\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Basic functionality for cellular complexes, fundamental groups and homology}}{7}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{ Data $\longrightarrow $ Cellular Complexes }}{7}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{RegularCWPolytope}}{7}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {1.1.2}\textcolor {Chapter }{CubicalComplex}}{7}{subsection.1.1.2}%
\contentsline {subsection}{\numberline {1.1.3}\textcolor {Chapter }{PureCubicalComplex}}{7}{subsection.1.1.3}%
\contentsline {subsection}{\numberline {1.1.4}\textcolor {Chapter }{PureCubicalKnot}}{8}{subsection.1.1.4}%
\contentsline {subsection}{\numberline {1.1.5}\textcolor {Chapter }{PurePermutahedralKnot}}{8}{subsection.1.1.5}%
\contentsline {subsection}{\numberline {1.1.6}\textcolor {Chapter }{PurePermutahedralComplex}}{8}{subsection.1.1.6}%
\contentsline {subsection}{\numberline {1.1.7}\textcolor {Chapter }{CayleyGraphOfGroup}}{8}{subsection.1.1.7}%
\contentsline {subsection}{\numberline {1.1.8}\textcolor {Chapter }{EquivariantEuclideanSpace}}{8}{subsection.1.1.8}%
\contentsline {subsection}{\numberline {1.1.9}\textcolor {Chapter }{EquivariantOrbitPolytope}}{9}{subsection.1.1.9}%
\contentsline {subsection}{\numberline {1.1.10}\textcolor {Chapter }{EquivariantTwoComplex}}{9}{subsection.1.1.10}%
\contentsline {subsection}{\numberline {1.1.11}\textcolor {Chapter }{QuillenComplex}}{9}{subsection.1.1.11}%
\contentsline {subsection}{\numberline {1.1.12}\textcolor {Chapter }{RestrictedEquivariantCWComplex}}{9}{subsection.1.1.12}%
\contentsline {subsection}{\numberline {1.1.13}\textcolor {Chapter }{RandomSimplicialGraph}}{9}{subsection.1.1.13}%
\contentsline {subsection}{\numberline {1.1.14}\textcolor {Chapter }{RandomSimplicialTwoComplex}}{9}{subsection.1.1.14}%
\contentsline {subsection}{\numberline {1.1.15}\textcolor {Chapter }{ReadCSVfileAsPureCubicalKnot}}{10}{subsection.1.1.15}%
\contentsline {subsection}{\numberline {1.1.16}\textcolor {Chapter }{ReadImageAsPureCubicalComplex}}{10}{subsection.1.1.16}%
\contentsline {subsection}{\numberline {1.1.17}\textcolor {Chapter }{ReadImageAsFilteredPureCubicalComplex}}{10}{subsection.1.1.17}%
\contentsline {subsection}{\numberline {1.1.18}\textcolor {Chapter }{ReadImageAsWeightFunction}}{10}{subsection.1.1.18}%
\contentsline {subsection}{\numberline {1.1.19}\textcolor {Chapter }{ReadPDBfileAsPureCubicalComplex}}{11}{subsection.1.1.19}%
\contentsline {subsection}{\numberline {1.1.20}\textcolor {Chapter }{ReadPDBfileAsPurepermutahedralComplex}}{11}{subsection.1.1.20}%
\contentsline {subsection}{\numberline {1.1.21}\textcolor {Chapter }{RegularCWPolytope}}{11}{subsection.1.1.21}%
\contentsline {subsection}{\numberline {1.1.22}\textcolor {Chapter }{SimplicialComplex}}{11}{subsection.1.1.22}%
\contentsline {subsection}{\numberline {1.1.23}\textcolor {Chapter }{SymmetricMatrixToFilteredGraph}}{12}{subsection.1.1.23}%
\contentsline {subsection}{\numberline {1.1.24}\textcolor {Chapter }{SymmetricMatrixToGraph}}{12}{subsection.1.1.24}%
\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{ Metric Spaces}}{12}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{CayleyMetric}}{12}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {1.2.2}\textcolor {Chapter }{EuclideanMetric}}{12}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {1.2.3}\textcolor {Chapter }{EuclideanSquaredMetric}}{12}{subsection.1.2.3}%
\contentsline {subsection}{\numberline {1.2.4}\textcolor {Chapter }{HammingMetric}}{13}{subsection.1.2.4}%
\contentsline {subsection}{\numberline {1.2.5}\textcolor {Chapter }{KendallMetric}}{13}{subsection.1.2.5}%
\contentsline {subsection}{\numberline {1.2.6}\textcolor {Chapter }{ManhattanMetric}}{13}{subsection.1.2.6}%
\contentsline {subsection}{\numberline {1.2.7}\textcolor {Chapter }{VectorsToSymmetricMatrix}}{13}{subsection.1.2.7}%
\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{ Cellular Complexes $\longrightarrow $ Cellular Complexes}}{13}{section.1.3}%
\contentsline {subsection}{\numberline {1.3.1}\textcolor {Chapter }{BoundaryMap}}{13}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {1.3.2}\textcolor {Chapter }{CliqueComplex}}{14}{subsection.1.3.2}%
\contentsline {subsection}{\numberline {1.3.3}\textcolor {Chapter }{ConcentricFiltration}}{14}{subsection.1.3.3}%
\contentsline {subsection}{\numberline {1.3.4}\textcolor {Chapter }{DirectProduct}}{14}{subsection.1.3.4}%
\contentsline {subsection}{\numberline {1.3.5}\textcolor {Chapter }{FiltrationTerm}}{14}{subsection.1.3.5}%
\contentsline {subsection}{\numberline {1.3.6}\textcolor {Chapter }{Graph}}{14}{subsection.1.3.6}%
\contentsline {subsection}{\numberline {1.3.7}\textcolor {Chapter }{HomotopyGraph}}{15}{subsection.1.3.7}%
\contentsline {subsection}{\numberline {1.3.8}\textcolor {Chapter }{Nerve}}{15}{subsection.1.3.8}%
\contentsline {subsection}{\numberline {1.3.9}\textcolor {Chapter }{RegularCWComplex}}{15}{subsection.1.3.9}%
\contentsline {subsection}{\numberline {1.3.10}\textcolor {Chapter }{RegularCWMap}}{15}{subsection.1.3.10}%
\contentsline {subsection}{\numberline {1.3.11}\textcolor {Chapter }{ThickeningFiltration}}{16}{subsection.1.3.11}%
\contentsline {section}{\numberline {1.4}\textcolor {Chapter }{ Cellular Complexes $\longrightarrow $ Cellular Complexes (Preserving Data Types)}}{16}{section.1.4}%
\contentsline {subsection}{\numberline {1.4.1}\textcolor {Chapter }{ContractedComplex}}{16}{subsection.1.4.1}%
\contentsline {subsection}{\numberline {1.4.2}\textcolor {Chapter }{ContractibleSubcomplex}}{16}{subsection.1.4.2}%
\contentsline {subsection}{\numberline {1.4.3}\textcolor {Chapter }{KnotReflection}}{17}{subsection.1.4.3}%
\contentsline {subsection}{\numberline {1.4.4}\textcolor {Chapter }{KnotSum}}{17}{subsection.1.4.4}%
\contentsline {subsection}{\numberline {1.4.5}\textcolor {Chapter }{OrientRegularCWComplex}}{17}{subsection.1.4.5}%
\contentsline {subsection}{\numberline {1.4.6}\textcolor {Chapter }{PathComponent}}{17}{subsection.1.4.6}%
\contentsline {subsection}{\numberline {1.4.7}\textcolor {Chapter }{PureComplexBoundary}}{17}{subsection.1.4.7}%
\contentsline {subsection}{\numberline {1.4.8}\textcolor {Chapter }{PureComplexComplement}}{18}{subsection.1.4.8}%
\contentsline {subsection}{\numberline {1.4.9}\textcolor {Chapter }{PureComplexDifference}}{18}{subsection.1.4.9}%
\contentsline {subsection}{\numberline {1.4.10}\textcolor {Chapter }{PureComplexInterstection}}{18}{subsection.1.4.10}%
\contentsline {subsection}{\numberline {1.4.11}\textcolor {Chapter }{PureComplexThickened}}{18}{subsection.1.4.11}%
\contentsline {subsection}{\numberline {1.4.12}\textcolor {Chapter }{PureComplexUnion}}{18}{subsection.1.4.12}%
\contentsline {subsection}{\numberline {1.4.13}\textcolor {Chapter }{SimplifiedComplex}}{18}{subsection.1.4.13}%
\contentsline {subsection}{\numberline {1.4.14}\textcolor {Chapter }{ZigZagContractedComplex}}{19}{subsection.1.4.14}%
\contentsline {section}{\numberline {1.5}\textcolor {Chapter }{ Cellular Complexes $\longrightarrow $ Homotopy Invariants}}{19}{section.1.5}%
\contentsline {subsection}{\numberline {1.5.1}\textcolor {Chapter }{AlexanderPolynomial}}{19}{subsection.1.5.1}%
\contentsline {subsection}{\numberline {1.5.2}\textcolor {Chapter }{BettiNumber}}{19}{subsection.1.5.2}%
\contentsline {subsection}{\numberline {1.5.3}\textcolor {Chapter }{EulerCharacteristic}}{20}{subsection.1.5.3}%
\contentsline {subsection}{\numberline {1.5.4}\textcolor {Chapter }{EulerIntegral}}{20}{subsection.1.5.4}%
\contentsline {subsection}{\numberline {1.5.5}\textcolor {Chapter }{FundamentalGroup}}{20}{subsection.1.5.5}%
\contentsline {subsection}{\numberline {1.5.6}\textcolor {Chapter }{FundamentalGroupOfQuotient}}{21}{subsection.1.5.6}%
\contentsline {subsection}{\numberline {1.5.7}\textcolor {Chapter }{IsAspherical}}{21}{subsection.1.5.7}%
\contentsline {subsection}{\numberline {1.5.8}\textcolor {Chapter }{KnotGroup}}{21}{subsection.1.5.8}%
\contentsline {subsection}{\numberline {1.5.9}\textcolor {Chapter }{PiZero}}{21}{subsection.1.5.9}%
\contentsline {subsection}{\numberline {1.5.10}\textcolor {Chapter }{PersistentBettiNumbers}}{21}{subsection.1.5.10}%
\contentsline {section}{\numberline {1.6}\textcolor {Chapter }{ Data $\longrightarrow $ Homotopy Invariants}}{22}{section.1.6}%
\contentsline {subsection}{\numberline {1.6.1}\textcolor {Chapter }{DendrogramMat}}{22}{subsection.1.6.1}%
\contentsline {section}{\numberline {1.7}\textcolor {Chapter }{ Cellular Complexes $\longrightarrow $ Non Homotopy Invariants}}{22}{section.1.7}%
\contentsline {subsection}{\numberline {1.7.1}\textcolor {Chapter }{ChainComplex}}{22}{subsection.1.7.1}%
\contentsline {subsection}{\numberline {1.7.2}\textcolor {Chapter }{ChainComplexEquivalence}}{23}{subsection.1.7.2}%
\contentsline {subsection}{\numberline {1.7.3}\textcolor {Chapter }{ChainComplexOfQuotient}}{23}{subsection.1.7.3}%
\contentsline {subsection}{\numberline {1.7.4}\textcolor {Chapter }{ChainMap}}{23}{subsection.1.7.4}%
\contentsline {subsection}{\numberline {1.7.5}\textcolor {Chapter }{CochainComplex}}{23}{subsection.1.7.5}%
\contentsline {subsection}{\numberline {1.7.6}\textcolor {Chapter }{CriticalCells}}{24}{subsection.1.7.6}%
\contentsline {subsection}{\numberline {1.7.7}\textcolor {Chapter }{DiagonalApproximation}}{24}{subsection.1.7.7}%
\contentsline {subsection}{\numberline {1.7.8}\textcolor {Chapter }{Size}}{24}{subsection.1.7.8}%
\contentsline {section}{\numberline {1.8}\textcolor {Chapter }{ (Co)chain Complexes $\longrightarrow $ (Co)chain Complexes}}{24}{section.1.8}%
\contentsline {subsection}{\numberline {1.8.1}\textcolor {Chapter }{FilteredTensorWithIntegers}}{24}{subsection.1.8.1}%
\contentsline {subsection}{\numberline {1.8.2}\textcolor {Chapter }{FilteredTensorWithIntegersModP}}{25}{subsection.1.8.2}%
\contentsline {subsection}{\numberline {1.8.3}\textcolor {Chapter }{HomToIntegers}}{25}{subsection.1.8.3}%
\contentsline {subsection}{\numberline {1.8.4}\textcolor {Chapter }{TensorWithIntegersModP}}{25}{subsection.1.8.4}%
\contentsline {section}{\numberline {1.9}\textcolor {Chapter }{ (Co)chain Complexes $\longrightarrow $ Homotopy Invariants}}{25}{section.1.9}%
\contentsline {subsection}{\numberline {1.9.1}\textcolor {Chapter }{Cohomology}}{25}{subsection.1.9.1}%
\contentsline {subsection}{\numberline {1.9.2}\textcolor {Chapter }{CupProduct}}{26}{subsection.1.9.2}%
\contentsline {subsection}{\numberline {1.9.3}\textcolor {Chapter }{Homology}}{26}{subsection.1.9.3}%
\contentsline {section}{\numberline {1.10}\textcolor {Chapter }{ Visualization}}{27}{section.1.10}%
\contentsline {subsection}{\numberline {1.10.1}\textcolor {Chapter }{BarCodeDisplay}}{27}{subsection.1.10.1}%
\contentsline {subsection}{\numberline {1.10.2}\textcolor {Chapter }{BarCodeCompactDisplay}}{27}{subsection.1.10.2}%
\contentsline {subsection}{\numberline {1.10.3}\textcolor {Chapter }{CayleyGraphOfGroup}}{27}{subsection.1.10.3}%
\contentsline {subsection}{\numberline {1.10.4}\textcolor {Chapter }{Display}}{27}{subsection.1.10.4}%
\contentsline {subsection}{\numberline {1.10.5}\textcolor {Chapter }{DisplayArcPresentation}}{27}{subsection.1.10.5}%
\contentsline {subsection}{\numberline {1.10.6}\textcolor {Chapter }{DisplayCSVKnotFile}}{28}{subsection.1.10.6}%
\contentsline {subsection}{\numberline {1.10.7}\textcolor {Chapter }{DisplayDendrogram}}{28}{subsection.1.10.7}%
\contentsline {subsection}{\numberline {1.10.8}\textcolor {Chapter }{DisplayDendrogramMat}}{28}{subsection.1.10.8}%
\contentsline {subsection}{\numberline {1.10.9}\textcolor {Chapter }{DisplayPDBfile}}{28}{subsection.1.10.9}%
\contentsline {subsection}{\numberline {1.10.10}\textcolor {Chapter }{OrbitPolytope}}{28}{subsection.1.10.10}%
\contentsline {subsection}{\numberline {1.10.11}\textcolor {Chapter }{ScatterPlot}}{29}{subsection.1.10.11}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Basic functionality for $\mathbb ZG$\texttt {\symbol {45}}resolutions and group cohomology}}{30}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{ Resolutions}}{30}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{EquivariantChainMap}}{30}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}\textcolor {Chapter }{FreeGResolution}}{30}{subsection.2.1.2}%
\contentsline {subsection}{\numberline {2.1.3}\textcolor {Chapter }{ResolutionBieberbachGroup}}{30}{subsection.2.1.3}%
\contentsline {subsection}{\numberline {2.1.4}\textcolor {Chapter }{ResolutionCubicalCrystGroup}}{31}{subsection.2.1.4}%
\contentsline {subsection}{\numberline {2.1.5}\textcolor {Chapter }{ResolutionFiniteGroup}}{31}{subsection.2.1.5}%
\contentsline {subsection}{\numberline {2.1.6}\textcolor {Chapter }{ResolutionNilpotentGroup}}{31}{subsection.2.1.6}%
\contentsline {subsection}{\numberline {2.1.7}\textcolor {Chapter }{ResolutionNormalSeries}}{31}{subsection.2.1.7}%
\contentsline {subsection}{\numberline {2.1.8}\textcolor {Chapter }{ResolutionPrimePowerGroup}}{31}{subsection.2.1.8}%
\contentsline {subsection}{\numberline {2.1.9}\textcolor {Chapter }{ResolutionSL2Z}}{32}{subsection.2.1.9}%
\contentsline {subsection}{\numberline {2.1.10}\textcolor {Chapter }{ResolutionSmallGroup}}{32}{subsection.2.1.10}%
\contentsline {subsection}{\numberline {2.1.11}\textcolor {Chapter }{ResolutionSubgroup}}{32}{subsection.2.1.11}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{ Algebras $\longrightarrow $ (Co)chain Complexes}}{32}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{LeibnizComplex}}{32}{subsection.2.2.1}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{ Resolutions $\longrightarrow $ (Co)chain Complexes}}{32}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{HomToIntegers}}{32}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{HomToIntegralModule}}{33}{subsection.2.3.2}%
\contentsline {subsection}{\numberline {2.3.3}\textcolor {Chapter }{TensorWithIntegers}}{33}{subsection.2.3.3}%
\contentsline {subsection}{\numberline {2.3.4}\textcolor {Chapter }{TensorWithIntegersModP}}{33}{subsection.2.3.4}%
\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{ Cohomology rings}}{34}{section.2.4}%
\contentsline {subsection}{\numberline {2.4.1}\textcolor {Chapter }{AreIsomorphicGradedAlgebras}}{34}{subsection.2.4.1}%
\contentsline {subsection}{\numberline {2.4.2}\textcolor {Chapter }{HAPDerivation}}{34}{subsection.2.4.2}%
\contentsline {subsection}{\numberline {2.4.3}\textcolor {Chapter }{HilbertPoincareSeries}}{34}{subsection.2.4.3}%
\contentsline {subsection}{\numberline {2.4.4}\textcolor {Chapter }{HomologyOfDerivation}}{34}{subsection.2.4.4}%
\contentsline {subsection}{\numberline {2.4.5}\textcolor {Chapter }{IntegralCohomologyGenerators}}{34}{subsection.2.4.5}%
\contentsline {subsection}{\numberline {2.4.6}\textcolor {Chapter }{LHSSpectralSequence}}{35}{subsection.2.4.6}%
\contentsline {subsection}{\numberline {2.4.7}\textcolor {Chapter }{LHSSpectralSequenceLastSheet}}{35}{subsection.2.4.7}%
\contentsline {subsection}{\numberline {2.4.8}\textcolor {Chapter }{ModPCohomologyGenerators}}{35}{subsection.2.4.8}%
\contentsline {subsection}{\numberline {2.4.9}\textcolor {Chapter }{ModPCohomologyRing ( )}}{35}{subsection.2.4.9}%
\contentsline {subsection}{\numberline {2.4.10}\textcolor {Chapter }{Mod2CohomologyRingPresentation}}{36}{subsection.2.4.10}%
\contentsline {section}{\numberline {2.5}\textcolor {Chapter }{ Group Invariants}}{36}{section.2.5}%
\contentsline {subsection}{\numberline {2.5.1}\textcolor {Chapter }{GroupCohomology}}{36}{subsection.2.5.1}%
\contentsline {subsection}{\numberline {2.5.2}\textcolor {Chapter }{GroupHomology}}{36}{subsection.2.5.2}%
\contentsline {subsection}{\numberline {2.5.3}\textcolor {Chapter }{PrimePartDerivedFunctor}}{37}{subsection.2.5.3}%
\contentsline {subsection}{\numberline {2.5.4}\textcolor {Chapter }{PoincareSeries}}{37}{subsection.2.5.4}%
\contentsline {subsection}{\numberline {2.5.5}\textcolor {Chapter }{PoincareSeries}}{37}{subsection.2.5.5}%
\contentsline {subsection}{\numberline {2.5.6}\textcolor {Chapter }{RankHomologyPGroup}}{38}{subsection.2.5.6}%
\contentsline {section}{\numberline {2.6}\textcolor {Chapter }{ $\mathbb F_p$\texttt {\symbol {45}}modules}}{38}{section.2.6}%
\contentsline {subsection}{\numberline {2.6.1}\textcolor {Chapter }{GroupAlgebraAsFpGModule}}{38}{subsection.2.6.1}%
\contentsline {subsection}{\numberline {2.6.2}\textcolor {Chapter }{Radical}}{38}{subsection.2.6.2}%
\contentsline {subsection}{\numberline {2.6.3}\textcolor {Chapter }{RadicalSeries}}{38}{subsection.2.6.3}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Basic functionality for homological group theory}}{39}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{ Cocycles}}{39}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{CcGroup}}{39}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {3.1.2}\textcolor {Chapter }{CocycleCondition}}{39}{subsection.3.1.2}%
\contentsline {subsection}{\numberline {3.1.3}\textcolor {Chapter }{StandardCocycle}}{39}{subsection.3.1.3}%
\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{ G\texttt {\symbol {45}}Outer Groups}}{40}{section.3.2}%
\contentsline {subsection}{\numberline {3.2.1}\textcolor {Chapter }{ActedGroup}}{40}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {3.2.2}\textcolor {Chapter }{ActingGroup}}{40}{subsection.3.2.2}%
\contentsline {subsection}{\numberline {3.2.3}\textcolor {Chapter }{Centre}}{40}{subsection.3.2.3}%
\contentsline {subsection}{\numberline {3.2.4}\textcolor {Chapter }{GOuterGroup}}{40}{subsection.3.2.4}%
\contentsline {section}{\numberline {3.3}\textcolor {Chapter }{ $G$\texttt {\symbol {45}}cocomplexes}}{41}{section.3.3}%
\contentsline {subsection}{\numberline {3.3.1}\textcolor {Chapter }{CohomologyModule}}{41}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {3.3.2}\textcolor {Chapter }{HomToGModule}}{41}{subsection.3.3.2}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Basic functionality for parallel computation}}{42}{chapter.4}%
\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{ Six Core Functions}}{42}{section.4.1}%
\contentsline {subsection}{\numberline {4.1.1}\textcolor {Chapter }{ChildCreate}}{42}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {4.1.2}\textcolor {Chapter }{ChildCreate}}{42}{subsection.4.1.2}%
\contentsline {chapter}{\numberline {5}\textcolor {Chapter }{Resolutions of the ground ring}}{44}{chapter.5}%
\contentsline {section}{\numberline {5.1}\textcolor {Chapter }{ {\nobreakspace }}}{44}{section.5.1}%
\contentsline {subsection}{\numberline {5.1.1}\textcolor {Chapter }{TietzeReducedResolution}}{44}{subsection.5.1.1}%
\contentsline {subsection}{\numberline {5.1.2}\textcolor {Chapter }{ResolutionArithmeticGroup}}{44}{subsection.5.1.2}%
\contentsline {subsection}{\numberline {5.1.3}\textcolor {Chapter }{FreeGResolution}}{45}{subsection.5.1.3}%
\contentsline {subsection}{\numberline {5.1.4}\textcolor {Chapter }{ResolutionGTree}}{45}{subsection.5.1.4}%
\contentsline {subsection}{\numberline {5.1.5}\textcolor {Chapter }{ResolutionSL2Z}}{45}{subsection.5.1.5}%
\contentsline {subsection}{\numberline {5.1.6}\textcolor {Chapter }{ResolutionAbelianGroup}}{45}{subsection.5.1.6}%
\contentsline {subsection}{\numberline {5.1.7}\textcolor {Chapter }{ResolutionAlmostCrystalGroup}}{46}{subsection.5.1.7}%
\contentsline {subsection}{\numberline {5.1.8}\textcolor {Chapter }{ResolutionAlmostCrystalQuotient}}{46}{subsection.5.1.8}%
\contentsline {subsection}{\numberline {5.1.9}\textcolor {Chapter }{ResolutionArtinGroup}}{46}{subsection.5.1.9}%
\contentsline {subsection}{\numberline {5.1.10}\textcolor {Chapter }{ResolutionAsphericalPresentation}}{47}{subsection.5.1.10}%
\contentsline {subsection}{\numberline {5.1.11}\textcolor {Chapter }{ResolutionBieberbachGroup}}{47}{subsection.5.1.11}%
\contentsline {subsection}{\numberline {5.1.12}\textcolor {Chapter }{ResolutionCoxeterGroup}}{47}{subsection.5.1.12}%
\contentsline {subsection}{\numberline {5.1.13}\textcolor {Chapter }{ResolutionDirectProduct}}{47}{subsection.5.1.13}%
\contentsline {subsection}{\numberline {5.1.14}\textcolor {Chapter }{ResolutionExtension}}{48}{subsection.5.1.14}%
\contentsline {subsection}{\numberline {5.1.15}\textcolor {Chapter }{ResolutionFiniteDirectProduct}}{48}{subsection.5.1.15}%
\contentsline {subsection}{\numberline {5.1.16}\textcolor {Chapter }{ResolutionFiniteExtension}}{48}{subsection.5.1.16}%
\contentsline {subsection}{\numberline {5.1.17}\textcolor {Chapter }{ResolutionFiniteGroup}}{48}{subsection.5.1.17}%
\contentsline {subsection}{\numberline {5.1.18}\textcolor {Chapter }{ResolutionFiniteSubgroup}}{49}{subsection.5.1.18}%
\contentsline {subsection}{\numberline {5.1.19}\textcolor {Chapter }{ResolutionGraphOfGroups}}{49}{subsection.5.1.19}%
\contentsline {subsection}{\numberline {5.1.20}\textcolor {Chapter }{ResolutionNilpotentGroup}}{49}{subsection.5.1.20}%
\contentsline {subsection}{\numberline {5.1.21}\textcolor {Chapter }{ResolutionNormalSeries}}{50}{subsection.5.1.21}%
\contentsline {subsection}{\numberline {5.1.22}\textcolor {Chapter }{ResolutionPrimePowerGroup}}{50}{subsection.5.1.22}%
\contentsline {subsection}{\numberline {5.1.23}\textcolor {Chapter }{ResolutionSmallFpGroup}}{50}{subsection.5.1.23}%
\contentsline {subsection}{\numberline {5.1.24}\textcolor {Chapter }{ResolutionSubgroup}}{51}{subsection.5.1.24}%
\contentsline {subsection}{\numberline {5.1.25}\textcolor {Chapter }{ResolutionSubnormalSeries}}{51}{subsection.5.1.25}%
\contentsline {subsection}{\numberline {5.1.26}\textcolor {Chapter }{TwistedTensorProduct}}{51}{subsection.5.1.26}%
\contentsline {subsection}{\numberline {5.1.27}\textcolor {Chapter }{ConjugatedResolution}}{51}{subsection.5.1.27}%
\contentsline {subsection}{\numberline {5.1.28}\textcolor {Chapter }{RecalculateIncidenceNumbers}}{52}{subsection.5.1.28}%
\contentsline {chapter}{\numberline {6}\textcolor {Chapter }{ Resolutions of modules}}{53}{chapter.6}%
\contentsline {section}{\numberline {6.1}\textcolor {Chapter }{ {\nobreakspace }}}{53}{section.6.1}%
\contentsline {subsection}{\numberline {6.1.1}\textcolor {Chapter }{ResolutionFpGModule}}{53}{subsection.6.1.1}%
\contentsline {chapter}{\numberline {7}\textcolor {Chapter }{ Induced equivariant chain maps}}{54}{chapter.7}%
\contentsline {section}{\numberline {7.1}\textcolor {Chapter }{ {\nobreakspace }}}{54}{section.7.1}%
\contentsline {subsection}{\numberline {7.1.1}\textcolor {Chapter }{EquivariantChainMap}}{54}{subsection.7.1.1}%
\contentsline {chapter}{\numberline {8}\textcolor {Chapter }{ Functors}}{55}{chapter.8}%
\contentsline {section}{\numberline {8.1}\textcolor {Chapter }{ {\nobreakspace }}}{55}{section.8.1}%
\contentsline {subsection}{\numberline {8.1.1}\textcolor {Chapter }{ExtendScalars}}{55}{subsection.8.1.1}%
\contentsline {subsection}{\numberline {8.1.2}\textcolor {Chapter }{HomToIntegers}}{55}{subsection.8.1.2}%
\contentsline {subsection}{\numberline {8.1.3}\textcolor {Chapter }{HomToIntegersModP}}{55}{subsection.8.1.3}%
\contentsline {subsection}{\numberline {8.1.4}\textcolor {Chapter }{HomToIntegralModule}}{55}{subsection.8.1.4}%
\contentsline {subsection}{\numberline {8.1.5}\textcolor {Chapter }{TensorWithIntegralModule}}{56}{subsection.8.1.5}%
\contentsline {subsection}{\numberline {8.1.6}\textcolor {Chapter }{HomToGModule}}{56}{subsection.8.1.6}%
\contentsline {subsection}{\numberline {8.1.7}\textcolor {Chapter }{InduceScalars}}{56}{subsection.8.1.7}%
\contentsline {subsection}{\numberline {8.1.8}\textcolor {Chapter }{LowerCentralSeriesLieAlgebra}}{56}{subsection.8.1.8}%
\contentsline {subsection}{\numberline {8.1.9}\textcolor {Chapter }{TensorWithIntegers}}{57}{subsection.8.1.9}%
\contentsline {subsection}{\numberline {8.1.10}\textcolor {Chapter }{FilteredTensorWithIntegers}}{57}{subsection.8.1.10}%
\contentsline {subsection}{\numberline {8.1.11}\textcolor {Chapter }{TensorWithTwistedIntegers}}{57}{subsection.8.1.11}%
\contentsline {subsection}{\numberline {8.1.12}\textcolor {Chapter }{TensorWithIntegersModP}}{57}{subsection.8.1.12}%
\contentsline {subsection}{\numberline {8.1.13}\textcolor {Chapter }{TensorWithTwistedIntegersModP}}{57}{subsection.8.1.13}%
\contentsline {subsection}{\numberline {8.1.14}\textcolor {Chapter }{TensorWithRationals}}{58}{subsection.8.1.14}%
\contentsline {chapter}{\numberline {9}\textcolor {Chapter }{ Chain complexes}}{59}{chapter.9}%
\contentsline {section}{\numberline {9.1}\textcolor {Chapter }{ {\nobreakspace }}}{59}{section.9.1}%
\contentsline {subsection}{\numberline {9.1.1}\textcolor {Chapter }{ChainComplex}}{59}{subsection.9.1.1}%
\contentsline {subsection}{\numberline {9.1.2}\textcolor {Chapter }{ChainComplexOfPair}}{59}{subsection.9.1.2}%
\contentsline {subsection}{\numberline {9.1.3}\textcolor {Chapter }{ChevalleyEilenbergComplex}}{59}{subsection.9.1.3}%
\contentsline {subsection}{\numberline {9.1.4}\textcolor {Chapter }{LeibnizComplex}}{60}{subsection.9.1.4}%
\contentsline {subsection}{\numberline {9.1.5}\textcolor {Chapter }{SuspendedChainComplex}}{60}{subsection.9.1.5}%
\contentsline {subsection}{\numberline {9.1.6}\textcolor {Chapter }{ReducedSuspendedChainComplex}}{60}{subsection.9.1.6}%
\contentsline {subsection}{\numberline {9.1.7}\textcolor {Chapter }{CoreducedChainComplex}}{60}{subsection.9.1.7}%
\contentsline {subsection}{\numberline {9.1.8}\textcolor {Chapter }{TensorProductOfChainComplexes}}{60}{subsection.9.1.8}%
\contentsline {subsection}{\numberline {9.1.9}\textcolor {Chapter }{LefschetzNumber}}{61}{subsection.9.1.9}%
\contentsline {chapter}{\numberline {10}\textcolor {Chapter }{ Sparse Chain complexes}}{62}{chapter.10}%
\contentsline {section}{\numberline {10.1}\textcolor {Chapter }{ {\nobreakspace }}}{62}{section.10.1}%
\contentsline {subsection}{\numberline {10.1.1}\textcolor {Chapter }{SparseMat}}{62}{subsection.10.1.1}%
\contentsline {subsection}{\numberline {10.1.2}\textcolor {Chapter }{TransposeOfSparseMat}}{62}{subsection.10.1.2}%
\contentsline {subsection}{\numberline {10.1.3}\textcolor {Chapter }{ReverseSparseMat}}{62}{subsection.10.1.3}%
\contentsline {subsection}{\numberline {10.1.4}\textcolor {Chapter }{SparseRowMult}}{62}{subsection.10.1.4}%
\contentsline {subsection}{\numberline {10.1.5}\textcolor {Chapter }{SparseRowInterchange}}{63}{subsection.10.1.5}%
\contentsline {subsection}{\numberline {10.1.6}\textcolor {Chapter }{SparseRowAdd}}{63}{subsection.10.1.6}%
\contentsline {subsection}{\numberline {10.1.7}\textcolor {Chapter }{SparseSemiEchelon}}{63}{subsection.10.1.7}%
\contentsline {subsection}{\numberline {10.1.8}\textcolor {Chapter }{RankMatDestructive}}{63}{subsection.10.1.8}%
\contentsline {subsection}{\numberline {10.1.9}\textcolor {Chapter }{RankMat}}{63}{subsection.10.1.9}%
\contentsline {subsection}{\numberline {10.1.10}\textcolor {Chapter }{SparseChainComplex}}{63}{subsection.10.1.10}%
\contentsline {subsection}{\numberline {10.1.11}\textcolor {Chapter }{SparseChainComplexOfRegularCWComplex}}{64}{subsection.10.1.11}%
\contentsline {subsection}{\numberline {10.1.12}\textcolor {Chapter }{SparseBoundaryMatrix}}{64}{subsection.10.1.12}%
\contentsline {subsection}{\numberline {10.1.13}\textcolor {Chapter }{Bettinumbers}}{64}{subsection.10.1.13}%
\contentsline {chapter}{\numberline {11}\textcolor {Chapter }{ Homology and cohomology groups}}{65}{chapter.11}%
\contentsline {section}{\numberline {11.1}\textcolor {Chapter }{ {\nobreakspace }}}{65}{section.11.1}%
\contentsline {subsection}{\numberline {11.1.1}\textcolor {Chapter }{Cohomology}}{65}{subsection.11.1.1}%
\contentsline {subsection}{\numberline {11.1.2}\textcolor {Chapter }{CohomologyModule}}{65}{subsection.11.1.2}%
\contentsline {subsection}{\numberline {11.1.3}\textcolor {Chapter }{CohomologyPrimePart}}{65}{subsection.11.1.3}%
\contentsline {subsection}{\numberline {11.1.4}\textcolor {Chapter }{GroupCohomology}}{66}{subsection.11.1.4}%
\contentsline {subsection}{\numberline {11.1.5}\textcolor {Chapter }{GroupHomology}}{66}{subsection.11.1.5}%
\contentsline {subsection}{\numberline {11.1.6}\textcolor {Chapter }{PersistentHomologyOfQuotientGroupSeries}}{67}{subsection.11.1.6}%
\contentsline {subsection}{\numberline {11.1.7}\textcolor {Chapter }{PersistentCohomologyOfQuotientGroupSeries}}{67}{subsection.11.1.7}%
\contentsline {subsection}{\numberline {11.1.8}\textcolor {Chapter }{UniversalBarCode}}{68}{subsection.11.1.8}%
\contentsline {subsection}{\numberline {11.1.9}\textcolor {Chapter }{PersistentHomologyOfSubGroupSeries}}{68}{subsection.11.1.9}%
\contentsline {subsection}{\numberline {11.1.10}\textcolor {Chapter }{PersistentHomologyOfFilteredChainComplex}}{68}{subsection.11.1.10}%
\contentsline {subsection}{\numberline {11.1.11}\textcolor {Chapter }{PersistentHomologyOfCommutativeDiagramOfPGroups}}{68}{subsection.11.1.11}%
\contentsline {subsection}{\numberline {11.1.12}\textcolor {Chapter }{PersistentHomologyOfFilteredPureCubicalComplex}}{69}{subsection.11.1.12}%
\contentsline {subsection}{\numberline {11.1.13}\textcolor {Chapter }{PersistentHomologyOfPureCubicalComplex}}{69}{subsection.11.1.13}%
\contentsline {subsection}{\numberline {11.1.14}\textcolor {Chapter }{ZZPersistentHomologyOfPureCubicalComplex}}{69}{subsection.11.1.14}%
\contentsline {subsection}{\numberline {11.1.15}\textcolor {Chapter }{RipsHomology}}{69}{subsection.11.1.15}%
\contentsline {subsection}{\numberline {11.1.16}\textcolor {Chapter }{BarCode}}{69}{subsection.11.1.16}%
\contentsline {subsection}{\numberline {11.1.17}\textcolor {Chapter }{BarCodeDisplay}}{70}{subsection.11.1.17}%
\contentsline {subsection}{\numberline {11.1.18}\textcolor {Chapter }{Homology}}{70}{subsection.11.1.18}%
\contentsline {subsection}{\numberline {11.1.19}\textcolor {Chapter }{HomologyPb}}{70}{subsection.11.1.19}%
\contentsline {subsection}{\numberline {11.1.20}\textcolor {Chapter }{HomologyVectorSpace}}{71}{subsection.11.1.20}%
\contentsline {subsection}{\numberline {11.1.21}\textcolor {Chapter }{HomologyPrimePart}}{71}{subsection.11.1.21}%
\contentsline {subsection}{\numberline {11.1.22}\textcolor {Chapter }{LeibnizAlgebraHomology}}{71}{subsection.11.1.22}%
\contentsline {subsection}{\numberline {11.1.23}\textcolor {Chapter }{LieAlgebraHomology}}{71}{subsection.11.1.23}%
\contentsline {subsection}{\numberline {11.1.24}\textcolor {Chapter }{PrimePartDerivedFunctor}}{71}{subsection.11.1.24}%
\contentsline {subsection}{\numberline {11.1.25}\textcolor {Chapter }{RankHomologyPGroup}}{72}{subsection.11.1.25}%
\contentsline {subsection}{\numberline {11.1.26}\textcolor {Chapter }{RankPrimeHomology}}{72}{subsection.11.1.26}%
\contentsline {chapter}{\numberline {12}\textcolor {Chapter }{ Poincare series}}{73}{chapter.12}%
\contentsline {section}{\numberline {12.1}\textcolor {Chapter }{ {\nobreakspace }}}{73}{section.12.1}%
\contentsline {subsection}{\numberline {12.1.1}\textcolor {Chapter }{EfficientNormalSubgroups}}{73}{subsection.12.1.1}%
\contentsline {subsection}{\numberline {12.1.2}\textcolor {Chapter }{ExpansionOfRationalFunction}}{73}{subsection.12.1.2}%
\contentsline {subsection}{\numberline {12.1.3}\textcolor {Chapter }{PoincareSeries}}{73}{subsection.12.1.3}%
\contentsline {subsection}{\numberline {12.1.4}\textcolor {Chapter }{PoincareSeriesPrimePart}}{74}{subsection.12.1.4}%
\contentsline {subsection}{\numberline {12.1.5}\textcolor {Chapter }{PoincareSeriesLHS}}{74}{subsection.12.1.5}%
\contentsline {subsection}{\numberline {12.1.6}\textcolor {Chapter }{Prank}}{74}{subsection.12.1.6}%
\contentsline {chapter}{\numberline {13}\textcolor {Chapter }{ Cohomology ring structure}}{75}{chapter.13}%
\contentsline {section}{\numberline {13.1}\textcolor {Chapter }{ {\nobreakspace }}}{75}{section.13.1}%
\contentsline {subsection}{\numberline {13.1.1}\textcolor {Chapter }{IntegralCupProduct}}{75}{subsection.13.1.1}%
\contentsline {subsection}{\numberline {13.1.2}\textcolor {Chapter }{IntegralRingGenerators}}{75}{subsection.13.1.2}%
\contentsline {subsection}{\numberline {13.1.3}\textcolor {Chapter }{ModPCohomologyGenerators}}{76}{subsection.13.1.3}%
\contentsline {subsection}{\numberline {13.1.4}\textcolor {Chapter }{ModPCohomologyRing ( )}}{76}{subsection.13.1.4}%
\contentsline {subsection}{\numberline {13.1.5}\textcolor {Chapter }{ModPRingGenerators}}{76}{subsection.13.1.5}%
\contentsline {subsection}{\numberline {13.1.6}\textcolor {Chapter }{Mod2CohomologyRingPresentation}}{76}{subsection.13.1.6}%
\contentsline {chapter}{\numberline {14}\textcolor {Chapter }{ Cohomology rings of $p$\texttt {\symbol {45}}groups (mainly $p=2)$}}{78}{chapter.14}%
\contentsline {section}{\numberline {14.1}\textcolor {Chapter }{ {\nobreakspace }}}{78}{section.14.1}%
\contentsline {subsection}{\numberline {14.1.1}\textcolor {Chapter }{Mod2CohomologyRingPresentation}}{78}{subsection.14.1.1}%
\contentsline {subsection}{\numberline {14.1.2}\textcolor {Chapter }{PoincareSeriesLHS}}{78}{subsection.14.1.2}%
\contentsline {chapter}{\numberline {15}\textcolor {Chapter }{ Commutator and nonabelian tensor computations}}{80}{chapter.15}%
\contentsline {section}{\numberline {15.1}\textcolor {Chapter }{ {\nobreakspace }}}{80}{section.15.1}%
\contentsline {subsection}{\numberline {15.1.1}\textcolor {Chapter }{BaerInvariant}}{80}{subsection.15.1.1}%
\contentsline {subsection}{\numberline {15.1.2}\textcolor {Chapter }{BogomolovMultiplier}}{80}{subsection.15.1.2}%
\contentsline {subsection}{\numberline {15.1.3}\textcolor {Chapter }{Bogomology}}{81}{subsection.15.1.3}%
\contentsline {subsection}{\numberline {15.1.4}\textcolor {Chapter }{Coclass}}{81}{subsection.15.1.4}%
\contentsline {subsection}{\numberline {15.1.5}\textcolor {Chapter }{EpiCentre}}{81}{subsection.15.1.5}%
\contentsline {subsection}{\numberline {15.1.6}\textcolor {Chapter }{NonabelianExteriorProduct}}{81}{subsection.15.1.6}%
\contentsline {subsection}{\numberline {15.1.7}\textcolor {Chapter }{NonabelianSymmetricKernel}}{82}{subsection.15.1.7}%
\contentsline {subsection}{\numberline {15.1.8}\textcolor {Chapter }{NonabelianSymmetricSquare}}{82}{subsection.15.1.8}%
\contentsline {subsection}{\numberline {15.1.9}\textcolor {Chapter }{NonabelianTensorProduct}}{82}{subsection.15.1.9}%
\contentsline {subsection}{\numberline {15.1.10}\textcolor {Chapter }{NonabelianTensorSquare}}{83}{subsection.15.1.10}%
\contentsline {subsection}{\numberline {15.1.11}\textcolor {Chapter }{RelativeSchurMultiplier}}{83}{subsection.15.1.11}%
\contentsline {subsection}{\numberline {15.1.12}\textcolor {Chapter }{TensorCentre}}{83}{subsection.15.1.12}%
\contentsline {subsection}{\numberline {15.1.13}\textcolor {Chapter }{ThirdHomotopyGroupOfSuspensionB}}{84}{subsection.15.1.13}%
\contentsline {subsection}{\numberline {15.1.14}\textcolor {Chapter }{UpperEpicentralSeries}}{84}{subsection.15.1.14}%
\contentsline {chapter}{\numberline {16}\textcolor {Chapter }{ Lie commutators and nonabelian Lie tensors}}{85}{chapter.16}%
\contentsline {section}{\numberline {16.1}\textcolor {Chapter }{ {\nobreakspace }}}{85}{section.16.1}%
\contentsline {subsection}{\numberline {16.1.1}\textcolor {Chapter }{LieCoveringHomomorphism}}{85}{subsection.16.1.1}%
\contentsline {subsection}{\numberline {16.1.2}\textcolor {Chapter }{LeibnizQuasiCoveringHomomorphism}}{85}{subsection.16.1.2}%
\contentsline {subsection}{\numberline {16.1.3}\textcolor {Chapter }{LieEpiCentre}}{86}{subsection.16.1.3}%
\contentsline {subsection}{\numberline {16.1.4}\textcolor {Chapter }{LieExteriorSquare}}{86}{subsection.16.1.4}%
\contentsline {subsection}{\numberline {16.1.5}\textcolor {Chapter }{LieTensorSquare}}{86}{subsection.16.1.5}%
\contentsline {subsection}{\numberline {16.1.6}\textcolor {Chapter }{LieTensorCentre}}{86}{subsection.16.1.6}%
\contentsline {chapter}{\numberline {17}\textcolor {Chapter }{ Generators and relators of groups}}{87}{chapter.17}%
\contentsline {section}{\numberline {17.1}\textcolor {Chapter }{ {\nobreakspace }}}{87}{section.17.1}%
\contentsline {subsection}{\numberline {17.1.1}\textcolor {Chapter }{CayleyGraphOfGroupDisplay}}{87}{subsection.17.1.1}%
\contentsline {subsection}{\numberline {17.1.2}\textcolor {Chapter }{IdentityAmongRelatorsDisplay}}{87}{subsection.17.1.2}%
\contentsline {subsection}{\numberline {17.1.3}\textcolor {Chapter }{IsAspherical}}{87}{subsection.17.1.3}%
\contentsline {subsection}{\numberline {17.1.4}\textcolor {Chapter }{PresentationOfResolution}}{88}{subsection.17.1.4}%
\contentsline {subsection}{\numberline {17.1.5}\textcolor {Chapter }{TorsionGeneratorsAbelianGroup}}{88}{subsection.17.1.5}%
\contentsline {chapter}{\numberline {18}\textcolor {Chapter }{ Orbit polytopes and fundamental domains}}{89}{chapter.18}%
\contentsline {section}{\numberline {18.1}\textcolor {Chapter }{ {\nobreakspace }}}{89}{section.18.1}%
\contentsline {subsection}{\numberline {18.1.1}\textcolor {Chapter }{CoxeterComplex}}{89}{subsection.18.1.1}%
\contentsline {subsection}{\numberline {18.1.2}\textcolor {Chapter }{ContractibleGcomplex}}{89}{subsection.18.1.2}%
\contentsline {subsection}{\numberline {18.1.3}\textcolor {Chapter }{QuotientOfContractibleGcomplex}}{90}{subsection.18.1.3}%
\contentsline {subsection}{\numberline {18.1.4}\textcolor {Chapter }{TruncatedGComplex}}{90}{subsection.18.1.4}%
\contentsline {subsection}{\numberline {18.1.5}\textcolor {Chapter }{FundamentalDomainStandardSpaceGroup}}{90}{subsection.18.1.5}%
\contentsline {subsection}{\numberline {18.1.6}\textcolor {Chapter }{OrbitPolytope}}{90}{subsection.18.1.6}%
\contentsline {subsection}{\numberline {18.1.7}\textcolor {Chapter }{PolytopalComplex}}{91}{subsection.18.1.7}%
\contentsline {subsection}{\numberline {18.1.8}\textcolor {Chapter }{PolytopalGenerators}}{91}{subsection.18.1.8}%
\contentsline {subsection}{\numberline {18.1.9}\textcolor {Chapter }{VectorStabilizer}}{92}{subsection.18.1.9}%
\contentsline {chapter}{\numberline {19}\textcolor {Chapter }{ Cocycles}}{93}{chapter.19}%
\contentsline {section}{\numberline {19.1}\textcolor {Chapter }{ {\nobreakspace }}}{93}{section.19.1}%
\contentsline {subsection}{\numberline {19.1.1}\textcolor {Chapter }{CcGroup}}{93}{subsection.19.1.1}%
\contentsline {subsection}{\numberline {19.1.2}\textcolor {Chapter }{CocycleCondition}}{93}{subsection.19.1.2}%
\contentsline {subsection}{\numberline {19.1.3}\textcolor {Chapter }{StandardCocycle}}{93}{subsection.19.1.3}%
\contentsline {subsection}{\numberline {19.1.4}\textcolor {Chapter }{Syzygy}}{94}{subsection.19.1.4}%
\contentsline {chapter}{\numberline {20}\textcolor {Chapter }{ Words in free $ZG$\texttt {\symbol {45}}modules }}{95}{chapter.20}%
\contentsline {section}{\numberline {20.1}\textcolor {Chapter }{ {\nobreakspace }}}{95}{section.20.1}%
\contentsline {subsection}{\numberline {20.1.1}\textcolor {Chapter }{AddFreeWords}}{95}{subsection.20.1.1}%
\contentsline {subsection}{\numberline {20.1.2}\textcolor {Chapter }{AddFreeWordsModP}}{95}{subsection.20.1.2}%
\contentsline {subsection}{\numberline {20.1.3}\textcolor {Chapter }{AlgebraicReduction}}{95}{subsection.20.1.3}%
\contentsline {subsection}{\numberline {20.1.4}\textcolor {Chapter }{MultiplyWord}}{95}{subsection.20.1.4}%
\contentsline {subsection}{\numberline {20.1.5}\textcolor {Chapter }{Negate}}{96}{subsection.20.1.5}%
\contentsline {subsection}{\numberline {20.1.6}\textcolor {Chapter }{NegateWord}}{96}{subsection.20.1.6}%
\contentsline {subsection}{\numberline {20.1.7}\textcolor {Chapter }{PrintZGword}}{96}{subsection.20.1.7}%
\contentsline {subsection}{\numberline {20.1.8}\textcolor {Chapter }{TietzeReduction}}{96}{subsection.20.1.8}%
\contentsline {subsection}{\numberline {20.1.9}\textcolor {Chapter }{ResolutionBoundaryOfWord}}{96}{subsection.20.1.9}%
\contentsline {chapter}{\numberline {21}\textcolor {Chapter }{ $FpG$\texttt {\symbol {45}}modules}}{97}{chapter.21}%
\contentsline {section}{\numberline {21.1}\textcolor {Chapter }{ {\nobreakspace }}}{97}{section.21.1}%
\contentsline {subsection}{\numberline {21.1.1}\textcolor {Chapter }{CompositionSeriesOfFpGModules}}{97}{subsection.21.1.1}%
\contentsline {subsection}{\numberline {21.1.2}\textcolor {Chapter }{DirectSumOfFpGModules}}{97}{subsection.21.1.2}%
\contentsline {subsection}{\numberline {21.1.3}\textcolor {Chapter }{FpGModule}}{97}{subsection.21.1.3}%
\contentsline {subsection}{\numberline {21.1.4}\textcolor {Chapter }{FpGModuleDualBasis}}{98}{subsection.21.1.4}%
\contentsline {subsection}{\numberline {21.1.5}\textcolor {Chapter }{FpGModuleHomomorphism}}{98}{subsection.21.1.5}%
\contentsline {subsection}{\numberline {21.1.6}\textcolor {Chapter }{DesuspensionFpGModule}}{98}{subsection.21.1.6}%
\contentsline {subsection}{\numberline {21.1.7}\textcolor {Chapter }{RadicalOfFpGModule}}{98}{subsection.21.1.7}%
\contentsline {subsection}{\numberline {21.1.8}\textcolor {Chapter }{RadicalSeriesOfFpGModule}}{99}{subsection.21.1.8}%
\contentsline {subsection}{\numberline {21.1.9}\textcolor {Chapter }{GeneratorsOfFpGModule}}{99}{subsection.21.1.9}%
\contentsline {subsection}{\numberline {21.1.10}\textcolor {Chapter }{ImageOfFpGModuleHomomorphism}}{99}{subsection.21.1.10}%
\contentsline {subsection}{\numberline {21.1.11}\textcolor {Chapter }{GroupAlgebraAsFpGModule}}{99}{subsection.21.1.11}%
\contentsline {subsection}{\numberline {21.1.12}\textcolor {Chapter }{IntersectionOfFpGModules}}{99}{subsection.21.1.12}%
\contentsline {subsection}{\numberline {21.1.13}\textcolor {Chapter }{IsFpGModuleHomomorphismData}}{99}{subsection.21.1.13}%
\contentsline {subsection}{\numberline {21.1.14}\textcolor {Chapter }{MaximalSubmoduleOfFpGModule}}{100}{subsection.21.1.14}%
\contentsline {subsection}{\numberline {21.1.15}\textcolor {Chapter }{MaximalSubmodulesOfFpGModule}}{100}{subsection.21.1.15}%
\contentsline {subsection}{\numberline {21.1.16}\textcolor {Chapter }{MultipleOfFpGModule}}{100}{subsection.21.1.16}%
\contentsline {subsection}{\numberline {21.1.17}\textcolor {Chapter }{ProjectedFpGModule}}{100}{subsection.21.1.17}%
\contentsline {subsection}{\numberline {21.1.18}\textcolor {Chapter }{RandomHomomorphismOfFpGModules}}{100}{subsection.21.1.18}%
\contentsline {subsection}{\numberline {21.1.19}\textcolor {Chapter }{Rank}}{101}{subsection.21.1.19}%
\contentsline {subsection}{\numberline {21.1.20}\textcolor {Chapter }{SumOfFpGModules}}{101}{subsection.21.1.20}%
\contentsline {subsection}{\numberline {21.1.21}\textcolor {Chapter }{SumOp}}{101}{subsection.21.1.21}%
\contentsline {subsection}{\numberline {21.1.22}\textcolor {Chapter }{VectorsToFpGModuleWords}}{101}{subsection.21.1.22}%
\contentsline {chapter}{\numberline {22}\textcolor {Chapter }{ Meataxe modules}}{102}{chapter.22}%
\contentsline {section}{\numberline {22.1}\textcolor {Chapter }{ {\nobreakspace }}}{102}{section.22.1}%
\contentsline {subsection}{\numberline {22.1.1}\textcolor {Chapter }{DesuspensionMtxModule}}{102}{subsection.22.1.1}%
\contentsline {subsection}{\numberline {22.1.2}\textcolor {Chapter }{FpG{\textunderscore }to{\textunderscore }MtxModule}}{102}{subsection.22.1.2}%
\contentsline {subsection}{\numberline {22.1.3}\textcolor {Chapter }{GeneratorsOfMtxModule}}{102}{subsection.22.1.3}%
\contentsline {chapter}{\numberline {23}\textcolor {Chapter }{ G\texttt {\symbol {45}}Outer Groups}}{103}{chapter.23}%
\contentsline {section}{\numberline {23.1}\textcolor {Chapter }{ {\nobreakspace }}}{103}{section.23.1}%
\contentsline {subsection}{\numberline {23.1.1}\textcolor {Chapter }{GOuterGroup}}{103}{subsection.23.1.1}%
\contentsline {subsection}{\numberline {23.1.2}\textcolor {Chapter }{GOuterGroupHomomorphismNC}}{103}{subsection.23.1.2}%
\contentsline {subsection}{\numberline {23.1.3}\textcolor {Chapter }{GOuterHomomorphismTester}}{103}{subsection.23.1.3}%
\contentsline {subsection}{\numberline {23.1.4}\textcolor {Chapter }{Centre}}{104}{subsection.23.1.4}%
\contentsline {subsection}{\numberline {23.1.5}\textcolor {Chapter }{DirectProductGog}}{104}{subsection.23.1.5}%
\contentsline {chapter}{\numberline {24}\textcolor {Chapter }{ Cat\texttt {\symbol {45}}1\texttt {\symbol {45}}groups}}{105}{chapter.24}%
\contentsline {section}{\numberline {24.1}\textcolor {Chapter }{ {\nobreakspace }}}{105}{section.24.1}%
\contentsline {subsection}{\numberline {24.1.1}\textcolor {Chapter }{AutomorphismGroupAsCatOneGroup}}{105}{subsection.24.1.1}%
\contentsline {subsection}{\numberline {24.1.2}\textcolor {Chapter }{HomotopyGroup}}{105}{subsection.24.1.2}%
\contentsline {subsection}{\numberline {24.1.3}\textcolor {Chapter }{HomotopyModule}}{105}{subsection.24.1.3}%
\contentsline {subsection}{\numberline {24.1.4}\textcolor {Chapter }{QuasiIsomorph}}{105}{subsection.24.1.4}%
\contentsline {subsection}{\numberline {24.1.5}\textcolor {Chapter }{ModuleAsCatOneGroup}}{106}{subsection.24.1.5}%
\contentsline {subsection}{\numberline {24.1.6}\textcolor {Chapter }{MooreComplex}}{106}{subsection.24.1.6}%
\contentsline {subsection}{\numberline {24.1.7}\textcolor {Chapter }{NormalSubgroupAsCatOneGroup}}{106}{subsection.24.1.7}%
\contentsline {subsection}{\numberline {24.1.8}\textcolor {Chapter }{XmodToHAP}}{106}{subsection.24.1.8}%
\contentsline {chapter}{\numberline {25}\textcolor {Chapter }{ Simplicial groups}}{107}{chapter.25}%
\contentsline {section}{\numberline {25.1}\textcolor {Chapter }{ {\nobreakspace }}}{107}{section.25.1}%
\contentsline {subsection}{\numberline {25.1.1}\textcolor {Chapter }{NerveOfCatOneGroup}}{107}{subsection.25.1.1}%
\contentsline {subsection}{\numberline {25.1.2}\textcolor {Chapter }{EilenbergMacLaneSimplicialGroup}}{107}{subsection.25.1.2}%
\contentsline {subsection}{\numberline {25.1.3}\textcolor {Chapter }{EilenbergMacLaneSimplicialGroupMap}}{107}{subsection.25.1.3}%
\contentsline {subsection}{\numberline {25.1.4}\textcolor {Chapter }{MooreComplex}}{108}{subsection.25.1.4}%
\contentsline {subsection}{\numberline {25.1.5}\textcolor {Chapter }{ChainComplexOfSimplicialGroup}}{108}{subsection.25.1.5}%
\contentsline {subsection}{\numberline {25.1.6}\textcolor {Chapter }{SimplicialGroupMap}}{108}{subsection.25.1.6}%
\contentsline {subsection}{\numberline {25.1.7}\textcolor {Chapter }{HomotopyGroup}}{108}{subsection.25.1.7}%
\contentsline {subsection}{\numberline {25.1.8}\textcolor {Chapter }{Representation of elements in the bar resolution}}{108}{subsection.25.1.8}%
\contentsline {subsection}{\numberline {25.1.9}\textcolor {Chapter }{BarResolutionBoundary}}{109}{subsection.25.1.9}%
\contentsline {subsection}{\numberline {25.1.10}\textcolor {Chapter }{BarResolutionHomotopy}}{109}{subsection.25.1.10}%
\contentsline {subsection}{\numberline {25.1.11}\textcolor {Chapter }{Representation of elements in the bar complex}}{109}{subsection.25.1.11}%
\contentsline {subsection}{\numberline {25.1.12}\textcolor {Chapter }{BarComplexBoundary}}{110}{subsection.25.1.12}%
\contentsline {subsection}{\numberline {25.1.13}\textcolor {Chapter }{BarResolutionEquivalence}}{110}{subsection.25.1.13}%
\contentsline {subsection}{\numberline {25.1.14}\textcolor {Chapter }{BarComplexEquivalence}}{110}{subsection.25.1.14}%
\contentsline {subsection}{\numberline {25.1.15}\textcolor {Chapter }{Representation of elements in the bar cocomplex}}{111}{subsection.25.1.15}%
\contentsline {subsection}{\numberline {25.1.16}\textcolor {Chapter }{BarCocomplexCoboundary}}{111}{subsection.25.1.16}%
\contentsline {chapter}{\numberline {26}\textcolor {Chapter }{ Coxeter diagrams and graphs of groups}}{112}{chapter.26}%
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\contentsline {subsection}{\numberline {35.1.9}\textcolor {Chapter }{ArrayAssignFunctions}}{152}{subsection.35.1.9}%
\contentsline {subsection}{\numberline {35.1.10}\textcolor {Chapter }{ArrayIterate}}{152}{subsection.35.1.10}%
\contentsline {subsection}{\numberline {35.1.11}\textcolor {Chapter }{BinaryArrayToTextFile}}{153}{subsection.35.1.11}%
\contentsline {subsection}{\numberline {35.1.12}\textcolor {Chapter }{FrameArray}}{153}{subsection.35.1.12}%
\contentsline {subsection}{\numberline {35.1.13}\textcolor {Chapter }{UnframeArray}}{153}{subsection.35.1.13}%
\contentsline {subsection}{\numberline {35.1.14}\textcolor {Chapter }{Add}}{153}{subsection.35.1.14}%
\contentsline {subsection}{\numberline {35.1.15}\textcolor {Chapter }{Append}}{153}{subsection.35.1.15}%
\contentsline {subsection}{\numberline {35.1.16}\textcolor {Chapter }{ListToPseudoList}}{153}{subsection.35.1.16}%
\contentsline {chapter}{\numberline {36}\textcolor {Chapter }{ Parallel Computation \texttt {\symbol {45}} Core Functions}}{155}{chapter.36}%
\contentsline {section}{\numberline {36.1}\textcolor {Chapter }{ {\nobreakspace }}}{155}{section.36.1}%
\contentsline {subsection}{\numberline {36.1.1}\textcolor {Chapter }{ChildProcess}}{155}{subsection.36.1.1}%
\contentsline {subsection}{\numberline {36.1.2}\textcolor {Chapter }{ChildClose}}{156}{subsection.36.1.2}%
\contentsline {subsection}{\numberline {36.1.3}\textcolor {Chapter }{ChildCommand}}{156}{subsection.36.1.3}%
\contentsline {subsection}{\numberline {36.1.4}\textcolor {Chapter }{NextAvailableChild}}{156}{subsection.36.1.4}%
\contentsline {subsection}{\numberline {36.1.5}\textcolor {Chapter }{IsAvailableChild}}{156}{subsection.36.1.5}%
\contentsline {subsection}{\numberline {36.1.6}\textcolor {Chapter }{ChildPut}}{156}{subsection.36.1.6}%
\contentsline {subsection}{\numberline {36.1.7}\textcolor {Chapter }{ChildGet}}{156}{subsection.36.1.7}%
\contentsline {subsection}{\numberline {36.1.8}\textcolor {Chapter }{HAPPrintTo}}{157}{subsection.36.1.8}%
\contentsline {subsection}{\numberline {36.1.9}\textcolor {Chapter }{HAPRead}}{157}{subsection.36.1.9}%
\contentsline {chapter}{\numberline {37}\textcolor {Chapter }{ Parallel Computation \texttt {\symbol {45}} Extra Functions}}{158}{chapter.37}%
\contentsline {section}{\numberline {37.1}\textcolor {Chapter }{ {\nobreakspace }}}{158}{section.37.1}%
\contentsline {subsection}{\numberline {37.1.1}\textcolor {Chapter }{ChildFunction}}{158}{subsection.37.1.1}%
\contentsline {subsection}{\numberline {37.1.2}\textcolor {Chapter }{ChildRead}}{158}{subsection.37.1.2}%
\contentsline {subsection}{\numberline {37.1.3}\textcolor {Chapter }{ChildReadEval}}{158}{subsection.37.1.3}%
\contentsline {subsection}{\numberline {37.1.4}\textcolor {Chapter }{ParallelList}}{158}{subsection.37.1.4}%
\contentsline {chapter}{\numberline {38}\textcolor {Chapter }{ Some functions for accessing basic data}}{159}{chapter.38}%
\contentsline {section}{\numberline {38.1}\textcolor {Chapter }{ {\nobreakspace }}}{159}{section.38.1}%
\contentsline {subsection}{\numberline {38.1.1}\textcolor {Chapter }{BoundaryMap}}{159}{subsection.38.1.1}%
\contentsline {subsection}{\numberline {38.1.2}\textcolor {Chapter }{BoundaryMatrix}}{159}{subsection.38.1.2}%
\contentsline {subsection}{\numberline {38.1.3}\textcolor {Chapter }{Dimension}}{159}{subsection.38.1.3}%
\contentsline {subsection}{\numberline {38.1.4}\textcolor {Chapter }{EvaluateProperty}}{159}{subsection.38.1.4}%
\contentsline {subsection}{\numberline {38.1.5}\textcolor {Chapter }{GroupOfResolution}}{160}{subsection.38.1.5}%
\contentsline {subsection}{\numberline {38.1.6}\textcolor {Chapter }{Length}}{160}{subsection.38.1.6}%
\contentsline {subsection}{\numberline {38.1.7}\textcolor {Chapter }{Map}}{160}{subsection.38.1.7}%
\contentsline {subsection}{\numberline {38.1.8}\textcolor {Chapter }{Source}}{160}{subsection.38.1.8}%
\contentsline {subsection}{\numberline {38.1.9}\textcolor {Chapter }{Target}}{160}{subsection.38.1.9}%
\contentsline {chapter}{\numberline {39}\textcolor {Chapter }{ Miscellaneous}}{161}{chapter.39}%
\contentsline {section}{\numberline {39.1}\textcolor {Chapter }{ {\nobreakspace }}}{161}{section.39.1}%
\contentsline {subsection}{\numberline {39.1.1}\textcolor {Chapter }{SL2Z}}{161}{subsection.39.1.1}%
\contentsline {subsection}{\numberline {39.1.2}\textcolor {Chapter }{BigStepLCS}}{161}{subsection.39.1.2}%
\contentsline {subsection}{\numberline {39.1.3}\textcolor {Chapter }{Classify}}{161}{subsection.39.1.3}%
\contentsline {subsection}{\numberline {39.1.4}\textcolor {Chapter }{RefineClassification}}{161}{subsection.39.1.4}%
\contentsline {subsection}{\numberline {39.1.5}\textcolor {Chapter }{Compose}}{162}{subsection.39.1.5}%
\contentsline {subsection}{\numberline {39.1.6}\textcolor {Chapter }{HAPcopyright}}{162}{subsection.39.1.6}%
\contentsline {subsection}{\numberline {39.1.7}\textcolor {Chapter }{IsLieAlgebraHomomorphism}}{162}{subsection.39.1.7}%
\contentsline {subsection}{\numberline {39.1.8}\textcolor {Chapter }{IsSuperperfect}}{162}{subsection.39.1.8}%
\contentsline {subsection}{\numberline {39.1.9}\textcolor {Chapter }{MakeHAPManual}}{162}{subsection.39.1.9}%
\contentsline {subsection}{\numberline {39.1.10}\textcolor {Chapter }{PermToMatrixGroup}}{162}{subsection.39.1.10}%
\contentsline {subsection}{\numberline {39.1.11}\textcolor {Chapter }{SolutionsMatDestructive}}{163}{subsection.39.1.11}%
\contentsline {subsection}{\numberline {39.1.12}\textcolor {Chapter }{LinearHomomorphismsPersistenceMat}}{163}{subsection.39.1.12}%
\contentsline {subsection}{\numberline {39.1.13}\textcolor {Chapter }{NormalSeriesToQuotientHomomorphisms}}{163}{subsection.39.1.13}%
\contentsline {subsection}{\numberline {39.1.14}\textcolor {Chapter }{TestHap}}{163}{subsection.39.1.14}%
\contentsline {chapter}{\numberline {40}\textcolor {Chapter }{HAP variables that are not yet documented}}{164}{chapter.40}%
\contentsline {section}{\numberline {40.1}\textcolor {Chapter }{ {\nobreakspace }}}{164}{section.40.1}%
\contentsline {chapter}{Index}{246}{section*.5}%
