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products/Sources/formale Sprachen/GAP/pkg/hap/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 19.6.2025 mit Größe 545 kB

SSL Undocumented.xml Sprache: XML

<Chapter><Heading>HAP variables that are not yet documented</Heading>
<Section><Heading> </Heading><C>2CoreducedChainComplex</C> Examples: 
 
<C>2x2matrix</C> Examples: 
 
<C>AbelianGOuterGroupToCatOneGroup</C> Examples: 
 
<C>AbelianInvariantsToTorsionCoefficients</C> Examples: 
 
<C>AcyclicSubcomplexOfPureCubicalComplex</C> Examples: <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>
 
 
<C>AddFirst</C> Examples: 
 
<C>AdjointGroupOfQuandle</C> Examples: <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>1</LinkText></URL>
 
 
<C>AlgebraicReduction_alt</C> Examples: 
 
<C>AppendFreeWord</C> Examples: 
 
<C>ArcDiagramToTubularSurface</C> Examples: 
 
<C>ArcPresentation</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap4.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>
 
 
<C>ArcPresentationToKnottedOneComplex</C> Examples: 
 
<C>AreIsoclinic</C> Examples: 
 
<C>AreStrictlyFundamentalCoordinates</C> Examples: 
 
<C>ArrayIterateBreak</C> Examples: 
 
<C>ArrayValueKD</C> Examples: 
 
<C>AsWordInSL2Z</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>AutomorphismGroupQuandleAsPerm_nonconnected</C> Examples: 
 
<C>AverageInnerProduct</C> Examples: 
 
<C>BarCodeOfFilteredPureCubicalComplex</C> Examples: 
 
<C>BarCodeOfSymmetricMatrix</C> Examples: 
 
<C>BarComplexOfMonoid</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BarycentricallySimplifiedComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BarycentricallySubdivideCell</C> Examples: 
 
<C>BettinumbersOfPureCubicalComplex_dim_2</C> Examples: 
 
<C>BianchiPolyhedron</C> Examples: <URL><Link>../tutorial/chap14.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BigStepUCS</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BocksteinHomology</C> Examples: 
 
<C>BogomolovMultiplier_viaTensorSquare</C> Examples: 
 
<C>BoundariesOfFilteredChainComplex</C> Examples: 
 
<C>BoundaryOfPureComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BoundaryOfPureRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>BoundaryOfRegularCWCell</C> Examples: 
 
<C>BoundaryPairOfPureRegularCWComplex</C> Examples: 
 
<C>BoundingPureComplex</C> Examples: 
 
<C>CR_ChainMapFromCocycle</C> Examples: 
 
<C>CR_CocyclesAndCoboundaries</C> Examples: 
 
<C>CR_IntegralClassToCocycle</C> Examples: 
 
<C>CR_IntegralCocycleToClass</C> Examples: 
 
<C>CR_IntegralCohomology</C> Examples: 
 
<C>CR_IntegralCycleToClass</C> Examples: 
 
<C>CWMap2ChainMap</C> Examples: 
 
<C>CWSubcomplexToRegularCWMap</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CanonicalRightCountableCosetElement</C> Examples: 
 
<C>CatOneGroupByCrossedModule</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CatOneGroupsByGroup</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CcElement</C> Examples: 
 
<C>Cedric_CheckThirdAxiomRow</C> Examples: 
 
<C>Cedric_ConjugateQuandleElement</C> Examples: 
 
<C>Cedric_FromAutGeReToAutQe</C> Examples: 
 
<C>Cedric_IsHomomorphism</C> Examples: 
 
<C>Cedric_Permute</C> Examples: 
 
<C>Cedric_Quandle1</C> Examples: 
 
<C>Cedric_Quandle2</C> Examples: 
 
<C>Cedric_Quandle3</C> Examples: 
 
<C>Cedric_Quandle4</C> Examples: 
 
<C>Cedric_Quandle5</C> Examples: 
 
<C>Cedric_Quandle6</C> Examples: 
 
<C>CellComplexBoundaryCheck</C> Examples: 
 
<C>ChainComplexEquivalenceOfRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ChainComplexHomeomorphismEquivalenceOfRegularCWComplex</C> Examples: 
 
<C>ChainComplexOfCubicalComplex</C> Examples: 
 
<C>ChainComplexOfCubicalPair</C> Examples: 
 
<C>ChainComplexOfRegularCWComplexWithVectorField</C> Examples: 
 
<C>ChainComplexOfSimplicialComplex</C> Examples: 
 
<C>ChainComplexOfSimplicialPair</C> Examples: 
 
<C>ChainComplexOfUniversalCover</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap4.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>
 
 
<C>ChainComplexToSparseChainComplex</C> Examples: 
 
<C>ChainComplexWithChainHomotopy</C> Examples: 
 
<C>ChainMapOfCubicalPairs</C> Examples: 
 
<C>ChainMapOfRegularCWMap</C> Examples: 
 
<C>ChevalleyEilenbergComplexOfModule</C> Examples: 
 
<C>ChildRestart</C> Examples: 
 
<C>ChildTransfer</C> Examples: 
 
<C>ClassifyingSpaceFiniteGroup</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ClosureCWCell</C> Examples: 
 
<C>CoClass</C> Examples: 
 
<C>CocriticalCellsOfRegularCWComplex</C> Examples: 
 
<C>CocyclicHadamardMatrices</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CocyclicMatrices</C> Examples: 
 
<C>CohomologicalData</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CohomologyHomomorphism</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>3</LinkText></URL>
 
 
<C>CohomologyHomomorphismOfRepresentation</C> Examples: 
 
<C>CohomologyModule_AsAutModule</C> Examples: 
 
<C>CohomologyModule_Gmap</C> Examples: 
 
<C>CohomologyRingOfSimplicialComplex</C> Examples: 
 
<C>CohomologySimplicialFreeAbelianGroup</C> Examples: 
 
<C>CombinationDisjointSets</C> Examples: 
 
<C>CommonEndomorphisms</C> Examples: 
 
<C>ComplementOfPureComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ComplementaryBasis</C> Examples: 
 
<C>ComposeCWMaps</C> Examples: 
 
<C>CompositionOfFpGModuleHomomorphisms</C> Examples: 
 
<C>CompositionSeriesOfFpGModule</C> Examples: 
 
<C>ConcentricallyFilteredPureCubicalComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CongruenceSubgroup</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap14.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>4</LinkText></URL>
 
 
<C>ConjugateSL2ZGroup</C> Examples: 
 
<C>ConnectingCohomologyHomomorphism</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ContractArray</C> Examples: 
 
<C>ContractCubicalComplex_dim2</C> Examples: 
 
<C>ContractCubicalComplex_dim3</C> Examples: 
 
<C>ContractMatrix</C> Examples: 
 
<C>ContractPermArray</C> Examples: 
 
<C>ContractPermMatrix</C> Examples: 
 
<C>ContractPureComplex</C> Examples: 
 
<C>ContractSimplicialComplex</C> Examples: 
 
<C>ContractSimplicialComplex_alt</C> Examples: 
 
<C>ContractedFilteredPureCubicalComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ContractedFilteredRegularCWComplex</C> Examples: 
 
<C>ContractedRegularCWComplex</C> Examples: 
 
<C>ContractibleSL2ZComplex</C> Examples: 
 
<C>ContractibleSL2ZComplex_alt</C> Examples: 
 
<C>ContractibleSubArray</C> Examples: 
 
<C>ContractibleSubMatrix</C> Examples: 
 
<C>ContractibleSubcomplexOfPureCubicalComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ConvertTorsionComplexToGcomplex</C> Examples: 
 
<C>CosetsQuandle</C> Examples: 
 
<C>CountingCellsOfBaryCentricSubdivision</C> Examples: 
 
<C>CountingNumberOfCellsInBaryCentricSubdivision</C> Examples: 
 
<C>CoverOfUnimodularPairs</C> Examples: 
 
<C>CoxeterComplex_alt</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CoxeterDiagramMatCoxeterGroup</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CoxeterWythoffComplex</C> Examples: 
 
<C>CreateCoxeterMatrix</C> Examples: <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CriticalBoundaryCells</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CropPureComplex</C> Examples: 
 
<C>CrossedInvariant</C> Examples: 
 
<C>CrossedModuleByAutomorphismGroup</C> Examples: 
 
<C>CrossedModuleByCatOneGroup</C> Examples: 
 
<C>CrossedModuleByNormalSubgroup</C> Examples: <URL><Link>../www/SideLinks/About/aboutNonabelian.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CrystCubicalTiling</C> Examples: 
 
<C>CrystFinitePartOfMatrix</C> Examples: 
 
<C>CrystGFullBasis</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap9.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>3</LinkText></URL>
 
 
<C>CrystGcomplex</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap9.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>3</LinkText></URL>
 
 
<C>CrystMatrix</C> Examples: 
 
<C>CrystTranslationMatrixToVector</C> Examples: 
 
<C>CrystallographicComplex</C> Examples: 
 
<C>CubicalToPermutahedralArray</C> Examples: 
 
<C>CupProductMatrix</C> Examples: 
 
<C>CupProductOfRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CupProductOfRegularCWComplexModP</C> Examples: 
 
<C>CupProductOfRegularCWComplex_alt</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CuspidalCohomologyHomomorphism</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>CyclesOfFilteredChainComplex</C> Examples: 
 
<C>DavisComplex</C> Examples: <URL><Link>../tutorial/chap9.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>4</LinkText></URL>
 
 
<C>DeformationRetract</C> Examples: 
 
<C>DensityMat</C> Examples: 
 
<C>DerivedGroupOfQuandle</C> Examples: <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>1</LinkText></URL>
 
 
<C>DiagonalChainMap</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>DijkgraafWittenInvariant</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>DirectProductOfGroupHomomorphisms</C> Examples: 
 
<C>DirectProductOfRegularCWComplexes</C> Examples: 
 
<C>DirectProductOfRegularCWComplexesLazy</C> Examples: 
 
<C>DirectProductOfSimplicialComplexes</C> Examples: 
 
<C>Display3DUnimodularPairs</C> Examples: 
 
<C>DisplayCSVknotFile</C> Examples: 
 
<C>DisplayUnimodularPairs</C> Examples: 
 
<C>DisplayVectorField</C> Examples: 
 
<C>E1CohomologyPage</C> Examples: 
 
<C>E1HomologyPage</C> Examples: 
 
<C>EilenbergMacLaneSimplicialFreeAbelianGroup</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ElementsLazy</C> Examples: 
 
<C>EquivariantCWComplexToRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap4.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>
 
 
<C>EquivariantCWComplexToRegularCWMap</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>3</LinkText></URL>
 
 
<C>EquivariantCWComplexToResolution</C> Examples: 
 
<C>ExcisedPureCubicalPair_dim_2</C> Examples: 
 
<C>ExtractTorsionSubcomplex</C> Examples: 
 
<C>FactorizationNParts</C> Examples: 
 
<C>FilteredChainComplexToFilteredSparseChainComplex</C> Examples: 
 
<C>FilteredCubicalComplexToFilteredRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>FilteredPureCubicalComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>
 
 
<C>FilteredPureCubicalComplexToCubicalComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>FiltrationTermOfGraph</C> Examples: 
 
<C>FiltrationTermOfPureCubicalComplex</C> Examples: 
 
<C>FiltrationTermOfRegularCWComplex</C> Examples: 
 
<C>FiltrationTerms</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>FirstHomologyCoveringCokernels</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>2</LinkText></URL>
 
 
<C>FirstHomologySimplicialTwoComplex</C> Examples: 
 
<C>FourthHomotopyGroupOfDoubleSuspensionB</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>Fp2PcpAbelianGroupHomomorphism</C> Examples: 
 
<C>FpGModuleSection</C> Examples: 
 
<C>FreeZGResolution</C> Examples: 
 
<C>FundamentalGroupOfRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL>
 
 
<C>FundamentalGroupOfRegularCWMap</C> Examples: 
 
<C>FundamentalGroupSimplicialTwoComplex</C> Examples: 
 
<C>FundamentalMultiplesOfStiefelWhitneyClasses</C> Examples: 
 
<C>GChainComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>1</LinkText></URL>
 
 
<C>GModuleAsCatOneGroup</C> Examples: 
 
<C>GammaSubgroupInSL3Z</C> Examples: 
 
<C>GaussCodeOfPureCubicalKnot</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutQuandles2.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutKnotsQuandles.html</Link><LinkText>4</LinkText></URL>
 
 
<C>GetTorsionPowerSubcomplex</C> Examples: 
 
<C>GetTorsionSubcomplex</C> Examples: 
 
<C>GraphOfRegularCWComplex</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap14.html</Link><LinkText>2</LinkText></URL>
 
 
<C>GraphOfResolutionsTest</C> Examples: 
 
<C>GraphOfResolutionsToGroups</C> Examples: 
 
<C>GroupHomomorphismToMatrix</C> Examples: 
 
<C>HAPCocontractRegularCWComplex</C> Examples: 
 
<C>HAPContractFilteredRegularCWComplex</C> Examples: 
 
<C>HAPContractRegularCWComplex</C> Examples: 
 
<C>HAPContractRegularCWComplex_Alt</C> Examples: 
 
<C>HAPPRIME_Algebra2Polynomial</C> Examples: 
 
<C>HAPPRIME_CohomologyRingWithoutResolution</C> Examples: 
 
<C>HAPPRIME_CombineIndeterminateMaps</C> Examples: 
 
<C>HAPPRIME_GradedAlgebraPresentationAvoidingIndeterminates</C> Examples: 
 
<C>HAPPRIME_LHSSpectralSequence</C> Examples: 
 
<C>HAPPRIME_MakeEliminationOrdering</C> Examples: 
 
<C>HAPPRIME_MapPolynomialIndeterminates</C> Examples: 
 
<C>HAPPRIME_Polynomial2Algebra</C> Examples: 
 
<C>HAPPRIME_RingHomomorphismsAreComposable</C> Examples: 
 
<C>HAPPRIME_SModule</C> Examples: 
 
<C>HAPPRIME_SingularGroebnerBasis</C> Examples: 
 
<C>HAPPRIME_SingularReducedGroebnerBasis</C> Examples: 
 
<C>HAPPRIME_SwitchGradedAlgebraRing</C> Examples: 
 
<C>HAPPRIME_SwitchPolynomialIndeterminates</C> Examples: 
 
<C>HAPPRIME_VersionWithSVN</C> Examples: 
 
<C>HAPQuadraticRing</C> Examples: 
 
<C>HAPRegularCWComplex</C> Examples: 
 
<C>HAPRegularCWPolytope</C> Examples: 
 
<C>HAPRemoveCellFromRegularCWComplex</C> Examples: 
 
<C>HAPRemoveVectorField</C> Examples: 
 
<C>HAPRingModIdeal</C> Examples: 
 
<C>HAPRingModIdealObj</C> Examples: 
 
<C>HAPTietzeReduction_Inf</C> Examples: 
 
<C>HAPTietzeReduction_OneLevel</C> Examples: 
 
<C>HAPTietzeReduction_OneStep</C> Examples: 
 
<C>HAP_4x4MatTo2x2Mat</C> Examples: 
 
<C>HAP_AddGenerator</C> Examples: 
 
<C>HAP_AllHomomorphisms</C> Examples: 
 
<C>HAP_AppendTo</C> Examples: 
 
<C>HAP_Are3IntersectingUnimodularPairs</C> Examples: 
 
<C>HAP_AreIntersectingUnimodularPairs</C> Examples: 
 
<C>HAP_AreStrictlyIntersectingUnimodularPairs</C> Examples: 
 
<C>HAP_AssociahedronBoundaries</C> Examples: 
 
<C>HAP_AssociahedronCells</C> Examples: 
 
<C>HAP_BarCodeCompactDisplayList</C> Examples: 
 
<C>HAP_BaryCentricSubdivisionGComplex</C> Examples: 
 
<C>HAP_BaryCentricSubdivisionRegularCWComplex</C> Examples: 
 
<C>HAP_BettiZeroMonotonic</C> Examples: 
 
<C>HAP_BianchiFundamentalRectangle</C> Examples: 
 
<C>HAP_BianchiRegularCWComplex</C> Examples: 
 
<C>HAP_BianchiTransformations</C> Examples: 
 
<C>HAP_Binlisttoint</C> Examples: 
 
<C>HAP_ChainComplexToEquivariantChainComplex</C> Examples: 
 
<C>HAP_CocyclesAndCoboundaries</C> Examples: 
 
<C>HAP_CocyclesAndCoboundariesModP</C> Examples: 
 
<C>HAP_CongruenceSubgroupGamma0</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap14.html</Link><LinkText>3</LinkText></URL>
 
 
<C>HAP_CongruenceSubgroupGamma0Ideal</C> Examples: 
 
<C>HAP_ConjugatedCongruenceSubgroup</C> Examples: 
 
<C>HAP_ConjugatedCongruenceSubgroupGamma0</C> Examples: 
 
<C>HAP_CriticalCellsDirected</C> Examples: 
 
<C>HAP_CupProductOfPresentation</C> Examples: 
 
<C>HAP_CupProductOfSimplicialComplex</C> Examples: 
 
<C>HAP_DisplayPlanarTree</C> Examples: 
 
<C>HAP_DisplayVectorField</C> Examples: 
 
<C>HAP_ElementsSL2Zfn</C> Examples: 
 
<C>HAP_FunctorialModPCohomologyRing</C> Examples: 
 
<C>HAP_GenericSL2OSubgroup</C> Examples: 
 
<C>HAP_GenericSL2ZConjugatedSubgroup</C> Examples: 
 
<C>HAP_GenericSL2ZSubgroup</C> Examples: 
 
<C>HAP_HeightOfPointOnSphere</C> Examples: 
 
<C>HAP_HomToIntModP_ChainComplex</C> Examples: 
 
<C>HAP_HomToIntModP_ChainMap</C> Examples: 
 
<C>HAP_HomToIntModP_CochainComplex</C> Examples: 
 
<C>HAP_HomToIntModP_CochainMap</C> Examples: 
 
<C>HAP_HomeoLinkingForm</C> Examples: 
 
<C>HAP_Hurewicz1Cycles</C> Examples: 
 
<C>HAP_IntegralClassToCocycle</C> Examples: 
 
<C>HAP_IntegralCocycleToClass</C> Examples: 
 
<C>HAP_IntegralCohomology</C> Examples: 
 
<C>HAP_IntersectionConjugatedCongruenceSubgroup</C> Examples: 
 
<C>HAP_IsRedundantUnimodularPair</C> Examples: 
 
<C>HAP_IsomorphismCcFpGroup</C> Examples: 
 
<C>HAP_KK_AddCell</C> Examples: 
 
<C>HAP_KnotGroupInv</C> Examples: 
 
<C>HAP_MultiplicationTableOfGroup</C> Examples: 
 
<C>HAP_MyIsBieberbachFpGroup</C> Examples: 
 
<C>HAP_MyIsFiniteFpGroup</C> Examples: 
 
<C>HAP_MyIsInfiniteFpGroup</C> Examples: 
 
<C>HAP_PHI</C> Examples: 
 
<C>HAP_PermBinlisttoint</C> Examples: 
 
<C>HAP_PlanarBinaryTrees</C> Examples: 
 
<C>HAP_PlanarTreeGraft</C> Examples: 
 
<C>HAP_PlanarTreeJoin</C> Examples: 
 
<C>HAP_PlanarTreeLeaves</C> Examples: 
 
<C>HAP_PlanarTreeRemovableEdge</C> Examples: 
 
<C>HAP_PlanarTreeRemoveEdge</C> Examples: 
 
<C>HAP_PrimePartModified</C> Examples: 
 
<C>HAP_PrincipalCongruenceSubgroup</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HAP_PrincipalCongruenceSubgroupIdeal</C> Examples: 
 
<C>HAP_PrintFloat</C> Examples: 
 
<C>HAP_PrintTo</C> Examples: 
 
<C>HAP_PureComplexSubcomplex</C> Examples: 
 
<C>HAP_PureCubicalPairToCWMap</C> Examples: 
 
<C>HAP_ResolutionAbelianGroupFromInvariants</C> Examples: 
 
<C>HAP_RightTransversalSL2ZSubgroups</C> Examples: 
 
<C>HAP_RightTransversalSL2ZSubgroups_alt</C> Examples: 
 
<C>HAP_SL2OSubgroupTree_fast</C> Examples: 
 
<C>HAP_SL2OSubgroupTree_slow</C> Examples: 
 
<C>HAP_SL2SubgroupTree</C> Examples: 
 
<C>HAP_SL2TreeDisplay</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HAP_SL2ZSubgroupTree_fast</C> Examples: 
 
<C>HAP_SL2ZSubgroupTree_slow</C> Examples: 
 
<C>HAP_Sequence2Boundaries</C> Examples: 
 
<C>HAP_SimplicialPairToCWMap</C> Examples: 
 
<C>HAP_SimplicialProjectivePlane</C> Examples: 
 
<C>HAP_SimplicialTorus</C> Examples: 
 
<C>HAP_SimplifiedGaussCode</C> Examples: 
 
<C>HAP_SqrtInequality</C> Examples: 
 
<C>HAP_SqrtStrictInequality</C> Examples: 
 
<C>HAP_StiefelWhitney</C> Examples: 
 
<C>HAP_SylowConjugatedHomomorphism</C> Examples: 
 
<C>HAP_SylowSubgroups</C> Examples: 
 
<C>HAP_Tensor</C> Examples: 
 
<C>HAP_TransversalCongruenceSubgroups</C> Examples: 
 
<C>HAP_TransversalCongruenceSubgroupsIdeal</C> Examples: 
 
<C>HAP_TransversalCongruenceSubgroupsIdeal_alt</C> Examples: 
 
<C>HAP_TransversalGamma0SubgroupsIdeal</C> Examples: 
 
<C>HAP_Triangulation</C> Examples: 
 
<C>HAP_TzPair</C> Examples: 
 
<C>HAP_UnimodularComplements</C> Examples: 
 
<C>HAP_VertexHeights</C> Examples: 
 
<C>HAP_WedgeSumOfSimplicialComplexes</C> Examples: 
 
<C>HAP_bockstein</C> Examples: 
 
<C>HAP_chain_bockstein</C> Examples: 
 
<C>HAP_coho_isoms</C> Examples: 
 
<C>HAP_nxnMatTo2nx2nMat</C> Examples: 
 
<C>HadamardGraph</C> Examples: 
 
<C>HapExample</C> Examples: 
 
<C>HapFile</C> Examples: <URL><Link>../tutorial/chap2.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap5.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap10.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../tutorial/chap11.html</Link><LinkText>4</LinkText></URL>
 
 
<C>Hap_int</C> Examples: 
 
<C>HasTrivialPostnikovInvariant</C> Examples: 
 
<C>HeckeComponent</C> Examples: 
 
<C>HeckeComponentWeight2</C> Examples: 
 
<C>HeckeOperator</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HenonOrbit</C> Examples: <URL><Link>../tutorial/chap2.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HomToGModule_hom</C> Examples: 
 
<C>HomToInt_ChainComplex</C> Examples: 
 
<C>HomToInt_ChainMap</C> Examples: 
 
<C>HomToInt_CochainComplex</C> Examples: 
 
<C>HomToModPModule</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HomogeneousPolynomials</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>HomogeneousPolynomials_Bianchi</C> Examples: 
 
<C>HomologicalGroupDecomposition</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap8.html</Link><LinkText>2</LinkText></URL>
 
 
<C>HomologyOfPureCubicalComplex</C> Examples: 
 
<C>HomologyPbs</C> Examples: 
 
<C>HomologySimplicialFreeAbelianGroup</C> Examples: 
 
<C>HomomorphismAsMatrix</C> Examples: 
 
<C>HomotopyCatOneGroup</C> Examples: 
 
<C>HomotopyCrossedModule</C> Examples: 
 
<C>HomotopyEquivalentLargerSubArray</C> Examples: 
 
<C>HomotopyEquivalentLargerSubArray3D</C> Examples: 
 
<C>HomotopyEquivalentLargerSubMatrix</C> Examples: 
 
<C>HomotopyEquivalentLargerSubPermArray</C> Examples: 
 
<C>HomotopyEquivalentLargerSubPermArray3D</C> Examples: 
 
<C>HomotopyEquivalentLargerSubPermMatrix</C> Examples: 
 
<C>HomotopyEquivalentMaximalPureSubcomplex</C> Examples: 
 
<C>HomotopyEquivalentMinimalPureSubcomplex</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubArray</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubArray3D</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubMatrix</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubPermArray</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubPermArray3D</C> Examples: 
 
<C>HomotopyEquivalentSmallerSubPermMatrix</C> Examples: 
 
<C>HomotopyLowerCentralSeries</C> Examples: 
 
<C>HomotopyLowerCentralSeriesOfCrossedModule</C> Examples: 
 
<C>HomotopyTruncation</C> Examples: 
 
<C>HopfSatohSurface</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>2</LinkText></URL>
 
 
<C>HybridSubdivision</C> Examples: 
 
<C>IdCatOneGroup</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>2</LinkText></URL>
 
 
<C>IdCrossedModule</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IdQuasiCatOneGroup</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IdQuasiCrossedModule</C> Examples: 
 
<C>IdentifyKnot</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IdentityAmongRelators</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutPeriodic.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>3</LinkText></URL>
 
 
<C>ImageOfGOuterGroupHomomorphism</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ImageOfMap</C> Examples: 
 
<C>InducedSteenrodHomomorphisms</C> Examples: 
 
<C>IntegerSimplicialComplex</C> Examples: <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IntegralCellularHomology</C> Examples: 
 
<C>IntegralCohomology</C> Examples: 
 
<C>IntegralCohomologyOfCochainComplex</C> Examples: 
 
<C>IntegralHomology</C> Examples: <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IntegralHomologyOfChainComplex</C> Examples: 
 
<C>IntersectionCWSubcomplex</C> Examples: 
 
<C>IsClosedManifold</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IsContractibleCube_higherdims</C> Examples: 
 
<C>IsCrystSameOrbit</C> Examples: 
 
<C>IsCrystSufficientLattice</C> Examples: 
 
<C>IsHadamardMatrix</C> Examples: 
 
<C>IsHapQuadraticInteger</C> Examples: 
 
<C>IsIntList</C> Examples: 
 
<C>IsIsomorphismOfAbelianFpGroups</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IsMetricMatrix</C> Examples: 
 
<C>IsPeriodicSpaceGroup</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap8.html</Link><LinkText>2</LinkText></URL>
 
 
<C>IsPureComplex</C> Examples: 
 
<C>IsPureRegularCWComplex</C> Examples: 
 
<C>IsQQUnimodularPair</C> Examples: 
 
<C>IsQUnimodularPair</C> Examples: 
 
<C>IsRigid</C> Examples: <URL><Link>../tutorial/chap9.html</Link><LinkText>1</LinkText></URL>
 
 
<C>IsRigidOnRight</C> Examples: 
 
<C>IsSphericalCoxeterGroup</C> Examples: 
 
<C>IsStrictlyFundamentalUnimodularPair</C> Examples: 
 
<C>IsUnimodularCollection</C> Examples: 
 
<C>IsoclinismClasses</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutBogomolov.html</Link><LinkText>2</LinkText></URL>
 
 
<C>IsomorphismCatOneGroups</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>2</LinkText></URL>
 
 
<C>IsomorphismCrossedModules</C> Examples: 
 
<C>KernelOfGOuterGroupHomomorphism</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>2</LinkText></URL>
 
 
<C>KernelOfMap</C> Examples: 
 
<C>KernelWG</C> Examples: 
 
<C>KinkArc2Presentation</C> Examples: 
 
<C>KnotComplement</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>3</LinkText></URL>
 
 
<C>KnotComplementWithBoundary</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>3</LinkText></URL>
 
 
<C>LazyList</C> Examples: 
 
<C>LefschetzNumberOfChainMap</C> Examples: 
 
<C>Lfunction</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>LiftColouredSurface</C> Examples: 
 
<C>LiftedRegularCWMap</C> Examples: 
 
<C>LinearHomomorphismsZZPersistenceMat</C> Examples: 
 
<C>LinkingForm</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>LinkingFormHomeomorphismInvariant</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>LinkingFormHomotopyInvariant</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ListsOfCellsToRegularCWComplex</C> Examples: 
 
<C>LowDimensionalCupProduct</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>MakeHAPprimeDoc</C> Examples: 
 
<C>ManifoldType</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>Mapper</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>Mapper_alt</C> Examples: 
 
<C>MatrixSize</C> Examples: 
 
<C>MaximalSimplicesOfSimplicialComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>MaximalSphericalCoxeterSubgroupsFromAbove</C> Examples: 
 
<C>MinimizeRingRelations</C> Examples: 
 
<C>Mod2SteenrodAlgebra</C> Examples: <URL><Link>../www/SideLinks/About/aboutModPRings.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ModPCohomologyPresentationBounds</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ModPCohomologyRing_alt</C> Examples: 
 
<C>ModPCohomologyRing_part_1</C> Examples: 
 
<C>ModPCohomologyRing_part_2</C> Examples: 
 
<C>ModPRingGeneratorsAlt</C> Examples: 
 
<C>ModPSteenrodAlgebra</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutModPRings.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ModularCohomology</C> Examples: 
 
<C>ModularEquivariantChainMap</C> Examples: 
 
<C>ModularHomology</C> Examples: 
 
<C>NeighbourhoodOfUnimodularPairs</C> Examples: 
 
<C>Nil3TensorSquare</C> Examples: 
 
<C>NonFreeResolutionFiniteSubgroup</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>NonManifoldVertices</C> Examples: 
 
<C>NonRegularCWBoundary</C> Examples: 
 
<C>NonabelianSymmetricKernel_alt</C> Examples: <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>1</LinkText></URL>
 
 
<C>NonabelianSymmetricSquare_inf</C> Examples: 
 
<C>NonabelianTensorProduct_Inf</C> Examples: 
 
<C>NonabelianTensorProduct_alt</C> Examples: 
 
<C>NonabelianTensorSquareAsCatOneGroup</C> Examples: 
 
<C>NonabelianTensorSquareAsCrossedModule</C> Examples: <URL><Link>../tutorial/chap12.html</Link><LinkText>1</LinkText></URL>
 
 
<C>NonabelianTensorSquare_inf</C> Examples: 
 
<C>NoncrossingPartitionsLatticeDisplay</C> Examples: <URL><Link>../www/SideLinks/About/aboutNoncrossing.html</Link><LinkText>1</LinkText></URL>
 
 
<C>NullspaceSparseMatDestructive</C> Examples: 
 
<C>NumberConnectedQuandles</C> Examples: 
 
<C>NumberGeneratorsOfGroupHomology</C> Examples: 
 
<C>NumberOfCrossingsInArc2Presentation</C> Examples: 
 
<C>NumberOfHomomorphisms_connected</C> Examples: 
 
<C>NumberOfHomomorphisms_groups</C> Examples: 
 
<C>NumberOfPrimeKnots</C> Examples: <URL><Link>../www/SideLinks/About/aboutQuandles2.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>2</LinkText></URL>
 
 
<C>NumberSmallCatOneGroups</C> Examples: 
 
<C>NumberSmallCrossedModules</C> Examples: 
 
<C>NumberSmallQuasiCatOneGroups</C> Examples: 
 
<C>NumberSmallQuasiCrossedModules</C> Examples: 
 
<C>OppositeGroup</C> Examples: 
 
<C>OrthogonalizeBasisByAverageInnerProduct</C> Examples: 
 
<C>PCentre</C> Examples: 
 
<C>PSubgroupGChainComplex</C> Examples: 
 
<C>PSubgroupSimplicialComplex</C> Examples: 
 
<C>PUpperCentralSeries</C> Examples: 
 
<C>ParallelPersistentBettiNumbers</C> Examples: 
 
<C>PartialIsoclinismClasses</C> Examples: <URL><Link>../www/SideLinks/About/aboutBogomolov.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PartsOfQuadraticInteger</C> Examples: 
 
<C>PathComponentOfPureComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PathComponentsCWSubcomplex</C> Examples: 
 
<C>PathComponentsOfSimplicialComplex_alt</C> Examples: 
 
<C>PathObjectForChainComplex</C> Examples: <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PermutahedralComplexToRegularCWComplex</C> Examples: <URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PermutahedralToCubicalArray</C> Examples: 
 
<C>PersistentBettiNumbersViaContractions</C> Examples: 
 
<C>PersistentHomologyOfCrossedModule</C> Examples: 
 
<C>PersistentHomologyOfFilteredPureCubicalComplex_alt</C> Examples: 
 
<C>PersistentHomologyOfFilteredSparseChainComplex</C> Examples: <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>
 
 
<C>PersistentHomologyOfPureCubicalComplex_Alt</C> Examples: 
 
<C>PersistentHomologyOfQuotientGroupSeries_Int</C> Examples: 
 
<C>PiZeroOfRegularCWComplex</C> Examples: 
 
<C>PoincareBipyramidCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PoincareCubeCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PoincareCubeCWComplexNS</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PoincareDodecahedronCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap11.html</Link><LinkText>2</LinkText></URL>
 
 
<C>PoincareOctahedronCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PoincarePrismCWComplex</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PoincareSeriesApproximation</C> Examples: 
 
<C>PoincareSeries_alt</C> Examples: 
 
<C>PolymakeFaceLattice</C> Examples: 
 
<C>PolytopalRepresentationComplex</C> Examples: 
 
<C>PrankAlt</C> Examples: 
 
<C>PresentationOfResolution_alt</C> Examples: 
 
<C>PrimePartDerivedFunctorHomomorphism</C> Examples: 
 
<C>PrimePartDerivedFunctorViaSubgroupChain</C> Examples: <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>
 
 
<C>PrimePartDerivedTwistedFunctor</C> Examples: 
 
<C>PrintAlgebraWordAsPolynomial</C> Examples: 
 
<C>PrintTorsionSubcomplex</C> Examples: 
 
<C>PureComplex</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap2.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap3.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../tutorial/chap5.html</Link><LinkText>4</LinkText></URL> ,
<URL><Link>../tutorial/chap10.html</Link><LinkText>5</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>6</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>7</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>8</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>9</LinkText></URL>
 
 
<C>PureCubicalComplexToCubicalComplex</C> Examples: <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>2</LinkText></URL>
 
 
<C>PureCubicalLink</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>2</LinkText></URL>
 
 
<C>PushoutOfFpGroups</C> Examples: 
 
<C>QNeighbourhoodOfUnimodularPairs</C> Examples: 
 
<C>QQNeighbourhoodOfUnimodularPairs</C> Examples: 
 
<C>QuadraticCharacter</C> Examples: 
 
<C>QuadraticIntegersByNorm</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>QuadraticNumber</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap14.html</Link><LinkText>3</LinkText></URL>
 
 
<C>QuadraticNumberConjugate</C> Examples: 
 
<C>QuadraticNumberField</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap14.html</Link><LinkText>3</LinkText></URL>
 
 
<C>QuandleIsomorphismRepresentatives</C> Examples: 
 
<C>QuotientByTorsionSubcomplex</C> Examples: 
 
<C>QuotientChainMap</C> Examples: 
 
<C>QuotientGroup</C> Examples: 
 
<C>QuotientQuasiIsomorph</C> Examples: 
 
<C>RadicalSeriesOfResolution</C> Examples: 
 
<C>RandomArc2Presentation</C> Examples: 
 
<C>RandomCellOfPureComplex</C> Examples: 
 
<C>ReadLinkImageAsGaussCode</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ReadMatrixAsPureCubicalComplex</C> Examples: 
 
<C>RecalculateIncidenceNumbers_NonFreeRes</C> Examples: 
 
<C>ReduceGenerators</C> Examples: 
 
<C>ReduceGenerators_alt</C> Examples: 
 
<C>ReflectedCubicalKnot</C> Examples: <URL><Link>../tutorial/chap2.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL> ,
<URL><Link>../tutorial/chap6.html</Link><LinkText>3</LinkText></URL> ,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>
 
 
<C>RegularCWAssociahedron</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWComplexComplement</C> Examples: <URL><Link>../tutorial/chap4.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWComplexReordered</C> Examples: 
 
<C>RegularCWComplexWithRemovedCell</C> Examples: <URL><Link>../tutorial/chap3.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWComplex_AttachCellDestructive</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWCube</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWMapToCWSubcomplex</C> Examples: 
 
<C>RegularCWOrbitPolytope</C> Examples: 
 
<C>RegularCWPermutahedron</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RegularCWPolygon</C> Examples: 
 
<C>RegularCWSimplex</C> Examples: <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>
 
 
<C>RelativeCentralQuotientSpaceGroup</C> Examples: 
 
<C>RelativeGroupHomology</C> Examples: 
 
<C>RelativeRightTransversal</C> Examples: 
 
<C>RemoveStar</C> Examples: 
 
<C>ResolutionAbelianBianchiSubgroup</C> Examples: 
 
<C>ResolutionAbelianGroup_alt</C> Examples: 
 
<C>ResolutionAbelianPcpGroup</C> Examples: 
 
<C>ResolutionAffineCrystGroup</C> Examples: 
 
<C>ResolutionArtinGroup_spherical</C> Examples: 
 
<C>ResolutionBoundaryOfWordOnRight</C> Examples: 
 
<C>ResolutionDirectProductLazy</C> Examples: 
 
<C>ResolutionFiniteCcGroup</C> Examples: 
 
<C>ResolutionFiniteCyclicGroup</C> Examples: 
 
<C>ResolutionGL2QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionGL3QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionGenericGroup</C> Examples: 
 
<C>ResolutionInfiniteCcGroup</C> Examples: <URL><Link>../tutorial/chap6.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionInfiniteCyclicGroup</C> Examples: 
 
<C>ResolutionPGL2QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionPGL3QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionPSL2QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ResolutionPrimePowerGroupSparse</C> Examples: 
 
<C>ResolutionSL2QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ResolutionSL2ZConjugated</C> Examples: 
 
<C>ResolutionSL2Z_alt</C> Examples: <URL><Link>../tutorial/chap13.html</Link><LinkText>1</LinkText></URL>
 
 
<C>ResolutionSpaceGroup</C> Examples: <URL><Link>../tutorial/chap8.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap11.html</Link><LinkText>2</LinkText></URL>
 
 
<C>ResolutionToEquivariantCWComplex</C> Examples: 
 
<C>ResolutionToResolutionOfFpGroup</C> Examples: <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>1</LinkText></URL>
 
 
<C>SL2QuadraticIntegers</C> Examples: <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL> ,
<URL><Link>../tutorial/chap13.html</Link><LinkText>2</LinkText></URL>
 
 
<C>SL2ZResolution</C> Examples: 
 
<C>SL2ZResolution_alt</C> Examples: 
 
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