
matrices, commutator 24.3
Matrix 51.9-8
matrix automorphisms 73.2-2
matrix spaces 61.9
MatrixAlgebra 62.5-4
MatrixAutomorphisms 71.22-1
MatrixByBlockMatrix 24.17-3
MatrixLieAlgebra 64.2-5
MatrixOfAction 62.11-15
MatScalarProducts 72.8-6
MatTom 70.7-10
MaximalAbelianQuotient 39.18-4
MaximalBlocks, for a group, an action domain, etc. 41.11-2
    for an external set 41.11-2
MaximalNormalSubgroups 39.19-9
MaximalSubgroupClassReps 39.19-6
MaximalSubgroups 39.19-7
MaximalSubgroups, for groups with pcgs 45.16
MaximalSubgroupsLattice 39.20-4
MaximalSubgroupsTom 70.9-12
Maximum, for a list 21.20-13
    for various objects 21.20-13
MaximumList 21.20-15
meet strategy 87.2-4
MeetEquivalenceRelations 33.6-3
MeetMaps 73.5-8
MeetOfPartialPerms 54.2-5
MemoryUsage 12.8-5
method 78.
Mid 19.2-4
MinimalElementCosetStabChain 43.10-13
MinimalGeneratingSet 39.22-3
MinimalGeneratingSet, for groups with pcgs 45.16
MinimalNonmonomialGroup 75.5-2
MinimalNormalSubgroups 39.19-10
MinimalPolynomial 66.8-1
    over a field 58.3-2
MinimalPolynomial, over a ring 66.8
MinimalStabChain 43.8-5
MinimalSupergroupsLattice 39.20-5
MinimalSupergroupsTom 70.9-13
MinimizedBombieriNorm 66.12-2
Minimum, for a list 21.20-14
    for various objects 21.20-14
MinimumList 21.20-15
MinusCharacter 73.6-5
mod 4.13
    arithmetic operators 4.13
    for character tables 71.7
mod, Integers 14.5-2
    Laurent polynomials 66.2
    lists 21.14-5
    rationals 4.13
mod, residue class rings 14.5
modular inverse 4.13
modular remainder 4.13
modular roots 15.4-5
ModuleByRestriction 62.11-21
ModuleOfExtension 46.8-7
modulo 4.13
    arithmetic operators 4.13
    residue class rings 14.5
ModuloPcgs 45.9-1
MoebiusMu 15.5-3
MoebiusTom 70.7-11
MolienSeries 72.12-1
MolienSeriesInfo 72.12-2
MolienSeriesWithGivenDenominator 72.12-4
Monoid, for a list 51.2-2
    for various generators 51.2-2
MonoidByGenerators 51.2-4
MonoidByMultiplicationTable 51.2-10
MonoidOfRewritingSystem 52.6-5
MonomialComparisonFunction 66.17-5
MonomialExtGrlexLess 66.17-14
MonomialExtrepComparisonFun 66.17-6
MonomialGrevlexOrdering 66.17-9
MonomialGrlexOrdering 66.17-8
MonomialLexOrdering 66.17-7
MonomialTotalDegreeLess 77.4
monomorphisms, find all 40.9-5
MorClassLoop 40.9-6
MostFrequentGeneratorFpGroup 47.6-8
MovedPoints, for a list or collection of permutations 42.3-3
    for a partial perm 54.3-9
    for a partial perm coll 54.3-9
    for a permutation 42.3-3
    for a transformation 53.5-5
    for a transformation coll 53.5-5
MTX 69.3-1
MTX.BasesCompositionSeries 69.7-9
MTX.BasesMaximalSubmodules 69.7-5
MTX.BasesMinimalSubmodules 69.7-4
MTX.BasesMinimalSupermodules 69.7-8
MTX.BasesSubmodules 69.7-3
MTX.BasisInOrbit 69.11-4
MTX.BasisModuleEndomorphisms 69.9-2
MTX.BasisModuleHomomorphisms 69.9-1
MTX.BasisRadical 69.7-6
MTX.BasisSocle 69.7-7
MTX.CollectedFactors 69.7-11
MTX.CompositionFactors 69.7-10
MTX.DegreeSplittingField 69.5-3
MTX.Dimension 69.4-2
MTX.Distinguish 69.10-5
MTX.Field 69.4-3
MTX.Generators 69.4-1
MTX.HomogeneousComponents 69.6-3
MTX.Homomorphism 69.10-3
MTX.Homomorphisms 69.10-4
MTX.Indecomposition 69.6-2
MTX.InducedAction 69.8-5
MTX.InducedActionFactorMatrix 69.8-4
MTX.InducedActionFactorModule 69.8-3
MTX.InducedActionMatrix 69.8-4
MTX.InducedActionMatrixNB 69.8-4
MTX.InducedActionSubmodule 69.8-2
MTX.InducedActionSubmoduleNB 69.8-2
MTX.InvariantBilinearForm 69.11-1
MTX.InvariantQuadraticForm 69.11-3
MTX.InvariantSesquilinearForm 69.11-2
MTX.IsAbsolutelyIrreducible 69.5-2
MTX.IsEquivalent 69.10-1
MTX.IsIndecomposable 69.6-1
MTX.IsIrreducible 69.5-1
MTX.IsomorphismIrred 69.10-2
MTX.IsomorphismModules 69.9-3
MTX.ModuleAutomorphisms 69.9-4
MTX.NormedBasisAndBaseChange 69.8-1
MTX.OrthogonalSign 69.11-5
MTX.ProperSubmoduleBasis 69.7-2
MTX.SubGModule 69.7-1
MTX.SubmoduleGModule 69.7-1
multiple indices 21.3
    assignment 21.4
multiplication 4.13
    matrices 24.3
    matrix and matrix list 24.3 24.3
    matrix and scalar 24.3
    matrix and vector 24.3
    operation 31.12-1
    scalar and matrix 24.3
    scalar and matrix list 24.3 24.3
    scalar and vector 23.2
    vector and matrix 24.3
    vector and matrix list 24.3
    vector and scalar 23.2
    vectors 23.2
MultiplicationTable, for a list of elements 35.3-5
    for a magma 35.3-5
multiplicative order of an integer 15.3-1
MultiplicativeNeutralElement 35.4-10
MultiplicativeZero 35.4-11
MultiplicativeZeroOp 31.10-4
multiplicity, of constituents of a group character 72.8-5
Multiplier 39.24-3
multisets 21.19
MultRowVector 23.4-3
Murnaghan components 72.11-4 72.11-5
MutableBasis 61.8-2
MutableBasisOfClosureUnderAction 62.9-11
MutableBasisOfIdealInNonassociativeAlgebra 62.9-13
MutableBasisOfNonassociativeAlgebra 62.9-12
MutableIdentityMat 77.4
MutableNullMat 77.4
Name 12.8-2
NameFunction 5.1-1
NameRNam 29.7-1
NamesFilter 13.2-2
NamesGVars 4.9-8
NamesLocalVariablesFunction 5.1-3
NamesOfComponents 79.10-1
NamesOfFusionSources 73.3-5
namespace 4.6-1 4.9
NamesSystemGVars 4.9-9
NamesUserGVars 4.9-10
NaturalCharacter, for a group 72.7-2
    for a homomorphism 72.7-2
NaturalHomomorphismByGenerators 32.8-3
NaturalHomomorphismByIdeal 56.8-4
    for an algebra and an ideal 62.10-7
NaturalHomomorphismByNormalSubgroup 39.18-1
NaturalHomomorphismByNormalSubgroupNC 39.18-1
NaturalHomomorphismBySubAlgebraModule 62.11-22
NaturalHomomorphismBySubspace 61.10-4
NaturalHomomorphismOfLieAlgebraFromNilpotentGroup 64.8-6
NaturalLeqPartialPerm 54.5-4
NaturalPartialOrder 54.7-5
NearAdditiveGroup 55.2-3
NearAdditiveGroupByGenerators 55.2-6
NearAdditiveMagma 55.2-1
NearAdditiveMagmaByGenerators 55.2-4
NearAdditiveMagmaWithZero 55.2-2
NearAdditiveMagmaWithZeroByGenerators 55.2-5
NearlyCharacterTablesFamily 71.4-3
negative number 4.13
NegativeRoots 64.6-8
NegativeRootVectors 64.6-10
NestingDepthA 21.12-4
NestingDepthM 21.12-5
NewAttribute 79.3-1
NewAttribute, example 80.5
NewCategory 79.1-1
NewConstructor 79.6-1
NewDictionary 28.2-1
NewFamily 79.7-1
NewFilter 79.4-1
NewFloat 19.2-7
NewInfoClass 7.4-1
newline 4.4
NewmanInfinityCriterion 47.16-2
NewOperation 79.5-1
NewProperty 79.3-2
NewRepresentation 79.2-1
NewRepresentation, example 80.6
NewType 79.8-1
NextIterator 30.8-5
NextPrimeInt 14.4-5
NF 60.1-2
NiceAlgebraMonomorphism 62.10-9
NiceBasis 61.11-4
NiceBasisFiltersInfo 61.12-2
NiceFreeLeftModule 61.11-1
NiceFreeLeftModuleInfo 61.11-3
NiceMonomorphism 40.5-2
NiceMonomorphismAutomGroup 40.8-2
NiceObject 40.5-3
NiceVector 61.11-2
NilpotencyClassOfGroup 39.15-4
NilpotentQuotientOfFpLieAlgebra 64.11-2
NK 18.4-5
NOAUTO 76.2-1
NonabelianExteriorSquare 39.24-5
NonnegativeIntegers 14.1-1
NonnegIntScalarProducts 73.5-15
NonNilpotentElement 64.9-6
Norm 58.3-4
    for a class function 72.8-7
Norm, of character 72.8-7
NormalBase 58.3-7
NormalClosure 39.11-4
NormalFormIntMat 25.2-9
NormalIntersection 39.11-5
NormalizedElementOfMagmaRingModuloRelations 65.4-3
NormalizedWhitespace 27.7-15
normalizer 39.11
Normalizer, for a group and a group element 39.11-1
    for two groups 39.11-1
NormalizerInGLnZ 44.6-7
NormalizerInGLnZBravaisGroup 44.6-14
NormalizersTom 70.9-4
NormalizerTom 70.9-4
NormalizeWhitespace 27.7-14
NormalSeriesByPcgs 45.11-18
NormalSubgroupClasses 71.23-3
NormalSubgroupClassesInfo 71.23-1
NormalSubgroups 39.19-8
NormedRowVector 23.2-1
NormedRowVectors 61.9-11
NormedVectors 77.4
not 20.4-3
NrArrangements 16.2-5
NrBasisVectors 61.8-3
NrCombinations 16.2-3
NrComponentsOfPartialPerm 54.3-19
NrComponentsOfTransformation 53.5-18
NrConjugacyClasses 39.10-5
    for a character table 71.8-5
NrConjugacyClassesGL 50.3-1
NrConjugacyClassesGU 50.3-1
NrConjugacyClassesPGL 50.3-1
NrConjugacyClassesPGU 50.3-1
NrConjugacyClassesPSL 50.3-1
NrConjugacyClassesPSU 50.3-1
NrConjugacyClassesSL 50.3-1
NrConjugacyClassesSLIsogeneous 50.3-1
NrConjugacyClassesSU 50.3-1
NrConjugacyClassesSUIsogeneous 50.3-1
NrDerangements 16.2-15
NrFixedPoints, for a partial perm 54.3-10
    for a partial perm coll 54.3-10
NrInputsOfStraightLineProgram 37.8-4
NrMovedPoints, for a list or collection of permutations 42.3-4
    for a partial perm 54.3-11
    for a partial perm coll 54.3-11
    for a permutation 42.3-4
    for a transformation 53.5-6
    for a transformation coll 53.5-6
NrOrderedPartitions 16.2-22
NrPartitions 16.2-20
NrPartitionsSet 16.2-17
NrPartitionTuples 16.2-31
NrPermutationsList 16.2-13
NrPolyhedralSubgroups 71.12-6
NrPrimitiveGroups 50.9-2
NrRestrictedPartitions 16.2-26
NrSubsTom 70.7-2
NrTransitiveGroups 50.6-2
NrTuples 16.2-11
NrUnorderedTuples 16.2-7
NthRootsInGroup 39.10-10
NullAlgebra 62.5-5
NullMat 24.5-2
NullspaceIntMat 25.1-1
NullspaceMat 24.7-4
NullspaceMatDestructive 24.7-5
NullspaceModQ 24.15-2
Number 21.20-21
number, Bell 16.1-3
    binomial 16.1-2
    Stirling, of the first kind 16.1-5
    Stirling, of the second kind 16.1-6
number field 60.2-2
number fields, Galois group 60.4
NumberArgumentsFunction 5.1-2
NumberFFVector 23.3-2
NumberIrreducibleSolvableGroups 50.11-2
NumberPerfectGroups 50.8-4
NumberPerfectLibraryGroups 50.8-5
NumberSmallGroups 50.7-4
NumberSmallRings 56.9-2
NumbersString 27.7-20
NumberSyllables 37.5-1
NumberTransformation 53.2-6
numerator, of a rational 17.2-4
NumeratorOfModuloPcgs 45.9-3
NumeratorOfRationalFunction 66.4-2
NumeratorRat 17.2-4
ObjByExtRep 79.16-1
    for creating a UEALattice element 64.14-3
Objectify 79.9-1
ObjectifyWithAttributes 79.9-2
obsolete 77.
OCOneCocycles 39.23-3
octal character codes 27.2
OctaveAlgebra 62.5-3
od 4.20
OldGeneratorsOfPresentation 48.9-2
Omega 39.14-1
    construct an orthogonal group 50.2-8
OmniGraffle 39.20-3
ONanScottType 43.5-1
OnBreak 6.4-3
OnBreakMessage 6.4-4
One 31.10-2
    for a partial perm 54.3-22
one cohomology 39.23
OneAttr 31.10-2
OneCoboundaries 39.23-2
OneCocycles, for a group and a pcgs 39.23-1
    for generators and a group 39.23-1
    for generators and a pcgs 39.23-1
    for two groups 39.23-1
OneFactorBound 66.12-4
OneImmutable 31.10-2
OneIrreducibleSolvableGroup 50.11-4
OneLibraryGroup 50.5
OneMutable 31.10-2
OneOfPcgs 45.4-6
OneOp 31.10-2
OnePrimitiveGroup 50.5
OneSameMutability 31.10-2
OneSM 31.10-2
OneSmallGroup 50.7-3
OneTransitiveGroup 50.5
OnIndeterminates, as a permutation action 41.2-13
OnLeftInverse 41.2-3
OnLines 41.2-12
OnLines, example 50.2-1
OnPairs 41.2-6
OnPoints 41.2-1
OnQuit 8.1-4
OnRight 41.2-2
OnSets 41.2-4
OnSetsDisjointSets 41.2-8
OnSetsSets 41.2-7
OnSetsTuples 41.2-9
OnSubspacesByCanonicalBasis 41.2-15
OnSubspacesByCanonicalBasisConcatenations 41.2-15
OnTuples 41.2-5
OnTuplesSets 41.2-10
OnTuplesTuples 41.2-11
PCore, see PCore 39.11-3
Operation 77.1
operation 78.
OperationAlgebraHomomorphism, action on a free left module 62.10-8
    action w.r.t. a basis of the module 62.10-8
OperationHomomorphism 77.1
operations, for booleans 20.4
Operations for algebraic elements 67.2
operators 4.7
    arithmetic 4.13
    associativity 4.13
    for cyclotomics 18.3
    for lists 21.11
    precedence 4.12
options 3.
    command line, filenames 3.1
    command line, internal 3.1
    under UNIX 3.1
or 20.4-1
Orbit 41.4-1
OrbitFusions 73.4-1
OrbitishFO 85.3-2
OrbitLength 41.4-4
OrbitLengths, for a group, a set of seeds, etc. 41.4-5
    for an external set 41.4-5
OrbitLengthsDomain, for a group and a set of seeds 41.4-6
    of an external set 41.4-6
OrbitPerms 43.2-1
OrbitPowerMaps 73.2-1
Orbits, as attributes for external sets 85.3
Orbits, attribute 41.4-2
    operation 41.4-2
OrbitsDomain, for a group and an action domain 41.4-3
    of an external set 41.4-3
OrbitsishOperation 85.3-1
OrbitsPerms 43.2-2
OrbitStabChain 43.10-6
OrbitStabilizer 41.5-1
OrbitStabilizerAlgorithm 41.5-3
Order 31.10-10
    for a class function 72.4-3
order, of a group 39.1
    of a list, collection or domain 30.4-6
    of the prime residue group 15.2-2
ordered partitions, internal representation 87.2-1
OrderedPartitions 16.2-21
ordering, booleans 20.3-2
    of records 29.5
OrderingByLessThanFunctionNC 34.2-1
OrderingByLessThanOrEqualFunctionNC 34.2-2
OrderingOfRewritingSystem 38.1-3
OrderingOnGenerators 34.4-4
OrderingsFamily 34.1-2
OrderMod 15.3-1
OrderOfRewritingSystem 38.1-3
OrdersClassRepresentatives 71.9-1
OrdersTom 70.7-2
Ordinal 27.9-2
ordinary character 72.8-1
OrdinaryCharacterTable, for a character table 71.8-4
    for a group 71.8-4
OrthogonalComponents 72.11-4
OrthogonalEmbeddings 25.6-1
OrthogonalEmbeddingsSpecialDimension 72.10-6
output, suppressing 6.1
OutputLogTo, for a filename 9.7-6
    for streams 10.4-7
    stop logging output 9.7-6
OutputTextFile 10.5-2
OutputTextNone 10.9-2
OutputTextString 10.7-2
OutputTextUser 10.6-2
Overlaps 19.2-4
overload 78.8
\(p\)-group 39.15-19
package 76.
PACKAGE_DEBUG 76.2-4
PACKAGE_ERROR 76.2-4
PACKAGE_INFO 76.2-4
PACKAGE_WARNING 76.2-4
PackageVariablesInfo 76.3-14
PadicCoefficients 25.4-3
PadicExtensionNumberFamily 68.2-1
PadicNumber, for a p-adic extension family and a list 68.2-2
    for a p-adic extension family and a rational 68.2-2
    for a pure p-adic numbers family and a list 68.2-2
    for pure padics 68.1-2
PadicValuation 56.5-10
Pager 2.4-1
PageSource 5.1-6
Parametrized 73.5-5
parametrized maps 73.
Parent 31.7-1
ParentPcgs 45.7-3
ParseRelators 47.2-3
partial order 33.2-6
PartialFactorization 14.4-9
PartialOrderByOrderingFunction 33.4-6
PartialOrderOfHasseDiagram 33.2-11
PartialPerm, for a dense image 54.2-1
    for a domain and image 54.2-1
PartialPermFamily 54.1-3
PartialPermOp 54.2-2
PartialPermOpNC 54.2-2
Partitions 16.2-18
partitions, improper, of an integer 16.2-21
    ordered, of an integer 16.2-21
    restricted, of an integer 16.2-25
PartitionsGreatestEQ 16.2-24
PartitionsGreatestLE 16.2-23
PartitionsSet 16.2-16
PartitionTuples 16.2-30
PcElementByExponents 45.5-6
PcElementByExponentsNC 45.5-6
PCentralLieAlgebra 64.8-5
PCentralNormalSeriesByPcgsPGroup 45.11-12
PCentralSeries 39.17-13
PcGroupCode 46.9-3
PcGroupFpGroup 46.4-1
PcGroupWithPcgs 46.5-1
Pcgs 45.2-1
Pcgs_OrbitStabilizer 45.15-2
PcgsByPcSequence 45.3-1
PcgsByPcSequenceNC 45.3-1
PcgsCentralSeries 45.11-6
PcgsChiefSeries 45.11-14
PcgsElementaryAbelianSeries, for a group 45.11-2
    for a list of normal subgroups 45.11-2
PcgsPCentralSeriesPGroup 45.11-10
PClassPGroup 39.15-21
PCore 39.11-3
PcSeries 45.4-4
perfect groups 50.8
PerfectGroup, for a pair [ order, index ] 50.8-2
    for group order (and index) 50.8-2
PerfectIdentification 50.8-3
PerfectResiduum 39.12-8
Perform 21.20-11
Permanent 16.4-1
PermBounds 72.14-3
PermCharInfo 72.13-1
PermCharInfoRelative 72.13-2
PermChars 72.14-1
PermCharsTom, from a character table 70.11-2
    via fusion map 70.11-2
PermComb 72.14-4
PermLeftQuoPartialPerm 54.5-1
PermLeftQuoPartialPermNC 54.5-1
PermLeftQuoTransformation 53.4-1
PermLeftQuoTransformationNC 53.4-1
PermList 42.5-2
PermListList 21.20-12
Permutation, for a group, an action domain, etc. 41.9-1
    for an external set 41.9-1
permutation character 73.7-2
permutation characters, possible 72.13
PermutationCharacter, for a group, an action domain, and a function 72.7-3
    for two groups 72.7-3
PermutationCycle 41.9-2
PermutationGModule 69.2-1
PermutationMat 24.5-5
PermutationOfImage 53.3-3
PermutationsFamily 42.1-3
PermutationsList 16.2-12
PermutationTom 70.5-2
Permuted 21.20-18
    as a permutation action 41.2-14
    for a class function 72.4-2
PGL 50.2-11
PGU 50.2-13
Phi 15.2-2
point stabilizer 41.5
PolynomialByExtRep 66.22-2
PolynomialByExtRepNC 66.22-2
PolynomialCoefficientsOfPolynomial 66.6-2
PolynomialDivisionAlgorithm 66.17-13
PolynomialModP 66.11-2
PolynomialReducedRemainder 66.17-12
PolynomialReduction 66.17-11
PolynomialRing, for a ring and a list of indeterminate numbers 66.15-1
    for a ring and a list of indeterminates 66.15-1
    for a ring and a list of names (and an exclusion list) 66.15-1
    for a ring and a rank (and an exclusion list) 66.15-1
POmega 50.2-16
PopOptions 8.1-2
Position 21.16-1
PositionBound 21.16-9
PositionCanonical 21.16-3
PositionFirstComponent 77.4
PositionNonZero 21.16-11
PositionNot 21.16-10
PositionNthOccurrence 21.16-4
PositionProperty 21.16-7
Positions 21.16-2
PositionSet 21.16-6
PositionsOp 21.16-2
PositionSorted 21.16-5
PositionSortedOp 21.16-5
PositionsProperty 21.16-8
PositionStream 10.3-7
PositionSublist 21.16-12
PositionWord 37.4-4
positive number 4.13
PositiveIntegers 14.1-1
PositiveRoots 64.6-7
PositiveRootVectors 64.6-9
possible permutation characters 72.13
PossibleClassFusions 73.3-6
PossibleFusionsCharTableTom 70.11-1
PossiblePowerMaps 73.1-2
power 4.13
    matrix 24.3
    meaning for class functions 72.4
    of words 37.4
power set 16.2-1
PowerMap 73.1-1
PowerMapByComposition 73.1-4
PowerMapOp 73.1-1
PowerMapsAllowedBySymmetrizations 73.6-6
PowerMod 56.7-9
PowerModCoeffs 23.7-5
PowerModInt 14.3-10
PowerPartition 16.2-29
PowerSubalgebraSeries 62.9-4
PQuotient 47.14-1
precedence 4.13
precedence test, for permutations 42.2-1
PrecisionFloat 19.2-3
Prefix 27.7-19
PrefrattiniSubgroup 39.12-7
PrefrattiniSubgroup, for groups with pcgs 45.16
PreImage, set of preimages of a collection under a general mapping 32.5-6
    set of preimages of the range of a general mapping 32.5-6
    unique preimage of an element under a general mapping 32.5-6
PreImageElm 32.5-3
PreImagePartialPerm 54.5-2
PreImages, set of preimages of a collection under a general mapping 32.5-7
    set of preimages of an elm under a general mapping 32.5-7
    set of preimages of the range of a general mapping 32.5-7
PreImagesElm 32.5-2
PreImagesOfTransformation 53.4-4
PreImagesRange 32.5-1
PreImagesRepresentative 32.5-4
PreImagesSet 32.5-5
preorder 33.2-5
PresentationFpGroup 48.1-1
PresentationNormalClosure 48.2-6
PresentationNormalClosureRrs 48.2-5
PresentationSubgroup 48.2-1
PresentationSubgroupMtc 48.2-4
PresentationSubgroupRrs, for a group and a coset table (and a string) 48.2-2
    for two groups (and a string) 48.2-2
PresentationViaCosetTable 48.1-5
previous result 6.1
PrevPrimeInt 14.4-6
PrimalityProof 14.4-3
primary subgroup generators 48.10-1
PrimaryGeneratorWords 48.2-3
prime residue group 15. 15.2
    exponent 15.2-3
    generator 15.3-3 15.3-4
    order 15.2-2
PrimeBlocks 71.11-1
PrimeBlocksOp 71.11-1
PrimeDivisors 14.4-8
PrimeField 58.2-4
PrimePGroup 39.15-20
PrimePowersInt 14.4-11
PrimeResidues 15.2-1
Primes 14.4-1
primitive 41.10-7
primitive root modulo an integer 15.3-3
PRIMITIVE_INDICES_MAGMA 50.10-3
PrimitiveElement 58.2-3
PrimitiveGroup 50.9-1
PrimitiveGroupsIterator 50.9-3
PrimitiveIdentification 50.10-1
PrimitiveIndexIrreducibleSolvableGroup 50.11-5
PrimitivePolynomial 66.11-1
PrimitiveRoot 59.3-3
PrimitiveRootMod 15.3-3
Print 6.3-4
PrintAmbiguity 73.5-14
PrintArray 24.5-10
PrintCharacterTable 71.13-5
PrintCSV 10.11-2
PrintFactorsInt 14.4-10
PrintFormattingStatus 10.4-8
PrintObj 6.3-5
    for a character table 71.13-2
    for a ffe 59.6-1
    for a string 27.1-4
    for a table of marks 70.4-2
    for class functions 72.5-2
PrintString 27.7-5
PrintTo 9.7-3
    for streams 10.4-4
ProbabilityShapes 66.11-4
procedure call 4.16
procedure call with arguments 4.16
Process 11.1-1
PROD_GF2MAT_GF2MAT_ADVANCED 24.16-2
PROD_GF2MAT_GF2MAT_SIMPLE 24.16-1
Product 21.20-25
product, of words 37.4
    rational functions 66.2
ProductCoeffs 23.7-2
ProductOfStraightLinePrograms 37.8-13
ProductSpace 62.9-3
ProductX 21.21-4
ProfileFunctions 7.7-5
ProfileGlobalFunctions 7.7-2
ProfileLineByLine 7.7-14
ProfileMethods 7.7-7
ProfileOperations 7.7-3
ProfileOperationsAndMethods 7.7-4
ProjectedInducedPcgs 45.10-2
ProjectedPcElement 45.10-1
Projection, example for direct products 49.1-1
    example for semidirect products 49.2-1
    example for subdirect products 49.3-1
    example for wreath products 49.4-1
Projection, for a domain 32.2-11
    for a domain and a positive integer 32.2-11
    for group products 49.6-2
    for two domains 32.2-11
ProjectionMap 73.5-3
projections, find all 40.9-4
ProjectiveActionHomomorphismMatrixGroup 44.3-2
ProjectiveActionOnFullSpace 44.3-1
ProjectiveGeneralLinearGroup 50.2-11
ProjectiveGeneralUnitaryGroup 50.2-13
ProjectiveOmega 50.2-16
ProjectiveOrder 24.14-3
ProjectiveSpecialLinearGroup 50.2-12
ProjectiveSpecialUnitaryGroup 50.2-14
ProjectiveSymplecticGroup 50.2-15
prompt 6.1
    partial 6.1
PRump 39.12-12
PseudoRandom 30.7-2
    for finitely presented groups 47.5-1
PSL 50.2-12
PSp 50.2-15
PSP 50.2-15
PSU 50.2-14
PthPowerImage, for basis and element 64.8-3
    for element 64.8-3
    for element and integer 64.8-3
PthPowerImages 64.8-2
PurePadicNumberFamily 68.1-1
PushOptions 8.1-1
Quadratic 18.5-4
quadratic residue 15.4-1 15.4-2 15.4-3
QuaternionAlgebra 62.5-1
QuaternionGroup 50.1-7
QUIET 77.4
QUIT 6.7-1
QUIT, emergency quit 6.7-1
quit, in emergency 6.7
QUIT_GAP 6.7-3
QUITTING 6.7-5
QuoInt 14.3-1
Quotient 56.1-9
quotient, for finitely presented groups 47.2-1
    matrices 24.3
    matrix and matrix list 24.3
    matrix and scalar 24.3
    of free monoid 52.5-1
    of free semigroup 52.2-1
    of words 37.4
    rational functions 66.2
    scalar and matrix 24.3
    scalar and matrix list 24.3
    vector and matrix 24.3
QuotientFromSCTable 62.4-8
QuotientMod 56.7-8
QuotientPolynomialsExtRep 66.23-3
QuotientRemainder 56.6-5
QuotientSemigroupCongruence 51.7-3
QuotientSemigroupHomomorphism 51.7-3
QuotientSemigroupPreimage 51.7-3
QuotRemLaurpols 66.5-6
\(r_N\) (irrational value) 18.4-2
RadicalGroup 39.12-9
RadicalOfAlgebra 62.9-16
Random 30.7-1
    for a list or collection 30.7-1
    for integers 14.2-12
    for lower and upper bound 30.7-1
    for random source and list 14.7-2
    for random source and two integers 14.7-2
    for rationals 17.2-7
random seed 30.7-3
RandomBinaryRelationOnPoints 33.3-2
RandomInvertibleMat 24.6-2
RandomIsomorphismTest 46.10-1
RandomList 30.7-3
RandomMat 24.6-1
RandomPartialPerm, for a positive integer 54.2-7
    for a set of positive integers 54.2-7
    for domain and image 54.2-7
RandomPrimitivePolynomial 59.5-3
RandomSource 14.7-5
RandomTransformation 53.2-7
RandomUnimodularMat 24.6-3
range 21.22
Range, of a general mapping 32.3-7
RankAction, for a group, an action domain, etc. 41.10-3
    for an external set 41.10-3
RankFilter 13.2-1
RankMat 24.7-1
RankOfPartialPerm 54.3-3
RankOfPartialPermCollection 54.3-3
RankOfPartialPermSemigroup 54.7-2
RankOfTransformation, for a transformation and a list 53.5-4
    for a transformation and a positive integer 53.5-4
RankPGroup 39.15-22
Rat 17.2-6
    for floats 19.2-8
    for strings 27.9-1
RationalClass 39.10-6
RationalClasses 39.10-7
RationalFunctionByExtRep 66.22-1
RationalFunctionByExtRepNC 66.22-1
RationalFunctionByExtRepWithCancellation 66.24-1
RationalFunctionsFamily 66.19-1
RationalizedMat 18.5-6
Rationals 17.1-1
RClassOfHClass 51.8-5
Read 9.7-1
    for streams 10.3-1
read eval print loop 6.1
ReadAll 10.3-5
ReadAllLine 10.8-3
ReadAsFunction 9.7-2
    for streams 10.3-2
ReadByte 10.3-3
ReadCommandLineHistory 6.9-3
ReadCSV 10.11-1
ReadLine 10.3-4
ReadlineInitLine 6.9-1
ReadPackage 76.3-1
ReadPkg 77.2
RealClasses 71.9-11
RealizableBrauerCharacters 72.15-4
RealPart 18.5-2
RecNames 29.1-2
record, component access 29.2
    component assignment 29.3
    component variable 29.2
    component variable assignment 29.3
record assignment, operation 29.7-3
record boundness test, operation 29.7-3
record component, operation 29.7-3
record unbind, operation 29.7-3
recursion 4.23
RedispatchOnCondition 78.5-1
redisplay a help section 2.2
redisplay with next help viewer 2.2
ReduceCoeffs 23.7-3
ReduceCoeffsMod 23.7-4
ReducedAdditiveInverse 38.2-1
ReducedCharacters 72.10-2
ReducedClassFunctions 72.10-1
ReducedComm 38.2-1
ReducedConfluentRewritingSystem 52.6-1
ReducedConjugate 38.2-1
ReducedDifference 38.2-1
ReducedForm 38.1-4
ReducedGroebnerBasis, for a list and a monomial ordering 66.18-2
    for an ideal and a monomial ordering 66.18-2
ReducedInverse 38.2-1
ReducedLeftQuotient 38.2-1
ReducedOne 38.2-1
ReducedPcElement 45.5-10
ReducedPower 38.2-1
ReducedProduct 38.2-1
ReducedQuotient 38.2-1
ReducedScalarProduct 38.2-1
ReducedSum 38.2-1
ReducedZero 38.2-1
ReduceRules 38.1-8
ReduceStabChain 43.11-5
Ree 50.1-13
ReeGroup 50.1-13
ReesCongruenceOfSemigroupIdeal 51.5-2
ReesMatrixSemigroup 51.9-1
ReesMatrixSemigroupElement 51.9-5
ReesMatrixSubsemigroup 51.9-2
ReesZeroMatrixSemigroup 51.9-1
ReesZeroMatrixSemigroupElement 51.9-5
ReesZeroMatrixSubsemigroup 51.9-2
RefinedPcGroup 46.4-9
ReflectionMat 24.5-9
reflexive relation 33.2-1
ReflexiveClosureBinaryRelation 33.4-1
regular 41.10-5
regular action 41.7-2
RegularActionHomomorphism 41.8-2
RegularModule 71.15-3
relations 32.
RelationsOfFpSemigroup 52.4-5
RelativeBasis 61.5-4
RelativeBasisNC 61.5-4
RelativeDiameter 19.2-4
relatively prime 4.13
RelativeOrderOfPcElement 45.5-1
RelativeOrders 45.4-1
RelativeOrders, of a pcgs 45.4-1
RelatorsOfFpGroup 47.4-3
remainder, operation 31.12-1
remainder of a quotient 14.3-3
RemInt 14.3-3
Remove 21.4-3
remove, an element from a set 21.19-5
RemoveCharacters 27.7-16
RemoveFile 9.7-8
RemoveOuterCoeffs 23.5-4
RemoveRelator 48.5-4
RemoveSet 21.19-5
RemoveStabChain 43.11-6
repeat loop 4.19
ReplacedString 27.7-13
representation, as a sum of two squares 15.7-1
RepresentationsOfObject 13.4-1
Representative 30.4-7
representative, of a list or collection 30.4-8
RepresentativeAction 41.6-1
RepresentativeLinearOperation 62.10-13
RepresentativeOperation 77.1
RepresentativesContainedRightCosets 39.9-2
RepresentativesFusions 73.4-2
RepresentativeSmallest 30.4-8
RepresentativesMinimalBlocks, for a group, an action domain, etc. 41.11-3
    for an external set 41.11-3
RepresentativesPerfectSubgroups 39.20-6
RepresentativesPowerMaps 73.2-2
RepresentativesSimpleSubgroups 39.20-6
RepresentativeTom 70.10-4
RepresentativeTomByGenerators 70.10-4
RepresentativeTomByGeneratorsNC 70.10-4
RequirePackage 77.2
Reread 9.7-9
REREADING 9.7-9
RereadPackage 76.3-1
RereadPkg 77.2
Reset 14.7-3
ResetFilterObj 79.4-3
ResetOptionsStack 8.1-3
residue, quadratic 15.4-1 15.4-2 15.4-3
RespectsAddition 32.10-1
RespectsAdditiveInverses 32.10-2
RespectsInverses 32.9-3
RespectsMultiplication 32.9-1
RespectsOne 32.9-2
RespectsScalarMultiplication 32.11-1
RespectsZero 32.10-3
RestrictedClassFunction 72.9-1
RestrictedClassFunctions 72.9-2
RestrictedLieAlgebraByStructureConstants 64.2-2
RestrictedMapping 32.2-12
RestrictedPartialPerm 54.2-3
RestrictedPartitions 16.2-25
RestrictedPerm 42.5-4
RestrictedPermNC 42.5-4
RestrictedTransformation 53.3-2
RestrictedTransformationNC 53.3-2
RestrictOutputsOfSLP 37.8-9
Resultant 66.6-7
ResultOfStraightLineProgram 37.8-5
return 6.4-2
    no value 4.24
    with value 4.24
return from break loop 6.4-2
ReturnFail 5.4-3
ReturnFalse 5.4-2
ReturnFirst 5.4-5
ReturnNothing 5.4-4
ReturnTrue 5.4-1
Reversed 21.20-7
ReverseNaturalPartialOrder 54.7-5
RewindStream 10.3-8
RewriteWord 47.9-4
right cosets 39.7
RightActingAlgebra 62.11-12
RightActingRingOfIdeal 56.2-10
RightAlgebraModule 62.11-5
RightAlgebraModuleByGenerators 62.11-2
RightCoset 39.7-1
RightCosets 39.7-2
RightCosetsNC 39.7-2
RightDerivations 64.2-6
RightIdeal 56.2-1
RightIdealByGenerators 56.2-6
RightIdealNC 56.2-2
RightModuleByHomomorphismToMatAlg 62.11-18
RightOne, for a partial perm 54.3-21
    for a transformation 53.5-22
RightShiftRowVector 23.5-2
RightTransversal 39.8-1
Ring, for a collection 56.1-2
    for ring elements 56.1-2
RingByGenerators 56.1-4
RingByStructureConstants 56.9-6
RingGeneralMappingByImages 56.8-1
RingHomomorphismByImages 56.8-2
RingHomomorphismByImagesNC 56.8-3
RingWithOne, for a collection 56.3-2
    for ring elements 56.3-2
RingWithOneByGenerators 56.3-3
RNamObj, for a positive integer 29.7-2
    for a string 29.7-2
root, of 1 modulo an integer 15.4-5
    of an integer 14.2-9
    of an integer modulo another 15.4-3
    of an integer, smallest 14.2-10
RootInt 14.2-9
RootMod 15.4-3
RootOfDefiningPolynomial 58.2-8
roots of unity 18.1-1
RootsMod 15.4-4
RootsOfPolynomial 66.5-4
RootsOfUPol 66.5-5
RootsUnityMod 15.4-5
RootSystem 64.6-5
Round 19.2-1
RoundCyc 18.1-9
row spaces 61.9
Rows 51.9-9
RREF 24.7-2
Rules 38.1-2
Runtime 7.6-2
Runtimes 7.6-1
\(s_N\) (irrational value) 18.4-3
SameBlock 71.11-2
save 3.3-1
SaveCommandLineHistory 6.9-3
SaveOnExitFile 6.7-6
SaveWorkspace 3.3-1
saving on exit 6.7
ScalarProduct, for characters 72.8-5
Schreier 48.2
Schreier-Sims, random 43.7
Schur multiplier 39.24-3
SchurCover 39.24-2
SchurCoverOfSymmetricGroup 39.24-10
scope 4.8
Sec 19.2-1
Sech 19.2-1
SecHMSM 27.10-8
secondary subgroup generators 48.10-1
SecondsDMYhms 27.10-10
SeekPositionStream 10.3-9
SemidirectProduct, for a group of automorphisms and a group 49.2-1
    for acting group, action, and a group 49.2-1
SemiEchelonBasis 61.9-8
SemiEchelonBasisNC 61.9-8
SemiEchelonMat 24.10-1
SemiEchelonMatDestructive 24.10-2
SemiEchelonMats 24.10-4
SemiEchelonMatsDestructive 24.10-5
SemiEchelonMatTransformation 24.10-3
semigroup 51.1-1
Semigroup, for a list 51.1-2
    for various generators 51.1-2
SemigroupByGenerators 51.1-5
SemigroupByMultiplicationTable 51.1-11
SemigroupIdealByGenerators 51.5-1
SemigroupOfRewritingSystem 52.6-4
semiregular 41.10-4
SemiSimpleType 64.6-1
sequence, Bernoulli 16.1-4
    Fibonacci 16.3-1
    Lucas 16.3-2
Set 30.3-7
set difference, of collections 30.5-4
set stabilizer 41.5
SetAssertionLevel 7.5-1
SetCommutator 46.4-4
SetConjugate 46.4-3
SetCrystGroupDefaultAction 44.7-2
SetCyclotomicsLimit 18.6-1
SetDefaultInfoOutput 7.4-6
SetElmWPObj 86.2-1
SetEntrySCTable 62.4-4
SetFilterObj 79.4-2
SetFloats 19.2-9
SetGasmanMessageStatus 7.11-2
SetHelpViewer 2.3-1
SetIndeterminateName 66.1-4
SetInfoHandler 7.4-6
SetInfoLevel 7.4-3
SetInfoOutput 7.4-6
SetName 12.8-1
SetNameObject 6.3-7
SetPackagePath 76.2-2
SetParent 31.7-1
SetPower 46.4-5
SetPrintFormattingStatus 10.4-8
SetRecursionTrapInterval 7.10-1
SetReducedMultiplication 47.3-4
Sets 21.
sets 21.19
setter 13.6
Setter 13.6-2
SetUserPreference 3.2-3
SetX 21.21-2
ShallowCopy 12.7-1
ShallowCopy, for lists 21.7
ShiftedCoeffs 23.7-6
ShiftedPadicNumber 68.1-4
short vectors spanning a lattice 25.5-1 72.10-4
ShortestVectors 25.6-2
ShortLexLeqPartialPerm 54.5-5
ShortLexOrdering 34.4-6
ShowAdditionTable 55.4-2
ShowArgument 7.1-2
ShowArguments 7.1-1
ShowDetails 7.1-3
ShowGcd 56.7-5
ShowImpliedFilters 13.2-3
ShowMethods 7.1-4
ShowMultiplicationTable 55.4-2
ShowOtherMethods 7.1-5
ShowPackageVariables 76.3-14
ShowUserPreferences 3.2-3
ShrinkAllocationPlist 21.9-1
ShrinkAllocationString 27.4-5
ShrinkRowVector 23.5-3
Shuffle 21.20-8
SiftedPcElement 45.5-8
SiftedPermutation 43.10-12
SiftedVector 61.9-12
Sigma 15.5-1
SigmaL 50.2-10
sign, of an integer 14.2-7
SignFloat 19.2-1
SignInt 14.2-7
SignPartition 16.2-27
SignPerm 42.4-1
SimpleGroup 39.15-13
SimpleGroupsIterator 39.15-14
SimpleLieAlgebra 64.2-7
SimpleSystem 64.6-11
SimplifiedFpGroup 48.1-6
SimplifyPresentation 48.6-2
SimsNo 50.10-2
SimultaneousEigenvalues 24.14-4
Sin 19.2-1
SinCos 19.2-1
SingleCollector 46.4-2
singlequote character 27.2
singlequotes 27.1
Sinh 19.2-1
SIntChar 27.8-3
Size 30.4-6
    for a character table 71.8-5
Size, for groups with pcgs 45.16
size, of a list or collection 30.4-6
SizeBlist 22.2-3
SizeConsiderFunction 39.21-4
SizeNumbersPerfectGroups 50.8-6
SizeOfFieldOfDefinition 72.15-3
SizesCentralisers 71.9-2
SizesCentralizers 71.9-2
SizesConjugacyClasses 71.9-3
SizeScreen 6.12-1
SizesPerfectGroups 50.8-1
SizeStabChain 43.10-3
SL, for dimension and a field size 50.2-2
    for dimension and a ring 50.2-2
SlotUsagePattern 37.8-14
smaller, associative words 37.3-2
    elements of finitely presented groups 47.3-2
    for pcwords 46.2-1
    for transformations 53.4
    nonassociative words 36.2-2
    rational functions 66.3
smaller or equal 4.12
smaller test 4.12
SmallerDegreePermutationRepresentation 43.3-2
SmallestGeneratorPerm 42.2-3
SmallestIdempotentPower, for a partial perm 54.3-17
    for a transformation 53.5-16
SmallestImageOfMovedPoint, for a partial permutation 54.3-14
    for a partial permutation coll 54.3-14
    for a transformation 53.5-9
    for a transformation coll 53.5-9
SmallestMovedPoint, for a list or collection of permutations 42.3-1
    for a partial perm 54.3-12
    for a partial perm coll 54.3-12
    for a permutation 42.3-1
    for a transformation 53.5-7
    for a transformation coll 53.5-7
SmallestRootInt 14.2-10
SmallGeneratingSet 39.22-4
SmallGroup, for a pair [ order, index ] 50.7-1
    for group order and index 50.7-1
SmallGroupsInformation 50.7-8
SmallRing 56.9-1
SmallSimpleGroup 39.15-15
Smith normal form 77.3
SmithNormalFormIntegerMat 25.2-6
SmithNormalFormIntegerMatTransforms 25.2-7
SMTX.AbsoluteIrreducibilityTest 69.12-8
SMTX.AlgEl 69.13-2
SMTX.AlgElCharPol 69.13-4
SMTX.AlgElCharPolFac 69.13-5
SMTX.AlgElMat 69.13-3
SMTX.AlgElNullspaceDimension 69.13-7
SMTX.AlgElNullspaceVec 69.13-6
SMTX.CentMat 69.13-8
SMTX.CentMatMinPoly 69.13-9
SMTX.CompleteBasis 69.12-11
SMTX.Getter 69.12-6
SMTX.GoodElementGModule 69.12-2
SMTX.IrreducibilityTest 69.12-7
SMTX.MatrixSum 69.12-10
SMTX.MinimalSubGModule 69.12-9
SMTX.MinimalSubGModules 69.12-4
SMTX.RandomIrreducibleSubGModule 69.12-1
SMTX.Setter 69.12-5
SMTX.SortHomGModule 69.12-3
SMTX.Subbasis 69.13-1
SO 50.2-7
Socle 39.12-10
SocleTypePrimitiveGroup 43.5-2
SolutionIntMat 25.1-2
SolutionMat 24.7-6
SolutionMatDestructive 24.7-7
SolutionNullspaceIntMat 25.1-3
SolvableQuotient, for a f.p. group and a list of primes 47.14-5
    for a f.p. group and a list of tuples 47.14-5
    for a f.p. group and a size 47.14-5
Sort 21.18-1
SortBy 21.18-1
Sorted Lists as Collections 30.3
SortedCharacters 71.21-2
SortedCharacterTable, relative to the table of a factor group 71.21-4
    w.r.t. a normal subgroup 71.21-4
    w.r.t. a series of normal subgroups 71.21-4
SortedList 30.3-6
SortedSparseActionHomomorphism 41.7-3
SortedTom 70.5-1
Sortex 21.18-3
SortingPerm 21.18-4
SortParallel 21.18-2
Source 32.3-8
SourceOfIsoclinicTable 71.20-4
SP, for dimension and a ring 50.2-5
Sp, for dimension and a ring 50.2-5
    for dimension and field size 50.2-5
SP, for dimension and field size 50.2-5
space 4.4
SparseActionHomomorphism 41.7-3
SparseCartanMatrix 64.7-2
SparseHashTable 28.7-1
SparseIntKey 28.5-2
special character sequences 27.2
SpecialLinearGroup, for dimension and a field size 50.2-2
    for dimension and a ring 50.2-2
SpecialOrthogonalGroup 50.2-7
SpecialPcgs, for a group 45.13-2
    for a pcgs 45.13-2
SpecialSemilinearGroup 50.2-10
SpecialUnitaryGroup 50.2-4
SplitCharacters 71.17-7
SplitExtension 46.8-6
    with specified homomorphism 46.8-10
SplitString 27.7-12
SplittingField 66.4-13
Spreadsheet 10.11
SQ, synonym of SolvableQuotient 47.14-5
Sqrt 31.12-5
Square 19.2-1
square root, of an integer 14.2-9
SquareRoots 35.4-12
SSortedList 30.3-7
StabChain, for a group (and a record) 43.8-1
    for a group and a base 43.8-1
StabChainBaseStrongGenerators 43.8-4
StabChainImmutable 43.8-1
StabChainMutable, for a group 43.8-1
    for a homomorphism 43.8-1
StabChainOp 43.8-1
StabChainOptions 43.8-2
Stabilizer 41.5-2
StabilizerOfExternalSet 41.12-10
StabilizerPcgs 45.15-1
Stack trace 6.4-5
StandardAssociate 56.5-5
StandardAssociateUnit 56.5-6
StandardizeTable 47.7-2
StandardWreathProduct 49.4-1
StarCyc 18.5-3
START_TEST 7.9-1
StartlineFunc 5.1-5
StartsWith 27.7-19
State 14.7-3
Stirling number of the first kind 16.1-5
Stirling number of the second kind 16.1-6
Stirling1 16.1-5
Stirling2 16.1-6
STOP_TEST 7.9-1
StoredGroebnerBasis 66.18-3
StoreFusion 73.3-4
StraightLineProgElm 37.9-2
StraightLineProgGens 37.9-3
StraightLineProgram, for a list of lines (and the number of generators) 37.8-2
    for a string and a list of generators names 37.8-2
StraightLineProgramNC, for a list of lines (and the number of generators) 37.8-2
    for a string and a list of generators names 37.8-2
StraightLineProgramsTom 70.10-2
StreamsFamily 10.1-9
StretchImportantSLPElement 37.9-5
strictly sorted list 21.17-4
String 27.7-6
    for a cyclotomic 18.1-6
StringDate 27.10-6
StringFactorizationWord 47.2-4
StringNumbers 27.7-21
StringOfResultOfStraightLineProgram 37.8-6
StringPP 27.7-9
strings, equality of 27.6-1
    inequality of 27.6-1
    lexicographic ordering of 27.6-2
StringTime 27.10-9
StripLineBreakCharacters 27.7-7
StrongGeneratorsStabChain 43.10-4
StronglyConnectedComponents 33.4-5
Struct 31.3
StructByGenerators 31.3
StructuralCopy 12.7-2
StructuralCopy, for lists 21.7
structure constant 71.12-7 71.12-8 71.12-9
StructureConstantsTable 62.4-2
StructureDescription 39.6-1
StructWithGenerators 31.3
SU 50.2-4
SubadditiveGroup 55.2-9
SubadditiveGroupNC 55.2-9
SubadditiveMagma 55.2-7
SubadditiveMagmaNC 55.2-7
SubadditiveMagmaWithZero 55.2-8
SubadditiveMagmaWithZeroNC 55.2-8
Subalgebra 62.6-1
SubAlgebraModule 62.11-16
SubalgebraNC 62.6-2
SubalgebraWithOne 62.6-3
SubalgebraWithOneNC 62.6-4
SubdirectProduct 49.3-1
SubdirectProducts 49.3-2
Subdomains 31.8
Subfield 58.2-1
SubfieldNC 58.2-1
Subfields 58.2-10
Subgroup 39.3-1
    for a group 39.3-1
subgroup fusions 73.3
subgroup generators tree 48.10-1
SubgroupByPcgs 45.7-9
SubgroupByProperty 39.3-11
SubgroupNC 39.3-1
SubgroupOfWholeGroupByCosetTable 47.8-2
SubgroupOfWholeGroupByQuotientSubgroup 47.13-1
SubgroupProperty 43.12-1
subgroups, polyhedral 71.12-6
SubgroupShell 39.3-12
SubgroupsSolvableGroup 39.21-3
sublist 21.3
    access 21.3
    assignment 21.4
    operation 21.3
sublist assignment, operation 21.4
Submagma 35.2-7
SubmagmaNC 35.2-7
SubmagmaWithInverses 35.2-9
SubmagmaWithInversesNC 35.2-9
SubmagmaWithOne 35.2-8
SubmagmaWithOneNC 35.2-8
Submodule 57.2-1
SubmoduleNC 57.2-2
Submonoid 51.2-3
SubmonoidNC 51.2-3
SubnearAdditiveGroup 55.2-9
SubnearAdditiveGroupNC 55.2-9
SubnearAdditiveMagma 55.2-7
SubnearAdditiveMagmaNC 55.2-7
SubnearAdditiveMagmaWithZero 55.2-8
SubnearAdditiveMagmaWithZeroNC 55.2-8
SubnormalSeries 39.17-4
Subring 56.1-7
SubringNC 56.1-7
Subrings 56.9-3
SubringWithOne 56.3-5
SubringWithOneNC 56.3-5
Subsemigroup 51.1-3
SubsemigroupNC 51.1-3
subset test, for collections 30.5-1
subsets 16.2-1
Subspace 61.2-2
SubspaceNC 61.2-2
Subspaces 61.4-1
SubstitutedWord, replace a subword by a given word 37.4-5
    replace an interval by a given word 37.4-5
SubsTom 70.7-1
Substruct 31.8
SubstructNC 31.8
SubSyllables 37.5-4
subtract, a set from another 21.19-8
SubtractBlist 22.4-4
subtraction 4.13
    matrices 24.3
    matrix and scalar 24.3
    rational functions 66.2
    scalar and matrix 24.3
    scalar and matrix list 24.3 24.3
    scalar and vector 23.2
    vector and scalar 23.2
    vectors 23.2
SubtractSet 21.19-8
Subword 37.4-3
Successors 33.2-9
Suffix 27.7-19
Sum 21.20-26
SumFactorizationFunctionPcgs 45.12-1
SumIntersectionMat 24.11-4
SumX 21.21-3
Sup 19.2-4
SupersolvableResiduum 39.12-11
support, email address 1.5
SupportedCharacterTableInfo 71.3-4
SurjectiveActionHomomorphismAttr 41.12-17
SuzukiGroup 50.1-12
SylowComplement 39.13-2
SylowSubgroup 39.13-1
SylowSystem 39.13-4
symmetric group, power map 16.2-29
symmetric power 72.11-2
symmetric relation 33.2-2
SymmetricClosureBinaryRelation 33.4-2
SymmetricGroup, for a degree 50.1-10
    for a domain 50.1-10
SymmetricInverseMonoid 54.7-3
SymmetricInverseSemigroup 54.7-3
SymmetricParentGroup 43.4-4
SymmetricParts 72.11-2
SymmetricPowerOfAlgebraModule 64.15-3
Symmetrizations 72.11-1
symmetrizations, orthogonal 72.11-4
    symplectic 72.11-5
SymplecticComponents 72.11-5
SymplecticGroup, for dimension and a ring 50.2-5
    for dimension and field size 50.2-5
syntax errors 6.1
system getter 13.5
system setter 13.5
Sz 50.1-12
\(t_N\) (irrational value) 18.4-3
table automorphisms 73.4-2 73.7-3
table of chapters for help books 2.2
table of sections for help books 2.2
TableAutomorphisms 71.22-2
TableOfMarks, for a group 70.3-1
    for a matrix 70.3-1
    for a string 70.3-1
TableOfMarksByLattice 70.3-2
TableOfMarksComponents 70.6-4
TableOfMarksCyclic 70.12-1
TableOfMarksDihedral 70.12-2
TableOfMarksFamily 70.6-3
TableOfMarksFrobenius 70.12-3
tables 71. 71.3
tabulator 4.4
Tan 19.2-1
Tanh 19.2-1
Tau 15.5-2
TCENUM 47.6-5
TeachingMode 6.13-1
TemporaryGlobalVarName 4.9-11
Tensored 72.8-20
TensorProductGModule 69.2-2
TensorProductOfAlgebraModules, for a list of algebra modules 64.15-1
    for two algebra modules 64.15-1
Test 7.9-2
test, for a primitive root 15.3-4
    for a rational 17.2-1
    for records 29.1-1
    for set equality 21.19-2
TestConsistencyMaps 73.5-12
TestDirectory 7.9-3
tester 13.6
Tester 13.6-1
TestHomogeneous 75.3-1
TestInducedFromNormalSubgroup 75.3-4
TestJacobi 62.4-6
TestMonomial, for a character 75.4-1
    for a character and a Boolean 75.4-1
    for a group 75.4-1
    for a group and a Boolean 75.4-1
TestMonomialQuick, for a character 75.4-4
    for a group 75.4-4
TestMonomialUseLattice 75.4-2
TestPackage 76.3-3
TestPackageAvailability 76.3-2
TestPerm1 72.14-2
TestPerm2 72.14-2
TestPerm3 72.14-2
TestPerm4 72.14-2
TestPerm5 72.14-2
TestQuasiPrimitive 75.3-3
TestRelativelySM, for a character 75.4-6
    for a character and a normal subgroup 75.4-6
    for a group 75.4-6
    for a group and a normal subgroup 75.4-6
TestSubnormallyMonomial, for a character 75.4-5
    for a group 75.4-5
then 4.17
ThreeGroup library 50.7
TietzeWordAbstractWord 48.3-1
time 7.6-3
Timeouts 5.3
Trace, for a field element 58.3-5
    for a matrix 58.3-5
    of a matrix 24.4-3
TraceAllMethods 7.3-2
TracedCosetFpGroup 47.6-2
TraceImmediateMethods 7.3-5
TraceMat 24.4-3
TraceMethods, for a list of operations 7.3-1
    for operations 7.3-1
TracePolynomial 58.3-3
TransferDiagram 73.5-11
Transformation, for a list and function 53.2-1
    for a source and destination 53.2-2
    for an image list 53.2-1
TransformationByImageAndKernel, for an image and kernel 53.2-3
TransformationFamily 53.1-3
TransformationList, for an image list 53.2-1
TransformationListList, for a source and destination 53.2-2
TransformationNumber 53.2-6
TransformationOp 53.2-5
TransformationOpNC 53.2-5
TransformingPermutations 71.22-3
TransformingPermutationsCharacterTables 71.22-4
transitive 41.10-1
transitive relation 33.2-3
TransitiveClosureBinaryRelation 33.4-3
TransitiveGroup 50.6-1
TransitiveIdentification 50.6-3
Transitivity, for a character 72.8-16
    for a group and an action domain 41.10-2
    for an external set 41.10-2
TranslatorSubalgebra 62.11-24
transporter 41.6
TransposedMat 24.5-6
TransposedMatAttr 24.5-6
TransposedMatDestructive 24.5-7
TransposedMatImmutable 24.5-6
TransposedMatMutable 24.5-6
TransposedMatOp 24.5-6
TransposedMatrixGroup 44.2-4
TriangulizedIntegerMat 25.2-1
TriangulizedIntegerMatTransform 25.2-2
TriangulizedMat 24.7-2
TriangulizedNullspaceMat 24.7-4
TriangulizedNullspaceMatDestructive 24.7-5
TriangulizeIntegerMat 25.2-3
TriangulizeMat 24.7-3
TrimPartialPerm 54.5-6
TrimTransformation 53.5-23
TrivialCharacter, for a character table 72.7-1
    for a group 72.7-1
TrivialGroup 50.1-1
TrivialIterator 30.8-7
TrivialSubalgebra 62.6-5
TrivialSubgroup 39.12-1
TrivialSubmagmaWithOne 35.4-13
TrivialSubmodule 57.2-4
TrivialSubmonoid 51.2-8
TrivialSubnearAdditiveMagmaWithZero 55.3-6
TrivialSubspace 61.3-2
Trunc 19.2-1
TryCosetTableInWholeGroup 47.8-1
TryGcdCancelExtRepPolynomials 66.24-2
TryNextMethod 78.4-1
tuple stabilizer 41.5
Tuples 16.2-8
TwoClosure 43.12-3
TwoCoboundaries 46.8-1
TwoCocycles 46.8-2
TwoCohomology 46.8-3
TwoGroup library 50.7
TwoSidedIdeal 56.2-1
TwoSidedIdealByGenerators 56.2-4
TwoSidedIdealNC 56.2-2
TwoSquares 15.7-1
type, boolean 20.
    cyclotomic 18.
    records 29.
    strings 27.1
TypeObj 13.9-1
TypeOfDefaultGeneralMapping 32.14-7
TzEliminate, for a presentation (and a generator) 48.7-1
    for a presentation (and an integer) 48.7-1
TzFindCyclicJoins 48.7-4
TzGo 48.6-1
TzGoGo 48.6-3
TzImagesOldGens 48.9-3
TzInitGeneratorImages 48.9-1
TzNewGenerator 48.5-2
TzOptions 48.11-1
TzPreImagesNewGens 48.9-4
TzPrint 48.4-6
TzPrintGeneratorImages 48.9-5
TzPrintGenerators 48.4-1
TzPrintLengths 48.4-3
TzPrintOptions 48.11-2
TzPrintPairs 48.4-7
TzPrintPresentation 48.4-5
TzPrintRelators 48.4-2
TzPrintStatus 48.4-4
TzSearch 48.7-2
TzSearchEqual 48.7-3
TzSort 48.1-2
TzSubstitute, for a presentation (and an integer and 0/1/2) 48.8-1
    for a presentation and a word 48.8-1
TzSubstituteCyclicJoins 48.8-2
\(u_N\) (irrational value) 18.4-3
UglyVector 61.11-2
Unbind, for multiple indices 21.5-2
    unbind a list entry 21.5-2
    unbind a record component 29.6-2
    unbind a variable 4.8-2
Unbind\. 29.7-3
Unbind\[\] 21.2-1
UnbindElmWPObj 86.2-1
UnbindGlobal 4.9-6
UncoverageLineByLine 7.7-17
UnderlyingCharacteristic, for a character 71.9-5
    for a character table 71.9-5
UnderlyingCharacterTable 72.2-1
UnderlyingElement, fp group elements 47.4-4
    fp semigroup elements 52.4-1
UnderlyingExternalSet 41.12-16
UnderlyingFamily 64.1-4
UnderlyingGeneralMapping 32.3-10
UnderlyingGroup, for character tables 71.6-1
    for tables of marks 70.7-7
UnderlyingInjectionZeroMagma 35.2-14
UnderlyingLeftModule 61.6-2
UnderlyingLieAlgebra 64.6-6
UnderlyingMagma 65.1-6
UnderlyingRelation 32.3-9
UnderlyingRingElement 64.1-5
UnderlyingSemigroup, for a Rees 0-matrix semigroup 51.9-10
    for a Rees matrix semigroup 51.9-10
UnInstallCharReadHookFunc 10.10-2
Union, for a list 30.5-3
    for various collections 30.5-3
union, of collections 30.5-3
    of sets 21.19-6
Union2 30.5-3
UnionBlist, for a list 22.3-1
    for various boolean lists 22.3-1
Unique 21.20-4
UniteBlist 22.4-1
UniteBlistList 22.4-2
UniteSet 21.19-6
Units 56.5-2
UnivariatenessTestRationalFunction 66.5-7
UnivariatePolynomial 66.5-1
UnivariatePolynomialByCoefficients 66.5-2
UnivariatePolynomialRing, for a ring (and a name and an exclusion list) 66.16-1
    for a ring (and an indeterminate number) 66.16-1
UnivariateRationalFunctionByCoefficients 66.14-1
UniversalEnvelopingAlgebra 64.10-1
UNIX, features 3.1
    options 3.1
UNIXSelect 10.2-3
Unknown 74.1-1
UnloadSmallGroupsData 50.7-9
UnorderedTuples 16.2-6
UnprofileFunctions 7.7-6
UnprofileLineByLine 7.7-16
UnprofileMethods 7.7-8
until 4.19
UntraceAllMethods 7.3-4
UntraceImmediateMethods 7.3-5
UntraceMethods, for a list of operations 7.3-3
    for operations 7.3-3
UpdateMap 73.5-7
UpEnv 6.5-1
UpperCentralSeriesOfGroup 39.17-12
UpperSubdiagonal 24.12-2
UseBasis 57.3-5
UseFactorRelation 31.13-2
UseIsomorphismRelation 31.13-3
UserPreference 3.2-3
UseSubsetRelation 31.13-1
utilities for editing GAP files 6.11
\(v_N\) (irrational value) 18.4-3
ValidatePackageInfo 76.3-13
Valuation 68.1-3
Value, for a univariate rat. function, a value (and a one) 66.7-1
    for rat. function, a list of indeterminates, a value (and a one) 66.7-1
ValueCochain 64.12-4
ValueGlobal 4.9-4
ValueMolienSeries 72.12-3
ValueOption 8.1-5
ValuePol 23.7-1
ValuesOfClassFunction 72.2-2
VectorSpace 61.2-1
VectorSpaceByPcgsOfElementaryAbelianGroup 45.14-1
vi 6.11
View 6.3-3
ViewObj 6.3-5
    for a character table 71.13-1
    for a ffe 59.6-1
    for a string 27.1-4
    for a table of marks 70.4-1
    for class functions 72.5-1
ViewString 27.7-3
vim 6.11
virtual character 72.8-2
virtual characters 72.
VirtualCharacter, for a character table and a list 72.6-2
    for a group and a list 72.6-2
\(w_N\) (irrational value) 18.4-3
WeakPointerObj 86.1-1
web sites, for GAP 1.5
WedgeGModule 69.2-3
WeekDay 27.10-5
WeightLexOrdering 34.4-8
WeightOfGenerators 34.4-10
WeightsTom 70.7-12
WeightVecFFE 23.6-1
WeylGroup 64.7-3
WeylOrbitIterator 64.7-7
Where 6.4-5
while loop 4.18
WordAlp 27.7-10
words, in generators 39.5
Wreath product embedding 49.4-4
WreathProduct 49.4-1
WreathProductImprimitiveAction 49.4-2
WreathProductOrdering 34.4-13
WreathProductProductAction 49.4-3
WriteAll 10.4-3
WriteByte 10.4-1
WriteGapIniFile 3.2-3
WriteLine 10.4-2
X, for a family and a number 66.1-1
    for a ring (and a name, and an exclusion list) 66.1-1
    for a ring (and a number) 66.1-1
\(x_N\) (irrational value) 18.4-3
\(y_N\) (irrational value) 18.4-3
Z, for field size 59.1-2
    for prime and degree 59.1-2
ZClassRepsQClass 44.6-9
Zero 31.10-3
    for a partial perm 54.3-23
ZeroAttr 31.10-3
ZeroCoefficient 65.2-5
ZeroCoefficientRatFun 66.21-4
ZeroImmutable 31.10-3
ZeroMapping 32.2-8
ZeroMutable 31.10-3
ZeroOp 31.10-3
ZeroSameMutability 31.10-3
ZeroSM 31.10-3
Zeta 19.2-1
ZippedProduct 66.23-2
ZippedSum 66.23-1
ZmodnZ 14.5-2
ZmodnZObj, for a residue class family and integer 14.5-3
    for two integers 14.5-3
ZmodpZ 14.5-2
ZmodpZNC 14.5-2
ZumbroichBase 60.3-1
Zuppos 39.20-8