| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/semigroups/doc/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 29.7.2025 mit Größe 72 kB |
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\GAPDocLabFile{semigroups}
\makelabel{semigroups:Title page}{}{X7D2C85EC87DD46E5} \makelabel{semigroups:Abstract}{}{X7AA6C5737B711C89} \makelabel{semigroups:Copyright}{}{X81488B807F2A1CF1} \makelabel{semigroups:Acknowledgements}{}{X82A988D47DFAFCFA} \makelabel{semigroups:Table of Contents}{}{X8537FEB07AF2BEC8} \makelabel{semigroups:The Semigroups package}{1}{X7D8D6DB37A0326BE} \makelabel{semigroups:Introduction}{1.1}{X7DFB63A97E67C0A1} \makelabel{semigroups:Overview}{1.2}{X8389AD927B74BA4A} \makelabel{semigroups:Installing Semigroups}{2}{X82398F3785F63754} \makelabel{semigroups:For those in a hurry}{2.1}{X7DA3059C79842BF3} \makelabel{semigroups:Compiling the kernel module}{2.2}{X849F6196875A6DF5} \makelabel{semigroups:Rebuilding the documentation}{2.3}{X857CBE5484CF703A} \makelabel{semigroups:Testing your installation}{2.4}{X7862D3F37C5BBDEF} \makelabel{semigroups:More information during a computation}{2.5}{X798CBC46800AB80F} \makelabel{semigroups:Bipartitions and blocks}{3}{X7C18DB427C9C0917} \makelabel{semigroups:The family and categories of bipartitions}{3.1}{X7850845886902F \makelabel{semigroups:Creating bipartitions}{3.2}{X85D77073820C7E72} \makelabel{semigroups:Changing the representation of a bipartition}{3.3}{X7C2C44D281A \makelabel{semigroups:Operators for bipartitions}{3.4}{X83F2C3C97E8FFA49} \makelabel{semigroups:Attributes for bipartitons}{3.5}{X87F3A304814797CE} \makelabel{semigroups:Creating blocks and their attributes}{3.6}{X87684C148592F831} \makelabel{semigroups:Actions on blocks}{3.7}{X7A45E0067F344683} \makelabel{semigroups:Semigroups of bipartitions}{3.8}{X876C963F830719E2} \makelabel{semigroups:Partitioned binary relations (PBRs)}{4}{X85A717D1790B7BB5} \makelabel{semigroups:The family and categories of PBRs}{4.1}{X7C40DA67826FF873} \makelabel{semigroups:Creating PBRs}{4.2}{X8758C4FB81D2C2A1} \makelabel{semigroups:Changing the representation of a PBR}{4.3}{X86B714987C01895F} \makelabel{semigroups:Operators for PBRs}{4.4}{X872B5817878660E5} 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\makelabel{semigroups:BLOCKSNC}{3.6.2}{X81302B217DCAAE6F} \makelabel{semigroups:ExtRepOfObj for a blocks}{3.6.3}{X7D2CB12279623CE2} \makelabel{semigroups:RankOfBlocks}{3.6.4}{X787D22AE7FA69239} \makelabel{semigroups:NrTransverseBlocks for blocks}{3.6.4}{X787D22AE7FA69239} \makelabel{semigroups:DegreeOfBlocks}{3.6.5}{X8527DC6A8771C2BE} \makelabel{semigroups:ProjectionFromBlocks}{3.6.6}{X815D99A983B2355F} \makelabel{semigroups:OnRightBlocks}{3.7.1}{X7B701DA37F75E77B} \makelabel{semigroups:OnLeftBlocks}{3.7.2}{X7A5A4AF57BEA2313} \makelabel{semigroups:IsBipartitionSemigroup}{3.8.1}{X810BFF647C4E191E} \makelabel{semigroups:IsBipartitionMonoid}{3.8.1}{X810BFF647C4E191E} \makelabel{semigroups:IsBlockBijectionSemigroup}{3.8.2}{X80C37124794636F3} \makelabel{semigroups:IsBlockBijectionMonoid}{3.8.2}{X80C37124794636F3} \makelabel{semigroups:IsPartialPermBipartitionSemigroup}{3.8.3}{X79A706A582ABE55 \makelabel{semigroups:IsPartialPermBipartitionMonoid}{3.8.3}{X79A706A582ABE558} \makelabel{semigroups:IsPermBipartitionGroup}{3.8.4}{X7DEE07577D7379AC} \makelabel{semigroups:DegreeOfBipartitionSemigroup}{3.8.5}{X8162E2BB7CF144F5} \makelabel{semigroups:IsPBR}{4.1.1}{X82CCBADC80AE2D15} \makelabel{semigroups:IsPBRCollection}{4.1.2}{X854A9CEA7AC14C0A} \makelabel{semigroups:IsPBRCollColl}{4.1.2}{X854A9CEA7AC14C0A} \makelabel{semigroups:PBR}{4.2.1}{X82A8646F7C70CF3B} \makelabel{semigroups:RandomPBR}{4.2.2}{X82FE736F7F11B157} \makelabel{semigroups:EmptyPBR}{4.2.3}{X8646781B7EAE04C0} \makelabel{semigroups:IdentityPBR}{4.2.4}{X80D20EA3816DC862} \makelabel{semigroups:UniversalPBR}{4.2.5}{X847BA0177D90E9D7} \makelabel{semigroups:AsPBR}{4.3.1}{X81CBBE6080439596} \makelabel{semigroups:AsTransformation for a PBR}{4.3.2}{X8407F516825A514A} \makelabel{semigroups:AsPartialPerm for a PBR}{4.3.3}{X795B1C16819905E8} \makelabel{semigroups:AsPermutation for a PBR}{4.3.4}{X86786B297FBCD064} \makelabel{semigroups:< (for PBRs)}{4.4}{X872B5817878660E5} \makelabel{semigroups:StarOp for a PBR}{4.5.1}{X7DFC277E80A50C2F} \makelabel{semigroups:Star for a PBR}{4.5.1}{X7DFC277E80A50C2F} \makelabel{semigroups:DegreeOfPBR}{4.5.2}{X785B576B7823D626} \makelabel{semigroups:DegreeOfPBRCollection}{4.5.2}{X785B576B7823D626} \makelabel{semigroups:ExtRepOfObj for a PBR}{4.5.3}{X78302D7E81BB1E54} \makelabel{semigroups:PBRNumber}{4.5.4}{X7F4C8A2B79E6D963} \makelabel{semigroups:NumberPBR}{4.5.4}{X7F4C8A2B79E6D963} \makelabel{semigroups:IsEmptyPBR}{4.5.5}{X82FD0AB179ED4AFD} \makelabel{semigroups:IsIdentityPBR}{4.5.6}{X7E263B2F7B838D6E} \makelabel{semigroups:IsUniversalPBR}{4.5.7}{X7A280FC27BAD0EF0} \makelabel{semigroups:IsBipartitionPBR}{4.5.8}{X81EC86397E098BC8} \makelabel{semigroups:IsBlockBijectionPBR}{4.5.8}{X81EC86397E098BC8} \makelabel{semigroups:IsTransformationPBR}{4.5.9}{X7AF425D17BBE9023} \makelabel{semigroups:IsDualTransformationPBR}{4.5.10}{X7962D03186B1AFDF} \makelabel{semigroups:IsPartialPermPBR}{4.5.11}{X7883CD5D824CC236} \makelabel{semigroups:IsPermPBR}{4.5.12}{X85B21BB0835FE166} \makelabel{semigroups:IsPBRSemigroup}{4.6.1}{X8554A3F878A4DC73} \makelabel{semigroups:IsPBRMonoid}{4.6.1}{X8554A3F878A4DC73} \makelabel{semigroups:DegreeOfPBRSemigroup}{4.6.2}{X80FC004C7B65B4C0} \makelabel{semigroups:IsMatrixOverSemiring}{5.1.1}{X8711618C7A8A1B60} \makelabel{semigroups:IsMatrixOverSemiringCollection}{5.1.2}{X86F696B883677D6B} \makelabel{semigroups:IsMatrixOverSemiringCollColl}{5.1.2}{X86F696B883677D6B} \makelabel{semigroups:DimensionOfMatrixOverSemiring}{5.1.3}{X7C1CDA817CE076FD} \makelabel{semigroups:DimensionOfMatrixOverSemiringCollection}{5.1.4}{X7FF0B2A78 \makelabel{semigroups:Matrix for a filter and a matrix}{5.1.5}{X7DCA234C86ED8BD3} \makelabel{semigroups:Matrix for a semiring and a matrix}{5.1.5}{X7DCA234C86ED8BD3} \makelabel{semigroups:AsMatrix for a filter and a matrix}{5.1.6}{X85426D8885431ECE} \makelabel{semigroups:AsMatrix for a filter, matrix, and threshold}{5.1.6}{X85426D8885 \makelabel{semigroups:AsMatrix for a filter, matrix, threshold, and period}{5.1.6}{X854 \makelabel{semigroups:RandomMatrix for a filter and a matrix}{5.1.7}{X82172D747D66C8CC \makelabel{semigroups:RandomMatrix for a semiring and a matrix}{5.1.7}{X82172D747D66C8 \makelabel{semigroups:IsBooleanMat}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsMatrixOverFiniteField}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsMaxPlusMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsMinPlusMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsTropicalMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsTropicalMaxPlusMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsTropicalMinPlusMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsNTPMatrix}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:Integers}{5.1.8}{X782480C686F1A663} \makelabel{semigroups:IsBooleanMatCollection}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsBooleanMatCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsMatrixOverFiniteFieldCollection}{5.1.9}{X86233A3E8651249 \makelabel{semigroups:IsMatrixOverFiniteFieldCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsMaxPlusMatrixCollection}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsMaxPlusMatrixCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsMinPlusMatrixCollection}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsMinPlusMatrixCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsTropicalMatrixCollection}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsTropicalMaxPlusMatrixCollection}{5.1.9}{X86233A3E8651249 \makelabel{semigroups:IsTropicalMaxPlusMatrixCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsTropicalMinPlusMatrixCollection}{5.1.9}{X86233A3E8651249 \makelabel{semigroups:IsTropicalMinPlusMatrixCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsNTPMatrixCollection}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:IsNTPMatrixCollColl}{5.1.9}{X86233A3E86512493} \makelabel{semigroups:AsList}{5.1.10}{X8289FCCC8274C89D} \makelabel{semigroups:AsMutableList}{5.1.10}{X8289FCCC8274C89D} \makelabel{semigroups:ThresholdTropicalMatrix}{5.1.11}{X7D21408E845E4648} \makelabel{semigroups:ThresholdNTPMatrix}{5.1.12}{X7874559881FE8779} \makelabel{semigroups:PeriodNTPMatrix}{5.1.12}{X7874559881FE8779} \makelabel{semigroups:< (for matrices over a semiring)}{5.2}{X807E402687741CDA} \makelabel{semigroups:BooleanMat}{5.3.1}{X84A16D4D7D015885} \makelabel{semigroups:AsBooleanMat}{5.3.2}{X7DA524567E0E7E16} \makelabel{semigroups:OnBlist}{5.3.4}{X8629FA5F7B682078} \makelabel{semigroups:Successors}{5.3.5}{X85E2FD8B82652876} \makelabel{semigroups:BooleanMatNumber}{5.3.6}{X7E0FD5878106AB66} \makelabel{semigroups:NumberBooleanMat}{5.3.6}{X7E0FD5878106AB66} \makelabel{semigroups:BlistNumber}{5.3.7}{X793A1C277C1D7D6D} \makelabel{semigroups:NumberBlist}{5.3.7}{X793A1C277C1D7D6D} \makelabel{semigroups:CanonicalBooleanMat for a perm group, perm group and boolean matrix \makelabel{semigroups:CanonicalBooleanMat for a perm group and boolean matrix}{5.3.8}{X \makelabel{semigroups:CanonicalBooleanMat}{5.3.8}{X7EEA5011862E6298} \makelabel{semigroups:IsRowTrimBooleanMat}{5.3.9}{X794C91597CC9F784} \makelabel{semigroups:IsColTrimBooleanMat}{5.3.9}{X794C91597CC9F784} \makelabel{semigroups:IsTrimBooleanMat}{5.3.9}{X794C91597CC9F784} \makelabel{semigroups:IsSymmetricBooleanMat}{5.3.10}{X7D22BA78790EFBC6} \makelabel{semigroups:IsReflexiveBooleanMat}{5.3.11}{X7C373B7D87044050} \makelabel{semigroups:IsTransitiveBooleanMat}{5.3.12}{X7CDAD39B856AC3E5} \makelabel{semigroups:IsAntiSymmetricBooleanMat}{5.3.13}{X8570C8A08549383D} \makelabel{semigroups:IsTotalBooleanMat}{5.3.14}{X7A68D87982A07C6F} \makelabel{semigroups:IsOntoBooleanMat}{5.3.14}{X7A68D87982A07C6F} \makelabel{semigroups:IsPartialOrderBooleanMat}{5.3.15}{X7D9BECEA7E9B72A7} \makelabel{semigroups:IsEquivalenceBooleanMat}{5.3.16}{X82EA957982B79827} \makelabel{semigroups:IsTransformationBooleanMat}{5.3.17}{X7E6B588887D34A0A} \makelabel{semigroups:RowSpaceBasis for a matrix over finite field}{5.4.1}{X857E626783 \makelabel{semigroups:RowSpaceTransformation for a matrix over finite field}{5.4.1}{X8 \makelabel{semigroups:RowSpaceTransformationInv for a matrix over finite field}{5.4.1} \makelabel{semigroups:RightInverse for a matrix over finite field}{5.4.2}{X8733B04781B \makelabel{semigroups:LeftInverse for a matrix over finite field}{5.4.2}{X8733B04781B6 \makelabel{semigroups:InverseOp for an integer matrix}{5.5.1}{X7BC66ECE8378068E} \makelabel{semigroups:IsTorsion for an integer matrix}{5.5.2}{X7CA636F080777C36} \makelabel{semigroups:Order}{5.5.3}{X84F59A2687C62763} \makelabel{semigroups:InverseOp}{5.6.1}{X82EC4F49877D6EB1} \makelabel{semigroups:RadialEigenvector}{5.6.2}{X83663A5387042B69} \makelabel{semigroups:SpectralRadius}{5.6.3}{X83FCFB368743E4BA} \makelabel{semigroups:UnweightedPrecedenceDigraph}{5.6.4}{X869F60527C2B9328} \makelabel{semigroups:IsMatrixOverSemiringSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsBooleanMatSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsMatrixOverFiniteFieldSemigroup}{5.7.1}{X7DC6EB0680B3E4DD \makelabel{semigroups:IsMaxPlusMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsMinPlusMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsTropicalMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsTropicalMaxPlusMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD \makelabel{semigroups:IsTropicalMinPlusMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD \makelabel{semigroups:IsNTPMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsIntegerMatrixSemigroup}{5.7.1}{X7DC6EB0680B3E4DD} \makelabel{semigroups:IsMatrixOverSemiringMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsBooleanMatMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsMatrixOverFiniteFieldMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsMaxPlusMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsMinPlusMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsTropicalMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsTropicalMaxPlusMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsTropicalMinPlusMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsNTPMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsIntegerMatrixMonoid}{5.7.2}{X8616225581BC7414} \makelabel{semigroups:IsFinite}{5.7.3}{X808A4061809A6E67} \makelabel{semigroups:IsTorsion}{5.7.4}{X80C6B26284721409} \makelabel{semigroups:NormalizeSemigroup}{5.7.5}{X873DE466868DA849} \makelabel{semigroups:IsActingSemigroup}{6.1.2}{X7F69D8FC7D578A0C} \makelabel{semigroups:CanUseFroidurePin}{6.1.4}{X7FEE8CFA87E7B872} \makelabel{semigroups:CanUseGapFroidurePin}{6.1.4}{X7FEE8CFA87E7B872} \makelabel{semigroups:CanUseLibsemigroupsFroidurePin}{6.1.4}{X7FEE8CFA87E7B872} \makelabel{semigroups:InverseMonoidByGenerators}{6.2.1}{X79A15C7C83BBA60B} \makelabel{semigroups:InverseSemigroupByGenerators}{6.2.1}{X79A15C7C83BBA60B} \makelabel{semigroups:SEMIGROUPS.DefaultOptionsRec}{6.3.1}{X78CF5DCC7C697BB3} \makelabel{semigroups:ClosureSemigroup}{6.4.1}{X7BE36790862AE26F} \makelabel{semigroups:ClosureMonoid}{6.4.1}{X7BE36790862AE26F} \makelabel{semigroups:ClosureInverseSemigroup}{6.4.1}{X7BE36790862AE26F} \makelabel{semigroups:ClosureInverseMonoid}{6.4.1}{X7BE36790862AE26F} \makelabel{semigroups:SubsemigroupByProperty for a semigroup and function}{6.4.2}{X7E \makelabel{semigroups:SubsemigroupByProperty for a semigroup, function, and limit on the \makelabel{semigroups:InverseSubsemigroupByProperty}{6.4.3}{X832AEDCC7BA9E5F5} \makelabel{semigroups:IsomorphismSemigroup}{6.5.1}{X838F18E87F765697} \makelabel{semigroups:IsomorphismMonoid}{6.5.2}{X83D03BE678C9974F} \makelabel{semigroups:AsSemigroup}{6.5.3}{X80ED104F85AE5134} \makelabel{semigroups:AsMonoid}{6.5.4}{X7B22038F832B9C0F} \makelabel{semigroups:IsomorphismPermGroup}{6.5.5}{X80B7B1C783AA1567} \makelabel{semigroups:RZMSNormalization}{6.5.6}{X870210EA7912B52A} \makelabel{semigroups:RMSNormalization}{6.5.7}{X80DE617E841E5BA0} \makelabel{semigroups:IsomorphismReesMatrixSemigroup for a semigroup}{6.5.8}{X7E2EC \makelabel{semigroups:IsomorphismReesZeroMatrixSemigroup}{6.5.8}{X7E2ECC577A1CF7 \makelabel{semigroups:IsomorphismReesMatrixSemigroupOverPermGroup}{6.5.8}{X7E2EC \makelabel{semigroups:IsomorphismReesZeroMatrixSemigroupOverPermGroup}{6.5.8}{X7 \makelabel{semigroups:AntiIsomorphismDualFpSemigroup}{6.5.9}{X820BB66381737F2D} \makelabel{semigroups:AntiIsomorphismDualFpMonoid}{6.5.9}{X820BB66381737F2D} \makelabel{semigroups:EmbeddingFpMonoid}{6.5.10}{X7873016586653A44} \makelabel{semigroups:RandomSemigroup}{6.6.1}{X789DE9AB79FCFEB5} \makelabel{semigroups:RandomMonoid}{6.6.1}{X789DE9AB79FCFEB5} \makelabel{semigroups:RandomInverseSemigroup}{6.6.1}{X789DE9AB79FCFEB5} \makelabel{semigroups:RandomInverseMonoid}{6.6.1}{X789DE9AB79FCFEB5} \makelabel{semigroups:CatalanMonoid}{7.1.1}{X84C4C81380B0239D} \makelabel{semigroups:EndomorphismsPartition}{7.1.2}{X85C1D4307D0F5FF7} \makelabel{semigroups:PartialTransformationMonoid}{7.1.3}{X808A27F87E5AC598} \makelabel{semigroups:SingularTransformationSemigroup}{7.1.4}{X7894EE357D103806} \makelabel{semigroups:SingularTransformationMonoid}{7.1.4}{X7894EE357D103806} \makelabel{semigroups:OrderEndomorphisms monoid of order preserving transformations}{ \makelabel{semigroups:SingularOrderEndomorphisms}{7.1.5}{X80E80A0A83B57483} \makelabel{semigroups:OrderAntiEndomorphisms}{7.1.5}{X80E80A0A83B57483} \makelabel{semigroups:PartialOrderEndomorphisms}{7.1.5}{X80E80A0A83B57483} \makelabel{semigroups:PartialOrderAntiEndomorphisms}{7.1.5}{X80E80A0A83B57483} \makelabel{semigroups:EndomorphismMonoid for a digraph}{7.1.6}{X868955247F2AFAA5} \makelabel{semigroups:EndomorphismMonoid for a digraph and vertex coloring}{7.1.6}{X86 \makelabel{semigroups:MunnSemigroup}{7.2.1}{X78FBE6DD7BCA30C1} \makelabel{semigroups:RookMonoid}{7.2.2}{X82D9619B7845CAEB} \makelabel{semigroups:POI monoid of order preserving partial perms}{7.2.3}{X85D841AE83 \makelabel{semigroups:PODI monoid of order preserving or reversing partial perms}{7.2.3} \makelabel{semigroups:POPI monoid of orientation preserving partial perms}{7.2.3}{X85D \makelabel{semigroups:PORI monoid of orientation preserving or reversing partial perms}{ \makelabel{semigroups:PartitionMonoid}{7.3.1}{X7E4B61FF7CCFD74A} \makelabel{semigroups:RookPartitionMonoid}{7.3.1}{X7E4B61FF7CCFD74A} \makelabel{semigroups:SingularPartitionMonoid}{7.3.1}{X7E4B61FF7CCFD74A} \makelabel{semigroups:BrauerMonoid}{7.3.2}{X79D33B2E7BA3073A} \makelabel{semigroups:PartialBrauerMonoid}{7.3.2}{X79D33B2E7BA3073A} \makelabel{semigroups:SingularBrauerMonoid}{7.3.2}{X79D33B2E7BA3073A} \makelabel{semigroups:JonesMonoid}{7.3.3}{X8378FC8B840B9706} \makelabel{semigroups:TemperleyLiebMonoid}{7.3.3}{X8378FC8B840B9706} \makelabel{semigroups:SingularJonesMonoid}{7.3.3}{X8378FC8B840B9706} \makelabel{semigroups:PartialJonesMonoid}{7.3.4}{X8458B0F7874484CE} \makelabel{semigroups:AnnularJonesMonoid}{7.3.5}{X7DB8CB067CBE1254} \makelabel{semigroups:MotzkinMonoid}{7.3.6}{X8375152F7AB52B7B} \makelabel{semigroups:DualSymmetricInverseSemigroup}{7.3.7}{X83C7587C81B985BA} \makelabel{semigroups:DualSymmetricInverseMonoid}{7.3.7}{X83C7587C81B985BA} \makelabel{semigroups:SingularDualSymmetricInverseMonoid}{7.3.7}{X83C7587C81B985 \makelabel{semigroups:PartialDualSymmetricInverseMonoid}{7.3.7}{X83C7587C81B985B \makelabel{semigroups:UniformBlockBijectionMonoid}{7.3.8}{X8301C61384168D6F} \makelabel{semigroups:FactorisableDualSymmetricInverseMonoid}{7.3.8}{X8301C61384 \makelabel{semigroups:SingularUniformBlockBijectionMonoid}{7.3.8}{X8301C61384168 \makelabel{semigroups:PartialUniformBlockBijectionMonoid}{7.3.8}{X8301C61384168D \makelabel{semigroups:SingularFactorisableDualSymmetricInverseMonoid}{7.3.8}{X83 \makelabel{semigroups:PlanarUniformBlockBijectionMonoid}{7.3.8}{X8301C61384168D6 \makelabel{semigroups:SingularPlanarUniformBlockBijectionMonoid}{7.3.8}{X8301C61 \makelabel{semigroups:PlanarPartitionMonoid}{7.3.9}{X8444092A7967A029} \makelabel{semigroups:SingularPlanarPartitionMonoid}{7.3.9}{X8444092A7967A029} \makelabel{semigroups:ModularPartitionMonoid}{7.3.10}{X7F208DC584C0B9D1} \makelabel{semigroups:SingularModularPartitionMonoid}{7.3.10}{X7F208DC584C0B9D1} \makelabel{semigroups:PlanarModularPartitionMonoid}{7.3.10}{X7F208DC584C0B9D1} \makelabel{semigroups:SingularPlanarModularPartitionMonoid}{7.3.10}{X7F208DC584C \makelabel{semigroups:ApsisMonoid}{7.3.11}{X7C82B25F8441928E} \makelabel{semigroups:SingularApsisMonoid}{7.3.11}{X7C82B25F8441928E} \makelabel{semigroups:CrossedApsisMonoid}{7.3.11}{X7C82B25F8441928E} \makelabel{semigroups:SingularCrossedApsisMonoid}{7.3.11}{X7C82B25F8441928E} \makelabel{semigroups:FullPBRMonoid}{7.4.1}{X7DBB30AA83663CE8} \makelabel{semigroups:FullMatrixMonoid}{7.5.1}{X7D4B473A7D7735E3} \makelabel{semigroups:GeneralLinearMonoid}{7.5.1}{X7D4B473A7D7735E3} \makelabel{semigroups:GLM}{7.5.1}{X7D4B473A7D7735E3} \makelabel{semigroups:SpecialLinearMonoid}{7.5.2}{X785924807B60F187} \makelabel{semigroups:SLM}{7.5.2}{X785924807B60F187} \makelabel{semigroups:IsFullMatrixMonoid}{7.5.3}{X860B2A4382CA8F87} \makelabel{semigroups:IsGeneralLinearMonoid}{7.5.3}{X860B2A4382CA8F87} \makelabel{semigroups:FullBooleanMatMonoid}{7.6.1}{X7B20103D84E010EF} \makelabel{semigroups:RegularBooleanMatMonoid}{7.6.2}{X7A43263981F2F2AF} \makelabel{semigroups:ReflexiveBooleanMatMonoid}{7.6.3}{X78DF50747A28098C} \makelabel{semigroups:HallMonoid}{7.6.4}{X79EF0EA68782CFCA} \makelabel{semigroups:GossipMonoid}{7.6.5}{X7F083600787C78FF} \makelabel{semigroups:TriangularBooleanMatMonoid}{7.6.6}{X81BBCF2E84239521} \makelabel{semigroups:UnitriangularBooleanMatMonoid}{7.6.6}{X81BBCF2E84239521} \makelabel{semigroups:FullTropicalMaxPlusMonoid}{7.7.1}{X81E937B6852A9C69} \makelabel{semigroups:FullTropicalMinPlusMonoid}{7.7.2}{X85EDC03180768931} \makelabel{semigroups:TrivialSemigroup}{7.8.1}{X82B07E907B3A55F0} \makelabel{semigroups:MonogenicSemigroup}{7.8.2}{X8411EBD97A220921} \makelabel{semigroups:RectangularBand}{7.8.3}{X7E4DFDE27BF8B8F7} \makelabel{semigroups:FreeSemilattice}{7.8.4}{X7982E0667ECEB265} \makelabel{semigroups:ZeroSemigroup}{7.8.5}{X801FC1D97D832A6F} \makelabel{semigroups:LeftZeroSemigroup}{7.8.6}{X8672CFA47CA620B2} \makelabel{semigroups:RightZeroSemigroup}{7.8.6}{X8672CFA47CA620B2} \makelabel{semigroups:BrandtSemigroup}{7.8.7}{X7E2B20C77D47F7FB} \makelabel{semigroups:FreeBand for a given rank}{7.9.1}{X7B2A65F382DB36EC} \makelabel{semigroups:FreeBand for a list of names}{7.9.1}{X7B2A65F382DB36EC} \makelabel{semigroups:FreeBand for various names}{7.9.1}{X7B2A65F382DB36EC} \makelabel{semigroups:IsFreeBandCategory}{7.9.2}{X7F5658DC7E56C4A6} \makelabel{semigroups:IsFreeBand for a given semigroup}{7.9.3}{X7B1CD5FC7E034B88} \makelabel{semigroups:IsFreeBandElement}{7.9.4}{X7DECF69087BB3B16} \makelabel{semigroups:IsFreeBandElementCollection}{7.9.5}{X842839C87DAAA43C} \makelabel{semigroups:IsFreeBandSubsemigroup}{7.9.6}{X7AEF4CD1857E7DCC} \makelabel{semigroups:ContentOfFreeBandElement}{7.9.7}{X808CAEC17BF271D1} \makelabel{semigroups:ContentOfFreeBandElementCollection}{7.9.7}{X808CAEC17BF271 \makelabel{semigroups:EqualInFreeBand}{7.9.8}{X7CD9426180587CA4} \makelabel{semigroups:GreensDClassOfElement for a free band and element}{7.9.9}{X85DC5 \makelabel{semigroups:GraphInverseSemigroup}{7.10.1}{X7A9EEFD386D6F630} \makelabel{semigroups:Range for a graph inverse semigroup element}{7.10.2}{X8187F0FF78 \makelabel{semigroups:Source for a graph inverse semigroup element}{7.10.2}{X8187F0FF7 \makelabel{semigroups:IsVertex for a graph inverse semigroup element}{7.10.3}{X7DEE927 \makelabel{semigroups:IsGraphInverseSemigroup}{7.10.4}{X7BFDF88B799B05A0} \makelabel{semigroups:IsGraphInverseSemigroupElement}{7.10.4}{X7BFDF88B799B05A0} \makelabel{semigroups:GraphOfGraphInverseSemigroup}{7.10.5}{X7BE287A385A058BC} \makelabel{semigroups:IsGraphInverseSemigroupElementCollection}{7.10.6}{X870128E \makelabel{semigroups:IsGraphInverseSubsemigroup}{7.10.7}{X7BC6D5107ED09DBA} \makelabel{semigroups:VerticesOfGraphInverseSemigroup}{7.10.8}{X7DF1ACC27CC998EB \makelabel{semigroups:IndexOfVertexOfGraphInverseSemigroup}{7.10.9}{X87500BC7822 \makelabel{semigroups:FreeInverseSemigroup for a given rank}{7.11.1}{X7F3F9DED8003CB \makelabel{semigroups:FreeInverseSemigroup for a list of names}{7.11.1}{X7F3F9DED8003 \makelabel{semigroups:FreeInverseSemigroup for various names}{7.11.1}{X7F3F9DED8003 \makelabel{semigroups:IsFreeInverseSemigroupCategory}{7.11.2}{X7CE4CFD886220179} \makelabel{semigroups:IsFreeInverseSemigroup}{7.11.3}{X7B91643B827DA6DB} \makelabel{semigroups:IsFreeInverseSemigroupElement}{7.11.4}{X7999FE0286283CC2} \makelabel{semigroups:IsFreeInverseSemigroupElementCollection}{7.11.5}{X813A2917 \makelabel{semigroups:CanonicalForm for a free inverse semigroup element}{7.11.6}{X7DB \makelabel{semigroups:MinimalWord for free inverse semigroup element}{7.11.7}{X87BB5D \makelabel{semigroups:DirectProduct}{8.1.1}{X861BA02C7902A4F4} \makelabel{semigroups:DirectProductOp}{8.1.1}{X861BA02C7902A4F4} \makelabel{semigroups:WreathProduct}{8.1.2}{X8786EFBC78D7D6ED} \makelabel{semigroups:DualSemigroup}{8.2.1}{X79F2643C8642A3B0} \makelabel{semigroups:IsDualSemigroupRep}{8.2.2}{X83403224821CD079} \makelabel{semigroups:IsDualSemigroupElement}{8.2.3}{X79BAAA397FC1FA2E} \makelabel{semigroups:AntiIsomorphismDualSemigroup}{8.2.4}{X7CB64FA378EC715B} \makelabel{semigroups:StrongSemilatticeOfSemigroups}{8.3.1}{X82C3F9C9861EEDFE} \makelabel{semigroups:SSSE}{8.3.2}{X798DE3E581978834} \makelabel{semigroups:IsSSSE}{8.3.3}{X7B7B70F37C9C3836} \makelabel{semigroups:IsStrongSemilatticeOfSemigroups}{8.3.4}{X838F24247D4DBE18} \makelabel{semigroups:SemilatticeOfStrongSemilatticeOfSemigroups}{8.3.5}{X87100C \makelabel{semigroups:SemigroupsOfStrongSemilatticeOfSemigroups}{8.3.6}{X79E6C08 \makelabel{semigroups:HomomorphismsOfStrongSemilatticeOfSemigroups}{8.3.7}{X8066 \makelabel{semigroups:IsMcAlisterTripleSemigroup}{8.4.1}{X85C00EB085774624} \makelabel{semigroups:McAlisterTripleSemigroup}{8.4.2}{X7B5FF3A27BB057F2} \makelabel{semigroups:McAlisterTripleSemigroupGroup}{8.4.3}{X7A54FDB186CD2E94} \makelabel{semigroups:McAlisterTripleSemigroupPartialOrder}{8.4.4}{X8046966B7F9A \makelabel{semigroups:McAlisterTripleSemigroupSemilattice}{8.4.5}{X86C0C3EF84517 \makelabel{semigroups:McAlisterTripleSemigroupAction}{8.4.6}{X86D6442E85881DEA} \makelabel{semigroups:IsMcAlisterTripleSemigroupElement}{8.4.7}{X7B4EC9FC82249A8 \makelabel{semigroups:IsMTSE}{8.4.7}{X7B4EC9FC82249A83} \makelabel{semigroups:McAlisterTripleSemigroupElement}{8.4.8}{X854BFB1C7BA57985} \makelabel{semigroups:MTSE}{8.4.8}{X854BFB1C7BA57985} \makelabel{semigroups:SemigroupIdeal}{9.1.1}{X78E15B0184A1DC14} \makelabel{semigroups:Ideals for a semigroup}{9.1.2}{X7AF9B33881D185C6} \makelabel{semigroups:GeneratorsOfSemigroupIdeal}{9.2.1}{X87BB45DB844D41BC} \makelabel{semigroups:MinimalIdealGeneratingSet}{9.2.2}{X8777E71A82C2BAF9} \makelabel{semigroups:SupersemigroupOfIdeal}{9.2.3}{X7DB8699784FA4114} \makelabel{semigroups:DClassOfHClass}{10.1.1}{X87558FEF805D24E1} \makelabel{semigroups:DClassOfLClass}{10.1.1}{X87558FEF805D24E1} \makelabel{semigroups:DClassOfRClass}{10.1.1}{X87558FEF805D24E1} \makelabel{semigroups:LClassOfHClass}{10.1.1}{X87558FEF805D24E1} \makelabel{semigroups:RClassOfHClass}{10.1.1}{X87558FEF805D24E1} \makelabel{semigroups:GreensDClassOfElement}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:DClass}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:GreensHClassOfElement}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:GreensHClassOfElement for a Rees matrix semigroup}{10.1.2}{X81B \makelabel{semigroups:HClass}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:HClass for a Rees matrix semigroup}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:GreensLClassOfElement}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:LClass}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:GreensRClassOfElement}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:RClass}{10.1.2}{X81B7AD4C7C552867} \makelabel{semigroups:GreensDClassOfElementNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:DClassNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:GreensHClassOfElementNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:HClassNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:GreensLClassOfElementNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:LClassNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:GreensRClassOfElementNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:RClassNC}{10.1.3}{X7B44317786571F8B} \makelabel{semigroups:GreensDClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:DClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:GreensHClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:HClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:GreensJClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:JClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:GreensLClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:LClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:GreensRClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:RClasses}{10.1.4}{X7D51218A80234DE5} \makelabel{semigroups:DClassReps}{10.1.5}{X865387A87FAAC395} \makelabel{semigroups:HClassReps}{10.1.5}{X865387A87FAAC395} \makelabel{semigroups:LClassReps}{10.1.5}{X865387A87FAAC395} \makelabel{semigroups:RClassReps}{10.1.5}{X865387A87FAAC395} \makelabel{semigroups:MinimalDClass}{10.1.6}{X81E5A04F7DA3A1E1} \makelabel{semigroups:MaximalDClasses}{10.1.7}{X834172F4787A565B} \makelabel{semigroups:MaximalLClasses}{10.1.7}{X834172F4787A565B} \makelabel{semigroups:MaximalRClasses}{10.1.7}{X834172F4787A565B} \makelabel{semigroups:NrRegularDClasses}{10.1.8}{X7AA3F0A77D0043FB} \makelabel{semigroups:RegularDClasses}{10.1.8}{X7AA3F0A77D0043FB} \makelabel{semigroups:NrDClasses}{10.1.9}{X7E45FD9F7BADDFBD} \makelabel{semigroups:NrHClasses}{10.1.9}{X7E45FD9F7BADDFBD} \makelabel{semigroups:NrLClasses}{10.1.9}{X7E45FD9F7BADDFBD} \makelabel{semigroups:NrRClasses}{10.1.9}{X7E45FD9F7BADDFBD} \makelabel{semigroups:PartialOrderOfDClasses}{10.1.10}{X8140814084748101} \makelabel{semigroups:PartialOrderOfLClasses}{10.1.10}{X8140814084748101} \makelabel{semigroups:PartialOrderOfRClasses}{10.1.10}{X8140814084748101} \makelabel{semigroups:LengthOfLongestDClassChain}{10.1.11}{X83B0EDA57F1D2F97} \makelabel{semigroups:IsGreensDGreaterThanFunc}{10.1.12}{X7E872C5381D0DD8A} \makelabel{semigroups:IteratorOfDClassReps}{10.2.1}{X8566F84A7F6D4193} \makelabel{semigroups:IteratorOfHClassReps}{10.2.1}{X8566F84A7F6D4193} \makelabel{semigroups:IteratorOfLClassReps}{10.2.1}{X8566F84A7F6D4193} \makelabel{semigroups:IteratorOfDClasses}{10.2.2}{X867D7B8982915960} \makelabel{semigroups:IteratorOfRClasses}{10.2.2}{X867D7B8982915960} \makelabel{semigroups:IsRegularGreensClass}{10.3.2}{X859DD1C079C80DCC} \makelabel{semigroups:IsGreensClassNC}{10.3.3}{X7E9BD34B8021045A} \makelabel{semigroups:GroupHClass}{10.4.1}{X8723756387DD4C0F} \makelabel{semigroups:SchutzenbergerGroup}{10.4.2}{X84F1321E8217D2A8} \makelabel{semigroups:StructureDescriptionSchutzenbergerGroups}{10.4.3}{X8120212 \makelabel{semigroups:StructureDescriptionMaximalSubgroups}{10.4.4}{X838F43FE79A \makelabel{semigroups:MultiplicativeNeutralElement for an H-class}{10.4.5}{X8459E40 \makelabel{semigroups:StructureDescription for an H-class}{10.4.6}{X85B34FFB82C8312 \makelabel{semigroups:InjectionPrincipalFactor}{10.4.7}{X7EBB4F1981CC2AE9} \makelabel{semigroups:InjectionNormalizedPrincipalFactor}{10.4.7}{X7EBB4F1981CC2 \makelabel{semigroups:IsomorphismReesMatrixSemigroup for a D-class}{10.4.7}{X7EBB4F \makelabel{semigroups:PrincipalFactor}{10.4.8}{X86C6D777847AAEC7} \makelabel{semigroups:NormalizedPrincipalFactor}{10.4.8}{X86C6D777847AAEC7} \makelabel{semigroups:LeftGreensMultiplier}{10.5.1}{X7EDE3F03879B2B12} \makelabel{semigroups:RightGreensMultiplier}{10.5.1}{X7EDE3F03879B2B12} \makelabel{semigroups:AsListCanonical}{11.1.1}{X7AC3FAA5826516AD} \makelabel{semigroups:EnumeratorCanonical}{11.1.1}{X7AC3FAA5826516AD} \makelabel{semigroups:IteratorCanonical}{11.1.1}{X7AC3FAA5826516AD} \makelabel{semigroups:PositionCanonical}{11.1.2}{X7B4B10AE81602D4E} \makelabel{semigroups:Enumerate}{11.1.3}{X7BCD5342793C7A7E} \makelabel{semigroups:IsEnumerated}{11.1.4}{X877FAAA67F834897} \makelabel{semigroups:RightCayleyDigraph}{11.2.1}{X7EA002E27B10CCE0} \makelabel{semigroups:LeftCayleyDigraph}{11.2.1}{X7EA002E27B10CCE0} \makelabel{semigroups:Random for a semigroup}{11.3.1}{X7BB7FDFE7AFFD672} \makelabel{semigroups:IndexPeriodOfSemigroupElement}{11.4.1}{X869AC4247E2BA4A2} \makelabel{semigroups:SmallestIdempotentPower}{11.4.2}{X84E1A41F84B70DBB} \makelabel{semigroups:OneInverseOfSemigroupElement}{11.5.1}{X7BDAC0B581B71D0F} \makelabel{semigroups:EvaluateWord}{11.6.1}{X799D2F3C866B9AED} \makelabel{semigroups:Factorization}{11.6.2}{X8357294D7B164106} \makelabel{semigroups:MinimalFactorization}{11.6.3}{X83A4D71382C5B6C3} \makelabel{semigroups:NonTrivialFactorization}{11.6.4}{X86261F4682DC9842} \makelabel{semigroups:Generators}{11.7.1}{X7BD5B55C802805B4} \makelabel{semigroups:SmallGeneratingSet}{11.7.2}{X814DBABC878D5232} \makelabel{semigroups:SmallSemigroupGeneratingSet}{11.7.2}{X814DBABC878D5232} \makelabel{semigroups:SmallMonoidGeneratingSet}{11.7.2}{X814DBABC878D5232} \makelabel{semigroups:SmallInverseSemigroupGeneratingSet}{11.7.2}{X814DBABC878D5 \makelabel{semigroups:SmallInverseMonoidGeneratingSet}{11.7.2}{X814DBABC878D5232 \makelabel{semigroups:IrredundantGeneratingSubset}{11.7.3}{X7F88DA9487720D2B} \makelabel{semigroups:MinimalSemigroupGeneratingSet}{11.7.4}{X8409DBED7996D495} \makelabel{semigroups:MinimalMonoidGeneratingSet}{11.7.4}{X8409DBED7996D495} \makelabel{semigroups:MinimalInverseSemigroupGeneratingSet}{11.7.4}{X8409DBED799 \makelabel{semigroups:MinimalInverseMonoidGeneratingSet}{11.7.4}{X8409DBED7996D4 \makelabel{semigroups:GeneratorsSmallest for a semigroup}{11.7.5}{X82B02F0887AD1B78 \makelabel{semigroups:IndecomposableElements}{11.7.6}{X7B4CD8937858A895} \makelabel{semigroups:MinimalIdeal}{11.8.1}{X7BC68589879C3BE9} \makelabel{semigroups:RepresentativeOfMinimalIdeal}{11.8.2}{X7CA6744182D07C5B} \makelabel{semigroups:RepresentativeOfMinimalDClass}{11.8.2}{X7CA6744182D07C5B} \makelabel{semigroups:MultiplicativeZero}{11.8.3}{X7B39F93C8136D642} \makelabel{semigroups:UnderlyingSemigroupOfSemigroupWithAdjoinedZero}{11.8.4}{X7 \makelabel{semigroups:GroupOfUnits}{11.9.1}{X811AEDD88280C277} \makelabel{semigroups:Idempotents}{11.10.1}{X7C651C9C78398FFF} \makelabel{semigroups:NrIdempotents}{11.10.2}{X7CFC4DB387452320} \makelabel{semigroups:IdempotentGeneratedSubsemigroup}{11.10.3}{X83970D028143B79 \makelabel{semigroups:MaximalSubsemigroups for a finite semigroup}{11.11.1}{X860A10E \makelabel{semigroups:MaximalSubsemigroups for a finite semigroup and a record}{11.11.1 \makelabel{semigroups:NrMaximalSubsemigroups}{11.11.2}{X7A52B4117BCEF379} \makelabel{semigroups:IsMaximalSubsemigroup}{11.11.3}{X82D74C2478A49FD5} \makelabel{semigroups:ComponentRepsOfTransformationSemigroup}{11.12.1}{X8065DBC4 \makelabel{semigroups:ComponentsOfTransformationSemigroup}{11.12.2}{X8706A72A7F3 \makelabel{semigroups:CyclesOfTransformationSemigroup}{11.12.3}{X7AA697B186301F5 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2026-03-28