GAP (semigroups) - Index

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### Index

`*` (for bipartitions) 5.4
`<` (for bipartitions) 5.4
`=` (for bipartitions) 5.4
`\<`, for Green's classes 4.4-1
`AsBipartition` 5.3-1
`AsBipartitionSemigroup` 2.4-1
`AsBlockBijection` 5.3-2
`AsBlockBijectionSemigroup` 2.4-1
`AsLookupTable` 7.2-5
`AsPartialPerm`, for a bipartition 5.3-4
`AsPartialPermSemigroup` 2.4-1
`AsPermutation`, for a bipartition 5.3-5
`AsRMSCongruenceByLinkedTriple` 7.3-7
`AsRZMSCongruenceByLinkedTriple` 7.3-7
`AsSemigroupCongruenceByGeneratingPairs` 7.3-6
`AsTransformation`, for a bipartition 5.3-3
`AsTransformationSemigroup` 2.4-1
`Bipartition` 5.2-1
`BipartitionByIntRep` 5.2-2
`BipartitionFamily` 5.1-3
`BlocksNC` 5.6-1
`BrauerMonoid` 2.5-3
`CanonicalForm`, for a free inverse semigroup element 6.3-1
`CanonicalRepresentative` 7.3-5
`CharacterTableOfInverseSemigroup` 4.7-16
`ClosureInverseSemigroup` 2.2-1
`ClosureSemigroup` 2.2-2
`ComponentRepsOfPartialPermSemigroup` 4.5-19
`ComponentRepsOfTransformationSemigroup` 4.5-15
`ComponentsOfPartialPermSemigroup` 4.5-20
`ComponentsOfTransformationSemigroup` 4.5-16
`CongruenceClasses` 7.2-2
`CongruenceClassOfElement` 7.2-1
`CongruencesOfSemigroup` 7.2-4
`CyclesOfPartialPerm` 4.5-21
`CyclesOfPartialPermSemigroup` 4.5-22
`CyclesOfTransformationSemigroup` 4.5-17
`DClass` 4.2-2
`DClasses` 4.3-1
`DClassNC` 4.2-3
`DClassOfHClass` 4.2-1
`DClassOfLClass` 4.2-1
`DClassOfRClass` 4.2-1
`DClassReps` 4.3-4
`DegreeOfBipartition` 5.5-1
`DegreeOfBipartitionCollection` 5.5-1
`DegreeOfBipartitionSemigroup` 5.9-5
`DegreeOfBlocks` 5.6-4
`DotDClasses` 4.8-2
`DotDClasses`, for a semigroup 4.8-2
`DotSemilatticeOfIdempotents` 4.8-3
`DualSymmetricInverseMonoid` 2.5-6
`DualSymmetricInverseSemigroup` 2.5-6
`EndomorphismsPartition` 2.5-1
`EnumeratePosition` 9.1-1
`EvaluateWord` 4.1-1
`ExtRepOfBipartition` 5.5-3
`ExtRepOfBlocks` 5.6-2
`FactorisableDualSymmetricInverseSemigroup` 2.5-5
`Factorization` 4.1-2
`FreeBand`, for a given rank 6.4-1
`FreeBand`, for a list of names 6.4-1
`FreeBand`, for various names 6.4-1
`FreeInverseSemigroup`, for a given rank 6.1-1
`FreeInverseSemigroup`, for a list of names 6.1-1
`FreeInverseSemigroup`, for various names 6.1-1
`FullMatrixSemigroup` 2.5-8
`GeneralLinearSemigroup` 2.5-8
`Generators` 4.5-1
`GeneratorsOfSemigroupIdeal` 3.2-1
`GeneratorsSmallest`, for a transformation semigroup 4.5-25
`GreensDClasses` 4.3-1
`GreensDClassOfElement` 4.2-2
`GreensDClassOfElement`, for a free band and a free band element 6.5-1
`GreensDClassOfElementNC` 4.2-3
`GreensHClasses` 4.3-1
`GreensHClassOfElement` 4.2-2
`GreensHClassOfElement`, for a Rees matrix semigroup 4.2-2
`GreensHClassOfElementNC` 4.2-3
`GreensJClasses` 4.3-1
`GreensLClasses` 4.3-1
`GreensLClassOfElement` 4.2-2
`GreensLClassOfElementNC` 4.2-3
`GreensRClasses` 4.3-1
`GreensRClassOfElement` 4.2-2
`GreensRClassOfElementNC` 4.2-3
`GroupHClass` 4.2-4
`GroupOfUnits` 4.5-2
`HClass` 4.2-2
`HClass`, for a Rees matrix semigroup 4.2-2
`HClasses` 4.3-1
`HClassNC` 4.2-3
`HClassReps` 4.3-4
`IdempotentGeneratedSubsemigroup` 4.5-5
`Idempotents` 4.5-3
`IdentityBipartition` 5.2-3
`InfoSemigroups` 1.5-1
`InjectionPrincipalFactor` 4.4-2
`InverseLeftBlocks` 5.7-5
`InverseRightBlocks` 5.7-4
`InverseSubsemigroupByProperty` 2.2-4
`IrredundantGeneratingSubset` 4.5-6
`IsAperiodicSemigroup` 4.6-16
`IsBand` 4.6-1
`IsBipartition` 5.1-1
`IsBipartitionCollection` 5.1-2
`IsBipartitionMonoid` 5.9-1
`IsBipartitionSemigroup` 5.9-1
`IsBipartitionSemigroupGreensClass` 4.4-16
`IsBlockBijection` 5.5-13
`IsBlockBijectionMonoid` 5.9-2
`IsBlockBijectionSemigroup` 5.9-2
`IsBlockGroup` 4.6-2
`IsBrandtSemigroup` 4.7-2
`IsCliffordSemigroup` 4.7-1
`IsCombinatorialSemigroup` 4.6-16
`IsCommutativeSemigroup` 4.6-3
`IsCompletelyRegularSemigroup` 4.6-4
`IsCompletelySimpleSemigroup` 4.6-18
`IsCongruenceFreeSemigroup` 4.6-5
`IsDTrivial` 4.6-16
`IsDualTransBipartition` 5.5-10
`IsEUnitaryInverseSemigroup` 4.7-3
`IsFactorisableSemigroup` 4.7-4
`IsFreeBand`, for a given semigroup 6.4-3
`IsFreeBandCategory` 6.4-2
`IsFreeBandElement` 6.4-4
`IsFreeBandSubsemigroup` 6.4-5
`IsFreeInverseSemigroup` 6.1-3
`IsFreeInverseSemigroupCategory` 6.1-2
`IsFreeInverseSemigroupElement` 6.1-4
`IsFullMatrixSemigroup` 2.5-9
`IsGeneralLinearSemigroup` 2.5-9
`IsGreensClassNC` 4.4-14
`IsGreensDLeq` 4.4-19
`IsGroupAsSemigroup` 4.6-6
`IsHTrivial` 4.6-16
`IsIdempotentGenerated` 4.6-7
`IsIsomorphicSemigroup` 8.1-1
`IsJoinIrreducible` 4.7-5
`IsLeftSimple` 4.6-8
`IsLeftZeroSemigroup` 4.6-9
`IsLinkedTriple` 7.3-4
`IsLTrivial` 4.6-16
`IsMajorantlyClosed` 4.7-6
`IsMaximalSubsemigroup` 4.5-9
`IsMonogenicInverseSemigroup` 4.7-7
`IsMonogenicSemigroup` 4.6-10
`IsMonoidAsSemigroup` 4.6-11
`IsomorphismBipartitionMonoid` 2.4-3
`IsomorphismBipartitionSemigroup` 2.4-3
`IsomorphismBlockBijectionMonoid` 2.4-4
`IsomorphismBlockBijectionSemigroup` 2.4-4
`IsomorphismPermGroup` 2.4-2
`IsomorphismReesMatrixSemigroup` 4.4-2
`IsomorphismSemigroups` 8.1-3
`IsOrthodoxSemigroup` 4.6-12
`IsPartialPermBipartition` 5.5-12
`IsPartialPermBipartitionMonoid` 5.9-3
`IsPartialPermBipartitionSemigroup` 5.9-3
`IsPartialPermSemigroupGreensClass` 4.4-17
`IsPermBipartition` 5.5-11
`IsPermBipartitionGroup` 5.9-4
`IsRectangularBand` 4.6-13
`IsRegularClass` 4.4-4
`IsRegularSemigroup` 4.6-14
`IsRightSimple` 4.6-8
`IsRightZeroSemigroup` 4.6-15
`IsRMSCongruenceByLinkedTriple` 7.3-1
`IsRTrivial` 4.6-16
`IsRZMSCongruenceByLinkedTriple` 7.3-1
`IsSemiBand` 4.6-7
`IsSemigroupWithCommutingIdempotents` 4.6-2
`IsSemilatticeAsSemigroup` 4.6-17
`IsSimpleSemigroup` 4.6-18
`IsSynchronizingSemigroup` 4.6-19
`IsSynchronizingTransformationCollection` 4.6-19
`IsTransBipartition` 5.5-9
`IsTransformationSemigroupGreensClass` 4.4-15
`IsTransitive`, for a transformation semigroup and a pos int 4.5-18
`IsTransitive`, for a transformation semigroup and a set 4.5-18
`IsUniformBlockBijection` 5.5-14
`IsUniversalSemigroupCongruence` 7.4-1
`IsZeroGroup` 4.6-20
`IsZeroRectangularBand` 4.6-21
`IsZeroSemigroup` 4.6-22
`IsZeroSimpleSemigroup` 4.6-23
`IteratorFromGeneratorsFile` 1.6-4
`IteratorOfDClasses` 4.3-3
`IteratorOfDClassReps` 4.3-2
`IteratorOfHClasses` 4.3-3
`IteratorOfHClassReps` 4.3-2
`IteratorOfLClasses` 4.3-3
`IteratorOfLClassReps` 4.3-2
`IteratorOfRClasses` 4.3-3
`IteratorOfRClassReps` 4.3-2
`JClasses` 4.3-1
`JoinIrreducibleDClasses` 4.7-8
`JoinSemigroupCongruences` 7.3-9
`JonesMonoid` 2.5-4
`LargestElementSemigroup` 4.5-24
`LClass` 4.2-2
`LClasses` 4.3-1
`LClassNC` 4.2-3
`LClassOfHClass` 4.2-1
`LClassReps` 4.3-4
`LeftBlocks` 5.5-5
`LeftOne`, for a bipartition 5.2-4
`LeftProjection` 5.2-4
`LookForInOrb` 9.1-2
`MajorantClosure` 4.7-9
`MaximalDClasses` 4.4-10
`MaximalSubsemigroups`, for a Rees (0-)matrix semigroup, and a group 4.5-8
`MaximalSubsemigroups`, for an acting semigroup 4.5-7
`MeetSemigroupCongruences` 7.3-8
`MinimalDClass` 4.4-9
`MinimalIdeal` 4.5-10
`MinimalIdealGeneratingSet` 3.2-2
`MinimalWord`, for free inverse semigroup element 6.3-2
`Minorants` 4.7-10
`MonogenicSemigroup` 2.5-14
`MultiplicativeNeutralElement`, for an H-class 4.4-13
`MultiplicativeZero` 4.5-12
`MunnSemigroup` 2.5-10
`NaturalLeqBlockBijection` 5.4-3
`NaturalLeqPartialPermBipartition` 5.4-2
`Normalizer`, for a perm group, semigroup, record 4.5-23
`Normalizer`, for a semigroup, record 4.5-23
`NrBlocks`, for a bipartition 5.5-8
`NrBlocks`, for blocks 5.5-8
`NrCongruenceClasses` 7.2-3
`NrDClasses` 4.4-6
`NrHClasses` 4.4-6
`NrIdempotents` 4.5-4
`NrLClasses` 4.4-6
`NrLeftBlocks` 5.5-6
`NrRClasses` 4.4-6
`NrRegularDClasses` 4.4-5
`NrRightBlocks` 5.5-7
`NrTransverseBlocks`, for a bipartition 5.5-2
`NrTransverseBlocks`, for blocks 5.6-3
`OnLeftBlocks` 5.7-2
`OnRightBlocks` 5.7-1
`OnRightBlocksBipartitionByPerm` 5.4-5
`OrbSCC` 9.2-1
`OrbSCCLookup` 9.2-2
`OrbSCCTruthTable` 9.2-3
`OrderEndomorphisms`, monoid of order preserving transformations 2.5-11
`PartialOrderOfDClasses` 4.4-7
`PartialPermLeqBipartition` 5.4-1
`PartialTransformationSemigroup` 2.5-7
`PartitionMonoid` 2.5-2
`PermLeftBlocks` 5.7-3
`PermLeftQuoBipartition` 5.4-4
`PermRightBlocks` 5.7-3
`POI`, monoid of order preserving partial perms 2.5-11
`POPI`, monoid of orientation preserving partial perms 2.5-11
`PrimitiveIdempotents` 4.7-11
`PrincipalFactor` 4.4-3
`Random`, for a semigroup 4.5-13
`RandomBinaryRelationMonoid` 2.1-4
`RandomBinaryRelationSemigroup` 2.1-4
`RandomBipartition` 5.2-7
`RandomBipartitionMonoid` 2.1-5
`RandomBipartitionSemigroup` 2.1-5
`RandomInverseMonoid` 2.1-1
`RandomInverseSemigroup` 2.1-1
`RandomPartialPermMonoid` 2.1-3
`RandomPartialPermSemigroup` 2.1-3
`RandomTransformationMonoid` 2.1-2
`RandomTransformationSemigroup` 2.1-2
`RankOfBipartition` 5.5-2
`RankOfBlocks` 5.6-3
`RClass` 4.2-2
`RClasses` 4.3-1
`RClassNC` 4.2-3
`RClassOfHClass` 4.2-1
`RClassReps` 4.3-4
`ReadGenerators` 1.6-2
`RectangularBand` 2.5-15
`RegularBinaryRelationSemigroup` 2.5-13
`RegularDClasses` 4.4-5
`RepresentativeOfMinimalDClass` 4.5-11
`RepresentativeOfMinimalIdeal` 4.5-11
`ReverseSchreierTreeOfSCC` 9.2-4
`RightBlocks` 5.5-4
`RightCosetsOfInverseSemigroup` 4.7-12
`RightOne`, for a bipartition 5.2-5
`RightProjection` 5.2-5
`RMSCongruenceByLinkedTriple` 7.3-2
`RMSCongruenceClassByLinkedTriple` 7.3-3
`RZMSCongruenceByLinkedTriple` 7.3-2
`RZMSCongruenceClassByLinkedTriple` 7.3-3
`SameMinorantsSubgroup` 4.7-13
`SchreierTreeOfSCC` 9.2-5
`SchutzenbergerGroup` 4.4-8
`SemigroupCongruence` 7.1-1
`SemigroupIdeal` 3.1-1
Semigroups package overview 1.
`SemigroupsDir` 1.6-1
`SemigroupsMakeDoc` 1.3-1
`SemigroupsOptionsRec` 2.3-1
`SemigroupsTestAll` 1.4-3
`SemigroupsTestInstall` 1.4-1
`SemigroupsTestManualExamples` 1.4-2
`SingularBrauerMonoid` 2.5-3
`SingularDualSymmetricInverseSemigroup` 2.5-6
`SingularFactorisableDualSymmetricInverseSemigroup` 2.5-5
`SingularJonesMonoid` 2.5-4
`SingularPartitionMonoid` 2.5-2
`SingularTransformationMonoid` 2.5-12
`SingularTransformationSemigroup` 2.5-12
`SmallerDegreePartialPermRepresentation` 4.7-14
`SmallestElementSemigroup` 4.5-24
`SmallestMultiplicationTable` 8.1-2
`SmallGeneratingSet` 4.5-14
`SmallInverseMonoidGeneratingSet` 4.5-14
`SmallInverseSemigroupGeneratingSet` 4.5-14
`SmallMonoidGeneratingSet` 4.5-14
`SmallSemigroupGeneratingSet` 4.5-14
`Splash` 4.8-1
`Star` 5.2-6
`StarOp` 5.2-6
`StructureDescription`, for an H-class 4.4-18
`StructureDescriptionMaximalSubgroups` 4.4-12
`StructureDescriptionSchutzenbergerGroups` 4.4-11
`SubsemigroupByProperty`, for a semigroup and function 2.2-3
`SubsemigroupByProperty`, for a semigroup, function, and limit on the size of the subsemigroup 2.2-3
`SupersemigroupOfIdeal` 3.2-3
`TemperleyLiebMonoid` 2.5-4
`TikzBipartition` 5.8-1
`TikzBlocks` 5.8-2
`TraceSchreierTreeOfSCCBack` 9.2-6
`TraceSchreierTreeOfSCCForward` 9.2-7
`UniversalSemigroupCongruence` 7.4-2
`VagnerPrestonRepresentation` 4.7-15
`WriteGenerators` 1.6-3
`ZeroSemigroup` 2.5-16

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