GAP (HAP commands) - Chapter 40: HAP variables that are not yet documented

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40 HAP variables that are not yet documented
40.1

### 40 HAP variables that are not yet documented

#### 40.1

`2CoreducedChainComplex` Examples:
`AbelianGOuterGroupToCatOneGroup` Examples:
`AbelianInvariantsToTorsionCoefficients` Examples:
`AcyclicSubcomplexOfPureCubicalComplex` Examples: 1
`AddFirst` Examples:
`AdjointGroupOfQuandle` Examples: 1
`AlgebraicReduction_alt` Examples:
`AppendFreeWord` Examples:
`ArcDiagramToTubularSurface` Examples:
`ArcPresentation` Examples: 1 , 2 , 3 , 4
`ArcPresentationToKnottedOneComplex` Examples:
`AreIsoclinic` Examples:
`ArrayIterateBreak` Examples:
`ArrayValueKD` Examples:
`AsWordInSL2Z` Examples:
`AutomorphismGroupQuandleAsPerm_nonconnected` Examples:
`AverageInnerProduct` Examples:
`BarCodeOfFilteredPureCubicalComplex` Examples:
`BarCodeOfSymmetricMatrix` Examples:
`BarComplexOfMonoid` Examples: 1
`BarycentricallySimplifiedComplex` Examples: 1
`BarycentricallySubdivideCell` Examples:
`BettinumbersOfPureCubicalComplex_dim_2` Examples:
`BocksteinHomology` Examples:
`BogomolovMultiplier_viaTensorSquare` Examples:
`BoundariesOfFilteredChainComplex` Examples:
`BoundaryOfPureComplex` Examples: 1
`BoundaryOfPureRegularCWComplex` Examples: 1
`BoundaryOfRegularCWCell` Examples:
`BoundaryPairOfPureRegularCWComplex` Examples:
`BoundingPureComplex` Examples:
`CR_ChainMapFromCocycle` Examples:
`CR_CocyclesAndCoboundaries` Examples:
`CR_IntegralClassToCocycle` Examples:
`CR_IntegralCocycleToClass` Examples:
`CR_IntegralCohomology` Examples:
`CR_IntegralCycleToClass` Examples:
`CWMap2ChainMap` Examples:
`CWSubcomplexToRegularCWMap` Examples: 1
`CanonicalRightCountableCosetElement` Examples:
`CatOneGroupByCrossedModule` Examples:
`CatOneGroupsByGroup` Examples:
`CcElement` Examples:
`Cedric_CheckThirdAxiomRow` Examples:
`Cedric_ConjugateQuandleElement` Examples:
`Cedric_FromAutGeReToAutQe` Examples:
`Cedric_IsHomomorphism` Examples:
`Cedric_Permute` Examples:
`Cedric_Quandle1` Examples:
`Cedric_Quandle2` Examples:
`Cedric_Quandle3` Examples:
`Cedric_Quandle4` Examples:
`Cedric_Quandle5` Examples:
`Cedric_Quandle6` Examples:
`CellComplexBoundaryCheck` Examples:
`ChainComplexEquivalenceOfRegularCWComplex` Examples: 1
`ChainComplexHomeomorphismEquivalenceOfRegularCWComplex` Examples:
`ChainComplexOfCubicalComplex` Examples:
`ChainComplexOfCubicalPair` Examples:
`ChainComplexOfRegularCWComplexWithVectorField` Examples:
`ChainComplexOfSimplicialComplex` Examples:
`ChainComplexOfSimplicialPair` Examples:
`ChainComplexOfUniversalCover` Examples: 1 , 2 , 3 , 4
`ChainComplexToSparseChainComplex` Examples:
`ChainComplexWithChainHomotopy` Examples:
`ChainMapOfCubicalPairs` Examples:
`ChainMapOfRegularCWMap` Examples:
`ChevalleyEilenbergComplexOfModule` Examples:
`ChildRestart` Examples:
`ClosureCWCell` Examples:
`CoClass` Examples:
`CocriticalCellsOfRegularCWComplex` Examples:
`CocyclicHadamardMatrices` Examples: 1
`CocyclicMatrices` Examples:
`CohomologicalData` Examples: 1
`CohomologyHomomorphism` Examples: 1 , 2
`CohomologyHomomorphismOfRepresentation` Examples:
`CohomologyModule_AsAutModule` Examples:
`CohomologyModule_Gmap` Examples:
`CohomologyRingOfSimplicialComplex` Examples:
`CohomologySimplicialFreeAbelianGroup` Examples:
`CombinationDisjointSets` Examples:
`CommonEndomorphisms` Examples:
`ComplementOfPureComplex` Examples: 1
`ComplementaryBasis` Examples:
`ComposeCWMaps` Examples:
`CompositionOfFpGModuleHomomorphisms` Examples:
`CompositionSeriesOfFpGModule` Examples:
`ConcentricallyFilteredPureCubicalComplex` Examples: 1
`CongruenceSubgroup` Examples: 1 , 2
`ConjugateSL2ZGroup` Examples:
`ConnectingCohomologyHomomorphism` Examples: 1 , 2
`ContractArray` Examples:
`ContractCubicalComplex_dim2` Examples:
`ContractCubicalComplex_dim3` Examples:
`ContractMatrix` Examples:
`ContractPermArray` Examples:
`ContractPermMatrix` Examples:
`ContractPureComplex` Examples:
`ContractSimplicialComplex` Examples:
`ContractSimplicialComplex_alt` Examples:
`ContractedFilteredPureCubicalComplex` Examples: 1
`ContractedFilteredRegularCWComplex` Examples:
`ContractedRegularCWComplex` Examples:
`ContractibleSL2ZComplex` Examples:
`ContractibleSL2ZComplex_alt` Examples:
`ContractibleSubArray` Examples:
`ContractibleSubMatrix` Examples:
`ContractibleSubcomplexOfPureCubicalComplex` Examples: 1
`ConvertTorsionComplexToGcomplex` Examples:
`CosetsQuandle` Examples:
`CountingCellsOfBaryCentricSubdivision` Examples:
`CountingNumberOfCellsInBaryCentricSubdivision` Examples:
`CoxeterComplex_alt` Examples: 1
`CoxeterDiagramMatCoxeterGroup` Examples:
`CoxeterWythoffComplex` Examples:
`CreateCoxeterMatrix` Examples: 1
`CriticalBoundaryCells` Examples: 1
`CropPureComplex` Examples:
`CrossedInvariant` Examples:
`CrossedModuleByAutomorphismGroup` Examples:
`CrossedModuleByCatOneGroup` Examples:
`CrossedModuleByNormalSubgroup` Examples: 1
`CrystCubicalTiling` Examples:
`CrystFinitePartOfMatrix` Examples:
`CrystGFullBasis` Examples: 1 , 2
`CrystGcomplex` Examples: 1 , 2
`CrystMatrix` Examples:
`CrystTranslationMatrixToVector` Examples:
`CrystallographicComplex` Examples:
`CubicalToPermutahedralArray` Examples:
`CupProductMatrix` Examples:
`CupProductOfRegularCWComplex` Examples: 1
`CupProductOfRegularCWComplex_alt` Examples: 1
`CuspidalCohomologyHomomorphism` Examples:
`CyclesOfFilteredChainComplex` Examples:
`DavisComplex` Examples: 1 , 2 , 3 , 4
`DeformationRetract` Examples:
`DensityMat` Examples:
`DerivedGroupOfQuandle` Examples: 1
`DiagonalChainMap` Examples:
`DijkgraafWittenInvariant` Examples: 1
`DirectProductOfGroupHomomorphisms` Examples:
`DirectProductOfRegularCWComplexes` Examples:
`DirectProductOfRegularCWComplexesLazy` Examples:
`DirectProductOfSimplicialComplexes` Examples:
`DisplayCSVknotFile` Examples:
`DisplayVectorField` Examples:
`E1CohomologyPage` Examples:
`E1HomologyPage` Examples:
`EilenbergMacLaneSimplicialFreeAbelianGroup` Examples:
`ElementsLazy` Examples:
`EquivariantCWComplexToRegularCWComplex` Examples: 1 , 2 , 3 , 4
`EquivariantCWComplexToRegularCWMap` Examples: 1 , 2 , 3
`EquivariantCWComplexToResolution` Examples:
`ExcisedPureCubicalPair_dim_2` Examples:
`ExtractTorsionSubcomplex` Examples:
`FactorizationNParts` Examples:
`FilteredChainComplexToFilteredSparseChainComplex` Examples:
`FilteredCubicalComplexToFilteredRegularCWComplex` Examples: 1
`FilteredPureCubicalComplexToCubicalComplex` Examples: 1
`FiltrationTermOfGraph` Examples:
`FiltrationTermOfPureCubicalComplex` Examples:
`FiltrationTermOfRegularCWComplex` Examples:
`FiltrationTerms` Examples: 1
`FirstHomologyCoveringCokernels` Examples: 1 , 2
`FirstHomologySimplicialTwoComplex` Examples:
`FourthHomotopyGroupOfDoubleSuspensionB` Examples:
`Fp2PcpAbelianGroupHomomorphism` Examples:
`FpGModuleSection` Examples:
`FreeZGResolution` Examples:
`FundamentalGroupOfRegularCWComplex` Examples: 1
`FundamentalGroupOfRegularCWMap` Examples:
`FundamentalGroupSimplicialTwoComplex` Examples:
`FundamentalMultiplesOfStiefelWhitneyClasses` Examples:
`GChainComplex` Examples: 1
`GModuleAsCatOneGroup` Examples:
`GammaSubgroupInSL3Z` Examples:
`GaussCodeOfPureCubicalKnot` Examples: 1 , 2 , 3 , 4
`GetTorsionPowerSubcomplex` Examples:
`GetTorsionSubcomplex` Examples:
`GraphOfRegularCWComplex` Examples:
`GraphOfResolutionsTest` Examples:
`GraphOfResolutionsToGroups` Examples:
`GroupHomomorphismToMatrix` Examples:
`HAPCocontractRegularCWComplex` Examples:
`HAPContractFilteredRegularCWComplex` Examples:
`HAPContractRegularCWComplex` Examples:
`HAPContractRegularCWComplex_Alt` Examples:
`HAPPRIME_Algebra2Polynomial` Examples:
`HAPPRIME_CohomologyRingWithoutResolution` Examples:
`HAPPRIME_CombineIndeterminateMaps` Examples:
`HAPPRIME_GradedAlgebraPresentationAvoidingIndeterminates` Examples:
`HAPPRIME_LHSSpectralSequence` Examples:
`HAPPRIME_MakeEliminationOrdering` Examples:
`HAPPRIME_MapPolynomialIndeterminates` Examples:
`HAPPRIME_Polynomial2Algebra` Examples:
`HAPPRIME_RingHomomorphismsAreComposable` Examples:
`HAPPRIME_SModule` Examples:
`HAPPRIME_SingularGroebnerBasis` Examples:
`HAPPRIME_SingularReducedGroebnerBasis` Examples:
`HAPPRIME_SwitchGradedAlgebraRing` Examples:
`HAPPRIME_SwitchPolynomialIndeterminates` Examples:
`HAPPRIME_VersionWithSVN` Examples:
`HAPRegularCWComplex` Examples:
`HAPRegularCWPolytope` Examples:
`HAPRemoveCellFromRegularCWComplex` Examples:
`HAPRemoveVectorField` Examples:
`HAPRingModIdeal` Examples:
`HAPRingModIdealObj` Examples:
`HAPTietzeReduction_Inf` Examples:
`HAPTietzeReduction_OneLevel` Examples:
`HAPTietzeReduction_OneStep` Examples:
`HAP_4x4MatTo2x2Mat` Examples:
`HAP_AddGenerator` Examples:
`HAP_AllHomomorphisms` Examples:
`HAP_AppendTo` Examples:
`HAP_AssociahedronBoundaries` Examples:
`HAP_AssociahedronCells` Examples:
`HAP_BaryCentricSubdivisionGComplex` Examples:
`HAP_BaryCentricSubdivisionRegularCWComplex` Examples:
`HAP_Binlisttoint` Examples:
`HAP_ChainComplexToEquivariantChainComplex` Examples:
`HAP_CocyclesAndCoboundaries` Examples:
`HAP_CongruenceSubgroupGamma0` Examples: 1
`HAP_CongruenceSubgroupGamma0Ideal` Examples:
`HAP_ConjugatedCongruenceSubgroup` Examples:
`HAP_ConjugatedCongruenceSubgroupGamma0` Examples:
`HAP_CriticalCellsDirected` Examples:
`HAP_CupProductOfPresentation` Examples:
`HAP_CupProductOfSimplicialComplex` Examples:
`HAP_DisplayPlanarTree` Examples:
`HAP_DisplayVectorField` Examples:
`HAP_ElementsSL2Zfn` Examples:
`HAP_FunctorialModPCohomologyRing` Examples:
`HAP_GenericSL2OSubgroup` Examples:
`HAP_GenericSL2ZConjugatedSubgroup` Examples:
`HAP_GenericSL2ZSubgroup` Examples:
`HAP_HomToIntModP_ChainComplex` Examples:
`HAP_HomToIntModP_ChainMap` Examples:
`HAP_HomToIntModP_CochainComplex` Examples:
`HAP_HomToIntModP_CochainMap` Examples:
`HAP_HomeoLinkingForm` Examples:
`HAP_Hurewicz1Cycles` Examples:
`HAP_IntegralClassToCocycle` Examples:
`HAP_IntegralCocycleToClass` Examples:
`HAP_IntegralCohomology` Examples:
`HAP_KK_AddCell` Examples:
`HAP_KnotGroupInv` Examples:
`HAP_MyIsBieberbachFpGroup` Examples:
`HAP_MyIsFiniteFpGroup` Examples:
`HAP_MyIsInfiniteFpGroup` Examples:
`HAP_PHI` Examples:
`HAP_PermBinlisttoint` Examples:
`HAP_PlanarBinaryTrees` Examples:
`HAP_PlanarTreeGraft` Examples:
`HAP_PlanarTreeJoin` Examples:
`HAP_PlanarTreeLeaves` Examples:
`HAP_PlanarTreeRemovableEdge` Examples:
`HAP_PlanarTreeRemoveEdge` Examples:
`HAP_PrimePartModified` Examples:
`HAP_PrincipalCongruenceSubgroup` Examples:
`HAP_PrincipalCongruenceSubgroupIdeal` Examples:
`HAP_PrintTo` Examples:
`HAP_PureComplexSubcomplex` Examples:
`HAP_PureCubicalPairToCWMap` Examples:
`HAP_ResolutionAbelianGroupFromInvariants` Examples:
`HAP_RightTransversalSL2ZSubgroups` Examples:
`HAP_SL2OSubgroupTree_slow` Examples:
`HAP_SL2SubgroupTree` Examples:
`HAP_SL2TreeDisplay` Examples:
`HAP_SL2ZSubgroupTree_fast` Examples:
`HAP_SL2ZSubgroupTree_slow` Examples:
`HAP_Sequence2Boundaries` Examples:
`HAP_SimplicialPairToCWMap` Examples:
`HAP_SimplicialProjectivePlane` Examples:
`HAP_SimplicialTorus` Examples:
`HAP_SimplifiedGaussCode` Examples:
`HAP_StiefelWhitney` Examples:
`HAP_SylowSubgroups` Examples:
`HAP_Tensor` Examples:
`HAP_TransversalCongruenceSubgroups` Examples:
`HAP_TransversalCongruenceSubgroupsIdeal` Examples:
`HAP_TransversalCongruenceSubgroupsIdeal_alt` Examples:
`HAP_TransversalGamma0SubgroupsIdeal` Examples:
`HAP_Triangulation` Examples:
`HAP_TzPair` Examples:
`HAP_WedgeSumOfSimplicialComplexes` Examples:
`HAP_bockstein` Examples:
`HAP_chain_bockstein` Examples:
`HAP_coho_isoms` Examples:
`HAP_nxnMatTo2nx2nMat` Examples:
`HadamardGraph` Examples:
`HapExample` Examples:
`HapFile` Examples: 1 , 2 , 3 , 4
`HasTrivialPostnikovInvariant` Examples:
`HeckeOperator` Examples:
`HeckeOperatorWeight2` Examples:
`HenonOrbit` Examples: 1
`HomToGModule_hom` Examples:
`HomToInt_ChainComplex` Examples:
`HomToInt_ChainMap` Examples:
`HomToInt_CochainComplex` Examples:
`HomToModPModule` Examples: 1
`HomogeneousPolynomials` Examples:
`HomogeneousPolynomials_Bianchi` Examples:
`HomologicalGroupDecomposition` Examples: 1
`HomologyOfPureCubicalComplex` Examples:
`HomologyPbs` Examples:
`HomologySimplicialFreeAbelianGroup` Examples:
`HomomorphismAsMatrix` Examples:
`HomotopyCatOneGroup` Examples:
`HomotopyCrossedModule` Examples:
`HomotopyEquivalentLargerSubArray` Examples:
`HomotopyEquivalentLargerSubArray3D` Examples:
`HomotopyEquivalentLargerSubMatrix` Examples:
`HomotopyEquivalentLargerSubPermArray` Examples:
`HomotopyEquivalentLargerSubPermArray3D` Examples:
`HomotopyEquivalentLargerSubPermMatrix` Examples:
`HomotopyEquivalentMaximalPureSubcomplex` Examples:
`HomotopyEquivalentMinimalPureSubcomplex` Examples:
`HomotopyEquivalentSmallerSubArray` Examples:
`HomotopyEquivalentSmallerSubArray3D` Examples:
`HomotopyEquivalentSmallerSubMatrix` Examples:
`HomotopyEquivalentSmallerSubPermArray` Examples:
`HomotopyEquivalentSmallerSubPermArray3D` Examples:
`HomotopyEquivalentSmallerSubPermMatrix` Examples:
`HomotopyLowerCentralSeries` Examples:
`HomotopyLowerCentralSeriesOfCrossedModule` Examples:
`HomotopyTruncation` Examples:
`HopfSatohSurface` Examples: 1 , 2
`HybridSubdivision` Examples:
`IdCatOneGroup` Examples: 1
`IdCrossedModule` Examples:
`IdQuasiCatOneGroup` Examples:
`IdQuasiCrossedModule` Examples:
`IdentifyKnot` Examples: 1
`IdentityAmongRelators` Examples: 1 , 2 , 3
`ImageOfGOuterGroupHomomorphism` Examples: 1 , 2
`ImageOfMap` Examples:
`InducedSteenrodHomomorphisms` Examples:
`IntegerSimplicialComplex` Examples: 1
`IntegralCellularHomology` Examples:
`IntegralCohomology` Examples:
`IntegralCohomologyOfCochainComplex` Examples:
`IntegralHomology` Examples: 1
`IntegralHomologyOfChainComplex` Examples:
`IntersectionCWSubcomplex` Examples:
`IsClosedManifold` Examples: 1
`IsContractibleCube_higherdims` Examples:
`IsCrystSameOrbit` Examples:
`IsCrystSufficientLattice` Examples:
`IsHadamardMatrix` Examples:
`IsIntList` Examples:
`IsIsomorphismOfAbelianFpGroups` Examples: 1
`IsMetricMatrix` Examples:
`IsPeriodicSpaceGroup` Examples: 1
`IsPureComplex` Examples:
`IsPureRegularCWComplex` Examples:
`IsRigid` Examples: 1
`IsRigidOnRight` Examples:
`IsSphericalCoxeterGroup` Examples:
`IsoclinismClasses` Examples: 1 , 2
`IsomorphismCatOneGroups` Examples: 1
`IsomorphismCrossedModules` Examples:
`KernelOfGOuterGroupHomomorphism` Examples: 1 , 2
`KernelOfMap` Examples:
`KernelWG` Examples:
`KinkArc2Presentation` Examples:
`KnotComplement` Examples: 1 , 2 , 3
`KnotComplementWithBoundary` Examples: 1 , 2 , 3
`LazyList` Examples:
`LefschetzNumberOfChainMap` Examples:
`Lfunction` Examples:
`LiftColouredSurface` Examples:
`LiftedRegularCWMap` Examples:
`LinearHomomorphismsZZPersistenceMat` Examples:
`LinkingForm` Examples: 1
`LinkingFormHomeomorphismInvariant` Examples: 1
`LinkingFormHomotopyInvariant` Examples: 1
`ListsOfCellsToRegularCWComplex` Examples:
`LowDimensionalCupProduct` Examples: 1
`MakeHAPprimeDoc` Examples:
`ManifoldType` Examples: 1
`Mapper` Examples: 1
`Mapper_alt` Examples:
`MatrixSize` Examples:
`MaximalSimplicesOfSimplicialComplex` Examples: 1
`MaximalSphericalCoxeterSubgroupsFromAbove` Examples:
`MinimizeRingRelations` Examples:
`Mod2SteenrodAlgebra` Examples: 1
`ModPCohomologyRing_alt` Examples:
`ModPCohomologyRing_part_1` Examples:
`ModPCohomologyRing_part_2` Examples:
`ModPRingGeneratorsAlt` Examples:
`ModPSteenrodAlgebra` Examples: 1 , 2
`ModularCohomology` Examples:
`ModularEquivariantChainMap` Examples:
`ModularHomology` Examples:
`Nil3TensorSquare` Examples:
`NonFreeResolutionFiniteSubgroup` Examples:
`NonManifoldVertices` Examples:
`NonRegularCWBoundary` Examples:
`NonabelianSymmetricKernel_alt` Examples: 1
`NonabelianSymmetricSquare_inf` Examples:
`NonabelianTensorProduct_Inf` Examples:
`NonabelianTensorProduct_alt` Examples:
`NonabelianTensorSquareAsCatOneGroup` Examples:
`NonabelianTensorSquareAsCrossedModule` Examples:
`NonabelianTensorSquare_inf` Examples:
`NoncrossingPartitionsLatticeDisplay` Examples: 1
`NullspaceSparseMatDestructive` Examples:
`NumberConnectedQuandles` Examples:
`NumberGeneratorsOfGroupHomology` Examples:
`NumberOfCrossingsInArc2Presentation` Examples:
`NumberOfHomomorphisms_connected` Examples:
`NumberOfHomomorphisms_groups` Examples:
`NumberOfPrimeKnots` Examples: 1 , 2
`NumberSmallCatOneGroups` Examples:
`NumberSmallCrossedModules` Examples:
`NumberSmallQuasiCatOneGroups` Examples:
`NumberSmallQuasiCrossedModules` Examples:
`OppositeGroup` Examples:
`OrthogonalizeBasisByAverageInnerProduct` Examples:
`PCentre` Examples:
`PSubgroupGChainComplex` Examples:
`PSubgroupSimplicialComplex` Examples:
`PUpperCentralSeries` Examples:
`PartialIsoclinismClasses` Examples: 1
`PartsOfQuadraticInteger` Examples:
`PathComponentOfPureComplex` Examples: 1
`PathComponentsCWSubcomplex` Examples:
`PathComponentsOfSimplicialComplex_alt` Examples:
`PathObjectForChainComplex` Examples: 1
`PermutahedralComplexToRegularCWComplex` Examples: 1
`PermutahedralToCubicalArray` Examples:
`PersistentBettiNumbersViaContractions` Examples:
`PersistentHomologyOfCrossedModule` Examples:
`PersistentHomologyOfFilteredPureCubicalComplex_alt` Examples:
`PersistentHomologyOfFilteredSparseChainComplex` Examples: 1 , 2
`PersistentHomologyOfPureCubicalComplex_Alt` Examples:
`PersistentHomologyOfQuotientGroupSeries_Int` Examples:
`PiZeroOfRegularCWComplex` Examples:
`PoincareBipyramidCWComplex` Examples: 1
`PoincareCubeCWComplex` Examples: 1
`PoincareCubeCWComplexNS` Examples: 1
`PoincareDodecahedronCWComplex` Examples: 1 , 2
`PoincareOctahedronCWComplex` Examples: 1
`PoincarePrismCWComplex` Examples: 1
`PoincareSeriesApproximation` Examples:
`PoincareSeries_alt` Examples:
`PolymakeFaceLattice` Examples:
`PolytopalRepresentationComplex` Examples:
`PrankAlt` Examples:
`PresentationOfResolution_alt` Examples:
`PrimePartDerivedFunctorHomomorphism` Examples:
`PrimePartDerivedFunctorViaSubgroupChain` Examples:
`PrimePartDerivedTwistedFunctor` Examples:
`PrintAlgebraWordAsPolynomial` Examples:
`PrintTorsionSubcomplex` Examples:
`PureComplex` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9
`PureCubicalComplexToCubicalComplex` Examples: 1 , 2
`PureCubicalLink` Examples: 1 , 2
`PushoutOfFpGroups` Examples:
`QuadraticCharacter` Examples:
`QuadraticNumberField` Examples: 1
`QuandleIsomorphismRepresentatives` Examples:
`QuotientByTorsionSubcomplex` Examples:
`QuotientChainMap` Examples:
`QuotientGroup` Examples:
`QuotientQuasiIsomorph` Examples:
`RadicalSeriesOfResolution` Examples:
`RandomArc2Presentation` Examples:
`RandomCellOfPureComplex` Examples:
`ReadLinkImageAsGaussCode` Examples: 1
`ReadMatrixAsPureCubicalComplex` Examples:
`ReduceGenerators` Examples:
`ReduceGenerators_alt` Examples:
`ReflectedCubicalKnot` Examples: 1 , 2 , 3 , 4
`RegularCWAssociahedron` Examples:
`RegularCWComplexComplement` Examples: 1
`RegularCWComplexWithRemovedCell` Examples: 1
`RegularCWComplex_AttachCellDestructive` Examples: 1
`RegularCWCube` Examples:
`RegularCWMapToCWSubcomplex` Examples:
`RegularCWOrbitPolytope` Examples:
`RegularCWPermutahedron` Examples:
`RegularCWPolygon` Examples:
`RegularCWSimplex` Examples:
`RelativeCentralQuotientSpaceGroup` Examples:
`RelativeGroupHomology` Examples:
`RelativeRightTransversal` Examples:
`RemoveStar` Examples:
`ResolutionAbelianGroup_alt` Examples:
`ResolutionAbelianPcpGroup` Examples:
`ResolutionAffineCrystGroup` Examples:
`ResolutionBoundaryOfWordOnRight` Examples:
`ResolutionDirectProductLazy` Examples:
`ResolutionFiniteCyclicGroup` Examples:
`ResolutionGL2QuadraticIntegers` Examples:
`ResolutionGL3QuadraticIntegers` Examples:
`ResolutionGenericGroup` Examples:
`ResolutionInfiniteCyclicGroup` Examples:
`ResolutionPGL2QuadraticIntegers` Examples:
`ResolutionPGL3QuadraticIntegers` Examples:
`ResolutionPSL2QuadraticIntegers` Examples: 1
`ResolutionPrimePowerGroupSparse` Examples:
`ResolutionSL2QuadraticIntegers` Examples: 1
`ResolutionSL2ZConjugated` Examples:
`ResolutionSL2Z_alt` Examples:
`ResolutionSpaceGroup` Examples: 1
`ResolutionToEquivariantCWComplex` Examples:
`ResolutionToResolutionOfFpGroup` Examples: 1
`SL2QuadraticIntegers` Examples: 1
`SL2ZResolution` Examples:
`SL2ZResolution_alt` Examples:
`SL2ZTree` Examples:
`SL2ZmElementsDecomposition` Examples:
`SequentialRegularCWComplexComplement` Examples:
`SignatureOfSymmetricMatrix` Examples: 1
`SignedPermutationGroup` Examples: 1
`SimplicesToSimplicialComplex` Examples: 1 , 2 , 3 , 4
`SimplicialComplexToRegularCWComplex_alt` Examples:
`SimplicialK3Surface` Examples: 1
`SimplicialNerveOfFilteredGraph` Examples: 1 , 2
`SimplicialNerveOfTwoComplex` Examples:
`SimplifiedQuandlePresentation` Examples:
`SimplifiedRegularCWComplex` Examples: 1
`SimplifiedSparseChainComplex` Examples:
`SmallCatOneGroup` Examples: 1
`SmallCrossedModule` Examples:
`SmallQuasiCatOneGroup` Examples:
`SmallQuasiCrossedModule` Examples:
`SmoothedFpGroup` Examples:
`SparseChainComplexOfCubicalComplex` Examples:
`SparseChainComplexOfCubicalPair` Examples:
`SparseChainComplexOfFilteredRegularCWComplex` Examples:
`SparseChainComplexOfRegularCWComplexWithVectorField` Examples:
`SparseChainComplexOfSimplicialComplex` Examples:
`SparseChainComplexToChainComplex` Examples:
`SparseChainMapOfCubicalPairs` Examples:
`SparseFilteredChainComplexOfFilteredCubicalComplex` Examples:
`SparseFilteredChainComplexOfFilteredSimplicialComplex` Examples: 1 , 2
`SparseMattoMat` Examples: 1
`SparseRowReduce` Examples:
`SphericalKnotComplement` Examples: 1
`Spin` Examples:
`SpunAboutHyperplane` Examples:
`SpunKnotComplement` Examples: 1
`SpunLinkComplement` Examples:
`StrongGeneratorsOfDerivedSubgroup` Examples:
`StrongGeneratorsOfDerivedSubgroup_alt` Examples:
`StructuralCopyOfFilteredRegularCWComplex` Examples:
`SubQuasiIsomorph` Examples:
`SubdivideCell` Examples:
`Suspension_alt` Examples:
`SylowSubgroupOfCatOneGroup` Examples:
`SymmetricCentre` Examples:
`SymmetricCommutativityGroup` Examples:
`TensorNonFreeResolutionWithRationals` Examples:
`TensorWithBurnsideRing` Examples: 1 , 2
`TensorWithComplexRepresentationRing` Examples: 1 , 2
`TensorWithComplexRepresentationRingOnRight` Examples:
`TensorWithIntegersModPSparse` Examples:
`TensorWithIntegersOverSubgroup` Examples: 1 , 2 , 3 , 4
`TensorWithIntegersSparse` Examples:
`TensorWithModPModule` Examples: 1
`TestHapBook` Examples:
`TestHapQuick` Examples:
`ThickenedHEPureCubicalComplex` Examples:
`ThickenedPureComplex` Examples: 1
`ThickenedPureCubicalComplex_dim2` Examples:
`ThirdHomotopyGroupOfSuspensionB_alt` Examples: 1
`ThreeManifoldViaDehnSurgery` Examples: 1
`ThreeManifoldWithBoundary` Examples: 1
`TransferChainMap` Examples: 1
`TransferCochainMap` Examples: 1
`TranslationSubGroup` Examples:
`TreeOfResolutionsToSL2Zcomplex` Examples:
`TruncatedRegularCWComplex` Examples:
`Tube` Examples:
`TupleOrbitReps` Examples:
`TupleOrbitReps_perm` Examples:
`TwistedResolution` Examples:
`UnboundedArrayAssign` Examples:
`UnitBall` Examples:
`UnitCubicalBall` Examples:
`UnitPermutahedralBall` Examples:
`UniversalBarCodeEval` Examples:
`UniversalCover` Examples: 1 , 2 , 3 , 4
`VectorToCrystMatrix` Examples:
`VectorsToOneSkeleton` Examples: 1
`VerticesOfRegularCWCell` Examples:
`View3dPureComplex` Examples:
`ViewArc2Presentation` Examples:
`ViewPureComplex` Examples:
`VirtuallySimplicialSubdivision` Examples:
`WeakCommutativityGroup` Examples:
`WirtingerGroup` Examples: 1
`WirtingerGroup_gc` Examples:
`WordModP` Examples:
`ZigZagContractedFilteredPureCubicalComplex` Examples:
`ZigZagContractedPureComplex` Examples: 1
`Sq` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`Category_Of_Groups` Examples: 1
`PreImagesElmNC` Examples:
`PreImagesNC` Examples:
`PreImagesSetNC` Examples:
`AsFpGroup` Examples:
`BarycentricSubdivision` Examples: 1 , 2
`Bockstein` Examples: 1 , 2 , 3
`CategoryArrow` Examples:
`CategoryObject` Examples:
`ClosedSurface` Examples: 1
`CoboundaryMatrix` Examples:
`CoefficientsOfPoincareSeries` Examples:
`CohomologyClass` Examples: 1 , 2
`CohomologyRing` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
`ComplexProjectiveSpace` Examples: 1
`CompositionRingHomomorphism` Examples:
`ConnectedComponentsQuandle` Examples:
`ConnectedSum` Examples: 1 , 2
`DegreeOfRepresentative` Examples:
`Dimensions` Examples:
`ExcisedPair` Examples:
`ExpandedComplex` Examples: 1
`FilteredRegularCWComplex` Examples: 1
`FundamentalGroupWithPathReps` Examples: 1 , 2
`GDerivedSubgroup` Examples:
`GModuleAsGOuterGroup` Examples: 1 , 2 , 3 , 4
`GOuterGroupHomomorphism` Examples: 1 , 2
`GOuterGroupHomomorphism` Examples: 1 , 2
`GradedAlgebraPresentation` Examples:
`GradedAlgebraPresentationNC` Examples:
`HAPDerivationNC` Examples:
`HAPRingHomomorphismByIndeterminateMap` Examples:
`HAPRingReductionHomomorphism` Examples:
`HAPRingReductionHomomorphism` Examples:
`HAPRingToSubringHomomorphism` Examples:
`HAPSubringToRingHomomorphism` Examples:
`HAPSubringToRingHomomorphism` Examples:
`HAPZeroRingHomomorphism` Examples:
`HAP_EquivalenceClasses` Examples:
`HomomorphismsImages` Examples:
`ImageOfDerivation` Examples:
`ImageOfRingHomomorphism` Examples:
`IsAssociatedGradedRing` Examples:
`KernelOfDerivation` Examples:
`LowerGCentralSeries` Examples:
`PathComponents` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PersistentHomology` Examples: 1 , 2
`PersistentHomology` Examples: 1 , 2
`PersistentHomology` Examples: 1 , 2
`PoincareSeriesAutoMem` Examples:
`PoincareSeriesAutoMem` Examples:
`PoincareSeriesAutoMemStop` Examples:
`PolynomialToRModuleRep` Examples:
`PreimageOfRingHomomorphism` Examples:
`PureComplexMeet` Examples:
`PureComplexRandomCell` Examples: 1
`PureComplexSubcomplex` Examples:
`Pushout` Examples:
`QuadraticIdeal` Examples: 1
`ReduceIdeal` Examples:
`ReducedPolynomialRingPresentation` Examples:
`ReducedPolynomialRingPresentationMap` Examples:
`RefinedColouring` Examples:
`Resolution` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34
`RightTransversal_alt` Examples:
`RingOfIntegers` Examples: 1
`SingularPolynomialNormalForm` Examples:
`SingularSetNormalFormIdeal` Examples:
`SingularSetNormalFormIdealNC` Examples:
`SparseChainComplexOfPair` Examples:
`Sphere` Examples: 1
`Sq` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`Standard2Cocycle` Examples:
`Standard2Cocycle` Examples:
`StandardNCocycle` Examples:
`StandardNCocycle` Examples:
`StarGraph` Examples:
`SubspaceBasisRepsByDegree` Examples:
`SubspaceDimensionDegree` Examples:
`Suspension` Examples: 1 , 2 , 3 , 4 , 5
`TrivialGModuleAsGOuterGroup` Examples: 1 , 2 , 3 , 4
`VertexLink` Examples:
`VertexStar` Examples:
`WedgeSum` Examples: 1
`TensorProductOp` Examples:
`Arity` Examples:
`AssociatedNumberField` Examples:
`AssociatedRing` Examples:
`Base` Examples: 1
`BaseElement` Examples:
`BaseRing` Examples:
`Cocycle` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7
`CoefficientModule` Examples:
`CohomologicalPeriod` Examples: 1
`CoxeterMatrix` Examples: 1
`DerivationImages` Examples:
`DerivationRelations` Examples:
`DerivationRing` Examples:
`Fibre` Examples:
`FibreElement` Examples:
`Generators` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`GeneratorsOfPresentationIdeal` Examples:
`GradedAlgebraPresentationFamily` Examples:
`HAPDerivationFamily` Examples:
`HAPPRIME_HilbertSeries` Examples:
`HAPRingHomomorphismFamily` Examples:
`HAP_MultiplicativeGenerators` Examples:
`IdentityMap` Examples:
`ImageGenerators` Examples:
`ImagePolynomialRing` Examples:
`ImageRelations` Examples:
`InCcGroup` Examples:
`IndeterminateAndExponentOfUnivariateMonomial` Examples:
`IndeterminateDegrees` Examples:
`IndeterminatesOfGradedAlgebraPresentation` Examples:
`IndeterminatesOfPolynomial` Examples:
`IndexInSL2O` Examples: 1
`InnerAutomorphismGroupQuandle` Examples:
`InnerAutomorphismGroupQuandleAsPerm` Examples:
`InverseRingHomomorphism` Examples:
`IsConnected` Examples: 1 , 2 , 3
`IsHomogeneousQuandle` Examples:
`IsLatinQuandle` Examples: 1
`MaximumDegreeForPresentation` Examples:
`ModPRingBasisAsPolynomials` Examples:
`ModPRingGeneratorDegrees` Examples:
`ModPRingNiceBasis` Examples:
`ModPRingNiceBasisAsPolynomials` Examples:
`Module` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
`NormOfIdeal` Examples:
`OuterAction` Examples:
`OuterGroup` Examples: 1 , 2 , 3 , 4
`PresentationIdeal` Examples:
`PresentationOfGradedStructureConstantAlgebra` Examples: 1
`Pullbacks` Examples:
`Pushouts` Examples:
`RightMultiplicationGroupOfQuandle` Examples: 1 , 2 , 3
`RightMultiplicationGroupOfQuandleAsPerm` Examples: 1
`SingularGroebnerBasis` Examples:
`SingularReducedGroebnerBasis` Examples:
`SourceGenerators` Examples:
`SourcePolynomialRing` Examples:
`SourceRelations` Examples:
`StarGraphAttr` Examples:
`TermsOfPolynomial` Examples:
`UnivariateMonomialsOfMonomial` Examples:
`CoefficientsRing` Examples:
`ElementsFamily` Examples:
`IndexInSL2Z` Examples:
`Name` Examples: 1 , 2 , 3 , 4 , 5 , 6
`Order` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`IsAbelianCategory` Examples:
`IsAdditiveCategory` Examples:
`IsCategoryName` Examples:
`IsCcGroup` Examples:
`IsCrystTranslationSubGroup` Examples:
`IsGOuterGroup` Examples:
`IsGOuterGroupHomomorphism` Examples:
`IsGammaSubgroupInSL3Z` Examples:
`IsHAPRationalMatrixGroup` Examples:
`IsHAPRationalSpecialLinearGroup` Examples:
`IsIdealOfQuadraticIntegers` Examples:
`IsPeriodic` Examples: 1 , 2
`IsPseudoListWithFunction` Examples:
`IsQuadraticNumberField` Examples:
`IsRingOfQuadraticIntegers` Examples:
`IsStandard2Cocycle` Examples:
`IsStandardNCocycle` Examples:
`IsCcElement` Examples:
`IsGradedAlgebraPresentation` Examples:
`IsHAPDerivation` Examples:
`IsHAPRingHomomorphism` Examples:
`IsHAPRingModIdealObj` Examples:
`IsHapCatOneGroup` Examples:
`IsHapCatOneGroupMorphism` Examples:
`IsHapChainComplex` Examples:
`IsHapChainMap` Examples:
`IsHapCochainComplex` Examples:
`IsHapCochainMap` Examples:
`IsHapCommutativeDiagram` Examples:
`IsHapConjQuandElt` Examples:
`IsHapCrossedModule` Examples:
`IsHapCrossedModuleMorphism` Examples:
`IsHapCubicalComplex` Examples:
`IsHapEquivariantCWComplex` Examples:
`IsHapEquivariantChainComplex` Examples:
`IsHapEquivariantChainMap` Examples:
`IsHapEquivariantNonFreeChainComplex` Examples:
`IsHapEquivariantSpectralSequencePage` Examples:
`IsHapFilteredChainComplex` Examples:
`IsHapFilteredCubicalComplex` Examples:
`IsHapFilteredGraph` Examples:
`IsHapFilteredPureCubicalComplex` Examples:
`IsHapFilteredRegularCWComplex` Examples:
`IsHapFilteredSimplicialComplex` Examples:
`IsHapFilteredSparseChainComplex` Examples:
`IsHapGCocomplex` Examples:
`IsHapGComplex` Examples:
`IsHapGComplexMap` Examples:
`IsHapGraph` Examples:
`IsHapOppositeElement` Examples:
`IsHapPureCubicalComplex` Examples:
`IsHapPureCubicalLink` Examples:
`IsHapPurePermutahedralComplex` Examples:
`IsHapQuandlePresentation` Examples:
`IsHapQuotientElement` Examples:
`IsHapRegularCWComplex` Examples:
`IsHapRegularCWMap` Examples:
`IsHapResolution` Examples:
`IsHapSimplicialComplex` Examples:
`IsHapSimplicialFreeAbelianGroup` Examples:
`IsHapSimplicialGroup` Examples:
`IsHapSimplicialGroupMorphism` Examples:
`IsHapSimplicialMap` Examples:
`IsHapSparseChainComplex` Examples:
`IsHapSparseChainMap` Examples:
`IsHapSparseMat` Examples:
`IsHapTorsionSubcomplex` Examples:
`IsPseudoList` Examples:
`IsCcElementRep` Examples:
`IsGradedAlgebraPresentationRep` Examples:
`IsHAPDerivationRep` Examples:
`IsHAPIdealRep` Examples:
`IsHAPRingHomomorphismIndeterminateMapRep` Examples:
`IsHAPRingReductionHomomorphismRep` Examples:
`IsHAPRingToSubringHomomorphismRep` Examples:
`IsHAPSubringToRingHomomorphismRep` Examples:
`IsHAPZeroRingHomomorphismRep` Examples:
`IsHapCatOneGroupMorphismRep` Examples:
`IsHapCatOneGroupRep` Examples:
`IsHapChainComplexRep` Examples:
`IsHapChainMapRep` Examples:
`IsHapCochainComplexRep` Examples:
`IsHapCochainMapRep` Examples:
`IsHapCommutativeDiagramRep` Examples:
`IsHapConjQuandEltRep` Examples:
`IsHapCrossedModuleMorphismRep` Examples:
`IsHapCrossedModuleRep` Examples:
`IsHapCubicalComplexRep` Examples:
`IsHapEquivariantCWComplexRep` Examples:
`IsHapEquivariantChainComplexRep` Examples:
`IsHapEquivariantChainMapRep` Examples:
`IsHapEquivariantNonFreeChainComplexRep` Examples:
`IsHapEquivariantSpectralSequencePageRep` Examples:
`IsHapFilteredChainComplexRep` Examples:
`IsHapFilteredCubicalComplexRep` Examples:
`IsHapFilteredGraphRep` Examples:
`IsHapFilteredPureCubicalComplexRep` Examples:
`IsHapFilteredRegularCWComplexRep` Examples:
`IsHapFilteredSimplicialComplexRep` Examples:
`IsHapFilteredSparseChainComplexRep` Examples:
`IsHapGCocomplexRep` Examples:
`IsHapGComplexMapRep` Examples:
`IsHapGComplexRep` Examples:
`IsHapGraphRep` Examples:
`IsHapOppositeElementRep` Examples:
`IsHapPureCubicalComplexRep` Examples:
`IsHapPureCubicalLinkRep` Examples:
`IsHapPurePermutahedralComplexRep` Examples:
`IsHapQuandlePresentationRep` Examples:
`IsHapQuotientElementRep` Examples:
`IsHapRegularCWComplexRep` Examples:
`IsHapRegularCWMapRep` Examples:
`IsHapResolutionRep` Examples:
`IsHapSimplicialComplexRep` Examples:
`IsHapSimplicialFreeAbelianGroupRep` Examples:
`IsHapSimplicialGroupMorphismRep` Examples:
`IsHapSimplicialGroupRep` Examples:
`IsHapSimplicialMapRep` Examples:
`IsHapSparseChainComplexRep` Examples:
`IsHapSparseChainMapRep` Examples:
`IsHapSparseMatRep` Examples:
`IsHapTorsionSubcomplexRep` Examples:
`IsPseudoListRep` Examples:
`IdealOfQuadraticIntegers` Examples:
`QuadraticNF` Examples:
`RingOfQuadraticIntegers` Examples:
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`` Examples:
`` Examples:
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`AdditiveInverseMutable` Examples:
`AsFpGroup` Examples:
`AsList` Examples:
`AsSSortedList` Examples:
`BarycentricSubdivision` Examples: 1 , 2
`BaseRing` Examples:
`Bockstein` Examples: 1 , 2 , 3
`CategoryArrow` Examples:
`CategoryObject` Examples:
`CoboundaryMatrix` Examples:
`CoefficientsOfPoincareSeries` Examples:
`CoefficientsRing` Examples:
`CohomologicalPeriod` Examples: 1
`CohomologyClass` Examples: 1 , 2
`CompositionRingHomomorphism` Examples:
`CompositionRingHomomorphism` Examples:
`CompositionRingHomomorphism` Examples:
`CompositionRingHomomorphism` Examples:
`CompositionRingHomomorphism` Examples:
`ConnectedComponentsQuandle` Examples:
`ConnectedSum` Examples: 1 , 2
`CoxeterMatrix` Examples: 1
`DefaultFieldOfMatrixGroup` Examples:
`DegreeOfRepresentative` Examples:
`DerivationImages` Examples:
`DerivationRelations` Examples:
`DerivationRing` Examples:
`Dimensions` Examples:
`Enumerator` Examples:
`ExcisedPair` Examples:
`FilteredRegularCWComplex` Examples: 1
`FundamentalGroupWithPathReps` Examples: 1 , 2
`GModuleAsGOuterGroup` Examples: 1 , 2 , 3 , 4
`GOuterGroupHomomorphism` Examples: 1 , 2
`GOuterGroupHomomorphism` Examples: 1 , 2
`Generators` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`GeneratorsOfMagmaWithInverses` Examples:
`GeneratorsOfMagmaWithInverses` Examples:
`GeneratorsOfPresentationIdeal` Examples:
`GradedAlgebraPresentation` Examples:
`GradedAlgebraPresentationNC` Examples:
`HAPDerivationNC` Examples:
`HAPPRIME_HilbertSeries` Examples:
`HAPRingHomomorphismByIndeterminateMap` Examples:
`HAPRingReductionHomomorphism` Examples:
`HAPRingReductionHomomorphism` Examples:
`HAPRingToSubringHomomorphism` Examples:
`HAPSubringToRingHomomorphism` Examples:
`HAPSubringToRingHomomorphism` Examples:
`HAPZeroRingHomomorphism` Examples:
`HAP_MultiplicativeGenerators` Examples:
`HomomorphismsImages` Examples:
`IdGroup` Examples: 1 , 2 , 3 , 4 , 5 , 6
`IdentityMap` Examples:
`ImageOfDerivation` Examples:
`ImageOfRingHomomorphism` Examples:
`ImageOfRingHomomorphism` Examples:
`ImageOfRingHomomorphism` Examples:
`ImageOfRingHomomorphism` Examples:
`ImageOfRingHomomorphism` Examples:
`IndeterminateAndExponentOfUnivariateMonomial` Examples:
`IndeterminateDegrees` Examples:
`IndeterminatesOfGradedAlgebraPresentation` Examples:
`IndeterminatesOfPolynomial` Examples:
`IndexInSL2O` Examples: 1
`IndexInSL2Z` Examples:
`InnerAutomorphismGroupQuandle` Examples:
`InnerAutomorphismGroupQuandleAsPerm` Examples:
`Int` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`InverseMutable` Examples:
`InverseMutable` Examples:
`InverseMutable` Examples:
`InverseRingHomomorphism` Examples:
`InverseRingHomomorphism` Examples:
`InverseRingHomomorphism` Examples:
`InverseRingHomomorphism` Examples:
`InverseRingHomomorphism` Examples:
`InverseSameMutability` Examples:
`IsAssociatedGradedRing` Examples:
`IsConnected` Examples: 1 , 2 , 3
`IsHomogeneousQuandle` Examples:
`IsLatinQuandle` Examples: 1
`IsMonomial` Examples:
`IsOne` Examples:
`IsPeriodic` Examples: 1 , 2
`Kernel` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`KernelOfDerivation` Examples:
`MaximumDegreeForPresentation` Examples:
`ModPRingBasisAsPolynomials` Examples:
`ModPRingGeneratorDegrees` Examples:
`ModPRingNiceBasis` Examples:
`ModPRingNiceBasisAsPolynomials` Examples:
`OneImmutable` Examples:
`OneMutable` Examples:
`PathComponents` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PreimageOfRingHomomorphism` Examples:
`PresentationIdeal` Examples:
`PresentationOfGradedStructureConstantAlgebra` Examples: 1
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`PrintObj` Examples:
`Projection` Examples:
`PureComplexMeet` Examples:
`PureComplexRandomCell` Examples: 1
`PureComplexSubcomplex` Examples:
`Pushout` Examples:
`QuadraticIdeal` Examples: 1
`Random` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16
`ReduceIdeal` Examples:
`ReducedPolynomialRingPresentation` Examples:
`ReducedPolynomialRingPresentationMap` Examples:
`RefinedColouring` Examples:
`Resolution` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34
`RightMultiplicationGroupOfQuandle` Examples: 1 , 2 , 3
`RightMultiplicationGroupOfQuandleAsPerm` Examples: 1
`RightTransversal` Examples:
`RingOfIntegers` Examples: 1
`SingularGroebnerBasis` Examples:
`SingularPolynomialNormalForm` Examples:
`SingularReducedGroebnerBasis` Examples:
`SingularSetNormalFormIdeal` Examples:
`SingularSetNormalFormIdealNC` Examples:
`SparseChainComplexOfPair` Examples:
`Sq` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`Standard2Cocycle` Examples:
`Standard2Cocycle` Examples:
`StandardNCocycle` Examples:
`StandardNCocycle` Examples:
`StarGraph` Examples:
`StarGraphAttr` Examples:
`SubspaceBasisRepsByDegree` Examples:
`SubspaceDimensionDegree` Examples:
`Suspension` Examples: 1 , 2 , 3 , 4 , 5
`TensorProductOp` Examples:
`TermsOfPolynomial` Examples:
`TrivialGModuleAsGOuterGroup` Examples: 1 , 2 , 3 , 4
`Units` Examples:
`Units` Examples:
`UnivariateMonomialsOfMonomial` Examples:
`VertexLink` Examples:
`VertexStar` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`ViewObj` Examples:
`WedgeSum` Examples: 1
`ZeroMutable` Examples:
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`mod` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`*` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`+` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43
`-` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`-` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`/` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`` Examples:
`` Examples:
`` Examples:
`` Examples:
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`=` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`AbelianInvariants` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`AbelianInvariants` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`BarycentricSubdivision` Examples: 1 , 2
`Bockstein` Examples: 1 , 2 , 3
`CanonicalRightCosetElement` Examples:
`ClosedSurface` Examples: 1
`CohomologyRing` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
`CohomologyRing` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
`ComplexProjectiveSpace` Examples: 1
`ConnectedSum` Examples: 1 , 2
`ConnectedSum` Examples: 1 , 2
`ConnectedSum` Examples: 1 , 2
`Dimensions` Examples:
`DirectProductOp` Examples:
`DirectProductOp` Examples:
`DirectProductOp` Examples:
`DirectProductOp` Examples:
`Discriminant` Examples:
`Discriminant` Examples:
`Embedding` Examples:
`ExpandedComplex` Examples: 1
`ExpandedComplex` Examples: 1
`ExpandedComplex` Examples: 1
`ExpandedComplex` Examples: 1
`GDerivedSubgroup` Examples:
`Generators` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`HAPRingReductionHomomorphism` Examples:
`HAPRingReductionHomomorphism` Examples:
`HAP_EquivalenceClasses` Examples:
`ImageOfRingHomomorphism` Examples:
`ImageOfRingHomomorphism` Examples:
`IndexNC` Examples:
`IndexNC` Examples:
`InverseMutable` Examples:
`InverseMutable` Examples:
`InverseMutable` Examples:
`InverseSameMutability` Examples:
`IsEmpty` Examples:
`IsEmpty` Examples:
`IsPrime` Examples: 1 , 2
`IsomorphismFpGroup` Examples: 1 , 2
`Iterator` Examples:
`KernelOfDerivation` Examples:
`ListOp` Examples:
`ListOp` Examples:
`LowerGCentralSeries` Examples:
`NaturalHomomorphism` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7
`Norm` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16
`Norm` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16
`OneImmutable` Examples:
`OneImmutable` Examples:
`Order` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`Order` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
`PersistentBettiNumbersAlt` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PersistentBettiNumbersAlt` Examples: 1
`PersistentHomology` Examples: 1 , 2
`PersistentHomology` Examples: 1 , 2
`Position` Examples: 1 , 2
`Position` Examples: 1 , 2
`Position` Examples: 1 , 2
`PositionCanonical` Examples:
`PreimageOfRingHomomorphism` Examples:
`Projection` Examples:
`PureComplexMeet` Examples:
`PureComplexRandomCell` Examples: 1
`PureComplexSubcomplex` Examples:
`QuadraticIdeal` Examples: 1
`Range` Examples: 1 , 2
`RankMatrixDestructive` Examples:
`ReduceIdeal` Examples:
`ReduceIdeal` Examples:
`ReducedPolynomialRingPresentation` Examples:
`ReducedPolynomialRingPresentation` Examples:
`ReducedPolynomialRingPresentationMap` Examples:
`ReducedPolynomialRingPresentationMap` Examples:
`ReducedPolynomialRingPresentationMap` Examples:
`RefinedColouring` Examples:
`RightTransversal` Examples:
`RightTransversal` Examples:
`RightTransversal` Examples:
`RightTransversal` Examples:
`RightTransversal` Examples:
`RightTransversal_alt` Examples:
`SingularPolynomialNormalForm` Examples:
`SparseChainComplexOfPair` Examples:
`Sphere` Examples: 1
`SubspaceBasisRepsByDegree` Examples:
`SubspaceDimensionDegree` Examples:
`Suspension` Examples: 1 , 2 , 3 , 4 , 5
`TensorProductOp` Examples:
`TensorProductOp` Examples:
`TensorProductOp` Examples:
`Trace` Examples:
`Units` Examples:
`WedgeSum` Examples: 1
`WedgeSum` Examples: 1
`WedgeSum` Examples: 1
`[]` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`[]` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`[]` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`^` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`in` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64
`mod` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39
`PathComponentOfSimplicialComplex` Examples:
`ResolutionSL2ZInvertedInteger` Examples:
`ViewGraph` Examples:
`InfoHAPprime` Examples:
`ASY_PATH` Examples:
`AutomorphismGroupAsCrossedModule` Examples:
`BROWSER_PATH` Examples:
`CATONEGROUP_DATA_PERM` Examples:
`CATONEGROUP_DATA_SIZE` Examples:
`Cedric_PlanarDiagram` Examples:
`ChildKill` Examples:
`DISPLAY_PATH` Examples:
`DOT_PATH` Examples:
`FilteredSimplicialComplexToFilteredCWComplex` Examples:
`GradedAlgebraPresentationType` Examples:
`HAPTEMPORARYFUNCTION` Examples:
`HAP_Knots` Examples:
`HAP_ROOT` Examples:
`HapCatOneGroup` Examples:
`HapCatOneGroupFamily` Examples:
`HapCatOneGroupMorphism` Examples:
`HapCatOneGroupMorphismFamily` Examples:
`HapChainComplex` Examples:
`HapChainComplexFamily` Examples:
`HapChainMap` Examples:
`HapChainMapFamily` Examples:
`HapCochainComplex` Examples:
`HapCochainComplexFamily` Examples:
`HapCochainMap` Examples:
`HapCochainMapFamily` Examples:
`HapCommutativeDiagram` Examples:
`HapCommutativeDiagramFamily` Examples:
`HapCrossedModule` Examples:
`HapCrossedModuleFamily` Examples:
`HapCrossedModuleMorphism` Examples:
`HapCrossedModuleMorphismFamily` Examples:
`HapCubicalComplex` Examples:
`HapCubicalComplexFamily` Examples:
`HapEquivariantCWComplex` Examples:
`HapEquivariantCWComplexFamily` Examples:
`HapEquivariantChainMap` Examples:
`HapEquivariantChainMapFamily` Examples:
`HapFPGModule` Examples:
`HapFPGModuleHomomorphism` Examples:
`HapFilteredChainComplex` Examples:
`HapFilteredChainComplexFamily` Examples:
`HapFilteredCubicalComplex` Examples:
`HapFilteredCubicalComplexFamily` Examples:
`HapFilteredGraph` Examples:
`HapFilteredGraphFamily` Examples:
`HapFilteredPureCubicalComplex` Examples:
`HapFilteredPureCubicalComplexFamily` Examples:
`HapFilteredRegularCWComplex` Examples:
`HapFilteredRegularCWComplexFamily` Examples:
`HapFilteredSimplicialComplex` Examples:
`HapFilteredSimplicialComplexFamily` Examples:
`HapFilteredSparseChainComplex` Examples:
`HapFilteredSparseChainComplexFamily` Examples:
`HapGChainComplex` Examples:
`HapGCocomplex` Examples:
`HapGCocomplexFamily` Examples:
`HapGComplex` Examples:
`HapGComplexFamily` Examples:
`HapGlobalDeclarationsAreAlreadyLoaded` Examples:
`HapGraph` Examples:
`HapGraphFamily` Examples:
`HapNonFreeResolution` Examples:
`HapOppositeElement` Examples:
`HapOppositeElementFamily` Examples:
`HapPureCubicalComplex` Examples:
`HapPureCubicalComplexFamily` Examples:
`HapPureCubicalLink` Examples:
`HapPureCubicalLinkFamily` Examples:
`HapPurePermutahedralComplex` Examples:
`HapPurePermutahedralComplexFamily` Examples:
`HapQuotientElement` Examples:
`HapQuotientElementFamily` Examples:
`HapRegularCWComplex` Examples:
`HapRegularCWComplexFamily` Examples:
`HapRegularCWMap` Examples:
`HapRegularCWMapFamily` Examples:
`HapResolution` Examples:
`HapResolutionFamily` Examples:
`HapSimplicialComplex` Examples:
`HapSimplicialComplexFamily` Examples:
`HapSimplicialGroup` Examples:
`HapSimplicialGroupFamily` Examples:
`HapSimplicialGroupMorphism` Examples:
`HapSimplicialGroupMorphismFamily` Examples:
`HapSimplicialMap` Examples:
`HapSimplicialMapFamily` Examples:
`HapSparseChainComplex` Examples:
`HapSparseChainComplexFamily` Examples:
`HapSparseChainMap` Examples:
`HapSparseChainMapFamily` Examples:
`HapSparseMat` Examples:
`HapSparseMatFamily` Examples:
`HomomorphismOfDirectProduct` Examples:
`IDQUASICATONEGROUP_DATA` Examples:
`IsHapChain` Examples:
`IsHapCochain` Examples:
`IsHapComplex` Examples:
`IsHapFPGModule` Examples:
`IsHapFPGModuleHomomorphism` Examples:
`IsHapGChainComplex` Examples:
`IsHapMap` Examples:
`IsHapNonFreeResolution` Examples:
`NEATO_PATH` Examples:
`NerveOfCover` Examples:
`POLYMAKE_PATH` Examples:
`PseudoList` Examples:
`PseudoListFamily` Examples:
`QUASICATONEGROUP_DATA_NOT` Examples:
`QUASICATONEGROUP_DATA_SIZE` Examples:
`ReadBioData` Examples:
`SMALLQUASICATONEGROUP_DATA` Examples:
`CATONEGROUP_DATA` Examples:
`COMPILED` Examples:
`Cedric_XYXYConnQuan` Examples:
`Cedric_XYXYQuandles` Examples:
`CommutingProbability` Examples:
`GroupIsomorphismRepresentatives` Examples:
`HAPAAA` Examples:
`HAPBARCODE` Examples:
`HAPDerivationType` Examples:
`HAPPRIME_LastLHSBicomplexSize` Examples:
`HAPPRIME_ShuffleRandomSource` Examples:
`HAPRIGXXX` Examples:
`HAP_GCOMPLEX_LIST` Examples:
`HAP_GCOMPLEX_SETUP` Examples:
`HAP_MOVES_DIM_2` Examples:
`HAP_MOVES_DIM_3` Examples:
`HAP_PERMMOVES_DIM_2` Examples:
`HAP_PERMMOVES_DIM_3` Examples:
`HAP_PoincareCubeManifoldEdgeDegrees` Examples:
`HAP_Test` Examples:
`HAP_XYXYXYXY` Examples:
`HAPchildFunctionToggle` Examples:
`HAPchildToggle` Examples:
`HAPchildren` Examples:
`HapConjQuandElt` Examples:
`HapConjQuandEltFamily` Examples:
`HapConstantPolRing` Examples:
`HapEquivariantChainComplex` Examples:
`HapEquivariantChainComplexFamily` Examples:
`HapEquivariantNonFreeChainComplex` Examples:
`HapEquivariantNonFreeChainComplexFamily` Examples:
`HapEquivariantSpectralSequencePage` Examples:
`HapEquivariantSpectralSequencePageFamily` Examples:
`HapGComplexMap` Examples:
`HapGComplexMapFamily` Examples:
`HapQuandlePresentation` Examples:
`HapQuandlePresentationFamily` Examples:
`HapRightTransversalSL2ZSubgroup` Examples:
`HapSL2ZConjugatedSubgroup` Examples:
`HapSL2ZSubgroup` Examples:
`HapSimplicialFreeAbelianGroup` Examples:
`HapSimplicialFreeAbelianGroupFamily` Examples:
`HapTorsionSubcomplex` Examples:
`HapTorsionSubcomplexFamily` Examples:
`IntersectionForm` Examples: 1 , 2
`IsHapRightTransversalSL2ZSubgroup` Examples:
`IsHapSL2ConjugatedSubgroup` Examples:
`IsHapSL2OSubgroup` Examples:
`IsHapSL2Subgroup` Examples:
`IsHapSL2ZConjugatedSubgroup` Examples:
`IsHapSL2ZSubgroup` Examples:
`RefinedColouring_gc` Examples:
`RefinedColouring_group` Examples:
`RegularCWAssociahedronWithDiscreteVectorField` Examples:
`RegularCWClosedSurface` Examples:
`RegularCWComplexWithAttachedRelatorCells` Examples: 1
`RegularCWComplex_DisjointUnion` Examples:
`RegularCWComplex_WedgeSum` Examples:
`RegularCWDiscreteSpace` Examples: 1
`RegularCWSphere` Examples: 1
`SimplicialComplexConnectedSum` Examples:
`SphericalKnotComplementWithBoundary` Examples:
`StemGroups` Examples:
`cat` Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28
`cnt` Examples:
`hap_cr` Examples:

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