\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Preface}}{23}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }The \textsf {GAP} System}}{23}{section.1.1}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Authors and Maintainers}}{25}{section.1.2}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Acknowledgements}}{26}{section.1.3}
\contentsline {section}{\numberline {1.4}\leavevmode {\color {Chapter }Copyright and License}}{26}{section.1.4}
\contentsline {section}{\numberline {1.5}\leavevmode {\color {Chapter }Further Information about \textsf {GAP}}}{27}{section.1.5}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }The Help System}}{28}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Invoking the Help}}{28}{section.2.1}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Browsing through the Sections}}{28}{section.2.2}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Changing the Help Viewer}}{29}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }SetHelpViewer}}{30}{subsection.2.3.1}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter }The Pager Command}}{31}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}\leavevmode {\color {Chapter }Pager}}{31}{subsection.2.4.1}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Running GAP}}{33}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Command Line Options}}{33}{section.3.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }The gap.ini and gaprc files}}{38}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }The gap.ini file}}{38}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }The gaprc file}}{38}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }Configuring User preferences}}{39}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}\leavevmode {\color {Chapter }DeclareUserPreference}}{40}{subsection.3.2.4}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Saving and Loading a Workspace}}{41}{section.3.3}
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\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter }Testing for the System Architecture}}{42}{section.3.4}
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\contentsline {section}{\numberline {3.6}\leavevmode {\color {Chapter }Coloring the Prompt and Input}}{42}{section.3.6}
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\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }The Programming Language}}{45}{chapter.4}
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\contentsline {section}{\numberline {4.17}\leavevmode {\color {Chapter }If}}{61}{section.4.17}
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\contentsline {section}{\numberline {4.24}\leavevmode {\color {Chapter }Return (With or without Value)}}{70}{section.4.24}
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\contentsline {section}{\numberline {6.8}\leavevmode {\color {Chapter }Line Editing}}{94}{section.6.8}
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\contentsline {subsection}{\numberline {6.9.4}\leavevmode {\color {Chapter }Writing your own command line editing functions}}{98}{subsection.6.9.4}
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\contentsline {section}{\numberline {6.11}\leavevmode {\color {Chapter }Editor Support}}{100}{section.6.11}
\contentsline {section}{\numberline {6.12}\leavevmode {\color {Chapter }Changing the Screen Size}}{101}{section.6.12}
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\contentsline {section}{\numberline {6.13}\leavevmode {\color {Chapter }Teaching Mode}}{101}{section.6.13}
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\contentsline {chapter}{\numberline {7}\leavevmode {\color {Chapter }Debugging and Profiling Facilities}}{103}{chapter.7}
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\contentsline {section}{\numberline {39.19}\leavevmode {\color {Chapter }Sets of Subgroups}}{549}{section.39.19}
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\contentsline {chapter}{\numberline {41}\leavevmode {\color {Chapter }Group Actions}}{587}{chapter.41}
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\contentsline {chapter}{\numberline {42}\leavevmode {\color {Chapter }Permutations}}{610}{chapter.42}
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\contentsline {section}{\numberline {42.3}\leavevmode {\color {Chapter }Moved Points of Permutations}}{612}{section.42.3}
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\contentsline {subsection}{\numberline {42.3.3}\leavevmode {\color {Chapter }MovedPoints (for a permutation)}}{613}{subsection.42.3.3}
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\contentsline {section}{\numberline {42.5}\leavevmode {\color {Chapter }Creating Permutations}}{614}{section.42.5}
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\contentsline {chapter}{\numberline {44}\leavevmode {\color {Chapter }Matrix Groups}}{636}{chapter.44}
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\contentsline {section}{\numberline {45.11}\leavevmode {\color {Chapter }Pcgs and Normal Series}}{657}{section.45.11}
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\contentsline {subsection}{\numberline {45.11.2}\leavevmode {\color {Chapter }PcgsElementaryAbelianSeries (for a group)}}{657}{subsection.45.11.2}
\contentsline {subsection}{\numberline {45.11.3}\leavevmode {\color {Chapter }IndicesEANormalSteps}}{657}{subsection.45.11.3}
\contentsline {subsection}{\numberline {45.11.4}\leavevmode {\color {Chapter }EANormalSeriesByPcgs}}{658}{subsection.45.11.4}
\contentsline {subsection}{\numberline {45.11.5}\leavevmode {\color {Chapter }IsPcgsCentralSeries}}{658}{subsection.45.11.5}
\contentsline {subsection}{\numberline {45.11.6}\leavevmode {\color {Chapter }PcgsCentralSeries}}{658}{subsection.45.11.6}
\contentsline {subsection}{\numberline {45.11.7}\leavevmode {\color {Chapter }IndicesCentralNormalSteps}}{658}{subsection.45.11.7}
\contentsline {subsection}{\numberline {45.11.8}\leavevmode {\color {Chapter }CentralNormalSeriesByPcgs}}{659}{subsection.45.11.8}
\contentsline {subsection}{\numberline {45.11.9}\leavevmode {\color {Chapter }IsPcgsPCentralSeriesPGroup}}{659}{subsection.45.11.9}
\contentsline {subsection}{\numberline {45.11.10}\leavevmode {\color {Chapter }PcgsPCentralSeriesPGroup}}{659}{subsection.45.11.10}
\contentsline {subsection}{\numberline {45.11.11}\leavevmode {\color {Chapter }IndicesPCentralNormalStepsPGroup}}{659}{subsection.45.11.11}
\contentsline {subsection}{\numberline {45.11.12}\leavevmode {\color {Chapter }PCentralNormalSeriesByPcgsPGroup}}{659}{subsection.45.11.12}
\contentsline {subsection}{\numberline {45.11.13}\leavevmode {\color {Chapter }IsPcgsChiefSeries}}{660}{subsection.45.11.13}
\contentsline {subsection}{\numberline {45.11.14}\leavevmode {\color {Chapter }PcgsChiefSeries}}{660}{subsection.45.11.14}
\contentsline {subsection}{\numberline {45.11.15}\leavevmode {\color {Chapter }IndicesChiefNormalSteps}}{660}{subsection.45.11.15}
\contentsline {subsection}{\numberline {45.11.16}\leavevmode {\color {Chapter }ChiefNormalSeriesByPcgs}}{660}{subsection.45.11.16}
\contentsline {subsection}{\numberline {45.11.17}\leavevmode {\color {Chapter }IndicesNormalSteps}}{661}{subsection.45.11.17}
\contentsline {subsection}{\numberline {45.11.18}\leavevmode {\color {Chapter }NormalSeriesByPcgs}}{661}{subsection.45.11.18}
\contentsline {section}{\numberline {45.12}\leavevmode {\color {Chapter }Sum and Intersection of Pcgs}}{661}{section.45.12}
\contentsline {subsection}{\numberline {45.12.1}\leavevmode {\color {Chapter }SumFactorizationFunctionPcgs}}{661}{subsection.45.12.1}
\contentsline {section}{\numberline {45.13}\leavevmode {\color {Chapter }Special Pcgs}}{662}{section.45.13}
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\contentsline {subsection}{\numberline {45.13.2}\leavevmode {\color {Chapter }SpecialPcgs}}{663}{subsection.45.13.2}
\contentsline {subsection}{\numberline {45.13.3}\leavevmode {\color {Chapter }LGWeights}}{663}{subsection.45.13.3}
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\contentsline {subsection}{\numberline {45.13.7}\leavevmode {\color {Chapter }IsInducedPcgsWrtSpecialPcgs}}{664}{subsection.45.13.7}
\contentsline {subsection}{\numberline {45.13.8}\leavevmode {\color {Chapter }InducedPcgsWrtSpecialPcgs}}{664}{subsection.45.13.8}
\contentsline {section}{\numberline {45.14}\leavevmode {\color {Chapter }Action on Subfactors Defined by a Pcgs}}{664}{section.45.14}
\contentsline {subsection}{\numberline {45.14.1}\leavevmode {\color {Chapter }VectorSpaceByPcgsOfElementaryAbelianGroup}}{664}{subsection.45.14.1}
\contentsline {subsection}{\numberline {45.14.2}\leavevmode {\color {Chapter }LinearAction}}{664}{subsection.45.14.2}
\contentsline {subsection}{\numberline {45.14.3}\leavevmode {\color {Chapter }LinearActionLayer}}{665}{subsection.45.14.3}
\contentsline {subsection}{\numberline {45.14.4}\leavevmode {\color {Chapter }AffineAction}}{665}{subsection.45.14.4}
\contentsline {subsection}{\numberline {45.14.5}\leavevmode {\color {Chapter }AffineActionLayer}}{665}{subsection.45.14.5}
\contentsline {section}{\numberline {45.15}\leavevmode {\color {Chapter }Orbit Stabilizer Methods for Polycyclic Groups}}{666}{section.45.15}
\contentsline {subsection}{\numberline {45.15.1}\leavevmode {\color {Chapter }StabilizerPcgs}}{666}{subsection.45.15.1}
\contentsline {subsection}{\numberline {45.15.2}\leavevmode {\color {Chapter }Pcgs{\textunderscore }OrbitStabilizer}}{666}{subsection.45.15.2}
\contentsline {section}{\numberline {45.16}\leavevmode {\color {Chapter }Operations which have Special Methods for Groups with Pcgs}}{666}{section.45.16}
\contentsline {section}{\numberline {45.17}\leavevmode {\color {Chapter }Conjugacy Classes in Solvable Groups}}{666}{section.45.17}
\contentsline {subsection}{\numberline {45.17.1}\leavevmode {\color {Chapter }ClassesSolvableGroup}}{666}{subsection.45.17.1}
\contentsline {subsection}{\numberline {45.17.2}\leavevmode {\color {Chapter }CentralizerSizeLimitConsiderFunction}}{667}{subsection.45.17.2}
\contentsline {chapter}{\numberline {46}\leavevmode {\color {Chapter }Pc Groups}}{668}{chapter.46}
\contentsline {section}{\numberline {46.1}\leavevmode {\color {Chapter }The family pcgs}}{669}{section.46.1}
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\contentsline {subsection}{\numberline {46.1.3}\leavevmode {\color {Chapter }InducedPcgsWrtFamilyPcgs}}{669}{subsection.46.1.3}
\contentsline {subsection}{\numberline {46.1.4}\leavevmode {\color {Chapter }IsParentPcgsFamilyPcgs}}{669}{subsection.46.1.4}
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\contentsline {subsection}{\numberline {46.2.2}\leavevmode {\color {Chapter }Arithmetic operations for elements of pc groups}}{670}{subsection.46.2.2}
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\contentsline {subsection}{\numberline {46.3.2}\leavevmode {\color {Chapter }IsomorphismFpGroupByPcgs}}{671}{subsection.46.3.2}
\contentsline {section}{\numberline {46.4}\leavevmode {\color {Chapter }Constructing Pc Groups}}{671}{section.46.4}
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\contentsline {subsection}{\numberline {46.4.2}\leavevmode {\color {Chapter }SingleCollector}}{672}{subsection.46.4.2}
\contentsline {subsection}{\numberline {46.4.3}\leavevmode {\color {Chapter }SetConjugate}}{672}{subsection.46.4.3}
\contentsline {subsection}{\numberline {46.4.4}\leavevmode {\color {Chapter }SetCommutator}}{672}{subsection.46.4.4}
\contentsline {subsection}{\numberline {46.4.5}\leavevmode {\color {Chapter }SetPower}}{672}{subsection.46.4.5}
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\contentsline {subsection}{\numberline {46.4.7}\leavevmode {\color {Chapter }IsConfluent (for pc groups)}}{673}{subsection.46.4.7}
\contentsline {subsection}{\numberline {46.4.8}\leavevmode {\color {Chapter }IsomorphismRefinedPcGroup}}{673}{subsection.46.4.8}
\contentsline {subsection}{\numberline {46.4.9}\leavevmode {\color {Chapter }RefinedPcGroup}}{673}{subsection.46.4.9}
\contentsline {section}{\numberline {46.5}\leavevmode {\color {Chapter }Computing Pc Groups}}{674}{section.46.5}
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\contentsline {subsection}{\numberline {46.5.2}\leavevmode {\color {Chapter }IsomorphismPcGroup}}{674}{subsection.46.5.2}
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\contentsline {section}{\numberline {46.7}\leavevmode {\color {Chapter }Operations for Pc Groups}}{675}{section.46.7}
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\contentsline {subsection}{\numberline {46.8.2}\leavevmode {\color {Chapter }TwoCocycles}}{676}{subsection.46.8.2}
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\contentsline {subsection}{\numberline {46.8.5}\leavevmode {\color {Chapter }Extension}}{677}{subsection.46.8.5}
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\contentsline {subsection}{\numberline {46.8.9}\leavevmode {\color {Chapter }ExtensionRepresentatives}}{678}{subsection.46.8.9}
\contentsline {subsection}{\numberline {46.8.10}\leavevmode {\color {Chapter }SplitExtension (with specified homomorphism)}}{679}{subsection.46.8.10}
\contentsline {section}{\numberline {46.9}\leavevmode {\color {Chapter }Coding a Pc Presentation}}{679}{section.46.9}
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\contentsline {subsection}{\numberline {46.9.2}\leavevmode {\color {Chapter }CodePcGroup}}{680}{subsection.46.9.2}
\contentsline {subsection}{\numberline {46.9.3}\leavevmode {\color {Chapter }PcGroupCode}}{680}{subsection.46.9.3}
\contentsline {section}{\numberline {46.10}\leavevmode {\color {Chapter }Random Isomorphism Testing}}{680}{section.46.10}
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\contentsline {chapter}{\numberline {47}\leavevmode {\color {Chapter }Finitely Presented Groups}}{681}{chapter.47}
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\contentsline {subsection}{\numberline {47.1.2}\leavevmode {\color {Chapter }IsFpGroup}}{682}{subsection.47.1.2}
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\contentsline {section}{\numberline {47.2}\leavevmode {\color {Chapter }Creating Finitely Presented Groups}}{683}{section.47.2}
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\contentsline {subsection}{\numberline {47.2.2}\leavevmode {\color {Chapter }FactorGroupFpGroupByRels}}{683}{subsection.47.2.2}
\contentsline {subsection}{\numberline {47.2.3}\leavevmode {\color {Chapter }ParseRelators}}{683}{subsection.47.2.3}
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\contentsline {section}{\numberline {47.3}\leavevmode {\color {Chapter }Comparison of Elements of Finitely Presented Groups}}{684}{section.47.3}
\contentsline {subsection}{\numberline {47.3.1}\leavevmode {\color {Chapter }\texttt {\char 92\relax }= (for two elements in a f.p. group)}}{684}{subsection.47.3.1}
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\contentsline {section}{\numberline {47.4}\leavevmode {\color {Chapter }Preimages in the Free Group}}{685}{section.47.4}
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\contentsline {subsection}{\numberline {47.4.2}\leavevmode {\color {Chapter }FreeGeneratorsOfFpGroup}}{685}{subsection.47.4.2}
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\contentsline {subsection}{\numberline {47.4.5}\leavevmode {\color {Chapter }ElementOfFpGroup}}{686}{subsection.47.4.5}
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\contentsline {section}{\numberline {47.6}\leavevmode {\color {Chapter }Coset Tables and Coset Enumeration}}{687}{section.47.6}
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\contentsline {subsection}{\numberline {47.6.4}\leavevmode {\color {Chapter }CosetTableBySubgroup}}{689}{subsection.47.6.4}
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\contentsline {section}{\numberline {47.10}\leavevmode {\color {Chapter }Low Index Subgroups}}{694}{section.47.10}
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\contentsline {section}{\numberline {47.11}\leavevmode {\color {Chapter }Converting Groups to Finitely Presented Groups}}{695}{section.47.11}
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\contentsline {section}{\numberline {47.12}\leavevmode {\color {Chapter }New Presentations and Presentations for Subgroups}}{698}{section.47.12}
\contentsline {subsection}{\numberline {47.12.1}\leavevmode {\color {Chapter }IsomorphismSimplifiedFpGroup}}{699}{subsection.47.12.1}
\contentsline {section}{\numberline {47.13}\leavevmode {\color {Chapter }Preimages under Homomorphisms from an FpGroup}}{699}{section.47.13}
\contentsline {subsection}{\numberline {47.13.1}\leavevmode {\color {Chapter }SubgroupOfWholeGroupByQuotientSubgroup}}{700}{subsection.47.13.1}
\contentsline {subsection}{\numberline {47.13.2}\leavevmode {\color {Chapter }IsSubgroupOfWholeGroupByQuotientRep}}{700}{subsection.47.13.2}
\contentsline {subsection}{\numberline {47.13.3}\leavevmode {\color {Chapter }AsSubgroupOfWholeGroupByQuotient}}{700}{subsection.47.13.3}
\contentsline {subsection}{\numberline {47.13.4}\leavevmode {\color {Chapter }DefiningQuotientHomomorphism}}{700}{subsection.47.13.4}
\contentsline {section}{\numberline {47.14}\leavevmode {\color {Chapter }Quotient Methods}}{700}{section.47.14}
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\contentsline {subsection}{\numberline {47.14.2}\leavevmode {\color {Chapter }EpimorphismQuotientSystem}}{701}{subsection.47.14.2}
\contentsline {subsection}{\numberline {47.14.3}\leavevmode {\color {Chapter }EpimorphismPGroup}}{702}{subsection.47.14.3}
\contentsline {subsection}{\numberline {47.14.4}\leavevmode {\color {Chapter }EpimorphismNilpotentQuotient}}{702}{subsection.47.14.4}
\contentsline {subsection}{\numberline {47.14.5}\leavevmode {\color {Chapter }SolvableQuotient (for a f.p. group and a size)}}{702}{subsection.47.14.5}
\contentsline {subsection}{\numberline {47.14.6}\leavevmode {\color {Chapter }EpimorphismSolvableQuotient}}{703}{subsection.47.14.6}
\contentsline {subsection}{\numberline {47.14.7}\leavevmode {\color {Chapter }LargerQuotientBySubgroupAbelianization}}{703}{subsection.47.14.7}
\contentsline {section}{\numberline {47.15}\leavevmode {\color {Chapter }Abelian Invariants for Subgroups}}{703}{section.47.15}
\contentsline {subsection}{\numberline {47.15.1}\leavevmode {\color {Chapter }AbelianInvariantsSubgroupFpGroup}}{704}{subsection.47.15.1}
\contentsline {subsection}{\numberline {47.15.2}\leavevmode {\color {Chapter }AbelianInvariantsSubgroupFpGroupMtc}}{704}{subsection.47.15.2}
\contentsline {subsection}{\numberline {47.15.3}\leavevmode {\color {Chapter }AbelianInvariantsSubgroupFpGroupRrs}}{704}{subsection.47.15.3}
\contentsline {subsection}{\numberline {47.15.4}\leavevmode {\color {Chapter }AbelianInvariantsNormalClosureFpGroup}}{704}{subsection.47.15.4}
\contentsline {subsection}{\numberline {47.15.5}\leavevmode {\color {Chapter }AbelianInvariantsNormalClosureFpGroupRrs}}{704}{subsection.47.15.5}
\contentsline {section}{\numberline {47.16}\leavevmode {\color {Chapter }Testing Finiteness of Finitely Presented Groups}}{705}{section.47.16}
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\contentsline {subsection}{\numberline {47.16.2}\leavevmode {\color {Chapter }NewmanInfinityCriterion}}{706}{subsection.47.16.2}
\contentsline {chapter}{\numberline {48}\leavevmode {\color {Chapter }Presentations and Tietze Transformations}}{707}{chapter.48}
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\contentsline {subsection}{\numberline {48.1.2}\leavevmode {\color {Chapter }TzSort}}{708}{subsection.48.1.2}
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\contentsline {subsection}{\numberline {48.1.4}\leavevmode {\color {Chapter }FpGroupPresentation}}{708}{subsection.48.1.4}
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\contentsline {section}{\numberline {48.4}\leavevmode {\color {Chapter }Printing Presentations}}{715}{section.48.4}
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\contentsline {chapter}{\numberline {55}\leavevmode {\color {Chapter }Additive Magmas}}{850}{chapter.55}
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\contentsline {subsection}{\numberline {71.9.2}\leavevmode {\color {Chapter }SizesCentralizers}}{1093}{subsection.71.9.2}
\contentsline {subsection}{\numberline {71.9.3}\leavevmode {\color {Chapter }SizesConjugacyClasses}}{1093}{subsection.71.9.3}
\contentsline {subsection}{\numberline {71.9.4}\leavevmode {\color {Chapter }AutomorphismsOfTable}}{1093}{subsection.71.9.4}
\contentsline {subsection}{\numberline {71.9.5}\leavevmode {\color {Chapter }UnderlyingCharacteristic}}{1093}{subsection.71.9.5}
\contentsline {subsection}{\numberline {71.9.6}\leavevmode {\color {Chapter }Class Names and Character Names}}{1094}{subsection.71.9.6}
\contentsline {subsection}{\numberline {71.9.7}\leavevmode {\color {Chapter }Class Parameters and Character Parameters}}{1094}{subsection.71.9.7}
\contentsline {subsection}{\numberline {71.9.8}\leavevmode {\color {Chapter }Identifier (for character tables)}}{1095}{subsection.71.9.8}
\contentsline {subsection}{\numberline {71.9.9}\leavevmode {\color {Chapter }InfoText (for character tables)}}{1095}{subsection.71.9.9}
\contentsline {subsection}{\numberline {71.9.10}\leavevmode {\color {Chapter }InverseClasses}}{1095}{subsection.71.9.10}
\contentsline {subsection}{\numberline {71.9.11}\leavevmode {\color {Chapter }RealClasses}}{1096}{subsection.71.9.11}
\contentsline {subsection}{\numberline {71.9.12}\leavevmode {\color {Chapter }ClassOrbit}}{1096}{subsection.71.9.12}
\contentsline {subsection}{\numberline {71.9.13}\leavevmode {\color {Chapter }ClassRoots}}{1096}{subsection.71.9.13}
\contentsline {section}{\numberline {71.10}\leavevmode {\color {Chapter }Normal Subgroups Represented by Lists of Class Positions}}{1097}{section.71.10}
\contentsline {subsection}{\numberline {71.10.1}\leavevmode {\color {Chapter }ClassPositionsOfNormalSubgroups}}{1097}{subsection.71.10.1}
\contentsline {subsection}{\numberline {71.10.2}\leavevmode {\color {Chapter }ClassPositionsOfAgemo}}{1097}{subsection.71.10.2}
\contentsline {subsection}{\numberline {71.10.3}\leavevmode {\color {Chapter }ClassPositionsOfCentre (for a character table)}}{1097}{subsection.71.10.3}
\contentsline {subsection}{\numberline {71.10.4}\leavevmode {\color {Chapter }ClassPositionsOfDirectProductDecompositions}}{1097}{subsection.71.10.4}
\contentsline {subsection}{\numberline {71.10.5}\leavevmode {\color {Chapter }ClassPositionsOfDerivedSubgroup}}{1098}{subsection.71.10.5}
\contentsline {subsection}{\numberline {71.10.6}\leavevmode {\color {Chapter }ClassPositionsOfElementaryAbelianSeries}}{1098}{subsection.71.10.6}
\contentsline {subsection}{\numberline {71.10.7}\leavevmode {\color {Chapter }ClassPositionsOfFittingSubgroup}}{1098}{subsection.71.10.7}
\contentsline {subsection}{\numberline {71.10.8}\leavevmode {\color {Chapter }ClassPositionsOfLowerCentralSeries}}{1098}{subsection.71.10.8}
\contentsline {subsection}{\numberline {71.10.9}\leavevmode {\color {Chapter }ClassPositionsOfUpperCentralSeries}}{1099}{subsection.71.10.9}
\contentsline {subsection}{\numberline {71.10.10}\leavevmode {\color {Chapter }ClassPositionsOfSolvableRadical}}{1099}{subsection.71.10.10}
\contentsline {subsection}{\numberline {71.10.11}\leavevmode {\color {Chapter }ClassPositionsOfSupersolvableResiduum}}{1099}{subsection.71.10.11}
\contentsline {subsection}{\numberline {71.10.12}\leavevmode {\color {Chapter }ClassPositionsOfPCore}}{1099}{subsection.71.10.12}
\contentsline {subsection}{\numberline {71.10.13}\leavevmode {\color {Chapter }ClassPositionsOfNormalClosure}}{1100}{subsection.71.10.13}
\contentsline {section}{\numberline {71.11}\leavevmode {\color {Chapter }Operations Concerning Blocks}}{1100}{section.71.11}
\contentsline {subsection}{\numberline {71.11.1}\leavevmode {\color {Chapter }PrimeBlocks}}{1100}{subsection.71.11.1}
\contentsline {subsection}{\numberline {71.11.2}\leavevmode {\color {Chapter }SameBlock}}{1101}{subsection.71.11.2}
\contentsline {subsection}{\numberline {71.11.3}\leavevmode {\color {Chapter }BlocksInfo}}{1101}{subsection.71.11.3}
\contentsline {subsection}{\numberline {71.11.4}\leavevmode {\color {Chapter }DecompositionMatrix}}{1102}{subsection.71.11.4}
\contentsline {subsection}{\numberline {71.11.5}\leavevmode {\color {Chapter }LaTeXStringDecompositionMatrix}}{1103}{subsection.71.11.5}
\contentsline {section}{\numberline {71.12}\leavevmode {\color {Chapter }Other Operations for Character Tables}}{1104}{section.71.12}
\contentsline {subsection}{\numberline {71.12.1}\leavevmode {\color {Chapter }Index (for two character tables)}}{1104}{subsection.71.12.1}
\contentsline {subsection}{\numberline {71.12.2}\leavevmode {\color {Chapter }IsInternallyConsistent (for character tables)}}{1104}{subsection.71.12.2}
\contentsline {subsection}{\numberline {71.12.3}\leavevmode {\color {Chapter }IsPSolvableCharacterTable}}{1105}{subsection.71.12.3}
\contentsline {subsection}{\numberline {71.12.4}\leavevmode {\color {Chapter }IsClassFusionOfNormalSubgroup}}{1105}{subsection.71.12.4}
\contentsline {subsection}{\numberline {71.12.5}\leavevmode {\color {Chapter }Indicator}}{1105}{subsection.71.12.5}
\contentsline {subsection}{\numberline {71.12.6}\leavevmode {\color {Chapter }NrPolyhedralSubgroups}}{1106}{subsection.71.12.6}
\contentsline {subsection}{\numberline {71.12.7}\leavevmode {\color {Chapter }ClassMultiplicationCoefficient (for character tables)}}{1106}{subsection.71.12.7}
\contentsline {subsection}{\numberline {71.12.8}\leavevmode {\color {Chapter }ClassStructureCharTable}}{1107}{subsection.71.12.8}
\contentsline {subsection}{\numberline {71.12.9}\leavevmode {\color {Chapter }MatClassMultCoeffsCharTable}}{1107}{subsection.71.12.9}
\contentsline {section}{\numberline {71.13}\leavevmode {\color {Chapter }Printing Character Tables}}{1107}{section.71.13}
\contentsline {subsection}{\numberline {71.13.1}\leavevmode {\color {Chapter }ViewObj (for a character table)}}{1107}{subsection.71.13.1}
\contentsline {subsection}{\numberline {71.13.2}\leavevmode {\color {Chapter }PrintObj (for a character table)}}{1108}{subsection.71.13.2}
\contentsline {subsection}{\numberline {71.13.3}\leavevmode {\color {Chapter }Display (for a character table)}}{1108}{subsection.71.13.3}
\contentsline {subsection}{\numberline {71.13.4}\leavevmode {\color {Chapter }DisplayOptions}}{1110}{subsection.71.13.4}
\contentsline {subsection}{\numberline {71.13.5}\leavevmode {\color {Chapter }PrintCharacterTable}}{1111}{subsection.71.13.5}
\contentsline {section}{\numberline {71.14}\leavevmode {\color {Chapter }Computing the Irreducible Characters of a Group}}{1112}{section.71.14}
\contentsline {subsection}{\numberline {71.14.1}\leavevmode {\color {Chapter }IrrDixonSchneider}}{1112}{subsection.71.14.1}
\contentsline {subsection}{\numberline {71.14.2}\leavevmode {\color {Chapter }IrrConlon}}{1112}{subsection.71.14.2}
\contentsline {subsection}{\numberline {71.14.3}\leavevmode {\color {Chapter }IrrBaumClausen}}{1112}{subsection.71.14.3}
\contentsline {subsection}{\numberline {71.14.4}\leavevmode {\color {Chapter }IrreducibleRepresentations}}{1113}{subsection.71.14.4}
\contentsline {subsection}{\numberline {71.14.5}\leavevmode {\color {Chapter }IrreducibleRepresentationsDixon}}{1114}{subsection.71.14.5}
\contentsline {section}{\numberline {71.15}\leavevmode {\color {Chapter }Representations Given by Modules}}{1115}{section.71.15}
\contentsline {subsection}{\numberline {71.15.1}\leavevmode {\color {Chapter }IrreducibleModules}}{1115}{subsection.71.15.1}
\contentsline {subsection}{\numberline {71.15.2}\leavevmode {\color {Chapter }AbsolutelyIrreducibleModules}}{1115}{subsection.71.15.2}
\contentsline {subsection}{\numberline {71.15.3}\leavevmode {\color {Chapter }RegularModule}}{1115}{subsection.71.15.3}
\contentsline {section}{\numberline {71.16}\leavevmode {\color {Chapter }The Dixon-Schneider Algorithm}}{1115}{section.71.16}
\contentsline {section}{\numberline {71.17}\leavevmode {\color {Chapter }Advanced Methods for Dixon-Schneider Calculations}}{1116}{section.71.17}
\contentsline {subsection}{\numberline {71.17.1}\leavevmode {\color {Chapter }DixonRecord}}{1116}{subsection.71.17.1}
\contentsline {subsection}{\numberline {71.17.2}\leavevmode {\color {Chapter }DixonInit}}{1116}{subsection.71.17.2}
\contentsline {subsection}{\numberline {71.17.3}\leavevmode {\color {Chapter }DixontinI}}{1116}{subsection.71.17.3}
\contentsline {subsection}{\numberline {71.17.4}\leavevmode {\color {Chapter }DixonSplit}}{1117}{subsection.71.17.4}
\contentsline {subsection}{\numberline {71.17.5}\leavevmode {\color {Chapter }BestSplittingMatrix}}{1117}{subsection.71.17.5}
\contentsline {subsection}{\numberline {71.17.6}\leavevmode {\color {Chapter }DxIncludeIrreducibles}}{1117}{subsection.71.17.6}
\contentsline {subsection}{\numberline {71.17.7}\leavevmode {\color {Chapter }SplitCharacters}}{1117}{subsection.71.17.7}
\contentsline {subsection}{\numberline {71.17.8}\leavevmode {\color {Chapter }IsDxLargeGroup}}{1117}{subsection.71.17.8}
\contentsline {section}{\numberline {71.18}\leavevmode {\color {Chapter }Components of a Dixon Record}}{1118}{section.71.18}
\contentsline {section}{\numberline {71.19}\leavevmode {\color {Chapter }An Example of Advanced Dixon-Schneider Calculations}}{1118}{section.71.19}
\contentsline {section}{\numberline {71.20}\leavevmode {\color {Chapter }Constructing Character Tables from Others}}{1120}{section.71.20}
\contentsline {subsection}{\numberline {71.20.1}\leavevmode {\color {Chapter }CharacterTableDirectProduct}}{1121}{subsection.71.20.1}
\contentsline {subsection}{\numberline {71.20.2}\leavevmode {\color {Chapter }FactorsOfDirectProduct}}{1121}{subsection.71.20.2}
\contentsline {subsection}{\numberline {71.20.3}\leavevmode {\color {Chapter }CharacterTableFactorGroup}}{1122}{subsection.71.20.3}
\contentsline {subsection}{\numberline {71.20.4}\leavevmode {\color {Chapter }CharacterTableIsoclinic}}{1122}{subsection.71.20.4}
\contentsline {subsection}{\numberline {71.20.5}\leavevmode {\color {Chapter }CharacterTableOfNormalSubgroup}}{1123}{subsection.71.20.5}
\contentsline {subsection}{\numberline {71.20.6}\leavevmode {\color {Chapter }CharacterTableWreathSymmetric}}{1124}{subsection.71.20.6}
\contentsline {section}{\numberline {71.21}\leavevmode {\color {Chapter }Sorted Character Tables}}{1125}{section.71.21}
\contentsline {subsection}{\numberline {71.21.1}\leavevmode {\color {Chapter }CharacterTableWithSortedCharacters}}{1125}{subsection.71.21.1}
\contentsline {subsection}{\numberline {71.21.2}\leavevmode {\color {Chapter }SortedCharacters}}{1125}{subsection.71.21.2}
\contentsline {subsection}{\numberline {71.21.3}\leavevmode {\color {Chapter }CharacterTableWithSortedClasses}}{1125}{subsection.71.21.3}
\contentsline {subsection}{\numberline {71.21.4}\leavevmode {\color {Chapter }SortedCharacterTable (w.r.t. a normal subgroup)}}{1126}{subsection.71.21.4}
\contentsline {subsection}{\numberline {71.21.5}\leavevmode {\color {Chapter }ClassPermutation}}{1126}{subsection.71.21.5}
\contentsline {section}{\numberline {71.22}\leavevmode {\color {Chapter }Automorphisms and Equivalence of Character Tables}}{1127}{section.71.22}
\contentsline {subsection}{\numberline {71.22.1}\leavevmode {\color {Chapter }MatrixAutomorphisms}}{1127}{subsection.71.22.1}
\contentsline {subsection}{\numberline {71.22.2}\leavevmode {\color {Chapter }TableAutomorphisms}}{1128}{subsection.71.22.2}
\contentsline {subsection}{\numberline {71.22.3}\leavevmode {\color {Chapter }TransformingPermutations}}{1128}{subsection.71.22.3}
\contentsline {subsection}{\numberline {71.22.4}\leavevmode {\color {Chapter }TransformingPermutationsCharacterTables}}{1129}{subsection.71.22.4}
\contentsline {subsection}{\numberline {71.22.5}\leavevmode {\color {Chapter }FamiliesOfRows}}{1129}{subsection.71.22.5}
\contentsline {section}{\numberline {71.23}\leavevmode {\color {Chapter }Storing Normal Subgroup Information}}{1130}{section.71.23}
\contentsline {subsection}{\numberline {71.23.1}\leavevmode {\color {Chapter }NormalSubgroupClassesInfo}}{1130}{subsection.71.23.1}
\contentsline {subsection}{\numberline {71.23.2}\leavevmode {\color {Chapter }ClassPositionsOfNormalSubgroup}}{1130}{subsection.71.23.2}
\contentsline {subsection}{\numberline {71.23.3}\leavevmode {\color {Chapter }NormalSubgroupClasses}}{1131}{subsection.71.23.3}
\contentsline {subsection}{\numberline {71.23.4}\leavevmode {\color {Chapter }FactorGroupNormalSubgroupClasses}}{1131}{subsection.71.23.4}
\contentsline {chapter}{\numberline {72}\leavevmode {\color {Chapter }Class Functions}}{1132}{chapter.72}
\contentsline {section}{\numberline {72.1}\leavevmode {\color {Chapter }Why Class Functions?}}{1132}{section.72.1}
\contentsline {subsection}{\numberline {72.1.1}\leavevmode {\color {Chapter }IsClassFunction}}{1134}{subsection.72.1.1}
\contentsline {section}{\numberline {72.2}\leavevmode {\color {Chapter }Basic Operations for Class Functions}}{1135}{section.72.2}
\contentsline {subsection}{\numberline {72.2.1}\leavevmode {\color {Chapter }UnderlyingCharacterTable}}{1135}{subsection.72.2.1}
\contentsline {subsection}{\numberline {72.2.2}\leavevmode {\color {Chapter }ValuesOfClassFunction}}{1135}{subsection.72.2.2}
\contentsline {section}{\numberline {72.3}\leavevmode {\color {Chapter }Comparison of Class Functions}}{1136}{section.72.3}
\contentsline {section}{\numberline {72.4}\leavevmode {\color {Chapter }Arithmetic Operations for Class Functions}}{1136}{section.72.4}
\contentsline {subsection}{\numberline {72.4.1}\leavevmode {\color {Chapter }Characteristic (for a class function)}}{1139}{subsection.72.4.1}
\contentsline {subsection}{\numberline {72.4.2}\leavevmode {\color {Chapter }ComplexConjugate (for a class function)}}{1139}{subsection.72.4.2}
\contentsline {subsection}{\numberline {72.4.3}\leavevmode {\color {Chapter }Order (for a class function)}}{1140}{subsection.72.4.3}
\contentsline {section}{\numberline {72.5}\leavevmode {\color {Chapter }Printing Class Functions}}{1140}{section.72.5}
\contentsline {subsection}{\numberline {72.5.1}\leavevmode {\color {Chapter }ViewObj (for class functions)}}{1140}{subsection.72.5.1}
\contentsline {subsection}{\numberline {72.5.2}\leavevmode {\color {Chapter }PrintObj (for class functions)}}{1140}{subsection.72.5.2}
\contentsline {subsection}{\numberline {72.5.3}\leavevmode {\color {Chapter }Display (for class functions)}}{1140}{subsection.72.5.3}
\contentsline {section}{\numberline {72.6}\leavevmode {\color {Chapter }Creating Class Functions from Values Lists}}{1141}{section.72.6}
\contentsline {subsection}{\numberline {72.6.1}\leavevmode {\color {Chapter }ClassFunction (for a character table and a list)}}{1141}{subsection.72.6.1}
\contentsline {subsection}{\numberline {72.6.2}\leavevmode {\color {Chapter }VirtualCharacter (for a character table and a list)}}{1141}{subsection.72.6.2}
\contentsline {subsection}{\numberline {72.6.3}\leavevmode {\color {Chapter }Character (for a character table and a list)}}{1141}{subsection.72.6.3}
\contentsline {subsection}{\numberline {72.6.4}\leavevmode {\color {Chapter }ClassFunctionSameType}}{1142}{subsection.72.6.4}
\contentsline {section}{\numberline {72.7}\leavevmode {\color {Chapter }Creating Class Functions using Groups}}{1142}{section.72.7}
\contentsline {subsection}{\numberline {72.7.1}\leavevmode {\color {Chapter }TrivialCharacter}}{1142}{subsection.72.7.1}
\contentsline {subsection}{\numberline {72.7.2}\leavevmode {\color {Chapter }NaturalCharacter (for a group)}}{1142}{subsection.72.7.2}
\contentsline {subsection}{\numberline {72.7.3}\leavevmode {\color {Chapter }PermutationCharacter}}{1143}{subsection.72.7.3}
\contentsline {section}{\numberline {72.8}\leavevmode {\color {Chapter }Operations for Class Functions}}{1143}{section.72.8}
\contentsline {subsection}{\numberline {72.8.1}\leavevmode {\color {Chapter }IsCharacter}}{1144}{subsection.72.8.1}
\contentsline {subsection}{\numberline {72.8.2}\leavevmode {\color {Chapter }IsVirtualCharacter}}{1144}{subsection.72.8.2}
\contentsline {subsection}{\numberline {72.8.3}\leavevmode {\color {Chapter }IsIrreducibleCharacter}}{1144}{subsection.72.8.3}
\contentsline {subsection}{\numberline {72.8.4}\leavevmode {\color {Chapter }DegreeOfCharacter}}{1144}{subsection.72.8.4}
\contentsline {subsection}{\numberline {72.8.5}\leavevmode {\color {Chapter }ScalarProduct (for characters)}}{1145}{subsection.72.8.5}
\contentsline {subsection}{\numberline {72.8.6}\leavevmode {\color {Chapter }MatScalarProducts}}{1145}{subsection.72.8.6}
\contentsline {subsection}{\numberline {72.8.7}\leavevmode {\color {Chapter }Norm (for a class function)}}{1145}{subsection.72.8.7}
\contentsline {subsection}{\numberline {72.8.8}\leavevmode {\color {Chapter }ConstituentsOfCharacter}}{1146}{subsection.72.8.8}
\contentsline {subsection}{\numberline {72.8.9}\leavevmode {\color {Chapter }KernelOfCharacter}}{1146}{subsection.72.8.9}
\contentsline {subsection}{\numberline {72.8.10}\leavevmode {\color {Chapter }ClassPositionsOfKernel}}{1146}{subsection.72.8.10}
\contentsline {subsection}{\numberline {72.8.11}\leavevmode {\color {Chapter }CentreOfCharacter}}{1147}{subsection.72.8.11}
\contentsline {subsection}{\numberline {72.8.12}\leavevmode {\color {Chapter }ClassPositionsOfCentre (for a character)}}{1147}{subsection.72.8.12}
\contentsline {subsection}{\numberline {72.8.13}\leavevmode {\color {Chapter }InertiaSubgroup}}{1147}{subsection.72.8.13}
\contentsline {subsection}{\numberline {72.8.14}\leavevmode {\color {Chapter }CycleStructureClass}}{1148}{subsection.72.8.14}
\contentsline {subsection}{\numberline {72.8.15}\leavevmode {\color {Chapter }IsTransitive (for a character)}}{1148}{subsection.72.8.15}
\contentsline {subsection}{\numberline {72.8.16}\leavevmode {\color {Chapter }Transitivity (for a character)}}{1148}{subsection.72.8.16}
\contentsline {subsection}{\numberline {72.8.17}\leavevmode {\color {Chapter }CentralCharacter}}{1148}{subsection.72.8.17}
\contentsline {subsection}{\numberline {72.8.18}\leavevmode {\color {Chapter }DeterminantOfCharacter}}{1148}{subsection.72.8.18}
\contentsline {subsection}{\numberline {72.8.19}\leavevmode {\color {Chapter }EigenvaluesChar}}{1149}{subsection.72.8.19}
\contentsline {subsection}{\numberline {72.8.20}\leavevmode {\color {Chapter }Tensored}}{1149}{subsection.72.8.20}
\contentsline {section}{\numberline {72.9}\leavevmode {\color {Chapter }Restricted and Induced Class Functions}}{1150}{section.72.9}
\contentsline {subsection}{\numberline {72.9.1}\leavevmode {\color {Chapter }RestrictedClassFunction}}{1150}{subsection.72.9.1}
\contentsline {subsection}{\numberline {72.9.2}\leavevmode {\color {Chapter }RestrictedClassFunctions}}{1150}{subsection.72.9.2}
\contentsline {subsection}{\numberline {72.9.3}\leavevmode {\color {Chapter }InducedClassFunction}}{1151}{subsection.72.9.3}
\contentsline {subsection}{\numberline {72.9.4}\leavevmode {\color {Chapter }InducedClassFunctions}}{1151}{subsection.72.9.4}
\contentsline {subsection}{\numberline {72.9.5}\leavevmode {\color {Chapter }InducedClassFunctionsByFusionMap}}{1151}{subsection.72.9.5}
\contentsline {subsection}{\numberline {72.9.6}\leavevmode {\color {Chapter }InducedCyclic}}{1152}{subsection.72.9.6}
\contentsline {section}{\numberline {72.10}\leavevmode {\color {Chapter }Reducing Virtual Characters}}{1152}{section.72.10}
\contentsline {subsection}{\numberline {72.10.1}\leavevmode {\color {Chapter }ReducedClassFunctions}}{1152}{subsection.72.10.1}
\contentsline {subsection}{\numberline {72.10.2}\leavevmode {\color {Chapter }ReducedCharacters}}{1153}{subsection.72.10.2}
\contentsline {subsection}{\numberline {72.10.3}\leavevmode {\color {Chapter }IrreducibleDifferences}}{1153}{subsection.72.10.3}
\contentsline {subsection}{\numberline {72.10.4}\leavevmode {\color {Chapter }LLL}}{1153}{subsection.72.10.4}
\contentsline {subsection}{\numberline {72.10.5}\leavevmode {\color {Chapter }Extract}}{1154}{subsection.72.10.5}
\contentsline {subsection}{\numberline {72.10.6}\leavevmode {\color {Chapter }OrthogonalEmbeddingsSpecialDimension}}{1155}{subsection.72.10.6}
\contentsline {subsection}{\numberline {72.10.7}\leavevmode {\color {Chapter }Decreased}}{1157}{subsection.72.10.7}
\contentsline {subsection}{\numberline {72.10.8}\leavevmode {\color {Chapter }DnLattice}}{1158}{subsection.72.10.8}
\contentsline {subsection}{\numberline {72.10.9}\leavevmode {\color {Chapter }DnLatticeIterative}}{1159}{subsection.72.10.9}
\contentsline {section}{\numberline {72.11}\leavevmode {\color {Chapter }Symmetrizations of Class Functions}}{1159}{section.72.11}
\contentsline {subsection}{\numberline {72.11.1}\leavevmode {\color {Chapter }Symmetrizations}}{1159}{subsection.72.11.1}
\contentsline {subsection}{\numberline {72.11.2}\leavevmode {\color {Chapter }SymmetricParts}}{1160}{subsection.72.11.2}
\contentsline {subsection}{\numberline {72.11.3}\leavevmode {\color {Chapter }AntiSymmetricParts}}{1160}{subsection.72.11.3}
\contentsline {subsection}{\numberline {72.11.4}\leavevmode {\color {Chapter }OrthogonalComponents}}{1160}{subsection.72.11.4}
\contentsline {subsection}{\numberline {72.11.5}\leavevmode {\color {Chapter }SymplecticComponents}}{1161}{subsection.72.11.5}
\contentsline {section}{\numberline {72.12}\leavevmode {\color {Chapter }Molien Series}}{1162}{section.72.12}
\contentsline {subsection}{\numberline {72.12.1}\leavevmode {\color {Chapter }MolienSeries}}{1162}{subsection.72.12.1}
\contentsline {subsection}{\numberline {72.12.2}\leavevmode {\color {Chapter }MolienSeriesInfo}}{1162}{subsection.72.12.2}
\contentsline {subsection}{\numberline {72.12.3}\leavevmode {\color {Chapter }ValueMolienSeries}}{1163}{subsection.72.12.3}
\contentsline {subsection}{\numberline {72.12.4}\leavevmode {\color {Chapter }MolienSeriesWithGivenDenominator}}{1164}{subsection.72.12.4}
\contentsline {section}{\numberline {72.13}\leavevmode {\color {Chapter }Possible Permutation Characters}}{1164}{section.72.13}
\contentsline {subsection}{\numberline {72.13.1}\leavevmode {\color {Chapter }PermCharInfo}}{1165}{subsection.72.13.1}
\contentsline {subsection}{\numberline {72.13.2}\leavevmode {\color {Chapter }PermCharInfoRelative}}{1166}{subsection.72.13.2}
\contentsline {section}{\numberline {72.14}\leavevmode {\color {Chapter }Computing Possible Permutation Characters}}{1167}{section.72.14}
\contentsline {subsection}{\numberline {72.14.1}\leavevmode {\color {Chapter }PermChars}}{1167}{subsection.72.14.1}
\contentsline {subsection}{\numberline {72.14.2}\leavevmode {\color {Chapter }TestPerm1, ..., TestPerm5}}{1169}{subsection.72.14.2}
\contentsline {subsection}{\numberline {72.14.3}\leavevmode {\color {Chapter }PermBounds}}{1170}{subsection.72.14.3}
\contentsline {subsection}{\numberline {72.14.4}\leavevmode {\color {Chapter }PermComb}}{1171}{subsection.72.14.4}
\contentsline {subsection}{\numberline {72.14.5}\leavevmode {\color {Chapter }Inequalities}}{1171}{subsection.72.14.5}
\contentsline {section}{\numberline {72.15}\leavevmode {\color {Chapter }Operations for Brauer Characters}}{1172}{section.72.15}
\contentsline {subsection}{\numberline {72.15.1}\leavevmode {\color {Chapter }FrobeniusCharacterValue}}{1172}{subsection.72.15.1}
\contentsline {subsection}{\numberline {72.15.2}\leavevmode {\color {Chapter }BrauerCharacterValue}}{1172}{subsection.72.15.2}
\contentsline {subsection}{\numberline {72.15.3}\leavevmode {\color {Chapter }SizeOfFieldOfDefinition}}{1173}{subsection.72.15.3}
\contentsline {subsection}{\numberline {72.15.4}\leavevmode {\color {Chapter }RealizableBrauerCharacters}}{1173}{subsection.72.15.4}
\contentsline {section}{\numberline {72.16}\leavevmode {\color {Chapter }Domains Generated by Class Functions}}{1173}{section.72.16}
\contentsline {chapter}{\numberline {73}\leavevmode {\color {Chapter }Maps Concerning Character Tables}}{1174}{chapter.73}
\contentsline {section}{\numberline {73.1}\leavevmode {\color {Chapter }Power Maps}}{1174}{section.73.1}
\contentsline {subsection}{\numberline {73.1.1}\leavevmode {\color {Chapter }PowerMap}}{1175}{subsection.73.1.1}
\contentsline {subsection}{\numberline {73.1.2}\leavevmode {\color {Chapter }PossiblePowerMaps}}{1176}{subsection.73.1.2}
\contentsline {subsection}{\numberline {73.1.3}\leavevmode {\color {Chapter }ElementOrdersPowerMap}}{1177}{subsection.73.1.3}
\contentsline {subsection}{\numberline {73.1.4}\leavevmode {\color {Chapter }PowerMapByComposition}}{1178}{subsection.73.1.4}
\contentsline {section}{\numberline {73.2}\leavevmode {\color {Chapter }Orbits on Sets of Possible Power Maps}}{1178}{section.73.2}
\contentsline {subsection}{\numberline {73.2.1}\leavevmode {\color {Chapter }OrbitPowerMaps}}{1178}{subsection.73.2.1}
\contentsline {subsection}{\numberline {73.2.2}\leavevmode {\color {Chapter }RepresentativesPowerMaps}}{1178}{subsection.73.2.2}
\contentsline {section}{\numberline {73.3}\leavevmode {\color {Chapter }Class Fusions between Character Tables}}{1179}{section.73.3}
\contentsline {subsection}{\numberline {73.3.1}\leavevmode {\color {Chapter }FusionConjugacyClasses}}{1180}{subsection.73.3.1}
\contentsline {subsection}{\numberline {73.3.2}\leavevmode {\color {Chapter }ComputedClassFusions}}{1181}{subsection.73.3.2}
\contentsline {subsection}{\numberline {73.3.3}\leavevmode {\color {Chapter }GetFusionMap}}{1181}{subsection.73.3.3}
\contentsline {subsection}{\numberline {73.3.4}\leavevmode {\color {Chapter }StoreFusion}}{1182}{subsection.73.3.4}
\contentsline {subsection}{\numberline {73.3.5}\leavevmode {\color {Chapter }NamesOfFusionSources}}{1182}{subsection.73.3.5}
\contentsline {subsection}{\numberline {73.3.6}\leavevmode {\color {Chapter }PossibleClassFusions}}{1183}{subsection.73.3.6}
\contentsline {subsection}{\numberline {73.3.7}\leavevmode {\color {Chapter }ConsiderStructureConstants}}{1184}{subsection.73.3.7}
\contentsline {section}{\numberline {73.4}\leavevmode {\color {Chapter }Orbits on Sets of Possible Class Fusions}}{1185}{section.73.4}
\contentsline {subsection}{\numberline {73.4.1}\leavevmode {\color {Chapter }OrbitFusions}}{1185}{subsection.73.4.1}
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\contentsline {section}{\numberline {73.5}\leavevmode {\color {Chapter }Parametrized Maps}}{1185}{section.73.5}
\contentsline {subsection}{\numberline {73.5.1}\leavevmode {\color {Chapter }CompositionMaps}}{1186}{subsection.73.5.1}
\contentsline {subsection}{\numberline {73.5.2}\leavevmode {\color {Chapter }InverseMap}}{1186}{subsection.73.5.2}
\contentsline {subsection}{\numberline {73.5.3}\leavevmode {\color {Chapter }ProjectionMap}}{1187}{subsection.73.5.3}
\contentsline {subsection}{\numberline {73.5.4}\leavevmode {\color {Chapter }Indirected}}{1187}{subsection.73.5.4}
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\contentsline {subsection}{\numberline {73.5.6}\leavevmode {\color {Chapter }ContainedMaps}}{1188}{subsection.73.5.6}
\contentsline {subsection}{\numberline {73.5.7}\leavevmode {\color {Chapter }UpdateMap}}{1188}{subsection.73.5.7}
\contentsline {subsection}{\numberline {73.5.8}\leavevmode {\color {Chapter }MeetMaps}}{1189}{subsection.73.5.8}
\contentsline {subsection}{\numberline {73.5.9}\leavevmode {\color {Chapter }CommutativeDiagram}}{1189}{subsection.73.5.9}
\contentsline {subsection}{\numberline {73.5.10}\leavevmode {\color {Chapter }CheckFixedPoints}}{1190}{subsection.73.5.10}
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\contentsline {subsection}{\numberline {73.5.12}\leavevmode {\color {Chapter }TestConsistencyMaps}}{1191}{subsection.73.5.12}
\contentsline {subsection}{\numberline {73.5.13}\leavevmode {\color {Chapter }Indeterminateness}}{1192}{subsection.73.5.13}
\contentsline {subsection}{\numberline {73.5.14}\leavevmode {\color {Chapter }PrintAmbiguity}}{1192}{subsection.73.5.14}
\contentsline {subsection}{\numberline {73.5.15}\leavevmode {\color {Chapter }ContainedSpecialVectors}}{1192}{subsection.73.5.15}
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\contentsline {subsection}{\numberline {73.6.2}\leavevmode {\color {Chapter }Congruences (for character tables)}}{1195}{subsection.73.6.2}
\contentsline {subsection}{\numberline {73.6.3}\leavevmode {\color {Chapter }ConsiderKernels}}{1196}{subsection.73.6.3}
\contentsline {subsection}{\numberline {73.6.4}\leavevmode {\color {Chapter }ConsiderSmallerPowerMaps}}{1196}{subsection.73.6.4}
\contentsline {subsection}{\numberline {73.6.5}\leavevmode {\color {Chapter }MinusCharacter}}{1196}{subsection.73.6.5}
\contentsline {subsection}{\numberline {73.6.6}\leavevmode {\color {Chapter }PowerMapsAllowedBySymmetrizations}}{1197}{subsection.73.6.6}
\contentsline {section}{\numberline {73.7}\leavevmode {\color {Chapter }Subroutines for the Construction of Class Fusions}}{1198}{section.73.7}
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\contentsline {subsection}{\numberline {73.7.2}\leavevmode {\color {Chapter }CheckPermChar}}{1198}{subsection.73.7.2}
\contentsline {subsection}{\numberline {73.7.3}\leavevmode {\color {Chapter }ConsiderTableAutomorphisms}}{1199}{subsection.73.7.3}
\contentsline {subsection}{\numberline {73.7.4}\leavevmode {\color {Chapter }FusionsAllowedByRestrictions}}{1199}{subsection.73.7.4}
\contentsline {chapter}{\numberline {74}\leavevmode {\color {Chapter }Unknowns}}{1201}{chapter.74}
\contentsline {section}{\numberline {74.1}\leavevmode {\color {Chapter }More about Unknowns}}{1201}{section.74.1}
\contentsline {subsection}{\numberline {74.1.1}\leavevmode {\color {Chapter }Unknown}}{1201}{subsection.74.1.1}
\contentsline {subsection}{\numberline {74.1.2}\leavevmode {\color {Chapter }LargestUnknown}}{1202}{subsection.74.1.2}
\contentsline {subsection}{\numberline {74.1.3}\leavevmode {\color {Chapter }IsUnknown}}{1202}{subsection.74.1.3}
\contentsline {subsection}{\numberline {74.1.4}\leavevmode {\color {Chapter }Comparison of Unknowns}}{1202}{subsection.74.1.4}
\contentsline {subsection}{\numberline {74.1.5}\leavevmode {\color {Chapter }Arithmetical Operations for Unknowns}}{1202}{subsection.74.1.5}
\contentsline {chapter}{\numberline {75}\leavevmode {\color {Chapter }Monomiality Questions}}{1204}{chapter.75}
\contentsline {section}{\numberline {75.1}\leavevmode {\color {Chapter }InfoMonomial (Info Class)}}{1205}{section.75.1}
\contentsline {subsection}{\numberline {75.1.1}\leavevmode {\color {Chapter }InfoMonomial}}{1205}{subsection.75.1.1}
\contentsline {section}{\numberline {75.2}\leavevmode {\color {Chapter }Character Degrees and Derived Length}}{1205}{section.75.2}
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\contentsline {subsection}{\numberline {75.2.2}\leavevmode {\color {Chapter }Delta}}{1205}{subsection.75.2.2}
\contentsline {subsection}{\numberline {75.2.3}\leavevmode {\color {Chapter }IsBergerCondition}}{1205}{subsection.75.2.3}
\contentsline {section}{\numberline {75.3}\leavevmode {\color {Chapter }Primitivity of Characters}}{1206}{section.75.3}
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\contentsline {subsection}{\numberline {75.3.2}\leavevmode {\color {Chapter }IsPrimitiveCharacter}}{1207}{subsection.75.3.2}
\contentsline {subsection}{\numberline {75.3.3}\leavevmode {\color {Chapter }TestQuasiPrimitive}}{1207}{subsection.75.3.3}
\contentsline {subsection}{\numberline {75.3.4}\leavevmode {\color {Chapter }TestInducedFromNormalSubgroup}}{1208}{subsection.75.3.4}
\contentsline {section}{\numberline {75.4}\leavevmode {\color {Chapter }Testing Monomiality}}{1208}{section.75.4}
\contentsline {subsection}{\numberline {75.4.1}\leavevmode {\color {Chapter }TestMonomial}}{1208}{subsection.75.4.1}
\contentsline {subsection}{\numberline {75.4.2}\leavevmode {\color {Chapter }TestMonomialUseLattice}}{1209}{subsection.75.4.2}
\contentsline {subsection}{\numberline {75.4.3}\leavevmode {\color {Chapter }IsMonomialNumber}}{1209}{subsection.75.4.3}
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\contentsline {subsection}{\numberline {75.4.5}\leavevmode {\color {Chapter }TestSubnormallyMonomial}}{1210}{subsection.75.4.5}
\contentsline {subsection}{\numberline {75.4.6}\leavevmode {\color {Chapter }TestRelativelySM}}{1211}{subsection.75.4.6}
\contentsline {section}{\numberline {75.5}\leavevmode {\color {Chapter }Minimal Nonmonomial Groups}}{1212}{section.75.5}
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\contentsline {subsection}{\numberline {75.5.2}\leavevmode {\color {Chapter }MinimalNonmonomialGroup}}{1212}{subsection.75.5.2}
\contentsline {chapter}{\numberline {76}\leavevmode {\color {Chapter }Using and Developing GAP Packages}}{1213}{chapter.76}
\contentsline {section}{\numberline {76.1}\leavevmode {\color {Chapter }Installing a GAP Package}}{1213}{section.76.1}
\contentsline {section}{\numberline {76.2}\leavevmode {\color {Chapter }Loading a GAP Package}}{1214}{section.76.2}
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\contentsline {subsection}{\numberline {76.2.3}\leavevmode {\color {Chapter }SetPackagePath}}{1215}{subsection.76.2.3}
\contentsline {subsection}{\numberline {76.2.4}\leavevmode {\color {Chapter }ExtendRootDirectories}}{1215}{subsection.76.2.4}
\contentsline {subsection}{\numberline {76.2.5}\leavevmode {\color {Chapter }DisplayPackageLoadingLog}}{1216}{subsection.76.2.5}
\contentsline {section}{\numberline {76.3}\leavevmode {\color {Chapter }Functions for GAP Packages}}{1217}{section.76.3}
\contentsline {subsection}{\numberline {76.3.1}\leavevmode {\color {Chapter }ReadPackage}}{1217}{subsection.76.3.1}
\contentsline {subsection}{\numberline {76.3.2}\leavevmode {\color {Chapter }TestPackageAvailability}}{1217}{subsection.76.3.2}
\contentsline {subsection}{\numberline {76.3.3}\leavevmode {\color {Chapter }IsPackageLoaded}}{1218}{subsection.76.3.3}
\contentsline {subsection}{\numberline {76.3.4}\leavevmode {\color {Chapter }IsPackageMarkedForLoading}}{1218}{subsection.76.3.4}
\contentsline {subsection}{\numberline {76.3.5}\leavevmode {\color {Chapter }TestPackage}}{1218}{subsection.76.3.5}
\contentsline {subsection}{\numberline {76.3.6}\leavevmode {\color {Chapter }InstalledPackageVersion}}{1219}{subsection.76.3.6}
\contentsline {subsection}{\numberline {76.3.7}\leavevmode {\color {Chapter }DirectoriesPackageLibrary}}{1219}{subsection.76.3.7}
\contentsline {subsection}{\numberline {76.3.8}\leavevmode {\color {Chapter }DirectoriesPackagePrograms}}{1220}{subsection.76.3.8}
\contentsline {subsection}{\numberline {76.3.9}\leavevmode {\color {Chapter }CompareVersionNumbers}}{1220}{subsection.76.3.9}
\contentsline {subsection}{\numberline {76.3.10}\leavevmode {\color {Chapter }DeclareAutoreadableVariables}}{1220}{subsection.76.3.10}
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\contentsline {subsection}{\numberline {76.3.12}\leavevmode {\color {Chapter }LoadDynamicModule}}{1221}{subsection.76.3.12}
\contentsline {subsection}{\numberline {76.3.13}\leavevmode {\color {Chapter }The PackageInfo.g File}}{1221}{subsection.76.3.13}
\contentsline {subsection}{\numberline {76.3.14}\leavevmode {\color {Chapter }ValidatePackageInfo}}{1221}{subsection.76.3.14}
\contentsline {subsection}{\numberline {76.3.15}\leavevmode {\color {Chapter }ShowPackageVariables}}{1222}{subsection.76.3.15}
\contentsline {subsection}{\numberline {76.3.16}\leavevmode {\color {Chapter }BibEntry}}{1223}{subsection.76.3.16}
\contentsline {subsection}{\numberline {76.3.17}\leavevmode {\color {Chapter }Cite}}{1224}{subsection.76.3.17}
\contentsline {section}{\numberline {76.4}\leavevmode {\color {Chapter }Guidelines for Writing a GAP Package}}{1224}{section.76.4}
\contentsline {section}{\numberline {76.5}\leavevmode {\color {Chapter }Structure of a GAP Package}}{1225}{section.76.5}
\contentsline {section}{\numberline {76.6}\leavevmode {\color {Chapter }Writing Documentation and Tools Needed}}{1228}{section.76.6}
\contentsline {section}{\numberline {76.7}\leavevmode {\color {Chapter }An Example of a GAP Package}}{1229}{section.76.7}
\contentsline {section}{\numberline {76.8}\leavevmode {\color {Chapter }File Structure}}{1230}{section.76.8}
\contentsline {section}{\numberline {76.9}\leavevmode {\color {Chapter }Creating the PackageInfo.g File}}{1231}{section.76.9}
\contentsline {section}{\numberline {76.10}\leavevmode {\color {Chapter }Functions and Variables and Choices of Their Names}}{1231}{section.76.10}
\contentsline {section}{\numberline {76.11}\leavevmode {\color {Chapter }Package Dependencies (Requesting one \textsf {GAP} Package from within Another)}}{1234}{section.76.11}
\contentsline {section}{\numberline {76.12}\leavevmode {\color {Chapter }Declaration and Implementation Part of a Package}}{1235}{section.76.12}
\contentsline {section}{\numberline {76.13}\leavevmode {\color {Chapter }Autoreadable Variables}}{1236}{section.76.13}
\contentsline {section}{\numberline {76.14}\leavevmode {\color {Chapter }Standalone Programs in a \textsf {GAP} Package}}{1237}{section.76.14}
\contentsline {subsection}{\numberline {76.14.1}\leavevmode {\color {Chapter }Installation of \textsf {GAP} Package Binaries}}{1237}{subsection.76.14.1}
\contentsline {subsection}{\numberline {76.14.2}\leavevmode {\color {Chapter }Test for the Existence of GAP Package Binaries}}{1237}{subsection.76.14.2}
\contentsline {subsection}{\numberline {76.14.3}\leavevmode {\color {Chapter }Calling of and Communication with External Binaries}}{1238}{subsection.76.14.3}
\contentsline {section}{\numberline {76.15}\leavevmode {\color {Chapter }Having an InfoClass}}{1239}{section.76.15}
\contentsline {section}{\numberline {76.16}\leavevmode {\color {Chapter }The Banner}}{1239}{section.76.16}
\contentsline {section}{\numberline {76.17}\leavevmode {\color {Chapter }Version Numbers}}{1239}{section.76.17}
\contentsline {section}{\numberline {76.18}\leavevmode {\color {Chapter }Testing a \textsf {GAP} package}}{1240}{section.76.18}
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\contentsline {subsection}{\numberline {76.18.3}\leavevmode {\color {Chapter }LoadAllPackages}}{1243}{subsection.76.18.3}
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\contentsline {section}{\numberline {76.19}\leavevmode {\color {Chapter }Access to the \textsf {GAP} Development Version}}{1244}{section.76.19}
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\contentsline {section}{\numberline {76.21}\leavevmode {\color {Chapter }Selecting a license for a \textsf {GAP} Package}}{1244}{section.76.21}
\contentsline {section}{\numberline {76.22}\leavevmode {\color {Chapter }Releasing a GAP Package}}{1244}{section.76.22}
\contentsline {section}{\numberline {76.23}\leavevmode {\color {Chapter }The homepage of a Package}}{1246}{section.76.23}
\contentsline {section}{\numberline {76.24}\leavevmode {\color {Chapter }Some things to keep in mind}}{1246}{section.76.24}
\contentsline {section}{\numberline {76.25}\leavevmode {\color {Chapter }Package release checklists}}{1247}{section.76.25}
\contentsline {subsection}{\numberline {76.25.1}\leavevmode {\color {Chapter }Checklist for releasing a new package}}{1247}{subsection.76.25.1}
\contentsline {subsection}{\numberline {76.25.2}\leavevmode {\color {Chapter }Checklist for upgrading the package for the next major release of \textsf {GAP}}}{1248}{subsection.76.25.2}
\contentsline {chapter}{\numberline {77}\leavevmode {\color {Chapter }Replaced and Removed Command Names}}{1249}{chapter.77}
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\contentsline {section}{\numberline {77.2}\leavevmode {\color {Chapter }Package Interface {\textendash } Obsolete Functions and Name Changes}}{1250}{section.77.2}
\contentsline {section}{\numberline {77.3}\leavevmode {\color {Chapter }Normal Forms of Integer Matrices {\textendash } Name Changes}}{1250}{section.77.3}
\contentsline {section}{\numberline {77.4}\leavevmode {\color {Chapter }Miscellaneous Name Changes or Removed Names}}{1250}{section.77.4}
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\contentsline {section}{\numberline {77.5}\leavevmode {\color {Chapter }The former .gaprc file}}{1251}{section.77.5}
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\contentsline {chapter}{\numberline {78}\leavevmode {\color {Chapter }Method Selection}}{1253}{chapter.78}
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\contentsline {section}{\numberline {78.2}\leavevmode {\color {Chapter }Method Installation}}{1253}{section.78.2}
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\contentsline {section}{\numberline {78.3}\leavevmode {\color {Chapter }Applicable Methods and Method Selection}}{1255}{section.78.3}
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\contentsline {section}{\numberline {78.8}\leavevmode {\color {Chapter }Operations and Mathematical Terms}}{1258}{section.78.8}
\contentsline {chapter}{\numberline {79}\leavevmode {\color {Chapter }Creating New Objects}}{1259}{chapter.79}
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\contentsline {section}{\numberline {79.4}\leavevmode {\color {Chapter }Creating Other Filters}}{1261}{section.79.4}
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\contentsline {subsection}{\numberline {79.4.2}\leavevmode {\color {Chapter }SetFilterObj}}{1262}{subsection.79.4.2}
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\contentsline {section}{\numberline {79.6}\leavevmode {\color {Chapter }Creating Constructors}}{1262}{section.79.6}
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\contentsline {section}{\numberline {79.7}\leavevmode {\color {Chapter }Creating Families}}{1264}{section.79.7}
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\contentsline {section}{\numberline {79.8}\leavevmode {\color {Chapter }Creating Types}}{1265}{section.79.8}
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\contentsline {section}{\numberline {79.9}\leavevmode {\color {Chapter }Creating Objects}}{1265}{section.79.9}
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\contentsline {section}{\numberline {79.10}\leavevmode {\color {Chapter }Component Objects}}{1266}{section.79.10}
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\contentsline {section}{\numberline {79.11}\leavevmode {\color {Chapter }Positional Objects}}{1268}{section.79.11}
\contentsline {section}{\numberline {79.12}\leavevmode {\color {Chapter }Implementing New List Objects}}{1269}{section.79.12}
\contentsline {section}{\numberline {79.13}\leavevmode {\color {Chapter }Example {\textendash } Constructing Enumerators}}{1270}{section.79.13}
\contentsline {section}{\numberline {79.14}\leavevmode {\color {Chapter }Example {\textendash } Constructing Iterators}}{1272}{section.79.14}
\contentsline {section}{\numberline {79.15}\leavevmode {\color {Chapter }Arithmetic Issues in the Implementation of New Kinds of Lists}}{1273}{section.79.15}
\contentsline {section}{\numberline {79.16}\leavevmode {\color {Chapter }External Representation}}{1274}{section.79.16}
\contentsline {subsection}{\numberline {79.16.1}\leavevmode {\color {Chapter }ExtRepOfObj}}{1275}{subsection.79.16.1}
\contentsline {section}{\numberline {79.17}\leavevmode {\color {Chapter }Mutability and Copying}}{1275}{section.79.17}
\contentsline {section}{\numberline {79.18}\leavevmode {\color {Chapter }Global Variables in the Library}}{1278}{section.79.18}
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\contentsline {subsection}{\numberline {79.18.4}\leavevmode {\color {Chapter }IsRepresentation}}{1278}{subsection.79.18.4}
\contentsline {subsection}{\numberline {79.18.5}\leavevmode {\color {Chapter }IsProperty}}{1278}{subsection.79.18.5}
\contentsline {subsection}{\numberline {79.18.6}\leavevmode {\color {Chapter }IsAttribute}}{1278}{subsection.79.18.6}
\contentsline {subsection}{\numberline {79.18.7}\leavevmode {\color {Chapter }CategoryByName}}{1278}{subsection.79.18.7}
\contentsline {subsection}{\numberline {79.18.8}\leavevmode {\color {Chapter }DeclareRepresentation}}{1279}{subsection.79.18.8}
\contentsline {subsection}{\numberline {79.18.9}\leavevmode {\color {Chapter }DeclareAttribute}}{1279}{subsection.79.18.9}
\contentsline {subsection}{\numberline {79.18.10}\leavevmode {\color {Chapter }DeclareProperty}}{1279}{subsection.79.18.10}
\contentsline {subsection}{\numberline {79.18.11}\leavevmode {\color {Chapter }DeclareFilter}}{1279}{subsection.79.18.11}
\contentsline {subsection}{\numberline {79.18.12}\leavevmode {\color {Chapter }DeclareOperation}}{1279}{subsection.79.18.12}
\contentsline {subsection}{\numberline {79.18.13}\leavevmode {\color {Chapter }DeclareConstructor}}{1279}{subsection.79.18.13}
\contentsline {subsection}{\numberline {79.18.14}\leavevmode {\color {Chapter }DeclareGlobalFunction}}{1279}{subsection.79.18.14}
\contentsline {subsection}{\numberline {79.18.15}\leavevmode {\color {Chapter }DeclareGlobalVariable}}{1280}{subsection.79.18.15}
\contentsline {subsection}{\numberline {79.18.16}\leavevmode {\color {Chapter }InstallValue}}{1280}{subsection.79.18.16}
\contentsline {subsection}{\numberline {79.18.17}\leavevmode {\color {Chapter }DeclareSynonym}}{1280}{subsection.79.18.17}
\contentsline {subsection}{\numberline {79.18.18}\leavevmode {\color {Chapter }FlushCaches}}{1281}{subsection.79.18.18}
\contentsline {subsection}{\numberline {79.18.19}\leavevmode {\color {Chapter }FilterByName}}{1281}{subsection.79.18.19}
\contentsline {section}{\numberline {79.19}\leavevmode {\color {Chapter }Declaration and Implementation Part}}{1281}{section.79.19}
\contentsline {chapter}{\numberline {80}\leavevmode {\color {Chapter }Examples of Extending the System}}{1283}{chapter.80}
\contentsline {section}{\numberline {80.1}\leavevmode {\color {Chapter }Addition of a Method}}{1283}{section.80.1}
\contentsline {section}{\numberline {80.2}\leavevmode {\color {Chapter }Extending the Range of Definition of an Existing Operation}}{1285}{section.80.2}
\contentsline {section}{\numberline {80.3}\leavevmode {\color {Chapter }Enforcing Property Tests}}{1285}{section.80.3}
\contentsline {section}{\numberline {80.4}\leavevmode {\color {Chapter }Adding a new Operation}}{1286}{section.80.4}
\contentsline {section}{\numberline {80.5}\leavevmode {\color {Chapter }Adding a new Attribute}}{1286}{section.80.5}
\contentsline {section}{\numberline {80.6}\leavevmode {\color {Chapter }Adding a new Representation}}{1287}{section.80.6}
\contentsline {section}{\numberline {80.7}\leavevmode {\color {Chapter }Components versus Attributes}}{1289}{section.80.7}
\contentsline {section}{\numberline {80.8}\leavevmode {\color {Chapter }Adding new Concepts}}{1289}{section.80.8}
\contentsline {subsection}{\numberline {80.8.1}\leavevmode {\color {Chapter }Example: M-groups}}{1290}{subsection.80.8.1}
\contentsline {subsection}{\numberline {80.8.2}\leavevmode {\color {Chapter }Example: Groups with a word length}}{1291}{subsection.80.8.2}
\contentsline {subsection}{\numberline {80.8.3}\leavevmode {\color {Chapter }Example: Groups with a decomposition as semidirect product}}{1291}{subsection.80.8.3}
\contentsline {section}{\numberline {80.9}\leavevmode {\color {Chapter }Creating Own Arithmetic Objects}}{1292}{section.80.9}
\contentsline {subsection}{\numberline {80.9.1}\leavevmode {\color {Chapter }ArithmeticElementCreator}}{1292}{subsection.80.9.1}
\contentsline {subsection}{\numberline {80.9.2}\leavevmode {\color {Chapter }Example: ArithmeticElementCreator}}{1293}{subsection.80.9.2}
\contentsline {chapter}{\numberline {81}\leavevmode {\color {Chapter }An Example {\textendash } Residue Class Rings}}{1295}{chapter.81}
\contentsline {section}{\numberline {81.1}\leavevmode {\color {Chapter }A First Attempt to Implement Elements of Residue Class Rings}}{1295}{section.81.1}
\contentsline {section}{\numberline {81.2}\leavevmode {\color {Chapter }Why Proceed in a Different Way?}}{1296}{section.81.2}
\contentsline {section}{\numberline {81.3}\leavevmode {\color {Chapter }A Second Attempt to Implement Elements of Residue Class Rings}}{1297}{section.81.3}
\contentsline {section}{\numberline {81.4}\leavevmode {\color {Chapter }Compatibility of Residue Class Rings with Prime Fields}}{1308}{section.81.4}
\contentsline {section}{\numberline {81.5}\leavevmode {\color {Chapter }Further Improvements in Implementing Residue Class Rings}}{1314}{section.81.5}
\contentsline {chapter}{\numberline {82}\leavevmode {\color {Chapter }An Example {\textendash } Designing Arithmetic Operations}}{1316}{chapter.82}
\contentsline {section}{\numberline {82.1}\leavevmode {\color {Chapter }New Arithmetic Operations vs. New Objects}}{1316}{section.82.1}
\contentsline {section}{\numberline {82.2}\leavevmode {\color {Chapter }Designing new Multiplicative Objects}}{1317}{section.82.2}
\contentsline {chapter}{\numberline {83}\leavevmode {\color {Chapter }Library Files}}{1324}{chapter.83}
\contentsline {section}{\numberline {83.1}\leavevmode {\color {Chapter }File Types}}{1324}{section.83.1}
\contentsline {section}{\numberline {83.2}\leavevmode {\color {Chapter }Finding Implementations in the Library}}{1324}{section.83.2}
\contentsline {section}{\numberline {83.3}\leavevmode {\color {Chapter }Undocumented Variables}}{1325}{section.83.3}
\contentsline {chapter}{\numberline {84}\leavevmode {\color {Chapter }Interface to the GAP Help System}}{1327}{chapter.84}
\contentsline {section}{\numberline {84.1}\leavevmode {\color {Chapter }Installing and Removing a Help Book}}{1327}{section.84.1}
\contentsline {subsection}{\numberline {84.1.1}\leavevmode {\color {Chapter }HELP{\textunderscore }ADD{\textunderscore }BOOK}}{1327}{subsection.84.1.1}
\contentsline {subsection}{\numberline {84.1.2}\leavevmode {\color {Chapter }HELP{\textunderscore }REMOVE{\textunderscore }BOOK}}{1328}{subsection.84.1.2}
\contentsline {section}{\numberline {84.2}\leavevmode {\color {Chapter }The manual.six File}}{1328}{section.84.2}
\contentsline {section}{\numberline {84.3}\leavevmode {\color {Chapter }The Help Book Handler}}{1328}{section.84.3}
\contentsline {section}{\numberline {84.4}\leavevmode {\color {Chapter }Introducing new Viewer for the Online Help}}{1330}{section.84.4}
\contentsline {subsection}{\numberline {84.4.1}\leavevmode {\color {Chapter }HELP{\textunderscore }VIEWER{\textunderscore }INFO}}{1330}{subsection.84.4.1}
\contentsline {chapter}{\numberline {85}\leavevmode {\color {Chapter }Function-Operation-Attribute Triples}}{1331}{chapter.85}
\contentsline {section}{\numberline {85.1}\leavevmode {\color {Chapter }Key Dependent Operations}}{1331}{section.85.1}
\contentsline {subsection}{\numberline {85.1.1}\leavevmode {\color {Chapter }KeyDependentOperation}}{1331}{subsection.85.1.1}
\contentsline {section}{\numberline {85.2}\leavevmode {\color {Chapter }In Parent Attributes}}{1333}{section.85.2}
\contentsline {subsection}{\numberline {85.2.1}\leavevmode {\color {Chapter }InParentFOA}}{1333}{subsection.85.2.1}
\contentsline {section}{\numberline {85.3}\leavevmode {\color {Chapter }Operation Functions}}{1333}{section.85.3}
\contentsline {subsection}{\numberline {85.3.1}\leavevmode {\color {Chapter }OrbitsishOperation}}{1334}{subsection.85.3.1}
\contentsline {subsection}{\numberline {85.3.2}\leavevmode {\color {Chapter }OrbitishFO}}{1335}{subsection.85.3.2}
\contentsline {subsection}{\numberline {85.3.3}\leavevmode {\color {Chapter }Example: Orbit and OrbitOp}}{1335}{subsection.85.3.3}
\contentsline {chapter}{\numberline {86}\leavevmode {\color {Chapter }Weak Pointers}}{1337}{chapter.86}
\contentsline {section}{\numberline {86.1}\leavevmode {\color {Chapter }Weak Pointer Objects}}{1337}{section.86.1}
\contentsline {subsection}{\numberline {86.1.1}\leavevmode {\color {Chapter }WeakPointerObj}}{1337}{subsection.86.1.1}
\contentsline {section}{\numberline {86.2}\leavevmode {\color {Chapter }Low Level Access Functions for Weak Pointer Objects}}{1338}{section.86.2}
\contentsline {subsection}{\numberline {86.2.1}\leavevmode {\color {Chapter }SetElmWPObj}}{1338}{subsection.86.2.1}
\contentsline {section}{\numberline {86.3}\leavevmode {\color {Chapter }Accessing Weak Pointer Objects as Lists}}{1339}{section.86.3}
\contentsline {section}{\numberline {86.4}\leavevmode {\color {Chapter }Copying Weak Pointer Objects}}{1339}{section.86.4}
\contentsline {section}{\numberline {86.5}\leavevmode {\color {Chapter }The GASMAN Interface for Weak Pointer Objects}}{1340}{section.86.5}
\contentsline {chapter}{\numberline {87}\leavevmode {\color {Chapter }More about Stabilizer Chains}}{1341}{chapter.87}
\contentsline {section}{\numberline {87.1}\leavevmode {\color {Chapter }Generalized Conjugation Technique}}{1341}{section.87.1}
\contentsline {section}{\numberline {87.2}\leavevmode {\color {Chapter }The General Backtrack Algorithm with Ordered Partitions}}{1342}{section.87.2}
\contentsline {subsection}{\numberline {87.2.1}\leavevmode {\color {Chapter }Internal representation of ordered partitions}}{1342}{subsection.87.2.1}
\contentsline {subsection}{\numberline {87.2.2}\leavevmode {\color {Chapter }Functions for setting up an R-base}}{1343}{subsection.87.2.2}
\contentsline {subsection}{\numberline {87.2.3}\leavevmode {\color {Chapter }Refinement functions for the backtrack search}}{1346}{subsection.87.2.3}
\contentsline {subsection}{\numberline {87.2.4}\leavevmode {\color {Chapter }Functions for meeting ordered partitions}}{1347}{subsection.87.2.4}
\contentsline {subsection}{\numberline {87.2.5}\leavevmode {\color {Chapter }Avoiding multiplication of permutations}}{1348}{subsection.87.2.5}
\contentsline {section}{\numberline {87.3}\leavevmode {\color {Chapter }Stabilizer Chains for Automorphisms Acting on Enumerators}}{1350}{section.87.3}
\contentsline {subsection}{\numberline {87.3.1}\leavevmode {\color {Chapter }An operation domain for automorphisms}}{1350}{subsection.87.3.1}
\contentsline {subsection}{\numberline {87.3.2}\leavevmode {\color {Chapter }Enumerators for cosets of characteristic factors}}{1351}{subsection.87.3.2}
\contentsline {subsection}{\numberline {87.3.3}\leavevmode {\color {Chapter }Making automorphisms act on such enumerators}}{1352}{subsection.87.3.3}
\contentsline {chapter}{References}{1362}{chapter*.3}
\contentsline {chapter}{Index}{1363}{section*.4}
