The GAP 4 Reference Manual - Index I

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

IdealByGenerators 51.2
IdempotentsTom 64.7
IdempotentsTomInfo 64.7
IdentificationOfConjugacyClasses 65.5
Identifier 64.7 65.7
Identity 28.9
IdentityFromSCTable 57.3
IdentityMapping 29.1
IdentityMat 23.3
IdGroup 45.6
IdsOfAllGroups 45.6
if statement 4.16
Image 29.3
Image, for Frobenius automorphisms 54.4
image, vector under matrix 23.1
ImageElm 29.3
ImageListOfTransformation 49.0
Images 29.3
ImagesElm 29.3
ImageSetOfTransformation 49.0
ImagesRepresentative 29.3
ImagesSet 29.3
ImagesSmallestGenerators 35.3
ImagesSource 29.3
Immutable 11.5
ImmutableBasis 56.5
iN 17.4
in, for collections 27.5
in, for lists 20.8
in, for strictly sorted lists 20.15
in, operation for 27.5
IndependentGeneratorsOfAbelianGroup 34.21
Indeterminate 60.1
IndeterminateName 60.1
Indeterminateness 67.3
IndeterminateNumberOfLaurentPolynomial 60.12
IndeterminateNumberOfUnivariateRationalFunction 60.1
IndeterminateOfUnivariateRationalFunction 60.1
IndeterminatesOfPolynomialRing 60.13
Index 34.3
IndexInWholeGroup 34.3
Indicator 65.9
IndicatorOp 65.9
IndicesInvolutaryGenerators 42.5
IndicesNormalSteps 40.11
IndicesOfAdjointBasis 57.8
IndicesStabChain 38.8
Indirected 67.3
InducedAutomorphism 35.6
InducedClassFunction 66.9
InducedClassFunctions 66.9
InducedCyclic 66.9
InducedPcgs 40.7
InducedPcgsByGenerators 40.7
InducedPcgsByGeneratorsNC 40.7
InducedPcgsByPcSequence 40.7
InducedPcgsByPcSequenceAndGenerators 40.7
InducedPcgsByPcSequenceNC 40.7
InducedPcgsWrtFamilyPcgs 41.1
InducedPcgsWrtSpecialPcgs 40.13
Inequalities 66.14
inequality test 4.11
inequality, of records 26.4
InertiaSubgroup 66.8
infinity 17.2
inflated class functions 66.9
Info 6.4
InfoAlgebra 57.0
InfoAttributes 12.5
InfoBckt 38.10
InfoCharacterTable 65.3
InfoCoh 34.22
InfoComplement 34.10
InfoCoset 34.8
InfoFpGroup 42.0
InfoGroup 34.2
InfoLattice 34.19
InfoLevel 6.4
InfoMatrix 23.0
InfoNumtheor 14.0
InfoOptions 7.0
InfoPcSubgroup 34.20
InfoText 65.7
InfoTom 64.6
InitFusion 67.5
InitPowerMap 67.4
InjectionZeroMagma 31.2
InnerAutomorphism 35.5
InnerAutomorphismsAutomorphismGroup 35.6
InputLogTo 8.7 9.4
InputTextFile 9.5
InputTextNone 9.8
InputTextString 9.7
InputTextUser 9.6
InsertTrivialStabilizer 38.9
InstallAtExit 5.6
installation 70.0
installation, under UNIX 70.4
installation, under Windows 70.10
InstallFactorMaintenance 28.12
Installing GAP 70.0
InstallIsomorphismMaintenance 28.12
InstallSubsetMaintenance 28.12
Int 13.1
integer part of a quotient 13.2
Integers 13.0
Integral matrices and lattices 24.0
IntegralizedMat 24.0
IntermediateGroup 34.16
IntermediateSubgroups 34.16
internet config 2.5 70.14
InterpolatedPolynomial 51.7
IntersectBlist 21.3
Intersection 27.4
intersection, of collections 27.4
intersection, of sets 20.15
Intersection2 27.4
IntersectionBlist 21.2
IntersectionsTom 64.9
IntersectSet 20.15
IntFFE 54.2
IntScalarProducts 67.3
IntVecFFE 54.2
InvariantBilinearForm 39.2
InvariantElementaryAbelianSeries 34.16
InvariantLattice 39.3
InvariantSesquilinearForm 39.2
InvariantSubgroupsElementaryAbelianGroup 34.20
Inverse 28.9
Inverse, group homomorphism 35.2
inverse, matrix 23.1
InverseClasses 65.7
InverseGeneralMapping 29.1
InverseMap 67.3
InverseMatMod 23.11
InverseOp 28.9
InverseRepresentative 38.8
IRIX 70.3
Irr 65.7
irrationalities 17.0
IrrBaumClausen 65.11
IrrConlon 65.11
IrrDixonSchneider 65.11
irreducible characters, computation 65.13
IrreducibleDifferences 66.10
IrreducibleRepresentations 65.11
IrreducibleSolvableGroup 45.4
IsAbelian 31.4
IsAbelianNumberField 55.2
IsAdditiveElement 28.13
IsAdditiveElementWithInverse 28.13
IsAdditiveElementWithZero 28.13
IsAdditiveGroup 50.1
IsAdditiveGroupGeneralMapping 29.9
IsAdditiveGroupHomomorphism 29.9
IsAdditivelyCommutative 50.3
IsAdditivelyCommutativeElement 28.14
IsAdditivelyCommutativeElementCollColl 28.14
IsAdditivelyCommutativeElementCollection 28.14
IsAdditivelyCommutativeElementFamily 28.14
IsAdditiveMagma 50.1
IsAdditiveMagmaWithInverses 50.1
IsAdditiveMagmaWithZero 50.1
IsAlgebra 57.7
IsAlgebraGeneralMapping 29.11
IsAlgebraHomomorphism 29.11
IsAlgebraicElement 61.2
IsAlgebraicExtension 61.1
IsAlgebraWithOne 57.7
IsAlgebraWithOneGeneralMapping 29.11
IsAlgebraWithOneHomomorphism 29.11
IsAlphaChar 25.2
IsAlternatingGroup 38.3
IsAnticommutative 51.4
IsAssociated 51.5
IsAssociative 31.4
IsAssociativeElement 28.14
IsAssociativeElementCollColl 28.14
IsAssociativeElementCollection 28.14
IsAssocWord 32.0
IsAssocWordWithInverse 32.0
IsAssocWordWithOne 32.0
IsAutomorphismGroup 35.6
IsBasis 56.4
IsBergerCondition 68.1
IsBijective 29.2
IsBinaryRelation 30.1
IsBlist 21.0
IsBool 19.0
IsBound, for lists M 20.5
IsBoundGlobal 4.9
IsBrauerTable 65.3
IsBravaisGroup 39.3
IsBuiltFromAdditiveMagmaWithInverses 33.3
IsBuiltFromGroup 33.3
IsBuiltFromMagma 33.3
IsBuiltFromMagmaWithInverses 33.3
IsBuiltFromMagmaWithOne 33.3
IsCanonicalBasis 56.4
IsCanonicalBasisFullMatrixModule 56.4
IsCanonicalBasisFullRowModule 56.4
IsCanonicalNiceMonomorphism 35.4
IsCanonicalPcgs 40.8
IsCentral 31.4
IsChar 25.0
IsCharacter 66.8
IsCharacteristicSubgroup 34.3
IsCharacterTable 65.3
IsCharacterTableInProgress 65.3
IsClassFunction 66.0
IsClosedStream 9.1
IsCollection 27.0
IsCollectionFamily 27.1
IsCommutative 31.4
IsCommutativeElement 28.14
IsCommutativeElementCollColl 28.14
IsCommutativeElementCollection 28.14
IsConfluent 33.1 41.4
IsConjugacyClassSubgroupsByStabilizerRep 34.18
IsConjugacyClassSubgroupsRep 34.18
IsConjugate 34.9
IsConjugatorAutomorphism 35.5
IsConstantRationalFunction 60.4
IsConstantTimeAccessGeneralMapping 29.12
IsConstantTimeAccessList 20.1
IsContainedInSpan 56.5
IsCopyable 11.5
IsCyc 17.1
IsCyclic 34.14
IsCyclotomic 17.1
IsCyclotomicMatrixGroup 39.3
IsDenseList 20.1
IsDiagonalMat 23.2
IsDigitChar 25.2
IsDirectoryPath 8.6
IsDistributive 51.4
IsDivisionRing 53.1
IsDomain 28.8
IsDoneIterator 27.7
IsDoubleCoset 34.8
IsDuplicateFree 20.13
IsDuplicateFreeList 20.13
IsDxLargeGroup 65.13
IsElementaryAbelian 34.14
IsElementOfFpSemigroup 48.0
IsElementOfFreeMagmaRing 59.2
IsElementOfFreeMagmaRingCollection 59.2
IsElementOfFreeMagmaRingFamily 59.2
IsElementOfMagmaRingModuloRelations 59.4
IsElementOfMagmaRingModuloRelationsCollection 59.4
IsElementOfMagmaRingModuloRelationsFamily 59.4
IsElementOfMagmaRingModuloSpanOfZeroFamily 59.5
IsEmpty 27.3
IsEmptyString 25.7
IsEndOfStream 9.3
IsEndoGeneralMapping 29.12
IsEqualSet 20.15
IsEquivalenceClass 30.2
IsEquivalenceRelation 30.2
IsEuclideanRing 51.6
IsEvenInt 13.1
IsExecuteableFile 8.6
IsExistingFile 8.6
IsExtAElement 28.13
IsExternalOrbit 36.10
IsExternalSet 36.10
IsExternalSubset 36.10
IsExtLElement 28.13
IsExtRElement 28.13
IsFamilyPcgs 41.1
IsFFE 54.1
IsFFECollColl 54.1
IsFFECollection 54.1
IsField 53.1
IsFieldHomomorphism 29.11
IsFinite 27.3
IsFiniteDimensional 52.3 57.7
IsFiniteFieldPolynomialRing 60.13
IsFinitelyGeneratedGroup 34.14
IsFiniteOrderElement 28.14
IsFiniteOrderElementCollColl 28.14
IsFiniteOrderElementCollection 28.14
IsFiniteOrdersPcgs 40.4
IsFixedStabilizer 38.9
IsFLMLOR 57.7
IsFLMLORWithOne 57.7
IsFpGroup 42.0
IsFpSemigroup 48.0
IsFreeGroup 32.1
IsFreeLeftModule 52.3
IsFreeMagmaRing 59.1
IsFreeMagmaRingWithOne 59.1
IsFromFpGroupGeneralMappingByImages 35.9
IsFromFpGroupStdGensGeneralMappingByImages 35.9
IsFromFpGroupStdGensHomomorphismByImages 35.9
IsFullHomModule 56.6
IsFullMatrixModule 52.3
IsFullRowModule 52.3
IsFullSubgroupGLorSLRespectingBilinearForm 39.2
IsFullSubgroupGLorSLRespectingSesquilinearForm 39.2
IsGaussianIntegers 55.3
IsGaussianRationals 55.0
IsGaussianSpace 56.2
IsGaussInt 17.1
IsGaussRat 17.1
IsGeneralizedDomain 28.8
IsGeneralLinearGroup 39.1
IsGeneralMapping 29.12
IsGeneralMappingFamily 29.13
IsGeneratorsOfStruct 28.3
IsGL 39.1
IsGreensClass 46.5
IsGreensDClass 46.5
IsGreensDClassEnumerator 46.5
IsGreensDRelation 46.5
IsGreensHClass 46.5
IsGreensHClassEnumerator 46.5
IsGreensHRelation 46.5
IsGreensJClass 46.5
IsGreensJClassEnumerator 46.5
IsGreensJRelation 46.5
IsGreensLClass 46.5
IsGreensLClassEnumerator 46.5
IsGreensLessThanOrEqual 46.5
IsGreensLRelation 46.5
IsGreensRClass 46.5
IsGreensRClassEnumerator 46.5
IsGreensRelation 46.5
IsGreensRRelation 46.5
IsGroup 34.2
IsGroupGeneralMapping 29.8
IsGroupGeneralMappingByAsGroupGeneralMappingByImages 35.9
IsGroupGeneralMappingByImages 35.9
IsGroupGeneralMappingByPcgs 35.9
IsGroupHClass 46.5
IsGroupHomomorphism 29.8
IsGroupOfAutomorphisms 35.6
IsGroupRing 59.1
IsHandledByNiceBasis 52.3
IsHandledByNiceMonomorphism 35.4
IsHomogeneousList 20.1
IsIdenticalObj 11.4
IsInducedPcgs 40.7
IsInducedPcgsWrtSpecialPcgs 40.13
IsInfinity 17.2
IsInjective 29.2
IsInnerAutomorphism 35.5
IsInputStream 9.1
IsInputTextNone 9.1
IsInputTextStream 9.1
IsInt 13.1
IsIntegerMatrixGroup 39.3
IsIntegers 13.0
IsIntegralBasis 56.4
IsIntegralCyclotomic 17.1
IsIntegralRing 51.4
IsInternallyConsistent 11.7 64.9 65.9
IsInternallyConsistent, for character tables 65.9
IsInternallyConsistent, for tables of marks 64.9
IsIrreducibleCharacter 66.8
IsIrreducibleRingElement 51.5
IsIterator 27.7
IsJacobianElement 28.14
IsJacobianElementCollColl 28.14
IsJacobianElementCollection 28.14
IsJacobianRing 51.4
IsKnuthBendixRewritingSystem 48.4
IsLaurentPolynomial 60.4
IsLaurentPolynomialDefaultRep 60.18
IsLDistributive 51.4
IsLeftIdeal 51.2
IsLeftIdealInParent 51.2
IsLeftModule 52.1
IsLeftModuleGeneralMapping 29.10
IsLeftModuleHomomorphism 29.10
IsLeftOperatorAdditiveGroup 52.1
IsLeftSemigroupIdeal 46.2
IsLeftSemigroupIdealEnumerator 46.2
IsLeftVectorSpace 56.2
IsLexicographicallyLess 20.16
IsLieAbelian 58.5
IsLieAlgebra 57.7
IsLieMatrix 23.0
IsLieNilpotent 58.5
IsLieObject 58.1
IsLieObjectCollection 58.1
IsLieSolvable 58.5
IsLinearMapping 29.10
IsList 20.1
IsListDefault 20.11
IsListOrCollection 27.2
IsLowerAlphaChar 25.2
IsLowerTriangularMat 23.2
IsMagma 31.1
IsMagmaHomomorphism 29.7
IsMagmaRingModuloRelations 59.4
IsMagmaRingModuloSpanOfZero 59.5
IsMagmaWithInverses 31.1
IsMagmaWithInversesIfNonzero 31.1
IsMagmaWithOne 31.1
IsMapping 29.2
IsMatrix 23.0
IsMatrixGroup 39.0
IsMatrixModuleRep 52.3
IsMinimalNonmonomial 68.4
IsModuloPcgs 40.9
IsMonoid 47.0
IsMonomialGroup 34.14
IsMonomialMatrix 23.2
IsMonomialNumber 68.3
IsMultiplicativeElement 28.13
IsMultiplicativeElementWithInverse 28.13
IsMultiplicativeElementWithOne 28.13
IsMultiplicativeElementWithZero 28.13
IsMultiplicativeZero 31.4
IsMutable 11.5
IsMutableBasis 56.5
IsNaturalAlternatingGroup 38.3
IsNaturalGL 39.1
IsNaturalGLnZ 39.3
IsNaturalSL 39.1
IsNaturalSymmetricGroup 38.3
IsNearAdditiveElement 28.13
IsNearAdditiveElementWithInverse 28.13
IsNearAdditiveElementWithZero 28.13
IsNearAdditiveGroup 50.1
IsNearAdditiveMagma 50.1
IsNearAdditiveMagmaWithInverses 50.1
IsNearAdditiveMagmaWithZero 50.1
IsNearlyCharacterTable 65.3
IsNearRingElement 28.13
IsNearRingElementWithInverse 28.13
IsNearRingElementWithOne 28.13
IsNegRat 15.1
IsNilpotentElement 58.9
IsNilpotentGroup 34.14
IsNonnegativeIntegers 13.0
IsNonSPGeneralMapping 29.13
IsNonTrivial 27.3
IsNormal 34.3
IsNormalBasis 56.4
IsNotIdenticalObj 11.4
IsNumberField 55.2
IsObject 11.1
IsOddInt 13.1
isomorphic, pc group 41.4 41.5
IsomorphismFpAlgebra 57.9
IsomorphismFpGroup 42.8
IsomorphismFpGroupByGenerators 42.8
IsomorphismFpGroupByPcgs 41.3
IsomorphismFpSemigroup 48.1
IsomorphismGroups 35.8
IsomorphismMatrixAlgebra 57.9
IsomorphismPcGroup 41.5
IsomorphismPermGroup 38.2
IsomorphismReesMatrixSemigroup 46.6
IsomorphismRefinedPcGroup 41.4
IsomorphismSpecialPcGroup 41.5
IsomorphismTransformationSemigroup 46.1
IsomorphismTypeFiniteSimpleGroup 34.14
IsOne 28.9
IsOrdinaryMatrix 23.0
IsOrdinaryTable 65.3
IsOutputStream 9.1
IsOutputTextNone 9.1
IsOutputTextStream 9.1
IsPadicExtensionNumber 62.2
IsPadicExtensionNumberFamily 62.2
IsParentPcgsFamilyPcgs 41.1
IsPcGroup 41.3
IsPcGroupGeneralMappingByImages 35.9
IsPcGroupHomomorphismByImages 35.9
IsPcgs 40.2
IsPcgsCentralSeries 40.11
IsPcgsElementaryAbelianSeries 40.11
IsPcgsPCentralSeriesPGroup 40.11
IsPerfectGroup 34.14
IsPerm 37.0
IsPermCollColl 37.0
IsPermCollection 37.0
IsPermGroup 38.0
IsPermGroupGeneralMappingByImages 35.9
IsPermGroupHomomorphismByImages 35.9
IsPGroup 34.14
IsPNilpotent 34.14
IsPolycyclicGroup 34.14
IsPolynomial 60.4
IsPolynomialDefaultRep 60.18
IsPolynomialRing 60.13
IsPosInt 13.1
IsPositiveIntegers 13.0
IsPosRat 15.1
IsPreimagesByAsGroupGeneralMappingByImages 35.9
IsPrime 51.5
IsPrimeField 53.2
IsPrimeInt 13.3
IsPrimeOrdersPcgs 40.4
IsPrimePowerInt 13.3
IsPrimitive 36.8
IsPrimitiveCharacter 68.2
IsPrimitiveRootMod 14.2
IsProbablyPrimeInt 13.3
IsPseudoCanonicalBasisFullHomModule 56.6
IsPSolvable 34.14
IsPSolvableCharacterTable 65.9
IsPSolvableCharacterTableOp 65.9
IsPurePadicNumber 62.1
IsPurePadicNumberFamily 62.1
IsQuasiPrimitive 68.2
IsQuaternion 57.7
IsQuaternionCollColl 57.7
IsQuaternionCollection 57.7
IsQuickPositionList 20.19
IsQuotientSemigroup 46.4
IsRange 20.18
IsRat 15.1
IsRationalFunction 60.4
IsRationalFunctionDefaultRep 60.18
IsRationalFunctionsFamily 60.16
IsRationalMatrixGroup 39.3
IsRationals 15.0
IsRationalsPolynomialRing 60.13
IsRDistributive 51.4
IsReadableFile 8.6
IsReadOnlyGlobal 4.9
IsRecord 26.0
IsRecordCollColl 26.0
IsRecordCollection 26.0
IsReduced 33.1
IsReesCongruence 46.3
IsReesCongruenceSemigroup 46.0
IsReesMatrixSemigroup 46.6
IsReesMatrixSemigroupElement 46.6
IsReesZeroMatrixSemigroup 46.6
IsReesZeroMatrixSemigroupElement 46.6
IsReflexiveBinaryRelation 30.1
IsRegular 36.8
IsRegularDClass 46.5
IsRegularSemigroup 46.0
IsRegularSemigroupElement 46.0
IsRestrictedLieAlgebra 58.8
IsRewritingSystem 33.1
IsRightCoset 34.6
IsRightIdeal 51.2
IsRightIdealInParent 51.2
IsRightModule 52.1
IsRightOperatorAdditiveGroup 52.1
IsRightSemigroupIdeal 46.2
IsRightSemigroupIdealEnumerator 46.2
IsRing 51.1
IsRingElement 28.13
IsRingElementWithInverse 28.13
IsRingElementWithOne 28.13
IsRingGeneralMapping 29.11
IsRingHomomorphism 29.11
IsRingWithOne 51.3
IsRingWithOneGeneralMapping 29.11
IsRingWithOneHomomorphism 29.11
IsRowModuleRep 52.3
IsRowVector 22.0
IsScalar 28.13
IsSemiEchelonized 56.4
IsSemigroup 46.0
IsSemigroupCongruence 46.3
IsSemigroupIdeal 46.2
IsSemigroupIdealEnumerator 46.2
IsSemiRegular 36.8
IsSet 20.13
IsSimpleAlgebra 57.7
IsSimpleGroup 34.14
IsSimpleSemigroup 46.0
IsSingleValued 29.2
IsSL 39.1
IsSolvableGroup 34.14
IsSortedList 20.13
IsSpecialLinearGroup 39.1
IsSpecialPcgs 40.13
IsSPGeneralMapping 29.13
IsSSortedList 20.13
IsStream 9.1
IsString 25.0
IsStringRep 25.7
IsStruct 28.5
IsSubgroup 34.3
IsSubgroupFpGroup 42.0
IsSubgroupOfWholeGroupByQuotientRep 42.9
IsSubgroupSL 39.1
IsSubnormal 34.3
IsSubsemigroupFpSemigroup 48.0
IsSubset 27.4
IsSubsetBlist 21.1
IsSubsetLocallyFiniteGroup 34.14
IsSubsetSet 20.15
IsSubspacesVectorSpace 56.2
IsSubstruct 28.7
IsSupersolvableGroup 34.14
IsSurjective 29.2
IsSymmetricBinaryRelation 30.1
IsSymmetricGroup 38.3
IsTable 20.1
IsTableOfMarks 64.6
IsTableOfMarksWithGens 64.10
IsToPcGroupGeneralMappingByImages 35.9
IsToPcGroupHomomorphismByImages 35.9
IsToPermGroupGeneralMappingByImages 35.9
IsToPermGroupHomomorphismByImages 35.9
IsTotal 29.2
IsTransformation 49.0
IsTransformationCollection 49.0
IsTransformationMonoid 46.1
IsTransformationSemigroup 46.1
IsTransitive, for class functions 66.8
IsTransitive.ctblfuns 66.8
IsTransitive.oprt 36.8
IsTransitiveBinaryRelation 30.1
IsTrivial 27.3
IsTwoSidedIdeal 51.2
IsTwoSidedIdealInParent 51.2
IsUniqueFactorizationRing 51.4
IsUnit 51.5
IsUnivariatePolynomial 60.4
IsUnivariatePolynomialRing 60.14
IsUnivariateRationalFunction 60.4
IsUnknown 18.0
IsUpperAlphaChar 25.2
IsUpperTriangularMat 23.2
IsVector 28.13
IsVectorSpace 56.2
IsVirtualCharacter 66.8
IsWholeFamily 27.3
IsWriteableFile 8.6
IsZero 28.9
IsZeroGroup 46.0
IsZeroSimpleSemigroup 46.0
IsZeroSquaredElement 28.14
IsZeroSquaredElementCollColl 28.14
IsZeroSquaredElementCollection 28.14
IsZeroSquaredRing 51.4
IsZmodnZObj 13.4
IsZmodnZObjNonprime 13.4
IsZmodpZObj 13.4
IsZmodpZObjLarge 13.4
IsZmodpZObjSmall 13.4
Iterated 20.16
Iterator 27.7
IteratorByBasis 56.4
IteratorList 27.7
IteratorSorted 27.7

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GAP 4 manual
July 1999