GAP (Semigroups) - Index

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### Index

`*` (for bipartitions) 3.4
`*` (for PBRs) 4.4
`*` (for matrices over a semiring) 5.2
`*` (for Rees (0-)matrix semigroup isomorphisms by triples) 14.3-7
`<` (for bipartitions) 3.4
`<` (for PBRs) 4.4
`<` (for matrices over a semiring) 5.2
`<` (for Rees (0-)matrix semigroup isomorphisms by triples) 14.3-7
`=` (for bipartitions) 3.4
`=` (for PBRs) 4.4
`=` (for matrices over a semiring) 5.2
`=` (for Rees (0-)matrix semigroup isomorphisms by triples) 14.3-7
`\<`, for Green's classes 10.3-1
`\in` 5.3-3
`^` (for Rees (0-)matrix semigroup isomorphisms by triples) 14.3-7
`AnnularJonesMonoid` 7.3-5
`AntiIsomorphismDualFpMonoid` 6.5-9
`AntiIsomorphismDualFpSemigroup` 6.5-9
`AntiIsomorphismDualSemigroup` 8.2-4
`ApsisMonoid` 7.3-11
`AsBipartition` 3.3-1
`AsBlockBijection` 3.3-2
`AsBooleanMat` 5.3-2
`AsCongruenceByWangPair` 13.8-3
`AsInverseSemigroupCongruenceByKernelTrace` 13.7-3
`AsList` 5.1-10
`AsListCanonical` 11.1-1
`AsMatrix`, for a filter and a matrix 5.1-6
for a filter, matrix, and threshold 5.1-6
for a filter, matrix, threshold, and period 5.1-6
`AsMonoid` 6.5-4
`AsMutableList` 5.1-10
`AsPartialPerm`, for a bipartition 3.3-4
for a PBR 4.3-3
`AsPBR` 4.3-1
`AsPermutation`, for a bipartition 3.3-5
for a PBR 4.3-4
`AsSemigroup` 6.5-3
`AsSemigroupCongruenceByGeneratingPairs` 13.6-6
`AsSemigroupHomomorphismByFunction`, for a semigroup homomorphism by images 14.1-6
`AsSemigroupHomomorphismByImages`, for a semigroup homomorphism by function 14.1-5
`AsSemigroupIsomorphismByFunction`, for a semigroup homomorphism by images 14.2-11
`AsTransformation`, for a bipartition 3.3-3
for a PBR 4.3-2
`AutomorphismGroup`, for a semigroup 14.2-7
`Bipartition` 3.2-1
`BipartitionByIntRep` 3.2-2
`Bitranslation`, for IsBitranslationsSemigroup, IsLeftTranslation, IsRightTranslation 18.1-6
`BlistNumber` 5.3-7
`BLOCKS_NC` 3.6-2
`BooleanMat` 5.3-1
`BooleanMatNumber` 5.3-6
`BrandtSemigroup` 7.8-6
`BrauerMonoid` 7.3-2
`CanonicalBlocks` 3.5-18
`CanonicalBooleanMat` 5.3-8
for a perm group and boolean matrix 5.3-8
for a perm group, perm group and boolean matrix 5.3-8
`CanonicalForm`, for a free inverse semigroup element 7.11-6
`CanonicalMultiplicationTable` 14.2-3
`CanonicalMultiplicationTablePerm` 14.2-4
`CanonicalReesMatrixSemigroup` 14.3-6
`CanonicalReesZeroMatrixSemigroup` 14.3-6
`CanonicalTransformation` 11.11-9
`CanUseFroidurePin` 6.1-4
`CanUseGapFroidurePin` 6.1-4
`CanUseLibsemigroupsFroidurePin` 6.1-4
`CatalanMonoid` 7.1-1
`CharacterTableOfInverseSemigroup` 11.14-10
`ClosureInverseMonoid` 6.4-1
`ClosureInverseSemigroup` 6.4-1
`ClosureMonoid` 6.4-1
`ClosureSemigroup` 6.4-1
`CodomainOfBipartition` 3.5-11
`ComponentRepsOfPartialPermSemigroup` 11.12-1
`ComponentRepsOfTransformationSemigroup` 11.11-1
`ComponentsOfPartialPermSemigroup` 11.12-2
`ComponentsOfTransformationSemigroup` 11.11-2
`CompositionMapping2`, for IsRMSIsoByTriple 14.3-4
for IsRZMSIsoByTriple 14.3-4
`CongruenceByWangPair` 13.8-2
`CongruencesOfPoset` 13.4-7
`CongruencesOfSemigroup`, for a semigroup 13.4-1
for a semigroup and a multiplicative element collection 13.4-1
`ContentOfFreeBandElement` 7.9-7
`ContentOfFreeBandElementCollection` 7.9-7
`CrossedApsisMonoid` 7.3-11
`CyclesOfPartialPerm` 11.12-3
`CyclesOfPartialPermSemigroup` 11.12-4
`CyclesOfTransformationSemigroup` 11.11-3
`DClass` 10.1-2
`DClasses` 10.1-4
`DClassNC` 10.1-3
`DClassOfHClass` 10.1-1
`DClassOfLClass` 10.1-1
`DClassOfRClass` 10.1-1
`DClassReps` 10.1-5
`DegreeOfBipartition` 3.5-1
`DegreeOfBipartitionCollection` 3.5-1
`DegreeOfBipartitionSemigroup` 3.8-5
`DegreeOfBlocks` 3.6-5
`DegreeOfPBR` 4.5-2
`DegreeOfPBRCollection` 4.5-2
`DegreeOfPBRSemigroup` 4.6-2
`DigraphOfAction`, for a transformation semigroup, list, and action 11.11-4
`DigraphOfActionOnPoints`, for a transformation semigroup 11.11-5
for a transformation semigroup and an integer 11.11-5
`DimensionOfMatrixOverSemiring` 5.1-3
`DimensionOfMatrixOverSemiringCollection` 5.1-4
`DirectProduct` 8.1-1
`DirectProductOp` 8.1-1
`DomainOfBipartition` 3.5-10
`DotLeftCayleyDigraph` 16.1-4
`DotRightCayleyDigraph` 16.1-4
`DotSemilatticeOfIdempotents` 16.1-3
`DotString` 16.1-1
for a Cayley digraph 16.1-2
`DualSemigroup` 8.2-1
`DualSymmetricInverseMonoid` 7.3-7
`DualSymmetricInverseSemigroup` 7.3-7
`ElementOfFpMonoid` 15.2-3
`ElementOfFpSemigroup` 15.2-2
`ELM_LIST` (for Rees (0-)matrix semigroup isomorphisms by triples) 14.3-7
`ELM_LIST`, for IsRMSIsoByTriple 14.3-3
`EmptyPBR` 4.2-3
`EndomorphismMonoid`, for a digraph 7.1-6
for a digraph and vertex coloring 7.1-6
`EndomorphismsPartition` 7.1-2
`Enumerate` 11.1-3
`EnumeratorCanonical` 11.1-1
`EqualInFreeBand` 7.9-8
`EquivalenceRelationCanonicalLookup`, for an equivalence relation over a finite semigroup 13.3-6
`EquivalenceRelationCanonicalPartition` 13.3-7
`EquivalenceRelationLookup`, for an equivalence relation over a finite semigroup 13.3-5
`EUnitaryInverseCover` 11.14-11
`EvaluateWord` 11.5-1
`ExtRepOfObj`, for a bipartition 3.5-3
for a blocks 3.6-3
for a PBR 4.5-3
`FactorisableDualSymmetricInverseMonoid` 7.3-8
`Factorization` 11.5-2
`FixedPointsOfTransformationSemigroup`, for a transformation semigroup 11.11-6
`FpTietzeIsomorphism` 15.8-4
`FreeBand`, for a given rank 7.9-1
for a list of names 7.9-1
for various names 7.9-1
`FreeInverseSemigroup`, for a given rank 7.11-1
for a list of names 7.11-1
for various names 7.11-1
`FreeMonoidAndAssignGeneratorVars` 15.2-4
`FreeSemigroupAndAssignGeneratorVars` 15.2-4
`FullBooleanMatMonoid` 7.6-1
`FullMatrixMonoid` 7.5-1
`FullPBRMonoid` 7.4-1
`FullTropicalMaxPlusMonoid` 7.7-1
`FullTropicalMinPlusMonoid` 7.7-2
`GeneralLinearMonoid` 7.5-1
`GeneratingCongruencesOfLattice` 13.8-4
`Generators` 11.6-1
`GeneratorsOfSemigroupIdeal` 9.2-1
`GeneratorsOfStzPresentation` 15.3-3
`GeneratorsSmallest`, for a semigroup 11.6-5
`GLM` 7.5-1
`GossipMonoid` 7.6-5
`GraphInverseSemigroup` 7.10-1
`GraphOfGraphInverseSemigroup` 7.10-5
`GreensDClasses` 10.1-4
`GreensDClassOfElement` 10.1-2
for a free band and element 7.9-9
`GreensDClassOfElementNC` 10.1-3
`GreensHClasses` 10.1-4
`GreensHClassOfElement` 10.1-2
for a Rees matrix semigroup 10.1-2
`GreensHClassOfElementNC` 10.1-3
`GreensJClasses` 10.1-4
`GreensLClasses` 10.1-4
`GreensLClassOfElement` 10.1-2
`GreensLClassOfElementNC` 10.1-3
`GreensRClasses` 10.1-4
`GreensRClassOfElement` 10.1-2
`GreensRClassOfElementNC` 10.1-3
`GroupHClass` 10.4-1
`GroupOfUnits` 11.8-1
`HallMonoid` 7.6-4
`HClass` 10.1-2
for a Rees matrix semigroup 10.1-2
`HClasses` 10.1-4
`HClassNC` 10.1-3
`HClassReps` 10.1-5
`HomomorphismsOfStrongSemilatticeOfSemigroups` 8.3-7
`Ideals`, for a semigroup 9.1-2
`IdempotentGeneratedSubsemigroup` 11.9-3
`Idempotents` 11.9-1
`IdentityBipartition` 3.2-3
`IdentityPBR` 4.2-4
`ImagesElm`, for IsRMSIsoByTriple 14.3-5
`ImageSetOfTranslation`, for IsSemigroupTranslation 18.1-16
`ImagesRepresentative`, for IsRMSIsoByTriple 14.3-5
`IndecomposableElements` 11.6-6
`IndexOfVertexOfGraphInverseSemigroup` 7.10-9
`IndexPeriodOfSemigroupElement` 11.4-1
`InfoSemigroups` 2.5-1
`InjectionNormalizedPrincipalFactor` 10.4-7
`InjectionPrincipalFactor` 10.4-7
`InnerLeftTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-13
`InnerRightTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-13
`InnerTranslationalHull`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-14
`Integers` 5.1-8
`IntRepOfBipartition` 3.5-4
`InverseMonoidByGenerators` 6.2-1
`InverseOp` 5.6-1
for an integer matrix 5.5-1
`InverseSemigroupByGenerators` 6.2-1
`InverseSemigroupCongruenceByKernelTrace` 13.7-2
`InverseSubsemigroupByProperty` 6.4-3
`IrredundantGeneratingSubset` 11.6-3
`IsActingSemigroup` 6.1-2
`IsAntiSymmetricBooleanMat` 5.3-13
`IsAperiodicSemigroup` 12.1-19
`IsBand` 12.1-1
`IsBipartition` 3.1-1
`IsBipartitionCollColl` 3.1-2
`IsBipartitionCollection` 3.1-2
`IsBipartitionMonoid` 3.8-1
`IsBipartitionPBR` 4.5-8
`IsBipartitionSemigroup` 3.8-1
`IsBitranslation`, for IsAssociativeElement and IsMultiplicativeElementWithOne 18.1-2
`IsBitranslationCollection` 18.1-3
`IsBlockBijection` 3.5-16
`IsBlockBijectionMonoid` 3.8-2
`IsBlockBijectionPBR` 4.5-8
`IsBlockBijectionSemigroup` 3.8-2
`IsBlockGroup` 12.1-2
`IsBlocks` 3.6-1
`IsBooleanMat` 5.1-8
`IsBooleanMatCollColl` 5.1-9
`IsBooleanMatCollection` 5.1-9
`IsBooleanMatMonoid` 5.7-2
`IsBooleanMatSemigroup` 5.7-1
`IsBrandtSemigroup` 12.2-2
`IsCliffordSemigroup` 12.2-1
`IsColTrimBooleanMat` 5.3-9
`IsCombinatorialSemigroup` 12.1-19
`IsCommutativeSemigroup` 12.1-3
`IsCompletelyRegularSemigroup` 12.1-4
`IsCompletelySimpleSemigroup` 12.1-22
`IsCongruenceByWangPair` 13.8-1
`IsCongruenceClass` 13.3-1
`IsCongruenceFreeSemigroup` 12.1-5
`IsCongruencePoset` 13.4-4
`IsConnectedTransformationSemigroup`, for a transformation semigroup 11.11-10
`IsDTrivial` 12.1-19
`IsDualSemigroupElement` 8.2-3
`IsDualSemigroupRep` 8.2-2
`IsDualTransBipartition` 3.5-13
`IsDualTransformationPBR` 4.5-10
`IsEmptyPBR` 4.5-5
`IsEnumerated` 11.1-4
`IsEquivalenceBooleanMat` 5.3-16
`IsEUnitaryInverseSemigroup` 12.2-3
`IsFactorisableInverseMonoid` 12.2-6
`IsFinite` 5.7-3
`IsFInverseMonoid` 12.2-5
`IsFInverseSemigroup` 12.2-4
`IsFreeBand`, for a given semigroup 7.9-3
`IsFreeBandCategory` 7.9-2
`IsFreeBandElement` 7.9-4
`IsFreeBandElementCollection` 7.9-5
`IsFreeBandSubsemigroup` 7.9-6
`IsFreeInverseSemigroup` 7.11-3
`IsFreeInverseSemigroupCategory` 7.11-2
`IsFreeInverseSemigroupElement` 7.11-4
`IsFreeInverseSemigroupElementCollection` 7.11-5
`IsFullMatrixMonoid` 7.5-3
`IsGeneralLinearMonoid` 7.5-3
`IsGraphInverseSemigroup` 7.10-4
`IsGraphInverseSemigroupElement` 7.10-4
`IsGraphInverseSemigroupElementCollection` 7.10-6
`IsGraphInverseSubsemigroup` 7.10-7
`IsGreensClassNC` 10.3-3
`IsGreensDGreaterThanFunc` 10.1-12
`IsGroupAsSemigroup` 12.1-7
`IsHTrivial` 12.1-19
`IsIdempotentGenerated` 12.1-8
`IsIdentityPBR` 4.5-6
`IsIntegerMatrixMonoid` 5.7-2
`IsIntegerMatrixSemigroup` 5.7-1
`IsInverseSemigroupCongruenceByKernelTrace` 13.7-1
`IsInverseSemigroupCongruenceClassByKernelTrace` 13.7-6
`IsIsomorphicSemigroup` 14.2-1
`IsJoinIrreducible` 12.2-7
`IsLeftCongruenceClass` 13.3-2
`IsLeftSemigroupCongruence` 13.1-2
`IsLeftSimple` 12.1-9
`IsLeftTranslation`, for IsSemigroupTranslation 18.1-1
`IsLeftTranslationCollection` 18.1-3
`IsLeftZeroSemigroup` 12.1-10
`IsLinkedTriple` 13.6-5
`IsLTrivial` 12.1-19
`IsMajorantlyClosed` 12.2-8
`IsMatrixOverFiniteField` 5.1-8
`IsMatrixOverFiniteFieldCollColl` 5.1-9
`IsMatrixOverFiniteFieldCollection` 5.1-9
`IsMatrixOverFiniteFieldMonoid` 5.7-2
`IsMatrixOverFiniteFieldSemigroup` 5.7-1
`IsMatrixOverSemiring` 5.1-1
`IsMatrixOverSemiringCollColl` 5.1-2
`IsMatrixOverSemiringCollection` 5.1-2
`IsMatrixOverSemiringMonoid` 5.7-2
`IsMatrixOverSemiringSemigroup` 5.7-1
`IsMaximalSubsemigroup` 11.10-3
`IsMaxPlusMatrix` 5.1-8
`IsMaxPlusMatrixCollColl` 5.1-9
`IsMaxPlusMatrixCollection` 5.1-9
`IsMaxPlusMatrixMonoid` 5.7-2
`IsMaxPlusMatrixSemigroup` 5.7-1
`IsMcAlisterTripleSemigroup` 8.4-1
`IsMcAlisterTripleSemigroupElement` 8.4-7
`IsMinPlusMatrix` 5.1-8
`IsMinPlusMatrixCollColl` 5.1-9
`IsMinPlusMatrixCollection` 5.1-9
`IsMinPlusMatrixMonoid` 5.7-2
`IsMinPlusMatrixSemigroup` 5.7-1
`IsMonogenicInverseMonoid` 12.2-10
`IsMonogenicInverseSemigroup` 12.2-9
`IsMonogenicMonoid` 12.1-12
`IsMonogenicSemigroup` 12.1-11
`IsMonoidAsSemigroup` 12.1-13
`IsMTSE` 8.4-7
`IsNTPMatrix` 5.1-8
`IsNTPMatrixCollColl` 5.1-9
`IsNTPMatrixCollection` 5.1-9
`IsNTPMatrixMonoid` 5.7-2
`IsNTPMatrixSemigroup` 5.7-1
`IsomorphismMonoid` 6.5-2
`IsomorphismPermGroup` 6.5-5
`IsomorphismReesMatrixSemigroup`, for a D-class 10.4-7
for a semigroup 6.5-8
`IsomorphismReesMatrixSemigroupOverPermGroup` 6.5-8
`IsomorphismReesZeroMatrixSemigroup` 6.5-8
`IsomorphismReesZeroMatrixSemigroupOverPermGroup` 6.5-8
`IsomorphismSemigroup` 6.5-1
`IsomorphismSemigroups` 14.2-6
`IsOntoBooleanMat` 5.3-14
`IsOrthodoxSemigroup` 12.1-14
`IsPartialOrderBooleanMat` 5.3-15
`IsPartialPermBipartition` 3.5-15
`IsPartialPermBipartitionMonoid` 3.8-3
`IsPartialPermBipartitionSemigroup` 3.8-3
`IsPartialPermPBR` 4.5-11
`IsPBR` 4.1-1
`IsPBRCollColl` 4.1-2
`IsPBRCollection` 4.1-2
`IsPBRMonoid` 4.6-1
`IsPBRSemigroup` 4.6-1
`IsPermBipartition` 3.5-14
`IsPermBipartitionGroup` 3.8-4
`IsPermPBR` 4.5-12
`IsRectangularBand` 12.1-15
`IsRectangularGroup` 12.1-16
`IsReesCongruenceClass` 13.9-2
`IsReflexiveBooleanMat` 5.3-11
`IsRegularGreensClass` 10.3-2
`IsRegularSemigroup` 12.1-17
`IsRightCongruenceClass` 13.3-3
`IsRightSemigroupCongruence` 13.1-3
`IsRightSimple` 12.1-9
`IsRightTranslation`, for IsSemigroupTranslation 18.1-1
`IsRightTranslationCollection` 18.1-3
`IsRightZeroSemigroup` 12.1-18
`IsRMSCongruenceByLinkedTriple` 13.6-1
`IsRMSCongruenceClassByLinkedTriple` 13.6-3
`IsRMSIsoByTriple` 14.3-1
`IsRowTrimBooleanMat` 5.3-9
`IsRTrivial` 12.1-19
`IsRZMSCongruenceByLinkedTriple` 13.6-1
`IsRZMSCongruenceClassByLinkedTriple` 13.6-3
`IsRZMSIsoByTriple` 14.3-1
`IsSelfDualSemigroup` 12.1-29
`IsSemiband` 12.1-8
`IsSemigroupCongruence` 13.1-1
`IsSemigroupHomomorphismByFunction` 14.1-4
`IsSemigroupHomomorphismByImages` 14.1-3
`IsSemigroupIsomorphismByFunction` 14.2-10
`IsSemigroupTranslation`, for IsAssociativeElement and IsMultiplicativeElementWithOne 18.1-1
`IsSemigroupTranslationCollection` 18.1-3
`IsSemigroupWithAdjoinedZero` 12.1-20
`IsSemilattice` 12.1-21
`IsSimpleSemigroup` 12.1-22
`IsSSSE` 8.3-3
`IsStrongSemilatticeOfSemigroups` 8.3-4
`IsStzPresentation` 15.3-2
`IsSubrelation` 13.5-1
`IsSuperrelation` 13.5-2
`IsSurjectiveSemigroup` 12.1-6
`IsSymmetricBooleanMat` 5.3-10
`IsSynchronizingSemigroup`, for a transformation semigroup 12.1-23
`IsTorsion` 5.7-4
for an integer matrix 5.5-2
`IsTotalBooleanMat` 5.3-14
`IsTransBipartition` 3.5-12
`IsTransformationBooleanMat` 5.3-17
`IsTransformationPBR` 4.5-9
`IsTransitive`, for a transformation semigroup and a pos int 11.11-7
for a transformation semigroup and a set 11.11-7
`IsTransitiveBooleanMat` 5.3-12
`IsTrimBooleanMat` 5.3-9
`IsTropicalMatrix` 5.1-8
`IsTropicalMatrixCollection` 5.1-9
`IsTropicalMatrixMonoid` 5.7-2
`IsTropicalMatrixSemigroup` 5.7-1
`IsTropicalMaxPlusMatrix` 5.1-8
`IsTropicalMaxPlusMatrixCollColl` 5.1-9
`IsTropicalMaxPlusMatrixCollection` 5.1-9
`IsTropicalMaxPlusMatrixMonoid` 5.7-2
`IsTropicalMaxPlusMatrixSemigroup` 5.7-1
`IsTropicalMinPlusMatrix` 5.1-8
`IsTropicalMinPlusMatrixCollColl` 5.1-9
`IsTropicalMinPlusMatrixCollection` 5.1-9
`IsTropicalMinPlusMatrixMonoid` 5.7-2
`IsTropicalMinPlusMatrixSemigroup` 5.7-1
`IsUniformBlockBijection` 3.5-17
`IsUnitRegularMonoid` 12.1-24
`IsUniversalPBR` 4.5-7
`IsUniversalSemigroupCongruence` 13.10-1
`IsUniversalSemigroupCongruenceClass` 13.10-2
`IsVertex`, for a graph inverse semigroup element 7.10-3
`IsZeroGroup` 12.1-25
`IsZeroRectangularBand` 12.1-26
`IsZeroSemigroup` 12.1-27
`IsZeroSimpleSemigroup` 12.1-28
`IteratorCanonical` 11.1-1
`IteratorFromGeneratorsFile` 17.1-3
`IteratorFromMultiplicationTableFile` 17.2-3
`IteratorOfDClasses` 10.2-2
`IteratorOfDClassReps` 10.2-1
`IteratorOfHClassReps` 10.2-1
`IteratorOfLClassReps` 10.2-1
`IteratorOfLeftCongruences`, for a semigroup 13.4-13
for a semigroup, and a positive integer 13.4-13
for a semigroup, positive integer, and list or collection 13.4-13
`IteratorOfRClasses` 10.2-2
`IteratorOfRightCongruences`, for a semigroup 13.4-13
for a semigroup, and a positive integer 13.4-13
for a semigroup, positive integer, and list or collection 13.4-13
`JClasses` 10.1-4
`JoinIrreducibleDClasses` 11.14-2
`JoinLeftSemigroupCongruences` 13.5-4
`JoinRightSemigroupCongruences` 13.5-4
`JoinSemigroupCongruences` 13.5-4
`JoinSemilatticeOfCongruences`, for a congruence poset and a function 13.4-10
for a list or collection and a function 13.4-10
`JonesMonoid` 7.3-3
`KernelOfSemigroupCongruence` 13.7-4
`KernelOfSemigroupHomomorphism` 14.1-7
`LargestElementSemigroup` 11.11-8
`LatticeOfCongruences`, for a semigroup 13.4-5
for a semigroup and a multiplicative element collection 13.4-5
`LatticeOfLeftCongruences`, for a semigroup 13.4-5
for a semigroup and a multiplicative element collection 13.4-5
`LatticeOfRightCongruences`, for a semigroup 13.4-5
for a semigroup and a multiplicative element collection 13.4-5
`LClass` 10.1-2
`LClasses` 10.1-4
`LClassNC` 10.1-3
`LClassOfHClass` 10.1-1
`LClassReps` 10.1-5
`LeftBlocks` 3.5-6
`LeftCayleyDigraph` 11.2-1
`LeftCongruencesOfSemigroup`, for a semigroup 13.4-1
for a semigroup and a multiplicative element collection 13.4-1
`LeftInverse`, for a matrix over finite field 5.4-2
`LeftOne`, for a bipartition 3.2-4
`LeftPartOfBitranslation` 18.1-4
`LeftProjection` 3.2-4
`LeftSemigroupCongruence` 13.2-2
`LeftTranslation`, for IsLeftTranslationsSemigroup, IsGeneralMapping 18.1-5
`LeftTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-10
`LeftTranslationsSemigroupOfFamily`, for IsFamily 18.1-8
`LeftZeroSemigroup` 7.8-5
`Length` 15.3-6
`LengthOfLongestDClassChain` 10.1-11
`MajorantClosure` 11.14-3
`Matrix`, for a filter and a matrix 5.1-5
for a semiring and a matrix 5.1-5
`MaximalDClasses` 10.1-7
`MaximalLClasses` 10.1-7
`MaximalRClasses` 10.1-7
`MaximalSubsemigroups`, for a finite semigroup 11.10-1
for a finite semigroup and a record 11.10-1
`McAlisterTripleSemigroup` 8.4-2
`McAlisterTripleSemigroupAction` 8.4-6
`McAlisterTripleSemigroupElement` 8.4-8
`McAlisterTripleSemigroupGroup` 8.4-3
`McAlisterTripleSemigroupPartialOrder` 8.4-4
`McAlisterTripleSemigroupSemilattice` 8.4-5
`MeetLeftSemigroupCongruences` 13.5-3
`MeetRightSemigroupCongruences` 13.5-3
`MeetSemigroupCongruences` 13.5-3
`MinimalCongruences`, for a congruence poset 13.4-11
for a list or collection 13.4-11
`MinimalCongruencesOfSemigroup`, for a semigroup 13.4-2
for a semigroup and a multiplicative element collection 13.4-2
`MinimalDClass` 10.1-6
`MinimalFactorization` 11.5-3
`MinimalFaithfulTransformationDegree` 14.2-13
`MinimalIdeal` 11.7-1
`MinimalIdealGeneratingSet` 9.2-2
`MinimalInverseMonoidGeneratingSet` 11.6-4
`MinimalInverseSemigroupGeneratingSet` 11.6-4
`MinimalLeftCongruencesOfSemigroup`, for a semigroup 13.4-2
for a semigroup and a multiplicative element collection 13.4-2
`MinimalMonoidGeneratingSet` 11.6-4
`MinimalRightCongruencesOfSemigroup`, for a semigroup 13.4-2
for a semigroup and a multiplicative element collection 13.4-2
`MinimalSemigroupGeneratingSet` 11.6-4
`MinimalWord`, for free inverse semigroup element 7.11-7
`MinimumGroupCongruence` 13.7-7
`Minorants` 11.14-4
`ModularPartitionMonoid` 7.3-10
`MonogenicSemigroup` 7.8-2
`MotzkinMonoid` 7.3-6
`MTSE` 8.4-8
`MultiplicativeNeutralElement`, for an H-class 10.4-5
`MultiplicativeZero` 11.7-3
`MunnSemigroup` 7.2-1
`NambooripadLeqRegularSemigroup` 11.15-1
`NambooripadPartialOrder` 11.15-2
`NaturalLeqBlockBijection` 3.4-3
`NaturalLeqInverseSemigroup` 11.14-1
`NaturalLeqPartialPermBipartition` 3.4-2
`NonTrivialEquivalenceClasses` 13.3-4
`NonTrivialFactorization` 11.5-4
`NormalizedPrincipalFactor` 10.4-8
`NormalizeSemigroup` 5.7-5
`NrBitranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-12
`NrBlocks`, for a bipartition 3.5-9
for blocks 3.5-9
`NrDClasses` 10.1-9
`NrHClasses` 10.1-9
`NrIdempotents` 11.9-2
`NrLClasses` 10.1-9
`NrLeftBlocks` 3.5-7
`NrLeftTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-12
`NrMaximalSubsemigroups` 11.10-2
`NrRClasses` 10.1-9
`NrRegularDClasses` 10.1-8
`NrRightBlocks` 3.5-8
`NrRightTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-12
`NrTransverseBlocks`, for a bipartition 3.5-2
for blocks 3.6-4
`NumberBlist` 5.3-7
`NumberBooleanMat` 5.3-6
`NumberOfLeftCongruences`, for a semigroup 13.4-12
for a semigroup, and a positive integer 13.4-12
for a semigroup, positive integer, and list or collection 13.4-12
`NumberOfRightCongruences`, for a semigroup 13.4-12
for a semigroup, and a positive integer 13.4-12
for a semigroup, positive integer, and list or collection 13.4-12
`NumberPBR` 4.5-4
`OnBlist` 5.3-4
`OnLeftBlocks` 3.7-2
`OnLeftCongruenceClasses` 13.3-8
`OnMultiplicationTable` 14.2-5
`OnRightBlocks` 3.7-1
`OnRightCongruenceClasses` 13.3-9
`Order` 5.5-3
`OrderAntiEndomorphisms` 7.1-5
`OrderEndomorphisms`, monoid of order preserving transformations 7.1-5
`ParseRelations` 15.2-1
`PartialBrauerMonoid` 7.3-2
`PartialDualSymmetricInverseMonoid` 7.3-7
`PartialJonesMonoid` 7.3-4
`PartialOrderAntiEndomorphisms` 7.1-5
`PartialOrderEndomorphisms` 7.1-5
`PartialOrderOfDClasses` 10.1-10
`PartialOrderOfLClasses` 10.1-10
`PartialOrderOfRClasses` 10.1-10
`PartialPermLeqBipartition` 3.4-1
`PartialTransformationMonoid` 7.1-3
`PartialUniformBlockBijectionMonoid` 7.3-8
`PartitionMonoid` 7.3-1
`PBR` 4.2-1
`PBRNumber` 4.5-4
`PeriodNTPMatrix` 5.1-12
`PermLeftQuoBipartition` 3.4-4
`PlanarModularPartitionMonoid` 7.3-10
`PlanarPartitionMonoid` 7.3-9
`PlanarUniformBlockBijectionMonoid` 7.3-8
`PODI`, monoid of order preserving or reversing partial perms 7.2-3
`POI`, monoid of order preserving partial perms 7.2-3
`POPI`, monoid of orientation preserving partial perms 7.2-3
`PORI`, monoid of orientation preserving or reversing partial perms 7.2-3
`PosetOfCongruences` 13.4-9
`PosetOfPrincipalCongruences`, for a semigroup 13.4-6
for a semigroup and a multiplicative element collection 13.4-6
`PosetOfPrincipalLeftCongruences`, for a semigroup 13.4-6
for a semigroup and a multiplicative element collection 13.4-6
`PosetOfPrincipalRightCongruences`, for a semigroup 13.4-6
for a semigroup and a multiplicative element collection 13.4-6
`PositionCanonical` 11.1-2
`PrimitiveIdempotents` 11.14-5
`PrincipalCongruencesOfSemigroup`, for a semigroup 13.4-3
for a semigroup and a multiplicative element collection 13.4-3
`PrincipalFactor` 10.4-8
`PrincipalLeftCongruencesOfSemigroup`, for a semigroup 13.4-3
for a semigroup and a multiplicative element collection 13.4-3
`PrincipalRightCongruencesOfSemigroup`, for a semigroup 13.4-3
for a semigroup and a multiplicative element collection 13.4-3
`ProjectionFromBlocks` 3.6-6
`RadialEigenvector` 5.6-2
`Random`, for a semigroup 11.3-1
`RandomBipartition` 3.2-7
`RandomBlockBijection` 3.2-7
`RandomInverseMonoid` 6.6-1
`RandomInverseSemigroup` 6.6-1
`RandomMatrix`, for a filter and a matrix 5.1-7
for a semiring and a matrix 5.1-7
`RandomMonoid` 6.6-1
`RandomPBR` 4.2-2
`RandomSemigroup` 6.6-1
`RandomWord`, for two integers 15.1-2
`Range`, for a graph inverse semigroup element 7.10-2
`RankOfBipartition` 3.5-2
`RankOfBlocks` 3.6-4
`RClass` 10.1-2
`RClasses` 10.1-4
`RClassNC` 10.1-3
`RClassOfHClass` 10.1-1
`RClassReps` 10.1-5
`ReadGenerators` 17.1-1
`ReadMultiplicationTable` 17.2-1
`RectangularBand` 7.8-3
`ReflexiveBooleanMatMonoid` 7.6-3
`RegularBooleanMatMonoid` 7.6-2
`RegularDClasses` 10.1-8
`RelationsOfStzPresentation` 15.3-4
`RepresentativeOfMinimalDClass` 11.7-2
`RepresentativeOfMinimalIdeal` 11.7-2
`RightBlocks` 3.5-5
`RightCayleyDigraph` 11.2-1
`RightCongruencesOfSemigroup`, for a semigroup 13.4-1
for a semigroup and a multiplicative element collection 13.4-1
`RightCosetsOfInverseSemigroup` 11.14-6
`RightInverse`, for a matrix over finite field 5.4-2
`RightOne`, for a bipartition 3.2-5
`RightPartOfBitranslation` 18.1-4
`RightProjection` 3.2-5
`RightSemigroupCongruence` 13.2-3
`RightTranslation`, for IsRightTranslationsSemigroup, IsGeneralMapping 18.1-5
`RightTranslations`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-10
`RightTranslationsSemigroupOfFamily`, for IsFamily 18.1-8
`RightZeroSemigroup` 7.8-5
`RMSCongruenceByLinkedTriple` 13.6-2
`RMSCongruenceClassByLinkedTriple` 13.6-4
`RMSIsoByTriple` 14.3-2
`RMSNormalization` 6.5-7
`RookMonoid` 7.2-2
`RookPartitionMonoid` 7.3-1
`RowSpaceBasis`, for a matrix over finite field 5.4-1
`RowSpaceTransformation`, for a matrix over finite field 5.4-1
`RowSpaceTransformationInv`, for a matrix over finite field 5.4-1
`RZMSCongruenceByLinkedTriple` 13.6-2
`RZMSCongruenceClassByLinkedTriple` 13.6-4
`RZMSConnectedComponents` 11.13-2
`RZMSDigraph` 11.13-1
`RZMSIsoByTriple` 14.3-2
`RZMSNormalization` 6.5-6
`SameMinorantsSubgroup` 11.14-7
`SchutzenbergerGroup` 10.4-2
`SemigroupCongruence` 13.2-1
`SemigroupHomomorphismByFunction` 14.1-2
`SemigroupHomomorphismByFunctionNC` 14.1-2
`SemigroupHomomorphismByImages`, for a semigroup and two lists 14.1-1
for two semigroups 14.1-1
for two semigroups and a list 14.1-1
for two semigroups and two lists 14.1-1
`SemigroupIdeal` 9.1-1
`SemigroupIdealOfReesCongruence` 13.9-1
`SemigroupIsomorphismByFunction` 14.2-9
`SemigroupIsomorphismByFunctionNC` 14.2-9
`SemigroupIsomorphismByImages`, for a semigroup and two list 14.2-8
for two semigroups 14.2-8
for two semigroups and a list 14.2-8
for two semigroups and two lists 14.2-8
Semigroups package overview 1.
`SEMIGROUPS.DefaultOptionsRec` 6.3-1
`SemigroupsOfStrongSemilatticeOfSemigroups` 8.3-6
`SemigroupsTestAll` 2.4-4
`SemigroupsTestExtreme` 2.4-3
`SemigroupsTestInstall` 2.4-1
`SemigroupsTestStandard` 2.4-2
`SemilatticeOfStrongSemilatticeOfSemigroups` 8.3-5
`SimplifiedFpSemigroup` 15.8-2
`SimplifyFpSemigroup` 15.8-1
`SingularApsisMonoid` 7.3-11
`SingularBrauerMonoid` 7.3-2
`SingularCrossedApsisMonoid` 7.3-11
`SingularDualSymmetricInverseMonoid` 7.3-7
`SingularFactorisableDualSymmetricInverseMonoid` 7.3-8
`SingularJonesMonoid` 7.3-3
`SingularModularPartitionMonoid` 7.3-10
`SingularOrderEndomorphisms` 7.1-5
`SingularPartitionMonoid` 7.3-1
`SingularPlanarModularPartitionMonoid` 7.3-10
`SingularPlanarPartitionMonoid` 7.3-9
`SingularPlanarUniformBlockBijectionMonoid` 7.3-8
`SingularTransformationMonoid` 7.1-4
`SingularTransformationSemigroup` 7.1-4
`SingularUniformBlockBijectionMonoid` 7.3-8
`SLM` 7.5-2
`SmallerDegreePartialPermRepresentation` 11.14-8
`SmallerDegreeTransformationRepresentation` 14.2-12
`SmallestElementSemigroup` 11.11-8
`SmallestIdempotentPower` 11.4-2
`SmallestMultiplicationTable` 14.2-2
`SmallGeneratingSet` 11.6-2
`SmallInverseMonoidGeneratingSet` 11.6-2
`SmallInverseSemigroupGeneratingSet` 11.6-2
`SmallMonoidGeneratingSet` 11.6-2
`SmallSemigroupGeneratingSet` 11.6-2
`Source`, for a graph inverse semigroup element 7.10-2
`SpecialLinearMonoid` 7.5-2
`SpectralRadius` 5.6-3
`SSSE` 8.3-2
`StandardiseWord` 15.1-3
`StandardizeWord` 15.1-3
`Star`, for a bipartition 3.2-6
for a PBR 4.5-1
`StarOp`, for a bipartition 3.2-6
for a PBR 4.5-1
`StringToWord`, for a string 15.1-4
`StrongSemilatticeOfSemigroups` 8.3-1
`StructureDescription`, for an H-class 10.4-6
`StructureDescriptionMaximalSubgroups` 10.4-4
`StructureDescriptionSchutzenbergerGroups` 10.4-3
`StzAddGenerator` 15.5-3
`StzAddRelation` 15.5-1
`StzIsomorphism` 15.6-3
`StzPresentation` 15.3-1
`StzPrintGenerators` 15.4-3
`StzPrintPresentation` 15.4-4
`StzPrintRelation` 15.4-2
`StzPrintRelations` 15.4-1
`StzRemoveGenerator` 15.5-4
`StzRemoveRelation` 15.5-2
`StzSimplifyOnce` 15.7-1
`StzSimplifyPresentation` 15.7-2
`StzSubstituteRelation` 15.5-5
`SubsemigroupByProperty`, for a semigroup and function 6.4-2
for a semigroup, function, and limit on the size of the subsemigroup 6.4-2
`Successors` 5.3-5
`SupersemigroupOfIdeal` 9.2-3
`TemperleyLiebMonoid` 7.3-3
`TexString` 16.2-1
`ThresholdNTPMatrix` 5.1-12
`ThresholdTropicalMatrix` 5.1-11
`TietzeBackwardMap` 15.6-2
`TietzeForwardMap` 15.6-1
`TikzLeftCayleyDigraph` 16.3-2
`TikzRightCayleyDigraph` 16.3-2
`TikzString` 16.3-1
`TraceOfSemigroupCongruence` 13.7-5
`TranslationalHull`, for IsSemigroup and CanUseFroidurePin and IsFinite 18.1-11
`TranslationalHullOfFamily`, for IsFamily 18.1-8
`TriangularBooleanMatMonoid` 7.6-6
`TrivialSemigroup` 7.8-1
`TypeBitranslations`, for IsBitranslationsSemigroup 18.1-9
`TypeLeftTranslationsSemigroupElements`, for IsLeftTranslationsSemigroup 18.1-9
`TypeRightTranslationsSemigroupElements`, for IsRightTranslationsSemigroup 18.1-9
`UnderlyingRepresentatives`, for IsTranslationsSemigroup 18.1-15
`UnderlyingSemigroup`, for IsBitranslationsSemigroup 18.1-7
for IsTranslationsSemigroup 18.1-7
`UnderlyingSemigroupOfCongruencePoset` 13.4-8
`UnderlyingSemigroupOfSemigroupWithAdjoinedZero` 11.7-4
`UniformBlockBijectionMonoid` 7.3-8
`UnitriangularBooleanMatMonoid` 7.6-6
`UniversalPBR` 4.2-5
`UniversalSemigroupCongruence` 13.10-3
`UnreducedFpSemigroup`, for a presentation 15.3-5
for a semigroup 15.8-3
`UnweightedPrecedenceDigraph` 5.6-4
`VagnerPrestonRepresentation` 11.14-9
`VerticesOfGraphInverseSemigroup` 7.10-8
`WordToString`, for a string and a list 15.1-1
`WreathProduct` 8.1-2
`WriteGenerators` 17.1-2
`WriteMultiplicationTable` 17.2-2
`ZeroSemigroup` 7.8-4

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