\begin{theindex}

  \item \texttt  {\texttt  {\char 92\relax }*}, \hyperpage{413}
    \subitem for pcwords, \hyperpage{653}
  \item \texttt{*}, \hyperpage{57}
    \subitem for character tables, \hyperpage{1079}
  \item \texttt  {\texttt  {\char 92\relax }+}, \hyperpage{413}
  \item \texttt{+}, \hyperpage{57}
  \item \texttt{-}, \hyperpage{57}
  \item \texttt  {-A}, \hyperpage{33}
  \item \texttt  {-B}, \hyperpage{34}
  \item \texttt{-C}, \hyperpage{38}
  \item \texttt  {-D}, \hyperpage{34}
  \item \texttt  {-E}, \hyperpage{34}
  \item \texttt  {-K}, \hyperpage{35}
  \item \texttt  {-L}, \hyperpage{35}
  \item \texttt  {-M}, \hyperpage{36}
  \item \texttt  {-O}, \hyperpage{36}
  \item \texttt{-P}, \hyperpage{38}
  \item \texttt  {-R}, \hyperpage{37}
  \item \texttt  {-T}, \hyperpage{37}
  \item \texttt{-U}, \hyperpage{38}
  \item \texttt{-W}, \hyperpage{38}
  \item \texttt  {-X}, \hyperpage{37}
  \item \texttt  {-a}, \hyperpage{33}
  \item \texttt  {-b}, \hyperpage{34}
  \item \texttt  {-e}, \hyperpage{34}
  \item \texttt  {-f}, \hyperpage{35}
  \item \texttt  {-g}, \hyperpage{35}
  \item \texttt  {-g -g}, \hyperpage{35}
  \item \texttt  {-h}, \hyperpage{35}
  \item \texttt  {-i}, \hyperpage{35}
  \item \texttt  {-infinity}, \hyperpage{228}
  \item \texttt  {-l}, \hyperpage{35}
  \item \texttt  {-m}, \hyperpage{36}
  \item \texttt  {-n}, \hyperpage{36}
  \item \texttt  {-o}, \hyperpage{36}
  \item \texttt{-p}, \hyperpage{38}
  \item \texttt  {-q}, \hyperpage{36}
  \item \texttt  {-r}, \hyperpage{37}
  \item \texttt  {-s}, \hyperpage{37}
  \item \texttt  {-x}, \hyperpage{37}
  \item \texttt  {-y}, \hyperpage{37}
  \item \texttt{-z}, \hyperpage{38}
  \item \texttt  {\texttt  {\char 92\relax }.}, \hyperpage{383}
  \item \texttt  {\texttt  {\char 92\relax }.\texttt  {\char 92\relax }:\texttt  {\char 92\relax }=}, 
		\hyperpage{383}
  \item \texttt  {\texttt  {\char 92\relax }/}, \hyperpage{413}
    \subitem for a free group and a list of elements, \hyperpage{666}
    \subitem for a free monoid and a list of pairs of elements, 
		\hyperpage{790}
    \subitem for a free semigroup and a list of pairs of elements, 
		\hyperpage{787}
  \item \texttt{/}, \hyperpage{57}
    \subitem for character tables, \hyperpage{1079}
  \item \texttt  {\texttt  {\char 92\relax }{\textless }}, 
		\hyperpage{412}
    \subitem for associative words, \hyperpage{476}
    \subitem for nonassociative words, \hyperpage{469}
    \subitem for pcwords, \hyperpage{653}
    \subitem for permutations, \hyperpage{595}
    \subitem for two elements in a f.p. group, \hyperpage{667}
    \subitem for two strings, \hyperpage{359}
  \item \texttt  {\texttt  {\char 92\relax }=}, \hyperpage{412}
    \subitem for associative words, \hyperpage{475}
    \subitem for nonassociative words, \hyperpage{469}
    \subitem for pcwords, \hyperpage{653}
    \subitem for permutations, \hyperpage{595}
    \subitem for two elements in a f.p. group, \hyperpage{667}
    \subitem for two elements in a f.p. semigroup, \hyperpage{788}
    \subitem for two strings, \hyperpage{358}
  \item \texttt  {\texttt  {\char 92\relax }[\texttt  {\char 92\relax }]}, 
		\hyperpage{251}
  \item \texttt  {\texttt  {\char 92\relax }[\texttt  {\char 92\relax }]\texttt  {\char 92\relax }:\texttt  {\char 92\relax }=}, 
		\hyperpage{251}
  \item \texttt{\texttt{\symbol{92}}*}
    \subitem for transformations, \hyperpage{801}
  \item \texttt{\texttt{\symbol{92}}/}
    \subitem for a transformation and a permutation, \hyperpage{801}
  \item \texttt{\texttt{\symbol{92}}{\textless}}
    \subitem for transformations, \hyperpage{802}
  \item \texttt{\texttt{\symbol{92}}=}
    \subitem for transformations, \hyperpage{802}
  \item \texttt{\texttt{\symbol{92}}\texttt{\symbol{94}}}
    \subitem for a positive integer and a transformation, 
		\hyperpage{801}
    \subitem for a transformation and a permutation, \hyperpage{801}
  \item \texttt  {\texttt  {\char 92\relax }'}, \hyperpage{355}
  \item \texttt  {\texttt  {\char 92\relax }XYZ}, \hyperpage{355}
  \item \texttt  {\texttt  {\char 92\relax }\texttt  {\char 92\relax }}, 
		\hyperpage{355}
  \item \texttt  {\texttt  {\char 92\relax }b}, \hyperpage{355}
  \item \texttt  {\texttt  {\char 92\relax }c}, \hyperpage{355}
  \item \texttt  {\texttt  {\char 92\relax }r}, \hyperpage{355}
  \item \texttt{\texttt{\symbol{94}}}
    \subitem for class functions, \hyperpage{1128}
  \item \texttt  {\texttt  {\char 92\relax }\texttt  {\char 94\relax }}, 
		\hyperpage{413}
    \subitem for a field and a pair of integers, \hyperpage{911}
    \subitem for a field and an integer, \hyperpage{911}
  \item \texttt{\texttt{\symbol{94}}}, \hyperpage{57}
  \item \texttt  {\texttt  {\char 92\relax }\texttt  {\char 123\relax }\texttt  {\char 92\relax }\texttt  {\char 125\relax }}, 
		\hyperpage{253}
  \item \texttt  {\texttt  {\char 92\relax }\texttt  {\char 123\relax }\texttt  {\char 92\relax }\texttt  {\char 125\relax }\texttt  {\char 92\relax }:\texttt  {\char 92\relax }=}, 
		\hyperpage{255}

  \indexspace

  \item abelian number field, \hyperpage{894}
  \item abelian number fields
    \subitem CanonicalBasis, \hyperpage{895}
    \subitem Galois group, \hyperpage{897}
  \item \texttt  {AbelianGroup}, \hyperpage{726}
  \item \texttt  {AbelianInvariants}, \hyperpage{528}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt{AbelianInvariants}
    \subitem for groups, \hyperpage{528}
  \item \texttt  {AbelianInvariantsMultiplier}, \hyperpage{549}
  \item \texttt  {Abelian}\discretionary {-}{}{}\texttt  {Invariants}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {Closure}\discretionary {-}{}{}\texttt  {Fp}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{687}
  \item \texttt  {Abelian}\discretionary {-}{}{}\texttt  {Invariants}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {Closure}\discretionary {-}{}{}\texttt  {Fp}\discretionary {-}{}{}\texttt  {GroupRrs}, 
		\hyperpage{687}
  \item \texttt  {AbelianInvariantsOfList}, \hyperpage{344}
  \item \texttt  {AbelianInvariantsSubgroupFpGroup}, \hyperpage{686}
  \item \texttt  {AbelianInvariantsSubgroupFpGroupMtc}, \hyperpage{686}
  \item \texttt  {AbelianInvariantsSubgroupFpGroupRrs}
    \subitem for a group and a coset table, \hyperpage{686}
    \subitem for two groups, \hyperpage{686}
  \item \texttt  {AbelianNumberField}, \hyperpage{893}
  \item \texttt  {AbelianSubfactorAction}, \hyperpage{582}
  \item About \textsf{GAP} manual, \hyperpage{23}
  \item \texttt  {AbsInt}, \hyperpage{179}
  \item absolute value of an integer, \hyperpage{179}
  \item \texttt  {AbsoluteDiameter}, \hyperpage{241}
  \item \texttt  {AbsoluteIrreducibleModules}, \hyperpage{1105}
  \item \texttt  {AbsolutelyIrreducibleModules}, \hyperpage{1105}
  \item \texttt  {AbsoluteValue}, \hyperpage{226}
  \item \texttt  {AbsolutIrreducibleModules}, \hyperpage{1106}
  \item abstract word, \hyperpage{467}
  \item \texttt  {AbstractWordTietzeWord}, \hyperpage{697}
  \item accessing
    \subitem list elements, \hyperpage{252}
    \subitem record elements, \hyperpage{378}
  \item \texttt  {AClosest}\discretionary {-}{}{}\texttt  {Vector}\discretionary {-}{}{}\texttt  {Combinations}\discretionary {-}{}{}\texttt  {Mat}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {VecFFE}, 
		\hyperpage{311}
  \item \texttt  {AClosest}\discretionary {-}{}{}\texttt  {Vector}\discretionary {-}{}{}\texttt  {Combinations}\discretionary {-}{}{}\texttt  {Mat}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {Vec}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {F}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {Coords}, 
		\hyperpage{311}
  \item \texttt  {Acos}, \hyperpage{240}
  \item \texttt  {Acosh}, \hyperpage{240}
  \item \texttt  {ActingAlgebra}, \hyperpage{949}
  \item \texttt  {ActingDomain}, \hyperpage{589}
  \item \texttt  {Action}
    \subitem for a group, an action domain, etc., \hyperpage{581}
    \subitem for an external set, \hyperpage{581}
  \item action
    \subitem by conjugation, \hyperpage{572}
    \subitem on blocks, \hyperpage{573}
    \subitem on sets, \hyperpage{573}
  \item \texttt  {ActionHomomorphism}
    \subitem for a group, an action domain, etc., \hyperpage{580}
    \subitem for an action image, \hyperpage{580}
    \subitem for an external set, \hyperpage{580}
  \item actions, \hyperpage{572}
  \item \texttt  {ActivateProfileColour}, \hyperpage{118}
  \item \texttt  {ActorOfExternalSet}, \hyperpage{592}
  \item \texttt  {Add}, \hyperpage{256}
  \item add
    \subitem an element to a set, \hyperpage{281}
  \item \texttt  {AddCoeffs}, \hyperpage{308}
  \item \texttt  {AddDictionary}, \hyperpage{374}
  \item \texttt  {AddGenerator}, \hyperpage{700}
  \item \texttt  {AddGeneratorsExtendSchreierTree}, \hyperpage{615}
  \item addition, \hyperpage{57}
    \subitem list and non-list, \hyperpage{266}
    \subitem matrices, \hyperpage{315}
    \subitem matrix and scalar, \hyperpage{316}
    \subitem operation, \hyperpage{413}
    \subitem rational functions, \hyperpage{996}
    \subitem scalar and matrix, \hyperpage{316}
    \subitem scalar and matrix list, \hyperpage{317}
    \subitem vector and scalar, \hyperpage{305}
    \subitem vectors, \hyperpage{305}
  \item \texttt  {AdditiveInverse}, \hyperpage{412}
  \item \texttt  {AdditiveInverseAttr}, \hyperpage{411}
  \item \texttt  {AdditiveInverseImmutable}, \hyperpage{411}
  \item \texttt  {AdditiveInverseMutable}, \hyperpage{412}
  \item \texttt  {AdditiveInverseOp}, \hyperpage{412}
  \item \texttt  {AdditiveInverseSameMutability}, \hyperpage{412}
  \item \texttt  {AdditiveInverseSM}, \hyperpage{412}
  \item \texttt  {AdditiveNeutralElement}, \hyperpage{846}
  \item \texttt  {AddRelator}, \hyperpage{701}
  \item \texttt  {AddRowVector}, \hyperpage{308}
  \item \texttt  {AddRule}, \hyperpage{492}
  \item \texttt  {AddRuleReduced}, \hyperpage{492}
  \item \texttt  {AddSet}, \hyperpage{281}
  \item \texttt  {AdjointAssociativeAlgebra}, \hyperpage{973}
  \item \texttt  {AdjointBasis}, \hyperpage{934}
  \item \texttt  {AdjointMatrix}, \hyperpage{973}
  \item \texttt  {AdjointModule}, \hyperpage{951}
  \item \texttt  {AffineAction}, \hyperpage{648}
  \item \texttt  {AffineActionLayer}, \hyperpage{648}
  \item \texttt  {Agemo}, \hyperpage{521}
  \item \texttt  {Algebra}, \hyperpage{921}
  \item \texttt  {AlgebraByStructureConstants}, \hyperpage{923}
  \item \texttt  {AlgebraGeneralMappingByImages}, \hyperpage{940}
  \item \texttt  {AlgebraHomomorphismByImages}, \hyperpage{941}
  \item \texttt  {AlgebraHomomorphismByImagesNC}, \hyperpage{941}
  \item \texttt  {AlgebraicExtension}, \hyperpage{1026}
  \item \texttt  {AlgebraWithOne}, \hyperpage{922}
  \item \texttt  {Algebra}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {One}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Images}, 
		\hyperpage{942}
  \item \texttt  {AlgebraWithOneHomomorphismByImages}, \hyperpage{942}
  \item \texttt  {Algebra}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {One}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {ImagesNC}, 
		\hyperpage{942}
  \item \texttt  {AllAutomorphisms}, \hyperpage{566}
  \item \texttt  {AllBlocks}, \hyperpage{588}
  \item \texttt  {AllEndomorphisms}, \hyperpage{566}
  \item \texttt  {AllHomomorphismClasses}, \hyperpage{566}
  \item \texttt  {AllHomomorphisms}, \hyperpage{566}
  \item \texttt  {AllIrreducibleSolvableGroups}, \hyperpage{752}
  \item \texttt{All\mbox{\texttt{\mdseries\slshape Library}}Groups}, 
		\hyperpage{737}
  \item \texttt{AllPrimitiveGroups}, \hyperpage{737}
  \item \texttt  {AllSmallGroups}, \hyperpage{741}
  \item \texttt  {AllSmallNonabelianSimpleGroups}, \hyperpage{526}
  \item \texttt  {AllSubgroups}, \hyperpage{537}
  \item \texttt{AllTransitiveGroups}, \hyperpage{737}
  \item \texttt  {Alpha}, \hyperpage{1195}
  \item \texttt  {AlternatingGroup}
    \subitem for a degree, \hyperpage{728}
    \subitem for a domain, \hyperpage{728}
  \item \texttt{and}, \hyperpage{247}
    \subitem for filters, \hyperpage{165}, \hyperpage{247}
  \item \texttt  {ANFAutomorphism}, \hyperpage{899}
  \item \texttt  {Anti}\discretionary {-}{}{}\texttt  {Isomorphism}\discretionary {-}{}{}\texttt  {Transformation}\discretionary {-}{}{}\texttt  {Semigroup}, 
		\hyperpage{816}
  \item antisymmetric relation, \hyperpage{443}
  \item \texttt  {AntiSymmetricParts}, \hyperpage{1150}
  \item \texttt  {Append}, \hyperpage{257}
  \item \texttt  {AppendTo}, \hyperpage{136}
    \subitem for streams, \hyperpage{145}
  \item \texttt  {ApplicableMethod}, \hyperpage{104}
  \item \texttt  {ApplicableMethodTypes}, \hyperpage{104}
  \item \texttt  {Apply}, \hyperpage{285}
  \item \texttt  {ApplySimpleReflection}, \hyperpage{969}
  \item \texttt  {Approximate}\discretionary {-}{}{}\texttt  {Suborbits}\discretionary {-}{}{}\texttt  {Stabilizer}\discretionary {-}{}{}\texttt  {Perm}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{613}
  \item \texttt  {ARC}\discretionary {-}{}{}\texttt  {H{\textunderscore }}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {S{\textunderscore }}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {C{\textunderscore }}\discretionary {-}{}{}\texttt  {O}\discretionary {-}{}{}\texttt  {S{\textunderscore }X}, 
		\hyperpage{42}
  \item \texttt  {ARC}\discretionary {-}{}{}\texttt  {H{\textunderscore }}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {S{\textunderscore }}\discretionary {-}{}{}\texttt  {UNIX}, 
		\hyperpage{42}
  \item \texttt  {ARC}\discretionary {-}{}{}\texttt  {H{\textunderscore }}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {S{\textunderscore }}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {N}\discretionary {-}{}{}\texttt  {DOWS}, 
		\hyperpage{42}
  \item \texttt{arg}
    \subitem special function argument, \hyperpage{66}
    \subitem special function argument, calling with, \hyperpage{55}
  \item \texttt  {Argument}
    \subitem for complex numbers, \hyperpage{241}
  \item arithmetic operators
    \subitem precedence, \hyperpage{58}
  \item \texttt  {ArithmeticElementCreator}, \hyperpage{1256}
  \item \texttt  {Arrangements}, \hyperpage{209}
  \item arrow notation for functions, \hyperpage{68}
  \item \texttt  {AsAlgebra}, \hyperpage{934}
  \item \texttt  {AsAlgebraWithOne}, \hyperpage{934}
  \item \texttt  {AsBinaryRelationOnPoints}
    \subitem for a binary relation, \hyperpage{445}
    \subitem for a permutation, \hyperpage{445}
    \subitem for a transformation, \hyperpage{445}
  \item \texttt  {AsBlockMatrix}, \hyperpage{338}
  \item \texttt  {AscendingChain}, \hyperpage{533}
  \item \texttt  {AsDivisionRing}, \hyperpage{876}
  \item \texttt  {AsDuplicateFreeList}, \hyperpage{284}
  \item \texttt  {AsField}, \hyperpage{876}
  \item \texttt  {AsGroup}, \hyperpage{498}
  \item \texttt  {AsGroupGeneralMappingByImages}, \hyperpage{556}
  \item \texttt  {Asin}, \hyperpage{240}
  \item \texttt  {Asinh}, \hyperpage{240}
  \item \texttt  {AsInternalFFE}, \hyperpage{887}
  \item \texttt  {AsLeftIdeal}, \hyperpage{854}
  \item \texttt  {AsLeftModule}, \hyperpage{869}
  \item \texttt  {AsList}, \hyperpage{389}
  \item \texttt  {AsMagma}, \hyperpage{460}
  \item \texttt  {AsMonoid}, \hyperpage{766}
  \item \texttt  {AsPartialPerm}
    \subitem for a permutation, \hyperpage{831}
    \subitem for a permutation and a positive integer, \hyperpage{831}
    \subitem for a permutation and a set of positive integers, 
		\hyperpage{831}
    \subitem for a transformation, \hyperpage{831}
    \subitem for a transformation and a positive integer, 
		\hyperpage{831}
    \subitem for a transformation and a set of positive integer, 
		\hyperpage{831}
  \item \texttt  {AsPermutation}, \hyperpage{599}
  \item \texttt  {AsPolynomial}, \hyperpage{999}
  \item \texttt  {AsRightIdeal}, \hyperpage{854}
  \item \texttt  {AsSemigroup}, \hyperpage{763}
  \item \texttt  {Assert}, \hyperpage{108}
  \item \texttt  {AssertionLevel}, \hyperpage{108}
  \item \texttt  {AsSet}, \hyperpage{390}
  \item \texttt  {AssignGeneratorVariables}, \hyperpage{475}
  \item assignment
    \subitem to a list, \hyperpage{254}
    \subitem to a record, \hyperpage{379}
    \subitem variable, \hyperpage{59}
  \item \texttt  {Assign}\discretionary {-}{}{}\texttt  {Nice}\discretionary {-}{}{}\texttt  {Monomorphism}\discretionary {-}{}{}\texttt  {Automorphism}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{565}
  \item \texttt  {AssociatedPartition}, \hyperpage{216}
  \item \texttt  {Associated}\discretionary {-}{}{}\texttt  {Rees}\discretionary {-}{}{}\texttt  {Matrix}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {Class}, 
		\hyperpage{783}
  \item \texttt  {Associates}, \hyperpage{858}
  \item associativity, \hyperpage{57}
  \item \texttt  {AssocWordByLetterRep}, \hyperpage{481}
  \item \texttt  {AsSortedList}, \hyperpage{390}
  \item \texttt  {AsSSortedList}, \hyperpage{390}
  \item \texttt{As\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{404}
  \item \texttt  {AsSubalgebra}, \hyperpage{935}
  \item \texttt  {AsSubalgebraWithOne}, \hyperpage{935}
  \item \texttt  {AsSubgroup}, \hyperpage{500}
  \item \texttt  {AsSubgroupOfWholeGroupByQuotient}, \hyperpage{683}
  \item \texttt  {AsSubmagma}, \hyperpage{460}
  \item \texttt  {AsSubmonoid}, \hyperpage{766}
  \item \texttt  {AsSubsemigroup}, \hyperpage{763}
  \item \texttt  {AsSubspace}, \hyperpage{901}
  \item \texttt{AsSub\mbox{\texttt{\mdseries\slshape struct}}}, 
		\hyperpage{407}
  \item \texttt  {AsTransformation}, \hyperpage{799}
  \item \texttt  {AsTwoSidedIdeal}, \hyperpage{854}
  \item \texttt  {AsVectorSpace}, \hyperpage{901}
  \item at exit functions, \hyperpage{92}
  \item \texttt  {Atan}, \hyperpage{240}
  \item \texttt  {Atan2}, \hyperpage{240}
  \item \texttt  {Atanh}, \hyperpage{240}
  \item \texttt  {AtlasIrrationality}, \hyperpage{232}
  \item atomic irrationalities, \hyperpage{229}
  \item \texttt  {AttributeValueNotSet}, \hyperpage{172}
  \item \texttt  {AugmentationIdeal}, \hyperpage{988}
  \item \texttt  {AugmentedCosetTableInWholeGroup}, \hyperpage{676}
  \item \texttt  {AugmentedCosetTableMtc}, \hyperpage{676}
  \item \texttt  {AugmentedCosetTableRrs}, \hyperpage{676}
  \item automatic loading of GAP packages, \hyperpage{1204}
  \item automorphism group
    \subitem of number fields, \hyperpage{897}
  \item \texttt  {AutomorphismDomain}, \hyperpage{563}
  \item \texttt  {AutomorphismGroup}, \hyperpage{563}
  \item \texttt{AutomorphismGroup}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {AutomorphismsOfTable}, \hyperpage{1084}

  \indexspace

  \item $b_N$ (irrational value), \hyperpage{229}
  \item backslash character, \hyperpage{355}
  \item backspace character, \hyperpage{355}
  \item Backtrace
    \subitem GAP3 name for Where, \hyperpage{89}
  \item \texttt{BANNER}, \hyperpage{1216}
  \item \texttt  {BaseFixedSpace}, \hyperpage{325}
  \item \texttt  {BaseIntersectionIntMats}, \hyperpage{340}
  \item \texttt  {BaseIntMat}, \hyperpage{340}
  \item \texttt  {BaseMat}, \hyperpage{330}
  \item \texttt  {BaseMatDestructive}, \hyperpage{330}
  \item \texttt  {BaseOfGroup}, \hyperpage{611}
  \item \texttt  {BaseOrthogonalSpaceMat}, \hyperpage{330}
  \item \texttt  {BaseStabChain}, \hyperpage{611}
  \item \texttt  {BaseSteinitzVectors}, \hyperpage{331}
  \item \texttt  {Basic}\discretionary {-}{}{}\texttt  {Spin}\discretionary {-}{}{}\texttt  {Representation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Symmetric}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{551}
  \item \texttt  {BasicWreathProductOrdering}, \hyperpage{455}
  \item \texttt  {Basis}, \hyperpage{904}
  \item \texttt  {BasisNC}, \hyperpage{904}
  \item \texttt  {BasisVectors}, \hyperpage{905}
  \item \texttt  {Bell}, \hyperpage{206}
  \item \texttt  {Bernoulli}, \hyperpage{206}
  \item \texttt  {BestQuoInt}, \hyperpage{181}
  \item \texttt  {BestSplittingMatrix}, \hyperpage{1107}
  \item \texttt  {BiAlgebraModule}, \hyperpage{947}
  \item \texttt  {BiAlgebraModuleByGenerators}, \hyperpage{946}
  \item \texttt  {BibEntry}, \hyperpage{1212}
  \item \texttt  {BilinearFormMat}, \hyperpage{967}
  \item binary relation, \hyperpage{442}
  \item \texttt  {BinaryRelationByElements}, \hyperpage{442}
  \item \texttt  {BinaryRelationOnPoints}, \hyperpage{445}
  \item \texttt  {BinaryRelationOnPointsNC}, \hyperpage{445}
  \item \texttt  {BindGlobal}, \hyperpage{53}
  \item \texttt  {Binomial}, \hyperpage{205}
  \item \texttt  {BisectInterval}, \hyperpage{241}
  \item blank, \hyperpage{47}
  \item \texttt  {BlistList}, \hyperpage{299}
  \item \texttt  {BlockMatrix}, \hyperpage{338}
  \item \texttt  {Blocks}
    \subitem for a group, an action domain, etc., \hyperpage{587}
    \subitem for an external set, \hyperpage{587}
  \item \texttt  {BlocksInfo}, \hyperpage{1092}
  \item \texttt  {BlownUpMat}, \hyperpage{333}
  \item \texttt  {BlownUpVector}, \hyperpage{333}
  \item \texttt  {BlowupInterval}, \hyperpage{241}
  \item \texttt  {BlowUpIsomorphism}, \hyperpage{621}
  \item body, \hyperpage{66}
  \item \texttt  {BombieriNorm}, \hyperpage{1008}
  \item bound, \hyperpage{50}
  \item Brauer character, \hyperpage{1134}
  \item \texttt  {BrauerCharacterValue}, \hyperpage{1162}
  \item \texttt  {BrauerTable}
    \subitem for a character table, and a prime integer, 
		\hyperpage{1072}
    \subitem for a group, and a prime integer, \hyperpage{1072}
  \item \texttt  {BrauerTableOp}, \hyperpage{1072}
  \item \texttt  {BravaisGroup}, \hyperpage{626}
  \item \texttt  {BravaisSubgroups}, \hyperpage{626}
  \item \texttt  {BravaisSupergroups}, \hyperpage{627}
  \item Break loop message, \hyperpage{88}
  \item \texttt{break} statement, \hyperpage{65}
  \item browsing backwards, \hyperpage{28}
  \item browsing backwards one chapter, \hyperpage{29}
  \item browsing forward, \hyperpage{28}
  \item browsing forward one chapter, \hyperpage{29}
  \item browsing the next section browsed, \hyperpage{29}
  \item browsing the previous section browsed, \hyperpage{29}

  \indexspace

  \item $c_N$ (irrational value), \hyperpage{229}
  \item \texttt  {CallFuncList}, \hyperpage{72}
  \item \texttt  {CallWithTimeout}, \hyperpage{73}
  \item \texttt  {CallWithTimeoutList}, \hyperpage{73}
  \item \texttt  {CanComputeIndex}, \hyperpage{553}
  \item \texttt  {CanComputeIsSubset}, \hyperpage{553}
  \item \texttt  {CanComputeSize}, \hyperpage{553}
  \item \texttt  {CanComputeSizeAnySubgroup}, \hyperpage{553}
  \item candidates
    \subitem for permutation characters, \hyperpage{1154}
  \item \texttt  {CanEasilyCompareElements}, \hyperpage{413}
  \item \texttt  {CanEasilyCompareElementsFamily}, \hyperpage{413}
  \item \texttt  {CanEasilyComputePcgs}, \hyperpage{629}
  \item \texttt  {Can}\discretionary {-}{}{}\texttt  {Easily}\discretionary {-}{}{}\texttt  {Compute}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Independent}\discretionary {-}{}{}\texttt  {Gens}\discretionary {-}{}{}\texttt  {Abelian}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{553}
  \item \texttt  {CanEasilySortElements}, \hyperpage{413}
  \item \texttt  {CanEasilySortElementsFamily}, \hyperpage{413}
  \item \texttt  {CanEasilyTestMembership}, \hyperpage{552}
  \item canonical basis
    \subitem for matrix spaces, \hyperpage{913}
    \subitem for row spaces, \hyperpage{913}
  \item \texttt  {CanonicalBasis}, \hyperpage{905}
  \item \texttt  {CanonicalGenerators}, \hyperpage{967}
  \item \texttt  {CanonicalPcElement}, \hyperpage{633}
  \item \texttt  {CanonicalPcgs}, \hyperpage{637}
  \item \texttt  {CanonicalPcgsByGeneratorsWithImages}, \hyperpage{639}
  \item \texttt  {Canonical}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Determinator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {ExternalSet}, 
		\hyperpage{592}
  \item \texttt  {Canonical}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {ExternalSet}, 
		\hyperpage{591}
  \item \texttt  {CanonicalRightCosetElement}, \hyperpage{508}
  \item Carmichael's lambda function, \hyperpage{196}
  \item carriage return character, \hyperpage{355}
  \item \texttt  {CartanMatrix}, \hyperpage{967}
  \item \texttt  {CartanSubalgebra}, \hyperpage{963}
  \item \texttt  {Cartesian}
    \subitem for a list, \hyperpage{287}
    \subitem for various objects, \hyperpage{287}
  \item \texttt  {CategoriesOfObject}, \hyperpage{168}
  \item \texttt  {CategoryCollections}, \hyperpage{385}
  \item \texttt  {CategoryFamily}, \hyperpage{1225}
  \item \texttt  {Ceil}, \hyperpage{241}
  \item \texttt  {Center}, \hyperpage{464}
  \item center, \hyperpage{464}
  \item central character, \hyperpage{1138}
  \item \texttt  {CentralCharacter}, \hyperpage{1138}
  \item \texttt  {CentralIdempotentsOfAlgebra}, \hyperpage{938}
  \item centraliser, \hyperpage{464}
  \item \texttt  {Centralizer}
    \subitem for a class of objects in a magma, \hyperpage{464}
    \subitem for a magma and a submagma, \hyperpage{464}
    \subitem for a magma and an element, \hyperpage{464}
  \item \texttt{Centralizer}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {CentralizerInGLnZ}, \hyperpage{626}
  \item \texttt  {CentralizerModulo}, \hyperpage{535}
  \item \texttt  {Centralizer}\discretionary {-}{}{}\texttt  {Size}\discretionary {-}{}{}\texttt  {Limit}\discretionary {-}{}{}\texttt  {Consider}\discretionary {-}{}{}\texttt  {Function}, 
		\hyperpage{650}
  \item \texttt  {CentralNormalSeriesByPcgs}, \hyperpage{642}
  \item \texttt  {Centre}, \hyperpage{464}
  \item \texttt{Centre}
    \subitem for groups with pcgs, \hyperpage{649}
  \item centre
    \subitem of a character, \hyperpage{1137}
  \item \texttt  {CentreOfCharacter}, \hyperpage{1137}
  \item \texttt  {CF}
    \subitem for (subfield and) conductor, \hyperpage{892}
    \subitem for (subfield and) generators, \hyperpage{892}
  \item \texttt  {ChangeStabChain}, \hyperpage{614}
  \item \texttt  {Character}
    \subitem for a character table and a list, \hyperpage{1131}
    \subitem for a group and a list, \hyperpage{1131}
  \item character tables, \hyperpage{1071}
    \subitem access to, \hyperpage{1071}
    \subitem calculate, \hyperpage{1071}
    \subitem infix operators, \hyperpage{1079}
    \subitem of groups, \hyperpage{1071}
  \item character value
    \subitem of group element using powering operator, \hyperpage{1128}
  \item \texttt  {CharacterDegrees}
    \subitem for a character table, \hyperpage{1079}
    \subitem for a group, \hyperpage{1079}
  \item \texttt  {Characteristic}, \hyperpage{408}
    \subitem for a class function, \hyperpage{1129}
  \item characteristic polynomial
    \subitem for field elements, \hyperpage{879}
  \item \texttt  {CharacteristicPolynomial}, \hyperpage{332}
  \item \texttt  {CharacterNames}, \hyperpage{1085}
  \item \texttt  {CharacterParameters}, \hyperpage{1085}
  \item characters, \hyperpage{1122}
    \subitem permutation, \hyperpage{1154}
    \subitem symmetrizations of, \hyperpage{1149}
  \item \texttt  {CharacterTable}
    \subitem for a group, \hyperpage{1071}
    \subitem for a string, \hyperpage{1071}
    \subitem for an ordinary character table, \hyperpage{1071}
  \item \texttt  {CharacterTableDirectProduct}, \hyperpage{1111}
  \item \texttt  {CharacterTableFactorGroup}, \hyperpage{1112}
  \item \texttt  {CharacterTableIsoclinic}, \hyperpage{1113}
  \item \texttt  {CharacterTableRegular}, \hyperpage{1072}
  \item \texttt  {CharacterTableWithSortedCharacters}, \hyperpage{1114}
  \item \texttt  {CharacterTableWithSortedClasses}, \hyperpage{1115}
  \item \texttt  {CharacterTableWithStoredGroup}, \hyperpage{1077}
  \item \texttt  {CharacterTableWreathSymmetric}, \hyperpage{1113}
  \item \texttt  {CharInt}, \hyperpage{365}
  \item \texttt  {CharsFamily}, \hyperpage{357}
  \item \texttt  {CharSInt}, \hyperpage{366}
  \item \texttt  {CheckDigitISBN}, \hyperpage{191}
  \item \texttt  {CheckDigitISBN13}, \hyperpage{191}
  \item \texttt  {CheckDigitPostalMoneyOrder}, \hyperpage{191}
  \item \texttt  {CheckDigitTestFunction}, \hyperpage{192}
  \item \texttt  {CheckDigitUPC}, \hyperpage{191}
  \item \texttt  {CheckFixedPoints}, \hyperpage{1180}
  \item \texttt  {CheckForHandlingByNiceBasis}, \hyperpage{920}
  \item \texttt  {CheckPermChar}, \hyperpage{1188}
  \item \texttt  {ChevalleyBasis}, \hyperpage{965}
  \item \texttt  {ChiefNormalSeriesByPcgs}, \hyperpage{643}
  \item \texttt  {ChiefSeries}, \hyperpage{530}
  \item \texttt  {ChiefSeriesThrough}, \hyperpage{530}
  \item \texttt  {ChiefSeriesUnderAction}, \hyperpage{530}
  \item Chinese remainder, \hyperpage{183}
  \item \texttt  {ChineseRem}, \hyperpage{183}
  \item \texttt  {Chomp}, \hyperpage{364}
  \item \texttt  {Cite}, \hyperpage{1213}
  \item \texttt  {CIUnivPols}, \hyperpage{996}
  \item class function, \hyperpage{1124}
  \item class function objects, \hyperpage{1124}
  \item class functions, \hyperpage{1175}
    \subitem as ring elements, \hyperpage{1127}
  \item class multiplication coefficient, \hyperpage{1097, 1098}
  \item \texttt  {ClassElementLattice}, \hyperpage{538}
  \item classes
    \subitem real, \hyperpage{1087}
  \item \texttt  {ClassesSolvableGroup}, \hyperpage{649}
  \item \texttt  {ClassFunction}
    \subitem for a character table and a list, \hyperpage{1131}
    \subitem for a group and a list, \hyperpage{1131}
  \item \texttt  {ClassFunctionSameType}, \hyperpage{1132}
  \item \texttt  {ClassMultiplicationCoefficient}
    \subitem for character tables, \hyperpage{1097}
  \item \texttt{ClassMultiplicationCoefficient}
    \subitem for character tables, \hyperpage{1097}
  \item \texttt  {ClassNames}, \hyperpage{1085}
  \item \texttt  {ClassNamesTom}, \hyperpage{1054}
  \item \texttt  {ClassOrbit}, \hyperpage{1087}
  \item \texttt  {ClassParameters}, \hyperpage{1085}
  \item \texttt  {ClassPermutation}, \hyperpage{1116}
  \item \texttt  {ClassPositionsOfAgemo}, \hyperpage{1088}
  \item \texttt  {ClassPositionsOfCenter}
    \subitem for a character table, \hyperpage{1088}
  \item \texttt  {ClassPositionsOfCentre}
    \subitem for a character, \hyperpage{1137}
    \subitem for a character table, \hyperpage{1088}
  \item \texttt  {ClassPositionsOfDerivedSubgroup}, \hyperpage{1089}
  \item \texttt  {Class}\discretionary {-}{}{}\texttt  {Positions}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Direct}\discretionary {-}{}{}\texttt  {Product}\discretionary {-}{}{}\texttt  {Decompositions}, 
		\hyperpage{1088}
  \item \texttt  {Class}\discretionary {-}{}{}\texttt  {Positions}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Elementary}\discretionary {-}{}{}\texttt  {Abelian}\discretionary {-}{}{}\texttt  {Series}, 
		\hyperpage{1089}
  \item \texttt  {ClassPositionsOfFittingSubgroup}, \hyperpage{1089}
  \item \texttt  {ClassPositionsOfKernel}, \hyperpage{1136}
  \item \texttt  {ClassPositionsOfLowerCentralSeries}, \hyperpage{1089}
  \item \texttt  {Class}\discretionary {-}{}{}\texttt  {Positions}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Maximal}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {Subgroups}, 
		\hyperpage{1088}
  \item \texttt  {Class}\discretionary {-}{}{}\texttt  {Positions}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {Subgroups}, 
		\hyperpage{1088}
  \item \texttt  {ClassPositionsOfNormalClosure}, \hyperpage{1090}
  \item \texttt  {ClassPositionsOfNormalSubgroup}, \hyperpage{1120}
  \item \texttt  {ClassPositionsOfNormalSubgroups}, \hyperpage{1088}
  \item \texttt  {ClassPositionsOfPCore}, \hyperpage{1090}
  \item \texttt  {Class}\discretionary {-}{}{}\texttt  {Positions}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Supersolvable}\discretionary {-}{}{}\texttt  {Residuum}, 
		\hyperpage{1090}
  \item \texttt  {ClassPositionsOfUpperCentralSeries}, \hyperpage{1090}
  \item \texttt  {ClassRoots}, \hyperpage{1087}
  \item \texttt  {ClassStructureCharTable}, \hyperpage{1097}
  \item \texttt  {ClassTypesTom}, \hyperpage{1053}
  \item \texttt  {CleanedTailPcElement}, \hyperpage{633}
  \item \texttt  {ClearCacheStats}, \hyperpage{118}
  \item \texttt  {ClearProfile}, \hyperpage{113}
  \item clone
    \subitem an object, \hyperpage{161}
  \item \texttt  {CloseMutableBasis}, \hyperpage{910}
  \item \texttt  {CloseStream}, \hyperpage{141}
  \item \texttt  {ClosureGroup}, \hyperpage{502}
  \item \texttt  {ClosureGroupAddElm}, \hyperpage{502}
  \item \texttt  {ClosureGroupCompare}, \hyperpage{502}
  \item \texttt  {ClosureGroupDefault}, \hyperpage{502}
  \item \texttt  {ClosureGroupIntest}, \hyperpage{502}
  \item \texttt  {ClosureLeftModule}, \hyperpage{870}
  \item \texttt  {ClosureNearAdditiveGroup}
    \subitem for a near-additive group and an element, \hyperpage{847}
    \subitem for two near-additive groups, \hyperpage{847}
  \item \texttt  {ClosureRing}
    \subitem for a ring and a ring element, \hyperpage{850}
    \subitem for two rings, \hyperpage{850}
  \item \texttt{Closure\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{403}
  \item \texttt  {ClosureSubgroup}, \hyperpage{503}
  \item \texttt  {ClosureSubgroupNC}, \hyperpage{503}
  \item \texttt  {Coboundaries}, \hyperpage{979}
  \item \texttt  {Cochain}, \hyperpage{978}
  \item \texttt  {CochainSpace}, \hyperpage{978}
  \item \texttt  {Cocycles}
    \subitem for Lie algebra module, \hyperpage{979}
  \item cocycles, \hyperpage{546}
  \item \texttt  {CodegreeOfPartialPerm}, \hyperpage{823}
  \item \texttt  {CodegreeOfPartialPermCollection}, \hyperpage{823}
  \item \texttt  {CodegreeOfPartialPermSemigroup}, \hyperpage{838}
  \item \texttt  {CodePcGroup}, \hyperpage{663}
  \item \texttt  {CodePcgs}, \hyperpage{662}
  \item coefficient
    \subitem binomial, \hyperpage{205}
  \item \texttt  {Coefficients}, \hyperpage{906}
  \item coefficients
    \subitem for cyclotomics, \hyperpage{226}
  \item \texttt  {CoefficientsAndMagmaElements}, \hyperpage{989}
  \item \texttt  {CoefficientsFamily}, \hyperpage{1020}
  \item \texttt  {CoefficientsMultiadic}, \hyperpage{183}
  \item \texttt  {CoefficientsOfLaurentPolynomial}, \hyperpage{1009}
  \item \texttt  {CoefficientsOfUnivariatePolynomial}, \hyperpage{1000}
  \item \texttt  {Coefficients}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Univariate}\discretionary {-}{}{}\texttt  {Rational}\discretionary {-}{}{}\texttt  {Function}, 
		\hyperpage{999}
  \item \texttt  {CoefficientsQadic}, \hyperpage{183}
  \item \texttt  {CoefficientsRing}, \hyperpage{1011}
  \item \texttt  {CoeffsCyc}, \hyperpage{226}
  \item \texttt  {CoeffsMod}, \hyperpage{309}
  \item cohomology, \hyperpage{546}
  \item \texttt  {COH}\discretionary {-}{}{}\texttt  {O}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {S{\textunderscore }}\discretionary {-}{}{}\texttt  {P}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {V}\discretionary {-}{}{}\texttt  {E{\textunderscore }}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {OUPS}, 
		\hyperpage{750}
  \item \texttt  {CoKernelOfAdditiveGeneralMapping}, \hyperpage{436}
  \item \texttt  {CoKernel}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Multiplicative}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}, 
		\hyperpage{435}
  \item \texttt  {CollapsedMat}, \hyperpage{1183}
  \item \texttt  {Collected}, \hyperpage{283}
  \item \texttt  {CollectionsFamily}, \hyperpage{384}
  \item \texttt  {ColorPrompt}, \hyperpage{43}
  \item \texttt  {Columns}, \hyperpage{782}
  \item \texttt  {Combinations}, \hyperpage{208}
  \item \texttt  {CombinatorialCollector}, \hyperpage{655}
  \item \texttt  {Comm}, \hyperpage{414}
  \item \texttt{Comm}
    \subitem for words, \hyperpage{476}
  \item comments, \hyperpage{47}
  \item \texttt  {CommutativeDiagram}, \hyperpage{1179}
  \item \texttt  {CommutatorFactorGroup}, \hyperpage{534}
  \item \texttt  {CommutatorLength}, \hyperpage{517}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {CommutatorSubgroup}, \hyperpage{516}
  \item \texttt  {Compacted}, \hyperpage{283}
  \item \texttt  {CompanionMat}, \hyperpage{334}
  \item \texttt  {CompareVersionNumbers}, \hyperpage{1209}
  \item comparison
    \subitem fp semigroup elements, \hyperpage{788}
    \subitem operation, \hyperpage{412}
    \subitem rational functions, \hyperpage{997}
  \item comparisons
    \subitem of booleans, \hyperpage{246}
    \subitem of lists, \hyperpage{262}
  \item \texttt  {CompatibleConjugacyClasses}, \hyperpage{1078}
  \item \texttt  {CompatiblePairs}, \hyperpage{661}
  \item \texttt  {ComplementClassesRepresentatives}, \hyperpage{515}
  \item \texttt  {ComplementClassesRepresentativesEA}, \hyperpage{548}
  \item \texttt  {ComplementIntMat}, \hyperpage{340}
  \item \texttt  {ComplementSystem}, \hyperpage{520}
  \item \texttt  {ComplexConjugate}, \hyperpage{233}
    \subitem for a class function, \hyperpage{1129}
  \item \texttt  {ComplexI}, \hyperpage{241}
  \item \texttt  {ComplexificationQuat}
    \subitem for a matrix, \hyperpage{927}
    \subitem for a vector, \hyperpage{927}
  \item \texttt  {ComponentPartialPermInt}, \hyperpage{834}
  \item \texttt  {ComponentRepsOfPartialPerm}, \hyperpage{829}
  \item \texttt  {ComponentRepsOfTransformation}, \hyperpage{810}
  \item \texttt  {ComponentsOfPartialPerm}, \hyperpage{829}
  \item \texttt  {ComponentsOfTransformation}, \hyperpage{809}
  \item \texttt  {ComponentTransformationInt}, \hyperpage{802}
  \item \texttt  {CompositionMapping}, \hyperpage{426}
  \item \texttt{CompositionMapping}
    \subitem for Frobenius automorphisms, \hyperpage{888}
  \item \texttt  {CompositionMapping2}, \hyperpage{426}
  \item \texttt  {CompositionMapping2General}, \hyperpage{426}
  \item \texttt  {CompositionMaps}, \hyperpage{1176}
  \item \texttt  {CompositionOfStraightLinePrograms}, \hyperpage{485}
  \item \texttt  {CompositionSeries}, \hyperpage{530}
  \item \texttt{CompositionSeries}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {ComputedBrauerTables}, \hyperpage{1072}
  \item \texttt  {ComputedClassFusions}, \hyperpage{1171}
  \item \texttt  {ComputedIndicators}, \hyperpage{1096}
  \item \texttt  {ComputedIsPSolubleCharacterTables}, \hyperpage{1095}
  \item \texttt  {ComputedIsPSolvableCharacterTables}, \hyperpage{1095}
  \item \texttt  {ComputedPowerMaps}, \hyperpage{1165}
  \item \texttt  {ComputedPrimeBlockss}, \hyperpage{1091}
  \item \texttt  {Concatenation}
    \subitem for a list of lists, \hyperpage{282}
    \subitem for several lists, \hyperpage{282}
  \item concatenation
    \subitem of lists, \hyperpage{282}
  \item \texttt  {Conductor}
    \subitem for a collection of cyclotomics, \hyperpage{225}
    \subitem for a cyclotomic, \hyperpage{225}
  \item \texttt  {ConfluentRws}, \hyperpage{491}
  \item \texttt  {Congruences}
    \subitem for character tables, \hyperpage{1185}
  \item \texttt  {ConjugacyClass}, \hyperpage{511}
  \item \texttt  {ConjugacyClasses}
    \subitem attribute, \hyperpage{511}
    \subitem for character tables, \hyperpage{1076}
  \item \texttt{ConjugacyClasses}
    \subitem for groups with pcgs, \hyperpage{649}
    \subitem for linear groups, \hyperpage{735}
  \item \texttt  {ConjugacyClassesByOrbits}, \hyperpage{512}
  \item \texttt  {ConjugacyClassesByRandomSearch}, \hyperpage{512}
  \item \texttt  {ConjugacyClassesMaximalSubgroups}, \hyperpage{536}
  \item \texttt  {ConjugacyClassesPerfectSubgroups}, \hyperpage{541}
  \item \texttt  {ConjugacyClassesSubgroups}, \hyperpage{536}
  \item \texttt  {ConjugacyClassSubgroups}, \hyperpage{535}
  \item conjugate
    \subitem matrix, \hyperpage{317}
    \subitem of a word, \hyperpage{476}
  \item \texttt  {ConjugateDominantWeight}, \hyperpage{970}
  \item \texttt  {ConjugateDominantWeightWithWord}, \hyperpage{970}
  \item \texttt  {ConjugateGroup}, \hyperpage{498}
  \item \texttt  {Conjugates}, \hyperpage{880}
  \item \texttt  {ConjugateSubgroup}, \hyperpage{501}
  \item \texttt  {ConjugateSubgroups}, \hyperpage{501}
  \item conjugation, \hyperpage{572}
  \item \texttt  {ConjugatorAutomorphism}, \hyperpage{561}
  \item \texttt  {ConjugatorAutomorphismNC}, \hyperpage{561}
  \item \texttt  {ConjugatorIsomorphism}, \hyperpage{561}
  \item \texttt  {ConjugatorOfConjugatorIsomorphism}, \hyperpage{562}
  \item \texttt  {ConsiderKernels}, \hyperpage{1186}
  \item \texttt  {ConsiderSmallerPowerMaps}, \hyperpage{1186}
  \item \texttt  {ConsiderStructureConstants}, \hyperpage{1174}
  \item \texttt  {ConsiderTableAutomorphisms}, \hyperpage{1189}
  \item \texttt  {ConstantTimeAccessList}, \hyperpage{277}
  \item \texttt  {ConstantTransformation}, \hyperpage{799}
  \item constituent
    \subitem of a group character, \hyperpage{1135}
  \item \texttt  {ConstituentsCompositionMapping}, \hyperpage{426}
  \item \texttt  {ConstituentsOfCharacter}, \hyperpage{1136}
  \item \texttt  {ContainedCharacters}, \hyperpage{1184}
  \item \texttt  {ContainedDecomposables}, \hyperpage{1184}
  \item \texttt  {ContainedMaps}, \hyperpage{1178}
  \item \texttt  {ContainedPossibleCharacters}, \hyperpage{1182}
  \item \texttt  {ContainedPossibleVirtualCharacters}, \hyperpage{1182}
  \item \texttt  {ContainedSpecialVectors}, \hyperpage{1182}
  \item \texttt  {ContainedTom}, \hyperpage{1059}
  \item \texttt  {ContainingTom}, \hyperpage{1059}
  \item \texttt{continue} statement, \hyperpage{65}
  \item \texttt  {Continued}\discretionary {-}{}{}\texttt  {Fraction}\discretionary {-}{}{}\texttt  {Approximation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Root}, 
		\hyperpage{202}
  \item \texttt  {ContinuedFractionExpansionOfRoot}, \hyperpage{202}
  \item convert
    \subitem to a string, \hyperpage{356}
  \item \texttt  {ConvertToBlistRep}, \hyperpage{302}
  \item \texttt  {ConvertToCharacterTable}, \hyperpage{1073}
  \item \texttt  {ConvertToCharacterTableNC}, \hyperpage{1073}
  \item \texttt  {ConvertToMatrixRep}
    \subitem for a list (and a field), \hyperpage{335}
    \subitem for a list (and a prime power), \hyperpage{335}
  \item \texttt  {ConvertToMatrixRepNC}
    \subitem for a list (and a field), \hyperpage{335}
    \subitem for a list (and a prime power), \hyperpage{336}
  \item \texttt  {ConvertToRangeRep}, \hyperpage{296}
  \item \texttt  {ConvertToStringRep}, \hyperpage{356}
  \item \texttt  {ConvertToTableOfMarks}, \hyperpage{1052}
  \item \texttt  {ConvertToVectorRep}
    \subitem for a list (and a field), \hyperpage{307}
    \subitem for a list (and a prime power), \hyperpage{307}
  \item \texttt  {ConvertToVectorRepNC}
    \subitem for a list (and a field), \hyperpage{307}
    \subitem for a list (and a prime power), \hyperpage{307}
  \item \texttt  {ConwayPolynomial}, \hyperpage{889}
  \item coprime, \hyperpage{58}
  \item Copy, \hyperpage{161}
  \item copy
    \subitem an object, \hyperpage{161}
  \item \texttt  {CopyListEntries}, \hyperpage{256}
  \item \texttt  {CopyOptionsDefaults}, \hyperpage{614}
  \item \texttt  {CopyStabChain}, \hyperpage{614}
  \item \texttt  {CopyToStringRep}, \hyperpage{356}
  \item \texttt  {Core}, \hyperpage{515}
  \item \texttt  {CorrespondingGeneratorsByModuloPcgs}, \hyperpage{639}
  \item \texttt  {Cos}, \hyperpage{240}
  \item coset, \hyperpage{507}
  \item \texttt  {CosetDecomposition}, \hyperpage{508}
  \item \texttt  {CosetLeadersMatFFE}, \hyperpage{311}
  \item \texttt  {CosetTable}, \hyperpage{671}
  \item \texttt  {CosetTableBySubgroup}, \hyperpage{672}
  \item \texttt  {CosetTableDefaultLimit}, \hyperpage{674}
  \item \texttt  {CosetTableDefaultMaxLimit}, \hyperpage{673}
  \item \texttt  {CosetTableFromGensAndRels}, \hyperpage{672}
  \item \texttt  {CosetTableInWholeGroup}, \hyperpage{675}
  \item \texttt  {CosetTableOfFpSemigroup}, \hyperpage{793}
  \item \texttt  {CosetTableStandard}, \hyperpage{675}
  \item \texttt  {Cosh}, \hyperpage{240}
  \item \texttt  {Cot}, \hyperpage{240}
  \item \texttt  {Coth}, \hyperpage{240}
  \item \texttt  {CoverageLineByLine}, \hyperpage{117}
  \item \texttt  {CrcFile}, \hyperpage{137}
  \item \texttt  {CrcString}, \hyperpage{368}
  \item \texttt  {CrystGroupDefaultAction}, \hyperpage{627}
  \item \texttt  {Csc}, \hyperpage{240}
  \item \texttt  {Csch}, \hyperpage{240}
  \item \texttt  {CubeRoot}, \hyperpage{241}
  \item \texttt  {Cycle}, \hyperpage{584}
  \item \texttt  {CycleIndex}
    \subitem for a permutation and an action domain, \hyperpage{585}
    \subitem for a permutation group and an action domain, 
		\hyperpage{585}
  \item \texttt  {CycleLength}, \hyperpage{584}
  \item \texttt  {CycleLengths}, \hyperpage{584}
  \item \texttt  {Cycles}, \hyperpage{584}
  \item \texttt  {CyclesOfTransformation}, \hyperpage{810}
  \item \texttt  {CycleStructureClass}, \hyperpage{1138}
  \item \texttt  {CycleStructurePerm}, \hyperpage{597}
  \item \texttt  {CycleTransformationInt}, \hyperpage{811}
  \item \texttt  {CyclicExtensionsTom}
    \subitem for a list of primes, \hyperpage{1059}
    \subitem for a prime, \hyperpage{1059}
  \item \texttt  {CyclicGroup}, \hyperpage{726}
  \item cyclotomic field elements, \hyperpage{223}
  \item cyclotomic fields
    \subitem CanonicalBasis, \hyperpage{895}
  \item \texttt  {CyclotomicField}
    \subitem for (subfield and) conductor, \hyperpage{892}
    \subitem for (subfield and) generators, \hyperpage{892}
  \item \texttt  {CyclotomicPolynomial}, \hyperpage{1006}
  \item \texttt  {Cyclotomics}, \hyperpage{223}
  \item \texttt{CyclotomicsFamily}, \hyperpage{224}

  \indexspace

  \item $d_N$ (irrational value), \hyperpage{229}
  \item Darstellungsgruppe
    \subitem see EpimorphismSchurCover, \hyperpage{549}
  \item data type
    \subitem unknown, \hyperpage{1191}
  \item \texttt  {DataType}, \hyperpage{176}
  \item \texttt  {DayDMY}, \hyperpage{368}
  \item \texttt  {DaysInMonth}, \hyperpage{368}
  \item \texttt  {DaysInYear}, \hyperpage{368}
  \item DEC, \hyperpage{344}
  \item DeclareAttribute
    \subitem \texttt{DeclareAttribute
      \subsubitem example}, \hyperpage{1255}
  \item \texttt  {DeclareAttribute}, \hyperpage{1243}
  \item \texttt{DeclareAttribute}
    \subitem example, \hyperpage{1250}
  \item \texttt{DeclareAutoPackage}, \hyperpage{1216}
  \item \texttt  {DeclareAutoreadableVariables}, \hyperpage{1210}
  \item \texttt  {DeclareCategory}, \hyperpage{1242}
  \item \texttt  {DeclareFilter}, \hyperpage{1243}
  \item \texttt  {DeclareGlobalFunction}, \hyperpage{1243}
  \item \texttt  {DeclareGlobalVariable}, \hyperpage{1244}
  \item \texttt  {DeclareHandlingByNiceBasis}, \hyperpage{919}
  \item \texttt  {DeclareInfoClass}, \hyperpage{106}
  \item \texttt  {DeclareOperation}, \hyperpage{1243}
  \item \texttt{DeclarePackage}, \hyperpage{1216}
  \item \texttt{DeclarePackageAutoDocumentation}, \hyperpage{1216}
  \item \texttt{DeclarePackageDocumentation}, \hyperpage{1216}
  \item \texttt  {DeclareProperty}, \hyperpage{1243}
  \item \texttt  {DeclareRepresentation}, \hyperpage{1242}
  \item \texttt{DeclareRepresentation}
    \subitem belongs to implementation part, \hyperpage{1245}
    \subitem example, \hyperpage{1251}
  \item \texttt  {DeclareSynonym}, \hyperpage{1244}
  \item \texttt  {DeclareSynonymAttr}, \hyperpage{1244}
  \item \texttt  {DeclareUserPreference}, \hyperpage{40}
  \item \texttt  {DecodeTree}, \hyperpage{712}
  \item decompose
    \subitem a group character, \hyperpage{1135}
  \item \texttt  {DecomposedFixedPointVector}, \hyperpage{1060}
  \item \texttt  {DecomposeTensorProduct}, \hyperpage{980}
  \item \texttt  {Decomposition}, \hyperpage{345}
  \item decomposition matrix, \hyperpage{344}
  \item \texttt  {DecompositionInt}, \hyperpage{346}
  \item \texttt  {DecompositionMatrix}, \hyperpage{1093}
  \item \texttt  {Decreased}, \hyperpage{1147}
  \item \texttt  {DEFAULTDISPLAYSTRING}, \hyperpage{359}
  \item \texttt  {DefaultField}
    \subitem for a list of generators, \hyperpage{875}
    \subitem for cyclotomics, \hyperpage{228}
    \subitem for finite field elements, \hyperpage{887}
    \subitem for several generators, \hyperpage{875}
  \item \texttt  {DefaultFieldByGenerators}, \hyperpage{875}
  \item \texttt  {DefaultFieldOfMatrix}, \hyperpage{318}
  \item \texttt  {DefaultFieldOfMatrixGroup}, \hyperpage{620}
  \item \texttt{DefaultInfoHandler}, \hyperpage{108}
  \item \texttt  {DefaultRing}
    \subitem for a collection, \hyperpage{849}
    \subitem for finite field elements, \hyperpage{887}
    \subitem for ring elements, \hyperpage{849}
  \item \texttt  {DefaultRingByGenerators}, \hyperpage{849}
  \item \texttt  {DefaultStabChainOptions}, \hyperpage{609}
  \item \texttt  {DEFAULTVIEWSTRING}, \hyperpage{360}
  \item \texttt  {DefiningPolynomial}, \hyperpage{877}
  \item \texttt  {DefiningQuotientHomomorphism}, \hyperpage{683}
  \item \texttt  {DegreeFFE}
    \subitem for a FFE, \hyperpage{885}
    \subitem for a matrix of FFEs, \hyperpage{885}
    \subitem for a vector of FFEs, \hyperpage{885}
  \item \texttt  {DegreeIndeterminate}, \hyperpage{1003}
  \item \texttt  {DegreeOfBinaryRelation}, \hyperpage{444}
  \item \texttt  {DegreeOfCharacter}, \hyperpage{1134}
  \item \texttt  {DegreeOfLaurentPolynomial}, \hyperpage{1001}
  \item \texttt  {DegreeOfPartialPerm}, \hyperpage{823}
  \item \texttt  {DegreeOfPartialPermCollection}, \hyperpage{823}
  \item \texttt  {DegreeOfPartialPermSemigroup}, \hyperpage{838}
  \item \texttt  {DegreeOfTransformation}, \hyperpage{803}
  \item \texttt  {DegreeOfTransformationCollection}, \hyperpage{803}
  \item \texttt  {DegreeOfTransformationSemigroup}, \hyperpage{814}
  \item \texttt  {DegreeOverPrimeField}, \hyperpage{877}
  \item \texttt  {Delta}, \hyperpage{1195}
  \item denominator
    \subitem of a rational, \hyperpage{222}
  \item \texttt  {DenominatorCyc}, \hyperpage{227}
  \item \texttt  {DenominatorOfModuloPcgs}, \hyperpage{638}
  \item \texttt  {DenominatorOfRationalFunction}, \hyperpage{998}
  \item \texttt  {DenominatorRat}, \hyperpage{222}
  \item \texttt  {DenseHashTable}, \hyperpage{375}
  \item \texttt  {DenseIntKey}, \hyperpage{375}
  \item deprecated, \hyperpage{1215}
  \item \texttt  {DepthOfPcElement}, \hyperpage{632}
  \item \texttt  {DepthOfUpperTriangularMatrix}, \hyperpage{332}
  \item \texttt  {Derangements}, \hyperpage{212}
  \item \texttt  {Derivations}, \hyperpage{960}
  \item \texttt  {Derivative}, \hyperpage{1004}
  \item \texttt  {DerivedLength}, \hyperpage{531}
  \item \texttt  {DerivedSeriesOfGroup}, \hyperpage{531}
  \item \texttt  {DerivedSubgroup}, \hyperpage{516}
  \item \texttt  {DerivedSubgroupsTom}, \hyperpage{1057}
  \item \texttt  {DerivedSubgroupsTomPossible}, \hyperpage{1058}
  \item \texttt  {DerivedSubgroupsTomUnique}, \hyperpage{1058}
  \item \texttt  {DerivedSubgroupTom}, \hyperpage{1057}
  \item \texttt  {DescriptionOfRootOfUnity}, \hyperpage{227}
  \item \texttt  {Determinant}, \hyperpage{318}
  \item determinant
    \subitem integer matrix, \hyperpage{344}
  \item determinant character, \hyperpage{1138}
  \item \texttt  {DeterminantIntMat}, \hyperpage{344}
  \item \texttt  {DeterminantMat}, \hyperpage{318}
  \item \texttt  {DeterminantMatDestructive}, \hyperpage{319}
  \item \texttt  {DeterminantMatDivFree}, \hyperpage{319}
  \item \texttt  {DeterminantOfCharacter}, \hyperpage{1138}
  \item \texttt  {DiagonalizeIntMat}, \hyperpage{343}
  \item \texttt  {DiagonalizeMat}, \hyperpage{328}
  \item \texttt  {DiagonalMat}, \hyperpage{320}
  \item \texttt  {DiagonalOfMat}, \hyperpage{331}
  \item \texttt  {DictionaryByPosition}, \hyperpage{373}
  \item \texttt  {DicyclicGroup}, \hyperpage{727}
  \item \texttt  {Difference}, \hyperpage{395}
  \item \texttt  {DifferenceBlist}, \hyperpage{300}
  \item \texttt  {DihedralGroup}, \hyperpage{727}
  \item \texttt  {Dimension}, \hyperpage{872}
  \item \texttt  {DimensionOfHighestWeightModule}, \hyperpage{981}
  \item \texttt  {DimensionOfMatrixGroup}, \hyperpage{620}
  \item \texttt  {DimensionOfVectors}, \hyperpage{912}
  \item \texttt  {DimensionsLoewyFactors}, \hyperpage{533}
  \item \texttt  {DimensionsMat}, \hyperpage{318}
  \item \texttt  {DirectoriesLibrary}, \hyperpage{132}
  \item \texttt  {DirectoriesPackageLibrary}, \hyperpage{1208}
  \item \texttt  {DirectoriesPackagePrograms}, \hyperpage{1209}
  \item \texttt  {DirectoriesSystemPrograms}, \hyperpage{132}
  \item \texttt  {Directory}, \hyperpage{131}
  \item \texttt  {DirectoryContents}, \hyperpage{132}
  \item \texttt  {DirectoryCurrent}, \hyperpage{132}
  \item \texttt  {DirectoryDesktop}, \hyperpage{132}
  \item \texttt  {DirectoryHome}, \hyperpage{133}
  \item \texttt  {DirectoryTemporary}, \hyperpage{131}
  \item \texttt  {DirectProduct}, \hyperpage{718}
  \item \texttt  {DirectProductOp}, \hyperpage{718}
  \item \texttt  {DirectSum}, \hyperpage{866}
  \item \texttt  {DirectSumDecomposition}
    \subitem for Lie algebras, \hyperpage{938}
  \item \texttt  {DirectSumOfAlgebraModules}
    \subitem for a list of Lie algebra modules, \hyperpage{953}
    \subitem for two Lie algebra modules, \hyperpage{953}
  \item \texttt  {DirectSumOfAlgebras}
    \subitem for a list of algebras, \hyperpage{937}
    \subitem for two algebras, \hyperpage{937}
  \item \texttt  {DirectSumOp}, \hyperpage{866}
  \item disable automatic loading, \hyperpage{1204}
  \item \texttt  {DisableAttributeValueStoring}, \hyperpage{173}
  \item \texttt  {Discriminant}, \hyperpage{1004}
  \item \texttt  {Display}, \hyperpage{84}
    \subitem for a character table, \hyperpage{1098}
    \subitem for a ffe, \hyperpage{890}
    \subitem for a table of marks, \hyperpage{1049}
    \subitem for class functions, \hyperpage{1130}
  \item \texttt  {DisplayCacheStats}, \hyperpage{118}
  \item \texttt  {DisplayCompositionSeries}, \hyperpage{531}
  \item \texttt  {DisplayEggBoxOfDClass}, \hyperpage{775}
  \item \texttt  {DisplayImfInvariants}, \hyperpage{755}
  \item \texttt  {DisplayInformationPerfectGroups}
    \subitem for a pair [ order, index ], \hyperpage{746}
    \subitem for group order (and index), \hyperpage{746}
  \item \texttt  {DisplayOptions}, \hyperpage{1100}
  \item \texttt  {DisplayOptionsStack}, \hyperpage{128}
  \item \texttt  {DisplayPackageLoadingLog}, \hyperpage{1206}
  \item \texttt  {DisplayProfile}, \hyperpage{112}
  \item \texttt  {DisplayString}, \hyperpage{359}
  \item \texttt  {DistancePerms}, \hyperpage{596}
  \item \texttt  {DistancesDistributionMatFFEVecFFE}, \hyperpage{310}
  \item \texttt  {DistancesDistributionVecFFEsVecFFE}, \hyperpage{310}
  \item \texttt  {DistanceVecFFE}, \hyperpage{310}
  \item division, \hyperpage{57}
    \subitem operation, \hyperpage{413}
  \item division rings, \hyperpage{874}
  \item \texttt  {DivisionRingByGenerators}, \hyperpage{876}
  \item divisors
    \subitem of an integer, \hyperpage{189}
  \item \texttt  {DivisorsInt}, \hyperpage{189}
  \item Dixon-Schneider algorithm, \hyperpage{1106}
  \item \texttt  {DixonInit}, \hyperpage{1107}
  \item \texttt  {DixonRecord}, \hyperpage{1107}
  \item \texttt  {DixonSplit}, \hyperpage{1107}
  \item \texttt  {DixontinI}, \hyperpage{1107}
  \item \texttt  {DMYDay}, \hyperpage{368}
  \item \texttt  {DMYhmsSeconds}, \hyperpage{370}
  \item \texttt  {DnLattice}, \hyperpage{1148}
  \item \texttt  {DnLatticeIterative}, \hyperpage{1149}
  \item \texttt{do}, \hyperpage{63}
  \item document formats
    \subitem for help books, \hyperpage{1291}
  \item document formats (text, dvi, ps, pdf, HTML), \hyperpage{29}
  \item \texttt  {Domain}, \hyperpage{408}
  \item \texttt  {DomainByGenerators}, \hyperpage{408}
  \item \texttt  {DomainOfPartialPerm}, \hyperpage{824}
  \item \texttt  {DomainOfPartialPermCollection}, \hyperpage{824}
  \item \texttt  {DominantCharacter}
    \subitem for a root system and a highest weight, \hyperpage{980}
    \subitem for a semisimple Lie algebra and a highest weight, 
		\hyperpage{980}
  \item \texttt  {DominantWeights}, \hyperpage{980}
  \item dot-file, \hyperpage{539}
  \item \texttt  {DotFileLatticeSubgroups}, \hyperpage{539}
  \item \texttt  {DoubleCoset}, \hyperpage{509}
  \item \texttt  {DoubleCosetRepsAndSizes}, \hyperpage{510}
  \item \texttt  {DoubleCosets}, \hyperpage{510}
  \item \texttt  {DoubleCosetsNC}, \hyperpage{510}
  \item \texttt  {DoubleCoverOfAlternatingGroup}, \hyperpage{552}
  \item \texttt  {DoubleHashArraySize}, \hyperpage{376}
  \item doublequote character, \hyperpage{355}
  \item doublequotes, \hyperpage{352}
  \item \texttt  {DownEnv}, \hyperpage{90}
  \item duplicate free, \hyperpage{276}
  \item \texttt  {DuplicateFreeList}, \hyperpage{283}
  \item \texttt  {DxIncludeIrreducibles}, \hyperpage{1108}

  \indexspace

  \item \texttt  {E}, \hyperpage{223}
  \item $e_N$ (irrational value), \hyperpage{229}
  \item \texttt  {EANormalSeriesByPcgs}, \hyperpage{641}
  \item \texttt  {Earns}
    \subitem for a group, an action domain, etc., \hyperpage{586}
    \subitem for an external set, \hyperpage{586}
  \item \texttt  {EB}, \hyperpage{229}
  \item \texttt  {EC}, \hyperpage{229}
  \item \texttt  {ED}, \hyperpage{229}
  \item \texttt  {Edit}, \hyperpage{99}
  \item \texttt  {EE}, \hyperpage{229}
  \item \texttt  {EF}, \hyperpage{229}
  \item \texttt  {EG}, \hyperpage{229}
  \item \texttt  {EggBoxOfDClass}, \hyperpage{775}
  \item \texttt  {EH}, \hyperpage{229}
  \item \texttt  {EI}, \hyperpage{230}
  \item \texttt  {Eigenspaces}, \hyperpage{326}
  \item \texttt  {Eigenvalues}, \hyperpage{326}
  \item \texttt  {EigenvaluesChar}, \hyperpage{1139}
  \item \texttt  {Eigenvectors}, \hyperpage{326}
  \item \texttt  {EJ}, \hyperpage{231}
  \item \texttt  {EK}, \hyperpage{231}
  \item \texttt  {EL}, \hyperpage{231}
  \item element test
    \subitem for lists, \hyperpage{261}
  \item \texttt  {ElementaryAbelianGroup}, \hyperpage{726}
  \item \texttt  {ElementaryAbelianSeries}
    \subitem for a group, \hyperpage{531}
    \subitem for a list, \hyperpage{531}
  \item \texttt  {ElementaryAbelianSeriesLargeSteps}, \hyperpage{531}
  \item \texttt  {ElementaryDivisorsMat}, \hyperpage{326}
  \item \texttt  {ElementaryDivisorsMatDestructive}, \hyperpage{326}
  \item \texttt  {Elementary}\discretionary {-}{}{}\texttt  {Divisors}\discretionary {-}{}{}\texttt  {TransformationsMat}, 
		\hyperpage{327}
  \item \texttt  {Elementary}\discretionary {-}{}{}\texttt  {Divisors}\discretionary {-}{}{}\texttt  {Transformations}\discretionary {-}{}{}\texttt  {Mat}\discretionary {-}{}{}\texttt  {Destructive}, 
		\hyperpage{327}
  \item \texttt  {ElementOfFpGroup}, \hyperpage{669}
  \item \texttt  {ElementOfFpSemigroup}, \hyperpage{789}
  \item \texttt  {ElementOfMagmaRing}, \hyperpage{989}
  \item \texttt  {ElementOrdersPowerMap}, \hyperpage{1167}
  \item \texttt  {ElementProperty}, \hyperpage{616}
  \item \texttt  {Elements}, \hyperpage{391}
  \item elements
    \subitem definition, \hyperpage{156}
    \subitem of a list or collection, \hyperpage{390}
  \item \texttt  {ElementsFamily}, \hyperpage{385}
  \item \texttt  {ElementsStabChain}, \hyperpage{612}
  \item \texttt{elif}, \hyperpage{60}
  \item \texttt  {EliminatedWord}, \hyperpage{478}
  \item \texttt  {EliminationOrdering}, \hyperpage{1017}
  \item ElmWPObj, \hyperpage{1301}
  \item \texttt  {ElmWPObj}, \hyperpage{1301}
  \item \texttt{else}, \hyperpage{60}
  \item \texttt  {EM}, \hyperpage{231}
  \item \texttt{emacs}, \hyperpage{99}
  \item email addresses, \hyperpage{27}
  \item \texttt  {Embedding}
    \subitem for a domain and a positive integer, \hyperpage{427}
    \subitem for group products, \hyperpage{724}
    \subitem for two domains, \hyperpage{427}
  \item \texttt{Embedding}
    \subitem example for direct products, \hyperpage{719}
    \subitem example for semidirect products, \hyperpage{720}
    \subitem example for wreath products, \hyperpage{722}
    \subitem for Lie algebras, \hyperpage{958}
    \subitem for magma rings, \hyperpage{989}
  \item embeddings
    \subitem find all, \hyperpage{567}
  \item \texttt  {EmptyBinaryRelation}
    \subitem for a degree, \hyperpage{443}
    \subitem for a domain, \hyperpage{443}
  \item \texttt  {EmptyMatrix}, \hyperpage{320}
  \item \texttt  {EmptyPartialPerm}, \hyperpage{822}
  \item \texttt  {EmptyPlist}, \hyperpage{262}
  \item \texttt  {EmptySCTable}, \hyperpage{924}
  \item \texttt  {EmptyStabChain}, \hyperpage{615}
  \item \texttt  {EmptyString}, \hyperpage{357}
  \item \texttt  {EnableAttributeValueStoring}, \hyperpage{173}
  \item \texttt  {End}, \hyperpage{916}
  \item \texttt{end}, \hyperpage{66}
  \item \texttt  {EndlineFunc}, \hyperpage{71}
  \item \texttt  {EndsWith}, \hyperpage{364}
  \item \texttt  {Enumerator}, \hyperpage{386}
  \item \texttt  {EnumeratorByBasis}, \hyperpage{907}
  \item \texttt  {EnumeratorByFunctions}
    \subitem for a domain and a record, \hyperpage{387}
    \subitem for a family and a record, \hyperpage{387}
  \item \texttt  {EnumeratorOfCombinations}, \hyperpage{208}
  \item \texttt  {EnumeratorOfTuples}, \hyperpage{211}
  \item \texttt  {EnumeratorSorted}, \hyperpage{386}
  \item environment, \hyperpage{66}
  \item \texttt  {Epicentre}, \hyperpage{550}
  \item \texttt  {EpimorphismFromFreeGroup}, \hyperpage{503}
  \item \texttt  {EpimorphismNilpotentQuotient}, \hyperpage{685}
  \item \texttt  {EpimorphismNonabelianExteriorSquare}, \hyperpage{550}
  \item \texttt  {EpimorphismPGroup}, \hyperpage{684}
  \item \texttt  {EpimorphismQuotientSystem}, \hyperpage{684}
  \item epimorphisms
    \subitem find all, \hyperpage{566}
  \item \texttt  {EpimorphismSchurCover}, \hyperpage{549}
  \item \texttt  {EpimorphismSolvableQuotient}, \hyperpage{685}
  \item \texttt  {EqFloat}, \hyperpage{241}
  \item equality
    \subitem associative words, \hyperpage{475}
    \subitem elements of finitely presented groups, \hyperpage{667}
    \subitem for pcwords, \hyperpage{653}
    \subitem for transformations, \hyperpage{802}
    \subitem nonassociative words, \hyperpage{469}
    \subitem of booleans, \hyperpage{246}
    \subitem of records, \hyperpage{381}
    \subitem operation, \hyperpage{412}
  \item equality test, \hyperpage{56}
    \subitem for permutations, \hyperpage{595}
  \item equivalence class, \hyperpage{448}
  \item equivalence relation, \hyperpage{444}, \hyperpage{447}
  \item \texttt  {EquivalenceClasses}
    \subitem attribute, \hyperpage{449}
  \item \texttt  {EquivalenceClassOfElement}, \hyperpage{449}
  \item \texttt  {EquivalenceClassOfElementNC}, \hyperpage{449}
  \item \texttt  {EquivalenceClassRelation}, \hyperpage{448}
  \item \texttt  {EquivalenceRelationByPairs}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationByPairsNC}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationByPartition}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationByPartitionNC}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationByProperty}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationByRelation}, \hyperpage{447}
  \item \texttt  {EquivalenceRelationPartition}, \hyperpage{448}
  \item \texttt  {ER}, \hyperpage{230}
  \item \texttt  {Erf}, \hyperpage{241}
  \item \texttt  {Error}, \hyperpage{91}
  \item \texttt  {ErrorCount}, \hyperpage{92}
  \item \texttt  {ErrorNoReturn}, \hyperpage{91}
  \item \texttt{ErrorNoTraceBack}, \hyperpage{87}
  \item errors
    \subitem syntax, \hyperpage{79}
  \item \texttt  {ES}, \hyperpage{230}
  \item escaped characters, \hyperpage{354}
  \item escaping non-special characters, \hyperpage{355}
  \item \texttt  {ET}, \hyperpage{230}
  \item \texttt  {EU}, \hyperpage{230}
  \item \texttt  {EuclideanDegree}, \hyperpage{860}
  \item \texttt  {EuclideanQuotient}, \hyperpage{861}
  \item \texttt  {EuclideanRemainder}, \hyperpage{861}
  \item Euler's totient function, \hyperpage{196}
  \item \texttt  {EulerianFunction}, \hyperpage{529}
  \item \texttt  {EulerianFunctionByTom}, \hyperpage{1060}
  \item \texttt  {EV}, \hyperpage{230}
  \item \texttt  {EvalStraightLineProgElm}, \hyperpage{489}
  \item \texttt  {EvalString}, \hyperpage{367}
  \item evaluation, \hyperpage{49}
    \subitem strings, \hyperpage{366}
  \item \texttt  {EW}, \hyperpage{230}
  \item \texttt  {EX}, \hyperpage{230}
  \item \texttt  {ExactSizeConsiderFunction}, \hyperpage{544}
  \item Excel, \hyperpage{152}
  \item \texttt  {Exec}, \hyperpage{155}
  \item execution, \hyperpage{59}
  \item exit, \hyperpage{92}
  \item \texttt  {Exp}, \hyperpage{240}
  \item \texttt  {Exp10}, \hyperpage{240}
  \item \texttt  {Exp2}, \hyperpage{240}
  \item Expanded form of monomials, \hyperpage{1021}
  \item \texttt  {Expm1}, \hyperpage{241}
  \item \texttt  {Exponent}, \hyperpage{529}
    \subitem for a character table, \hyperpage{1082}
  \item exponent
    \subitem of the prime residue group, \hyperpage{196}
  \item exponentiation
    \subitem operation, \hyperpage{413}
  \item \texttt  {ExponentOfPcElement}, \hyperpage{631}
  \item \texttt  {ExponentsConjugateLayer}, \hyperpage{634}
  \item \texttt  {ExponentsOfCommutator}, \hyperpage{634}
  \item \texttt  {ExponentsOfConjugate}, \hyperpage{634}
  \item \texttt  {ExponentsOfPcElement}, \hyperpage{631}
  \item \texttt  {ExponentsOfRelativePower}, \hyperpage{634}
  \item \texttt  {ExponentSumWord}, \hyperpage{477}
  \item \texttt  {ExponentSyllable}, \hyperpage{479}
  \item \texttt  {ExtendedPcgs}, \hyperpage{636}
  \item \texttt  {ExtendRootDirectories}, \hyperpage{1205}
  \item \texttt  {ExtendStabChain}, \hyperpage{614}
  \item \texttt  {Extension}, \hyperpage{660}
  \item \texttt  {ExtensionNC}, \hyperpage{660}
  \item \texttt  {ExtensionRepresentatives}, \hyperpage{661}
  \item \texttt  {Extensions}, \hyperpage{660}
  \item exterior power, \hyperpage{1150}
  \item \texttt  {ExteriorCentre}, \hyperpage{550}
  \item \texttt  {ExteriorPowerOfAlgebraModule}, \hyperpage{984}
  \item External representation of polynomials, \hyperpage{1021}
  \item \texttt  {ExternalOrbit}, \hyperpage{590}
  \item \texttt  {ExternalOrbits}
    \subitem for a group, an action domain, etc., \hyperpage{591}
    \subitem for an external set, \hyperpage{591}
  \item \texttt  {ExternalOrbitsStabilizers}
    \subitem for a group, an action domain, etc., \hyperpage{591}
    \subitem for an external set, \hyperpage{591}
  \item \texttt  {ExternalSet}, \hyperpage{589}
  \item \texttt{ExternalSet}
    \subitem computing orbits, \hyperpage{1296}
  \item \texttt  {ExternalSubset}, \hyperpage{590}
  \item \texttt  {Extract}, \hyperpage{1144}
  \item \texttt  {ExtraspecialGroup}, \hyperpage{728}
  \item \texttt  {ExtRepDenominatorRatFun}, \hyperpage{1022}
  \item \texttt  {ExtRepNumeratorRatFun}, \hyperpage{1022}
  \item \texttt  {ExtRepOfObj}, \hyperpage{1240}
    \subitem for a cyclotomic, \hyperpage{227}
  \item \texttt  {ExtRepPolynomialRatFun}, \hyperpage{1022}
  \item \texttt  {EY}, \hyperpage{230}

  \indexspace

  \item $f_N$ (irrational value), \hyperpage{229}
  \item \texttt  {FactorCosetAction}, \hyperpage{582}
    \subitem for fp groups, \hyperpage{672}
  \item \texttt  {FactorFreeSemigroupByRelations}, \hyperpage{787}
  \item \texttt  {FactorGroup}, \hyperpage{534}
  \item \texttt  {FactorGroupFpGroupByRels}, \hyperpage{666}
  \item \texttt  {FactorGroupNC}, \hyperpage{534}
  \item \texttt  {FactorGroupNormalSubgroupClasses}, \hyperpage{1120}
  \item \texttt  {FactorGroupTom}, \hyperpage{1061}
  \item \texttt  {Factorial}, \hyperpage{205}
  \item \texttt  {Factorization}, \hyperpage{504}
  \item factorization, \hyperpage{503}
  \item \texttt  {Factors}, \hyperpage{859}
    \subitem for polynomials over abelian number fields, 
		\hyperpage{894}
    \subitem of polynomial, \hyperpage{1006}
  \item \texttt  {FactorsInt}, \hyperpage{186}
    \subitem using Pollard's Rho, \hyperpage{186}
  \item \texttt  {FactorsOfDirectProduct}, \hyperpage{1112}
  \item \texttt  {FactorsSquarefree}, \hyperpage{1007}
  \item \texttt  {fail}, \hyperpage{245}
  \item \texttt  {FaithfulModule}
    \subitem for Lie algebras, \hyperpage{952}
  \item \texttt  {FamiliesOfGeneralMappingsAndRanges}, \hyperpage{440}
  \item \texttt  {FamiliesOfRows}, \hyperpage{1119}
  \item \texttt  {FamilyForOrdering}, \hyperpage{452}
  \item \texttt  {FamilyObj}, \hyperpage{165}
  \item \texttt  {FamilyPcgs}, \hyperpage{652}
  \item \texttt  {FamilyRange}, \hyperpage{440}
  \item \texttt  {FamilySource}, \hyperpage{440}
  \item features
    \subitem under UNIX, \hyperpage{33}
  \item \texttt{fi}, \hyperpage{60}
  \item \texttt  {Fibonacci}, \hyperpage{217}
  \item \texttt  {Field}
    \subitem for (a field and) a list of generators, \hyperpage{875}
    \subitem for several generators, \hyperpage{875}
  \item field homomorphisms
    \subitem Frobenius, \hyperpage{888}
  \item \texttt  {FieldByGenerators}, \hyperpage{876}
  \item \texttt  {FieldExtension}, \hyperpage{878}
  \item \texttt  {FieldOfMatrixGroup}, \hyperpage{620}
  \item \texttt  {FieldOverItselfByGenerators}, \hyperpage{877}
  \item fields, \hyperpage{874}
  \item \texttt  {FileDescriptorOfStream}, \hyperpage{141}
  \item \texttt  {Filename}
    \subitem for a directory and a string, \hyperpage{133}
    \subitem for a list of directories and a string, \hyperpage{133}
  \item \texttt  {FilenameFunc}, \hyperpage{71}
  \item \texttt  {Filtered}, \hyperpage{289}
  \item \texttt  {FindSl2}, \hyperpage{975}
  \item finiteness test
    \subitem for a list or collection, \hyperpage{391}
  \item \texttt  {First}, \hyperpage{290}
  \item \texttt  {FittingSubgroup}, \hyperpage{517}
  \item \texttt  {FixedPointsOfPartialPerm}
    \subitem for a partial perm, \hyperpage{825}
    \subitem for a partial perm coll, \hyperpage{825}
  \item \texttt  {Flat}, \hyperpage{284}
  \item \texttt  {FlatKernelOfTransformation}, \hyperpage{807}
  \item \texttt  {FLOAT}
    \subitem constants, \hyperpage{242}
  \item \texttt  {Float}, \hyperpage{243}
  \item \texttt  {Floor}, \hyperpage{241}
  \item flush character, \hyperpage{355}
  \item \texttt  {FlushCaches}, \hyperpage{1245}
  \item FOA triples, \hyperpage{1294}
  \item \texttt{for} loop, \hyperpage{63}
  \item \texttt  {ForAll}, \hyperpage{290}
  \item \texttt  {ForAny}, \hyperpage{290}
  \item \texttt  {FOR}\discretionary {-}{}{}\texttt  {C}\discretionary {-}{}{}\texttt  {E{\textunderscore }}\discretionary {-}{}{}\texttt  {Q}\discretionary {-}{}{}\texttt  {U}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {T{\textunderscore }GAP}, 
		\hyperpage{92}
  \item \texttt  {FpElmComparisonMethod}, \hyperpage{668}
  \item \texttt  {FpGroupPresentation}, \hyperpage{691}
  \item \texttt  {FpGrpMonSmgOfFpGrpMonSmgElement}, \hyperpage{787}
  \item \texttt  {FpLieAlgebraByCartanMatrix}, \hyperpage{976}
  \item \texttt  {Frac}, \hyperpage{241}
  \item Frame, \hyperpage{1150}
  \item \texttt  {FrattiniSubgroup}, \hyperpage{517}
  \item \texttt{FrattiniSubgroup}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {FreeAbelianGroup}, \hyperpage{727}
  \item \texttt  {FreeAlgebra}
    \subitem for ring and several names, \hyperpage{922}
    \subitem for ring, rank (and name), \hyperpage{922}
  \item \texttt  {FreeAlgebraWithOne}
    \subitem for ring and several names, \hyperpage{922}
    \subitem for ring, rank (and name), \hyperpage{922}
  \item \texttt  {FreeAssociativeAlgebra}
    \subitem for ring and several names, \hyperpage{923}
    \subitem for ring, rank (and name), \hyperpage{923}
  \item \texttt  {FreeAssociativeAlgebraWithOne}
    \subitem for ring and several names, \hyperpage{923}
    \subitem for ring, rank (and name), \hyperpage{923}
  \item \texttt  {FreeGeneratorsOfFpGroup}, \hyperpage{668}
  \item \texttt  {FreeGeneratorsOfFpSemigroup}, \hyperpage{789}
  \item \texttt  {FreeGeneratorsOfWholeGroup}, \hyperpage{668}
  \item \texttt  {FreeGroup}
    \subitem for a list of names, \hyperpage{474}
    \subitem for given rank, \hyperpage{474}
    \subitem for infinitely many generators, \hyperpage{474}
    \subitem for various names, \hyperpage{474}
  \item \texttt  {FreeGroupOfFpGroup}, \hyperpage{668}
  \item \texttt  {FreeLeftModule}, \hyperpage{871}
  \item \texttt  {FreeLieAlgebra}
    \subitem for ring and several names, \hyperpage{960}
    \subitem for ring, rank (and name), \hyperpage{960}
  \item \texttt  {FreeMagma}
    \subitem for a list of names, \hyperpage{471}
    \subitem for given rank, \hyperpage{471}
    \subitem for infinitely many generators, \hyperpage{471}
    \subitem for various names, \hyperpage{471}
  \item \texttt  {FreeMagmaRing}, \hyperpage{987}
  \item \texttt  {FreeMagmaWithOne}
    \subitem for a list of names, \hyperpage{471}
    \subitem for given rank, \hyperpage{471}
    \subitem for infinitely many generators, \hyperpage{471}
    \subitem for various names, \hyperpage{471}
  \item \texttt  {FreeMonoid}
    \subitem for a list of names, \hyperpage{767}
    \subitem for given rank, \hyperpage{767}
    \subitem for infinitely many generators, \hyperpage{767}
    \subitem for various names, \hyperpage{767}
  \item \texttt  {FreeMonoidOfRewritingSystem}, \hyperpage{792}
  \item \texttt  {FreeProduct}
    \subitem for a list, \hyperpage{723}
    \subitem for several groups, \hyperpage{723}
  \item \texttt  {FreeSemigroup}
    \subitem for a list of names, \hyperpage{764}
    \subitem for given rank, \hyperpage{764}
    \subitem for infinitely many generators, \hyperpage{764}
    \subitem for various names, \hyperpage{764}
  \item \texttt  {FreeSemigroupOfFpSemigroup}, \hyperpage{789}
  \item \texttt  {FreeSemigroupOfRewritingSystem}, \hyperpage{792}
  \item Frobenius automorphism, \hyperpage{888}
  \item \texttt  {FrobeniusAutomorphism}, \hyperpage{888}
  \item \texttt  {FrobeniusCharacterValue}, \hyperpage{1162}
  \item \texttt  {FullMatrixAlgebra}, \hyperpage{927}
  \item \texttt  {FullMatrixAlgebraCentralizer}, \hyperpage{937}
  \item \texttt  {FullMatrixLieAlgebra}, \hyperpage{960}
  \item \texttt  {FullMatrixModule}, \hyperpage{873}
  \item \texttt  {FullMatrixSpace}, \hyperpage{911}
  \item \texttt  {FullRowModule}, \hyperpage{873}
  \item \texttt  {FullRowSpace}, \hyperpage{911}
  \item \texttt  {FullTransformationMonoid}, \hyperpage{814}
  \item \texttt  {FullTransformationSemigroup}, \hyperpage{814}
  \item \texttt  {FunctionAction}, \hyperpage{589}
  \item \texttt  {FunctionField}
    \subitem for an integral ring and a list of indeterminate numbers, 
		\hyperpage{1013}
    \subitem for an integral ring and a list of indeterminates, 
		\hyperpage{1013}
    \subitem for an integral ring and a list of names (and an exclusion list), 
		\hyperpage{1013}
    \subitem for an integral ring and a rank (and an exclusion list), 
		\hyperpage{1013}
  \item \texttt{FunctionOperation}, \hyperpage{1215}
  \item functions
    \subitem as in mathematics, \hyperpage{424}
    \subitem as in programming language, \hyperpage{70}
    \subitem definition by arrow notation, \hyperpage{68}
    \subitem definition of, \hyperpage{66}
    \subitem recursive, \hyperpage{66}
    \subitem with a variable number of arguments, \hyperpage{66}
    \subitem with a variable number of arguments, calling, 
		\hyperpage{55}
  \item \texttt  {FunctionsFamily}, \hyperpage{77}
  \item \texttt  {FusionCharTableTom}, \hyperpage{1064}
  \item \texttt  {FusionConjugacyClasses}
    \subitem for a homomorphism, \hyperpage{1170}
    \subitem for two character tables, \hyperpage{1170}
    \subitem for two groups, \hyperpage{1170}
  \item \texttt  {FusionConjugacyClassesOp}
    \subitem for a homomorphism, \hyperpage{1170}
    \subitem for two character tables, \hyperpage{1170}
  \item fusions, \hyperpage{1169}
  \item \texttt  {FusionsAllowedByRestrictions}, \hyperpage{1189}
  \item \texttt  {FusionsTom}, \hyperpage{1054}

  \indexspace

  \item $G$-sets, \hyperpage{588}
    \subitem computing orbits, \hyperpage{1296}
  \item $g_N$ (irrational value), \hyperpage{229}
  \item \texttt{gac}, \hyperpage{1210}
  \item \texttt  {GaloisCyc}
    \subitem for a class function, \hyperpage{1129}
    \subitem for a cyclotomic, \hyperpage{233}
    \subitem for a list of cyclotomics, \hyperpage{233}
  \item \texttt  {GaloisField}
    \subitem for characteristic and degree, \hyperpage{887}
    \subitem for characteristic and polynomial, \hyperpage{887}
    \subitem for field size, \hyperpage{887}
    \subitem for subfield and degree, \hyperpage{887}
    \subitem for subfield and polynomial, \hyperpage{887}
  \item \texttt  {GaloisGroup}
    \subitem for abelian number fields, \hyperpage{898}
    \subitem of field, \hyperpage{879}
    \subitem of rational class of a group, \hyperpage{513}
  \item \texttt  {GaloisMat}, \hyperpage{234}
  \item \texttt  {GaloisStabilizer}, \hyperpage{895}
  \item \texttt  {GaloisType}, \hyperpage{1008}
  \item \texttt  {Gamma}, \hyperpage{241}
  \item \texttt  {GammaL}, \hyperpage{733}
  \item \texttt{gap.ini}, \hyperpage{38}
  \item \texttt  {Gap3CatalogueIdGroup}, \hyperpage{742}
  \item \texttt  {GAP{\textunderscore }}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {X}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {T{\textunderscore }}\discretionary {-}{}{}\texttt  {CODE}, 
		\hyperpage{92}
  \item \texttt  {GAPInfo}, \hyperpage{42}
  \item \texttt{GAPInfo.Architecture}, \hyperpage{1209}
  \item \texttt{GAPInfo.CommandLineOptions}, \hyperpage{33}
  \item \texttt{GAPInfo.Keywords}, \hyperpage{48}
  \item \texttt  {GAPInfo.ProfileThreshold}, \hyperpage{112}
  \item \texttt{GAPInfo.RootPaths}, \hyperpage{130}
  \item \texttt  {GAPInfo.TimeoutsSupported}, \hyperpage{74}
  \item \texttt{GAPInfo.UserGapRoot}, \hyperpage{130}
  \item \texttt{GAPInfo.Version}, \hyperpage{118}
  \item \texttt  {GapInputPcGroup}, \hyperpage{658}
  \item \texttt  {GapInputSCTable}, \hyperpage{925}
  \item \texttt  {GAPKB{\textunderscore }REW}, \hyperpage{791}
  \item \texttt{GAPTCENUM}, \hyperpage{672}
  \item \texttt  {GasmanLimits}, \hyperpage{126}
  \item \texttt  {GasmanMessageStatus}, \hyperpage{125}
  \item \texttt  {GasmanStatistics}, \hyperpage{125}
  \item Gaussian algorithm, \hyperpage{323}
  \item \texttt  {GaussianIntegers}, \hyperpage{899}
  \item \texttt  {GaussianRationals}, \hyperpage{893}
  \item \texttt  {Gcd}
    \subitem for (a ring and) a list of elements, \hyperpage{861}
    \subitem for (a ring and) several elements, \hyperpage{861}
  \item \texttt  {Gcdex}, \hyperpage{182}
  \item \texttt  {GcdInt}, \hyperpage{182}
  \item \texttt  {GcdOp}, \hyperpage{862}
  \item \texttt  {GcdRepresentation}
    \subitem for (a ring and) a list of elements, \hyperpage{862}
    \subitem for (a ring and) several elements, \hyperpage{862}
  \item \texttt  {GcdRepresentationOp}, \hyperpage{862}
  \item \texttt  {GeneralisedEigenspaces}, \hyperpage{326}
  \item \texttt  {GeneralisedEigenvalues}, \hyperpage{325}
  \item generalized characters, \hyperpage{1122}
  \item generalized conjugation technique, \hyperpage{1304}
  \item \texttt  {GeneralizedEigenspaces}, \hyperpage{326}
  \item \texttt  {GeneralizedEigenvalues}, \hyperpage{325}
  \item \texttt  {GeneralLinearGroup}
    \subitem for dimension and a ring, \hyperpage{730}
    \subitem for dimension and field size, \hyperpage{730}
  \item \texttt  {GeneralMappingByElements}, \hyperpage{425}
  \item \texttt  {GeneralMappingsFamily}, \hyperpage{440}
  \item \texttt  {GeneralOrthogonalGroup}, \hyperpage{732}
  \item \texttt  {GeneralSemilinearGroup}, \hyperpage{733}
  \item \texttt  {GeneralUnitaryGroup}, \hyperpage{731}
  \item generator
    \subitem of the prime residue group, \hyperpage{198}
  \item \texttt  {GeneratorsOfAdditiveGroup}, \hyperpage{846}
  \item \texttt  {GeneratorsOfAdditiveMagma}, \hyperpage{846}
  \item \texttt  {GeneratorsOfAdditiveMagmaWithZero}, \hyperpage{846}
  \item \texttt  {GeneratorsOfAlgebra}, \hyperpage{932}
  \item \texttt  {GeneratorsOfAlgebraModule}, \hyperpage{947}
  \item \texttt  {GeneratorsOfAlgebraWithOne}, \hyperpage{933}
  \item \texttt  {GeneratorsOfDivisionRing}, \hyperpage{876}
  \item \texttt  {GeneratorsOfDomain}, \hyperpage{407}
  \item \texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Equivalence}\discretionary {-}{}{}\texttt  {Relation}\discretionary {-}{}{}\texttt  {Partition}, 
		\hyperpage{448}
  \item \texttt  {GeneratorsOfField}, \hyperpage{876}
  \item \texttt  {GeneratorsOfGroup}, \hyperpage{497}
  \item \texttt  {GeneratorsOfIdeal}, \hyperpage{853}
  \item \texttt  {GeneratorsOfInverseMonoid}, \hyperpage{769}
  \item \texttt  {GeneratorsOfInverseSemigroup}, \hyperpage{769}
  \item \texttt  {GeneratorsOfLeftIdeal}, \hyperpage{853}
  \item \texttt  {GeneratorsOfLeftModule}, \hyperpage{868}
  \item \texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Left}\discretionary {-}{}{}\texttt  {Operator}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{868}
  \item \texttt  {GeneratorsOfLeftVectorSpace}, \hyperpage{902}
  \item \texttt  {GeneratorsOfMagma}, \hyperpage{463}
  \item \texttt  {GeneratorsOfMagmaWithInverses}, \hyperpage{464}
  \item \texttt  {GeneratorsOfMagmaWithOne}, \hyperpage{463}
  \item \texttt  {GeneratorsOfMonoid}, \hyperpage{767}
  \item \texttt  {GeneratorsOfNearAdditiveGroup}, \hyperpage{846}
  \item \texttt  {GeneratorsOfNearAdditiveMagma}, \hyperpage{846}
  \item \texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Near}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Zero}, 
		\hyperpage{846}
  \item \texttt  {GeneratorsOfPresentation}, \hyperpage{691}
  \item \texttt  {GeneratorsOfRightIdeal}, \hyperpage{854}
  \item \texttt  {GeneratorsOfRightModule}, \hyperpage{869}
  \item \texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Right}\discretionary {-}{}{}\texttt  {Operator}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{869}
  \item \texttt  {GeneratorsOfRing}, \hyperpage{850}
  \item \texttt  {GeneratorsOfRingWithOne}, \hyperpage{855}
  \item \texttt  {GeneratorsOfRws}, \hyperpage{492}
  \item \texttt  {GeneratorsOfSemigroup}, \hyperpage{763}
  \item \texttt{GeneratorsOf\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{403}
  \item \texttt  {GeneratorsOfTwoSidedIdeal}, \hyperpage{853}
  \item \texttt  {GeneratorsOfVectorSpace}, \hyperpage{902}
  \item \texttt  {GeneratorsPrimeResidues}, \hyperpage{196}
  \item \texttt  {GeneratorsSmallest}, \hyperpage{544}
  \item \texttt  {GeneratorsSubgroupsTom}, \hyperpage{1062}
  \item \texttt  {GeneratorSyllable}, \hyperpage{479}
  \item \texttt  {GetCyclotomicsLimit}, \hyperpage{236}
  \item \texttt  {GetFusionMap}, \hyperpage{1171}
  \item getting help, \hyperpage{28}
  \item \texttt  {GF}
    \subitem for characteristic and degree, \hyperpage{887}
    \subitem for characteristic and polynomial, \hyperpage{887}
    \subitem for field size, \hyperpage{887}
    \subitem for subfield and degree, \hyperpage{887}
    \subitem for subfield and polynomial, \hyperpage{887}
  \item \texttt  {GL}
    \subitem for dimension and a ring, \hyperpage{730}
    \subitem for dimension and field size, \hyperpage{730}
  \item \texttt  {GlobalMersenneTwister}, \hyperpage{193}
  \item \texttt  {GlobalRandomSource}, \hyperpage{193}
  \item \texttt  {GModuleByMats}
    \subitem for empty list, the dimension, and a field, 
		\hyperpage{1033}
    \subitem for generators and a field, \hyperpage{1033}
  \item \texttt  {GO}, \hyperpage{732}
  \item \texttt  {GQuotients}, \hyperpage{566}
  \item \texttt  {Grading}, \hyperpage{939}
  \item graphviz, \hyperpage{539}
  \item \texttt  {GreensDClasses}, \hyperpage{775}
  \item \texttt  {GreensDClassOfElement}, \hyperpage{775}
  \item \texttt  {GreensDRelation}, \hyperpage{774}
  \item \texttt  {GreensHClasses}, \hyperpage{775}
  \item \texttt  {GreensHClassOfElement}, \hyperpage{775}
  \item \texttt  {GreensHRelation}, \hyperpage{774}
  \item \texttt  {GreensJClasses}, \hyperpage{775}
  \item \texttt  {GreensJClassOfElement}, \hyperpage{775}
  \item \texttt  {GreensJRelation}, \hyperpage{774}
  \item \texttt  {GreensLClasses}, \hyperpage{775}
  \item \texttt  {GreensLClassOfElement}, \hyperpage{775}
  \item \texttt  {GreensLRelation}, \hyperpage{774}
  \item \texttt  {GreensRClasses}, \hyperpage{775}
  \item \texttt  {GreensRClassOfElement}, \hyperpage{775}
  \item \texttt  {GreensRRelation}, \hyperpage{774}
  \item \texttt  {GroebnerBasis}
    \subitem for a list and a monomial ordering, \hyperpage{1018}
    \subitem for an ideal and a monomial ordering, \hyperpage{1018}
  \item \texttt  {GroebnerBasisNC}, \hyperpage{1018}
  \item \texttt  {Group}
    \subitem for a list of generators (and an identity element), 
		\hyperpage{497}
    \subitem for several generators, \hyperpage{497}
  \item group actions, \hyperpage{571, 572}
    \subitem operations syntax, \hyperpage{571}
  \item group algebra, \hyperpage{986}
  \item group characters, \hyperpage{1122}
  \item group operations, \hyperpage{572}, \hyperpage{1215}
  \item group ring, \hyperpage{986}
  \item \texttt  {GroupByGenerators}, \hyperpage{497}
    \subitem with explicitly specified identity element, 
		\hyperpage{497}
  \item \texttt  {GroupByRws}, \hyperpage{656}
  \item \texttt  {GroupByRwsNC}, \hyperpage{656}
  \item \texttt  {GroupGeneralMappingByImages}, \hyperpage{555}
    \subitem from group to itself, \hyperpage{555}
  \item \texttt  {GroupGeneralMappingByImagesNC}, \hyperpage{555}
    \subitem from group to itself, \hyperpage{555}
  \item \texttt  {GroupHClassOfGreensDClass}, \hyperpage{775}
  \item \texttt  {GroupHomomorphismByFunction}
    \subitem by function (and inverse function) between two domains, 
		\hyperpage{556}
    \subitem by function and function that computes one preimage, 
		\hyperpage{556}
  \item \texttt  {GroupHomomorphismByImages}, \hyperpage{554}
  \item \texttt  {GroupHomomorphismByImagesNC}, \hyperpage{555}
  \item \texttt  {GroupOfPcgs}, \hyperpage{631}
  \item \texttt  {GroupRing}, \hyperpage{987}
  \item \texttt  {GroupStabChain}, \hyperpage{612}
  \item \texttt  {GroupWithGenerators}, \hyperpage{497}
  \item \texttt  {GrowthFunctionOfGroup}, \hyperpage{504}
    \subitem with word length limit, \hyperpage{504}
  \item \texttt  {GU}, \hyperpage{731}

  \indexspace

  \item $h_N$ (irrational value), \hyperpage{229}
  \item \texttt  {HallSubgroup}, \hyperpage{520}
  \item \texttt  {HallSystem}, \hyperpage{521}
  \item \texttt{HallSystem}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {HasAbelianFactorGroup}, \hyperpage{535}
  \item \texttt  {HasElementaryAbelianFactorGroup}, \hyperpage{535}
  \item \texttt  {HasIndeterminateName}, \hyperpage{995}
  \item \texttt  {HasParent}, \hyperpage{406}
  \item \texttt  {HasseDiagramBinaryRelation}, \hyperpage{446}
  \item \texttt  {HeadPcElementByNumber}, \hyperpage{633}
  \item \texttt  {HEL}\discretionary {-}{}{}\texttt  {P{\textunderscore }}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {D{\textunderscore }}\discretionary {-}{}{}\texttt  {BOOK}, 
		\hyperpage{1290}
  \item \texttt  {HEL}\discretionary {-}{}{}\texttt  {P{\textunderscore }}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {O}\discretionary {-}{}{}\texttt  {V}\discretionary {-}{}{}\texttt  {E{\textunderscore }}\discretionary {-}{}{}\texttt  {BOOK}, 
		\hyperpage{1291}
  \item \texttt  {HEL}\discretionary {-}{}{}\texttt  {P{\textunderscore }}\discretionary {-}{}{}\texttt  {V}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {R{\textunderscore }}\discretionary {-}{}{}\texttt  {INFO}, 
		\hyperpage{1293}
  \item \texttt  {HenselBound}, \hyperpage{1009}
  \item Hermite normal form, \hyperpage{1216}
  \item \texttt  {HermiteNormalFormIntegerMat}, \hyperpage{342}
  \item \texttt  {Hermite}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {Form}\discretionary {-}{}{}\texttt  {Integer}\discretionary {-}{}{}\texttt  {Mat}\discretionary {-}{}{}\texttt  {Transform}, 
		\hyperpage{342}
  \item \texttt  {HeuristicCancelPolynomialsExtRep}, \hyperpage{1025}
  \item \texttt  {HexStringInt}, \hyperpage{361}
  \item \texttt  {HighestWeightModule}, \hyperpage{983}
  \item \texttt  {HMSMSec}, \hyperpage{369}
  \item \texttt  {Hom}, \hyperpage{916}
  \item \texttt  {HomeEnumerator}, \hyperpage{590}
  \item \texttt  {HomomorphismQuotientSemigroup}, \hyperpage{773}
  \item homomorphisms
    \subitem find all, \hyperpage{565}
    \subitem Frobenius, field, \hyperpage{888}
  \item \texttt  {Hypothenuse}, \hyperpage{241}

  \indexspace

  \item $i_N$ (irrational value), \hyperpage{230}
  \item \texttt  {Ideal}, \hyperpage{851}
  \item \texttt  {IdealByGenerators}, \hyperpage{852}
  \item \texttt  {IdealNC}, \hyperpage{852}
  \item \texttt  {Ideals}, \hyperpage{866}
  \item \texttt  {Idempotent}, \hyperpage{797}
  \item \texttt  {Idempotents}, \hyperpage{464}
  \item \texttt  {IdempotentsTom}, \hyperpage{1055}
  \item \texttt  {IdempotentsTomInfo}, \hyperpage{1055}
  \item \texttt  {IdentificationOfConjugacyClasses}, \hyperpage{1077}
  \item \texttt  {Identifier}
    \subitem for character tables, \hyperpage{1086}
    \subitem for tables of marks, \hyperpage{1055}
  \item \texttt  {Identity}, \hyperpage{409}
  \item \texttt  {IdentityBinaryRelation}
    \subitem for a degree, \hyperpage{442}
    \subitem for a domain, \hyperpage{442}
  \item \texttt  {IdentityFromSCTable}, \hyperpage{926}
  \item \texttt  {IdentityMapping}, \hyperpage{427}
  \item \texttt  {IdentityMat}, \hyperpage{320}
  \item \texttt  {IdentityTransformation}, \hyperpage{799}
  \item \texttt  {IdFunc}, \hyperpage{76}
  \item \texttt  {IdGap3SolvableGroup}, \hyperpage{742}
  \item \texttt  {IdGroup}, \hyperpage{741}
  \item \texttt  {IdSmallGroup}, \hyperpage{741}
  \item \texttt  {IdsOfAllSmallGroups}, \hyperpage{742}
  \item \texttt{if} statement, \hyperpage{60}
  \item \texttt  {Image}
    \subitem set of images of a collection under a mapping, 
		\hyperpage{430}
    \subitem set of images of the source of a general mapping, 
		\hyperpage{430}
    \subitem unique image of an element under a mapping, 
		\hyperpage{430}
  \item \texttt{Image}
    \subitem for Frobenius automorphisms, \hyperpage{889}
  \item image
    \subitem vector under matrix, \hyperpage{317}
  \item \texttt  {ImageElm}, \hyperpage{430}
  \item \texttt  {ImageListOfPartialPerm}, \hyperpage{825}
  \item \texttt  {ImageListOfTransformation}, \hyperpage{804}
  \item \texttt  {ImageOfPartialPermCollection}, \hyperpage{824}
  \item \texttt  {Images}
    \subitem set of images of a collection under a mapping, 
		\hyperpage{430}
    \subitem set of images of an element under a mapping, 
		\hyperpage{430}
    \subitem set of images of the source of a general mapping, 
		\hyperpage{430}
  \item \texttt  {ImagesElm}, \hyperpage{429}
  \item \texttt  {ImageSetOfPartialPerm}, \hyperpage{825}
  \item \texttt  {ImageSetOfTransformation}, \hyperpage{804}
  \item \texttt  {ImagesRepresentative}, \hyperpage{429}
  \item \texttt  {ImagesSet}, \hyperpage{430}
  \item \texttt  {ImagesSmallestGenerators}, \hyperpage{559}
  \item \texttt  {ImagesSource}, \hyperpage{429}
  \item \texttt  {ImaginaryPart}, \hyperpage{233}
  \item \texttt  {ImfInvariants}, \hyperpage{758}
  \item \texttt  {ImfMatrixGroup}, \hyperpage{759}
  \item \texttt  {ImfNumberQClasses}, \hyperpage{755}
  \item \texttt  {ImfNumberQQClasses}, \hyperpage{755}
  \item \texttt  {ImfNumberZClasses}, \hyperpage{755}
  \item \texttt  {Immutable}, \hyperpage{160}
  \item \texttt  {ImmutableBasis}, \hyperpage{909}
  \item \texttt  {ImmutableMatrix}, \hyperpage{335}
  \item \texttt  {\texttt  {\char 92\relax }in}
    \subitem element test for lists, \hyperpage{261}
    \subitem for a collection, \hyperpage{395}
    \subitem for strictly sorted lists, \hyperpage{280}
  \item \texttt{\texttt{\symbol{92}}in}
    \subitem operation for testing membership, \hyperpage{395}
  \item \texttt{in}
    \subitem for lists, \hyperpage{261}
    \subitem operation for, \hyperpage{395}
  \item \texttt  {IncreaseInterval}, \hyperpage{241}
  \item \texttt  {IndependentGeneratorExponents}, \hyperpage{546}
  \item \texttt  {IndependentGeneratorsOfAbelianGroup}, \hyperpage{545}
  \item \texttt  {Indeterminate}
    \subitem for a family and a number, \hyperpage{994}
    \subitem for a ring (and a name, and an exclusion list), 
		\hyperpage{994}
    \subitem for a ring (and a number), \hyperpage{994}
  \item \texttt  {IndeterminateName}, \hyperpage{995}
  \item \texttt  {Indeterminateness}, \hyperpage{1181}
  \item \texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Number}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Laurent}\discretionary {-}{}{}\texttt  {Polynomial}, 
		\hyperpage{1010}
  \item \texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Number}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Univariate}\discretionary {-}{}{}\texttt  {Rational}\discretionary {-}{}{}\texttt  {Function}, 
		\hyperpage{995}
  \item \texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Univariate}\discretionary {-}{}{}\texttt  {Rational}\discretionary {-}{}{}\texttt  {Function}, 
		\hyperpage{995}
  \item \texttt  {IndeterminatesOfFunctionField}, \hyperpage{1011}
  \item \texttt  {IndeterminatesOfPolynomialRing}, \hyperpage{1011}
  \item \texttt  {Index}
    \subitem for a group and its subgroup, \hyperpage{499}
    \subitem for two character tables, \hyperpage{1095}
  \item \texttt  {IndexInWholeGroup}, \hyperpage{499}
  \item \texttt  {IndexNC}
    \subitem for a group and its subgroup, \hyperpage{499}
  \item \texttt  {IndexPeriodOfPartialPerm}, \hyperpage{828}
  \item \texttt  {IndexPeriodOfTransformation}, \hyperpage{808}
  \item \texttt  {Indicator}, \hyperpage{1096}
  \item \texttt  {IndicatorOp}, \hyperpage{1096}
  \item \texttt  {IndicesCentralNormalSteps}, \hyperpage{641}
  \item \texttt  {IndicesChiefNormalSteps}, \hyperpage{643}
  \item \texttt  {IndicesEANormalSteps}, \hyperpage{640}
  \item \texttt  {IndicesInvolutaryGenerators}, \hyperpage{674}
  \item \texttt  {IndicesNormalSteps}, \hyperpage{644}
  \item \texttt  {IndicesOfAdjointBasis}, \hyperpage{934}
  \item \texttt  {IndicesPCentralNormalStepsPGroup}, \hyperpage{642}
  \item \texttt  {IndicesStabChain}, \hyperpage{612}
  \item \texttt  {Indirected}, \hyperpage{1177}
  \item \texttt  {InducedAutomorphism}, \hyperpage{564}
  \item \texttt  {InducedClassFunction}
    \subitem for a given monomorphism, \hyperpage{1141}
    \subitem for a supergroup, \hyperpage{1141}
    \subitem for the character table of a supergroup, \hyperpage{1141}
  \item \texttt  {InducedClassFunctions}, \hyperpage{1141}
  \item \texttt  {InducedClassFunctionsByFusionMap}, \hyperpage{1141}
  \item \texttt  {InducedCyclic}, \hyperpage{1142}
  \item \texttt  {InducedPcgs}, \hyperpage{635}
  \item \texttt  {InducedPcgsByGenerators}, \hyperpage{636}
  \item \texttt  {InducedPcgsByGeneratorsNC}, \hyperpage{636}
  \item \texttt  {InducedPcgsByPcSequence}, \hyperpage{635}
  \item \texttt  {Induced}\discretionary {-}{}{}\texttt  {Pcgs}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Pc}\discretionary {-}{}{}\texttt  {Sequence}\discretionary {-}{}{}\texttt  {And}\discretionary {-}{}{}\texttt  {Generators}, 
		\hyperpage{636}
  \item \texttt  {InducedPcgsByPcSequenceNC}, \hyperpage{635}
  \item \texttt  {InducedPcgsWrtFamilyPcgs}, \hyperpage{652}
  \item \texttt  {InducedPcgsWrtSpecialPcgs}, \hyperpage{647}
  \item \texttt  {Inequalities}, \hyperpage{1161}
  \item inequality
    \subitem of booleans, \hyperpage{246}
    \subitem of records, \hyperpage{381}
  \item inequality test, \hyperpage{56}
  \item \texttt  {InertiaSubgroup}, \hyperpage{1137}
  \item \texttt  {Inf}, \hyperpage{241}
  \item \texttt  {infinity}, \hyperpage{228}
  \item inflated class functions, \hyperpage{1140}
  \item \texttt  {Info}, \hyperpage{107}
  \item \texttt  {InfoAlgebra}, \hyperpage{921}
  \item \texttt  {InfoAttributes}, \hyperpage{172}
  \item \texttt  {InfoBckt}, \hyperpage{617}
  \item \texttt  {InfoCharacterTable}, \hyperpage{1075}
  \item \texttt  {InfoCoh}, \hyperpage{549}
  \item \texttt  {InfoComplement}, \hyperpage{516}
  \item \texttt  {InfoCoset}, \hyperpage{511}
  \item \texttt  {InfoFpGroup}, \hyperpage{666}
  \item \texttt  {InfoGroebner}, \hyperpage{1019}
  \item \texttt  {InfoGroup}, \hyperpage{499}
  \item \texttt  {InfoLattice}, \hyperpage{541}
  \item \texttt  {InfoLevel}, \hyperpage{106}
  \item \texttt  {InfoMatrix}, \hyperpage{314}
  \item \texttt  {InfoMonomial}, \hyperpage{1195}
  \item \texttt  {InfoNumtheor}, \hyperpage{195}
  \item \texttt  {InfoObsolete}, \hyperpage{1216}
  \item \texttt  {InfoOptions}, \hyperpage{128}
  \item \texttt  {InfoPackageLoading}, \hyperpage{1206}
  \item \texttt  {InfoPcSubgroup}, \hyperpage{544}
  \item \texttt  {InfoPoly}, \hyperpage{1003}
  \item \texttt  {InfoText}, \hyperpage{163}
    \subitem for character tables, \hyperpage{1086}
  \item \texttt{InfoText}
    \subitem (for Conway polynomials), \hyperpage{889}
  \item \texttt  {InfoTom}, \hyperpage{1051}
  \item \texttt  {InfoWarning}, \hyperpage{108}
  \item \texttt  {Init}, \hyperpage{193}
  \item \texttt  {InitFusion}, \hyperpage{1188}
  \item \texttt  {InitPowerMap}, \hyperpage{1185}
  \item \texttt  {InjectionZeroMagma}, \hyperpage{460}
  \item inner product
    \subitem of group characters, \hyperpage{1135}
  \item \texttt  {InnerAutomorphism}, \hyperpage{561}
  \item \texttt  {InnerAutomorphismNC}, \hyperpage{561}
  \item \texttt  {InnerAutomorphismsAutomorphismGroup}, \hyperpage{564}
  \item \texttt  {InParentFOA}, \hyperpage{1295}
  \item \texttt  {InputFromUser}, \hyperpage{148}
  \item \texttt  {InputLogTo}
    \subitem for a filename, \hyperpage{137}
    \subitem for streams, \hyperpage{145}
    \subitem stop logging input, \hyperpage{137}
  \item \texttt  {InputOutputLocalProcess}, \hyperpage{149}
  \item \texttt  {InputTextFile}, \hyperpage{147}
  \item \texttt  {InputTextNone}, \hyperpage{151}
  \item \texttt  {InputTextString}, \hyperpage{148}
  \item \texttt  {InputTextUser}, \hyperpage{148}
  \item \texttt  {InsertTrivialStabilizer}, \hyperpage{615}
  \item \texttt  {InstallAtExit}, \hyperpage{93}
  \item \texttt  {InstallCharReadHookFunc}, \hyperpage{151}
  \item \texttt  {InstalledPackageVersion}, \hyperpage{1208}
  \item \texttt  {InstallFactorMaintenance}, \hyperpage{417}
  \item \texttt  {InstallFlushableValue}, \hyperpage{1244}
  \item \texttt  {InstallFlushableValueFromFunction}, \hyperpage{1244}
  \item \texttt  {InstallGlobalFunction}, \hyperpage{1243}
  \item \texttt  {InstallHandlingByNiceBasis}, \hyperpage{919}
  \item \texttt  {InstallImmediateMethod}, \hyperpage{1222}
  \item \texttt  {InstallIsomorphismMaintenance}, \hyperpage{417}
  \item \texttt  {InstallMethod}, \hyperpage{1220}
  \item \texttt  {InstallOtherMethod}, \hyperpage{1220}
  \item \texttt{InstallReadlineMacro}, \hyperpage{97}
  \item \texttt  {InstallSubsetMaintenance}, \hyperpage{416}
  \item \texttt  {InstallTrueMethod}, \hyperpage{1223}
  \item \texttt  {InstallValue}, \hyperpage{1244}
  \item \texttt  {Int}, \hyperpage{178}
    \subitem for a cyclotomic, \hyperpage{225}
    \subitem for a FFE, \hyperpage{885}
    \subitem for strings, \hyperpage{366}
  \item \texttt  {IntChar}, \hyperpage{365}
  \item integer part of a quotient, \hyperpage{181}
  \item \texttt  {Integers}
    \subitem global variable, \hyperpage{177}
  \item \texttt  {IntegralizedMat}, \hyperpage{346}
  \item \texttt  {IntegratedStraightLineProgram}, \hyperpage{486}
  \item \texttt  {IntermediateGroup}, \hyperpage{533}
  \item \texttt  {IntermediateResultOfSLP}, \hyperpage{487}
  \item \texttt  {Intermediate}\discretionary {-}{}{}\texttt  {Result}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {P}\discretionary {-}{}{}\texttt  {Without}\discretionary {-}{}{}\texttt  {Overwrite}, 
		\hyperpage{487}
  \item \texttt  {Intermediate}\discretionary {-}{}{}\texttt  {Results}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {P}\discretionary {-}{}{}\texttt  {Without}\discretionary {-}{}{}\texttt  {Overwrite}, 
		\hyperpage{487}
  \item \texttt  {IntermediateSubgroups}, \hyperpage{533}
  \item \texttt  {InterpolatedPolynomial}, \hyperpage{864}
  \item \texttt  {IntersectBlist}, \hyperpage{301}
  \item \texttt  {Intersection}
    \subitem for a list, \hyperpage{394}
    \subitem for various collections, \hyperpage{394}
  \item \texttt{Intersection}
    \subitem for groups with pcgs, \hyperpage{649}
  \item intersection
    \subitem of collections, \hyperpage{394}
    \subitem of sets, \hyperpage{282}
  \item \texttt  {Intersection2}, \hyperpage{394}
  \item \texttt  {IntersectionBlist}
    \subitem for a list, \hyperpage{300}
    \subitem for various boolean lists, \hyperpage{300}
  \item \texttt  {IntersectionsTom}, \hyperpage{1060}
  \item \texttt  {IntersectSet}, \hyperpage{282}
  \item \texttt  {IntFFE}, \hyperpage{885}
  \item \texttt  {IntFFESymm}
    \subitem for a FFE, \hyperpage{886}
    \subitem for a vector of FFEs, \hyperpage{886}
  \item \texttt  {IntHexString}, \hyperpage{366}
  \item \texttt  {IntScalarProducts}, \hyperpage{1182}
  \item \texttt  {IntVecFFE}, \hyperpage{886}
  \item \texttt  {InvariantBilinearForm}, \hyperpage{623}
  \item \texttt  {InvariantElementaryAbelianSeries}, \hyperpage{532}
  \item \texttt  {InvariantLattice}, \hyperpage{625}
  \item \texttt  {InvariantQuadraticForm}, \hyperpage{623}
  \item \texttt  {InvariantSesquilinearForm}, \hyperpage{623}
  \item \texttt  {Invariant}\discretionary {-}{}{}\texttt  {Subgroups}\discretionary {-}{}{}\texttt  {Elementary}\discretionary {-}{}{}\texttt  {Abelian}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{542}
  \item Inverse
    \subitem group homomorphism, \hyperpage{557}
  \item \texttt  {Inverse}, \hyperpage{411}
    \subitem for a pcword, \hyperpage{653}
    \subitem for a transformation, \hyperpage{808}
  \item inverse
    \subitem matrix, \hyperpage{317}
    \subitem of class function, \hyperpage{1127}
  \item \texttt  {InverseAttr}, \hyperpage{411}
  \item \texttt  {InverseClasses}, \hyperpage{1086}
  \item \texttt  {InverseGeneralMapping}, \hyperpage{425}
  \item \texttt  {InverseImmutable}, \hyperpage{411}
  \item \texttt  {InverseMap}, \hyperpage{1176}
  \item \texttt  {InverseMatMod}, \hyperpage{337}
  \item \texttt  {InverseMonoid}, \hyperpage{768}
  \item \texttt  {InverseMutable}, \hyperpage{411}
  \item \texttt  {InverseOfTransformation}, \hyperpage{808}
  \item \texttt  {InverseOp}, \hyperpage{411}
  \item \texttt  {InverseRepresentative}, \hyperpage{613}
  \item \texttt  {InverseSameMutability}, \hyperpage{411}
  \item \texttt  {InverseSemigroup}, \hyperpage{768}
  \item \texttt  {InverseSM}, \hyperpage{411}
  \item \texttt  {InversesOfSemigroupElement}, \hyperpage{770}
  \item \texttt{InvocationReadlineMacro}, \hyperpage{97}
  \item \texttt  {Irr}
    \subitem for a character table, \hyperpage{1080}
    \subitem for a group, \hyperpage{1080}
  \item irrationalities, \hyperpage{223}
  \item \texttt  {IrrBaumClausen}, \hyperpage{1103}
  \item \texttt  {IrrConlon}, \hyperpage{1103}
  \item \texttt  {IrrDixonSchneider}, \hyperpage{1103}
  \item irreducible character, \hyperpage{1134}
  \item irreducible characters
    \subitem computation, \hyperpage{1106}
  \item \texttt  {IrreducibleDifferences}, \hyperpage{1143}
  \item \texttt  {IrreducibleModules}, \hyperpage{1105}
  \item \texttt{IrreducibleModules}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {IrreducibleRepresentations}, \hyperpage{1104}
  \item \texttt  {IrreducibleRepresentationsDixon}, \hyperpage{1105}
  \item \texttt  {IrreducibleSolvableGroup}, \hyperpage{753}
  \item \texttt  {IrreducibleSolvableGroupMS}, \hyperpage{752}
  \item \texttt  {Is16BitsFamily}, \hyperpage{481}
  \item \texttt  {Is32BitsFamily}, \hyperpage{481}
  \item \texttt  {IsAbelian}, \hyperpage{465}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsAbelianNumberField}, \hyperpage{894}
  \item \texttt  {IsAbelianNumberFieldPolynomialRing}, \hyperpage{1012}
  \item \texttt  {IsAbelianTom}, \hyperpage{1057}
  \item \texttt  {IsAdditiveElement}, \hyperpage{418}
  \item \texttt  {IsAdditiveElementWithInverse}, \hyperpage{419}
  \item \texttt  {IsAdditiveElementWithZero}, \hyperpage{418}
  \item \texttt  {IsAdditiveGroup}, \hyperpage{843}
  \item \texttt  {IsAdditiveGroupGeneralMapping}, \hyperpage{436}
  \item \texttt  {IsAdditiveGroupHomomorphism}, \hyperpage{436}
  \item \texttt  {IsAdditivelyCommutative}, \hyperpage{846}
  \item \texttt  {IsAdditivelyCommutativeElement}, \hyperpage{422}
  \item \texttt  {IsAdditively}\discretionary {-}{}{}\texttt  {Commutative}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Coll}\discretionary {-}{}{}\texttt  {Coll}, 
		\hyperpage{422}
  \item \texttt  {IsAdditively}\discretionary {-}{}{}\texttt  {Commutative}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Collection}, 
		\hyperpage{422}
  \item \texttt  {IsAdditively}\discretionary {-}{}{}\texttt  {Commutative}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Family}, 
		\hyperpage{422}
  \item \texttt  {IsAdditiveMagma}, \hyperpage{843}
  \item \texttt  {IsAdditiveMagmaWithInverses}, \hyperpage{843}
  \item \texttt  {IsAdditiveMagmaWithZero}, \hyperpage{843}
  \item \texttt  {IsAlgebra}, \hyperpage{931}
  \item \texttt  {IsAlgebraGeneralMapping}, \hyperpage{438}
  \item \texttt  {IsAlgebraHomomorphism}, \hyperpage{438}
  \item \texttt  {IsAlgebraicElement}, \hyperpage{1028}
  \item \texttt  {IsAlgebraicExtension}, \hyperpage{1026}
  \item \texttt  {IsAlgebraModuleElement}, \hyperpage{948}
  \item \texttt  {IsAlgebraModuleElementCollection}, \hyperpage{948}
  \item \texttt  {IsAlgebraModuleElementFamily}, \hyperpage{948}
  \item \texttt  {IsAlgebraWithOne}, \hyperpage{931}
  \item \texttt  {IsAlgebraWithOneGeneralMapping}, \hyperpage{438}
  \item \texttt  {IsAlgebraWithOneHomomorphism}, \hyperpage{438}
  \item \texttt  {IsAlmostSimple}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsAlmostSimpleGroup}, \hyperpage{523}
  \item \texttt  {IsAlphaChar}, \hyperpage{358}
  \item \texttt  {IsAlternatingGroup}, \hyperpage{603}
  \item \texttt  {IsAnticommutative}, \hyperpage{857}
  \item \texttt  {IsAntisymmetricBinaryRelation}, \hyperpage{443}
  \item \texttt  {IsAssociated}, \hyperpage{858}
  \item \texttt  {IsAssociative}, \hyperpage{465}
  \item \texttt  {IsAssociativeElement}, \hyperpage{421}
  \item \texttt  {IsAssociativeElementCollColl}, \hyperpage{421}
  \item \texttt  {IsAssociativeElementCollection}, \hyperpage{421}
  \item \texttt  {IsAssocWord}, \hyperpage{474}
  \item \texttt  {IsAssocWordWithInverse}, \hyperpage{474}
  \item \texttt  {IsAssocWordWithOne}, \hyperpage{474}
  \item \texttt{IsAttributeStoringRep}, \hyperpage{1251}
  \item \texttt  {IsAutomorphismGroup}, \hyperpage{563}
  \item \texttt  {IsBasicWreathLessThanOrEqual}, \hyperpage{476}
  \item \texttt  {IsBasicWreathProductOrdering}, \hyperpage{455}
  \item \texttt  {IsBasis}, \hyperpage{904}
  \item \texttt  {IsBasisByNiceBasis}, \hyperpage{919}
  \item \texttt  {IsBasisOfAlgebraModuleElementSpace}, \hyperpage{949}
  \item \texttt  {IsBergerCondition}
    \subitem for a character, \hyperpage{1195}
    \subitem for a group, \hyperpage{1195}
  \item \texttt  {IsBijective}, \hyperpage{428}
  \item \texttt  {IsBinaryRelation}, \hyperpage{442}
  \item \texttt{IsBinaryRelation}
    \subitem same as IsEndoGeneralMapping, \hyperpage{442}
  \item \texttt  {IsBLetterAssocWordRep}, \hyperpage{480}
  \item \texttt  {IsBLetterWordsFamily}, \hyperpage{480}
  \item \texttt  {IsBlist}, \hyperpage{298}
  \item \texttt  {IsBlistRep}, \hyperpage{302}
  \item IsBlockMatrixRep, \hyperpage{338}
  \item \texttt  {IsBool}, \hyperpage{245}
  \item \texttt  {IsBound}
    \subitem for a global variable, \hyperpage{51}
    \subitem for a list index, \hyperpage{257}
    \subitem for a record component, \hyperpage{382}
    \subitem for multiple indices, \hyperpage{257}
  \item \texttt  {IsBound\texttt  {\char 92\relax }.}, \hyperpage{383}
  \item \texttt  {IsBound\texttt  {\char 92\relax }[\texttt  {\char 92\relax }]}, 
		\hyperpage{251}
  \item \texttt  {IsBoundElmWPObj}, \hyperpage{1301}
  \item \texttt  {IsBoundGlobal}, \hyperpage{52}
  \item \texttt  {IsBrauerTable}, \hyperpage{1074}
  \item \texttt  {IsBravaisGroup}, \hyperpage{626}
  \item \texttt  {IsBuilt}\discretionary {-}{}{}\texttt  {From}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Inverses}, 
		\hyperpage{493}
  \item \texttt  {IsBuiltFromGroup}, \hyperpage{493}
  \item \texttt  {IsBuiltFromMagma}, \hyperpage{493}
  \item \texttt  {IsBuiltFromMagmaWithInverses}, \hyperpage{493}
  \item \texttt  {IsBuiltFromMagmaWithOne}, \hyperpage{493}
  \item \texttt  {IsBuiltFromSemigroup}, \hyperpage{493}
  \item \texttt  {IsCanonicalBasis}, \hyperpage{907}
  \item \texttt  {IsCanonicalBasisFullMatrixModule}, \hyperpage{913}
  \item \texttt  {IsCanonicalBasisFullRowModule}, \hyperpage{913}
  \item \texttt  {IsCanonicalNiceMonomorphism}, \hyperpage{561}
  \item \texttt  {IsCanonicalPcgs}, \hyperpage{637}
  \item \texttt  {IsCentral}, \hyperpage{465}
  \item \texttt  {IsCentralFactor}, \hyperpage{550}
  \item \texttt  {IsChar}, \hyperpage{352}
  \item \texttt  {IsCharacter}, \hyperpage{1134}
  \item \texttt  {IsCharacteristicSubgroup}, \hyperpage{501}
  \item \texttt  {IsCharacterTable}, \hyperpage{1074}
  \item \texttt  {IsCharacterTableInProgress}, \hyperpage{1074}
  \item \texttt  {IsCharCollection}, \hyperpage{352}
  \item \texttt  {IsCheapConwayPolynomial}, \hyperpage{890}
  \item \texttt  {IsClassFunction}, \hyperpage{1124}
  \item \texttt  {IsClassFusionOfNormalSubgroup}, \hyperpage{1096}
  \item \texttt  {IsClosedStream}, \hyperpage{139}
  \item \texttt  {IsCochain}, \hyperpage{978}
  \item \texttt  {IsCochainCollection}, \hyperpage{978}
  \item \texttt  {IsCollection}, \hyperpage{384}
  \item \texttt  {IsCollectionFamily}, \hyperpage{385}
  \item \texttt  {IsCommutative}, \hyperpage{465}
  \item \texttt  {IsCommutativeElement}, \hyperpage{422}
  \item \texttt  {IsCommutativeElementCollColl}, \hyperpage{422}
  \item \texttt  {IsCommutativeElementCollection}, \hyperpage{422}
  \item \texttt{IsComponentObjectRep}, \hyperpage{1251}
  \item \texttt  {IsCompositionMappingRep}, \hyperpage{426}
  \item \texttt  {IsConfluent}
    \subitem for a rewriting system, \hyperpage{491}
    \subitem for an algebra with canonical rewriting system, 
		\hyperpage{491}
    \subitem for pc groups, \hyperpage{656}
  \item \texttt  {IsConjugacy}\discretionary {-}{}{}\texttt  {Class}\discretionary {-}{}{}\texttt  {Subgroups}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {StabilizerRep}, 
		\hyperpage{536}
  \item \texttt  {IsConjugacyClassSubgroupsRep}, \hyperpage{536}
  \item \texttt  {IsConjugate}
    \subitem for a group and two elements, \hyperpage{514}
    \subitem for a group and two groups, \hyperpage{514}
  \item \texttt  {IsConjugatorAutomorphism}, \hyperpage{562}
  \item \texttt  {IsConjugatorIsomorphism}, \hyperpage{562}
  \item \texttt  {IsConstantRationalFunction}, \hyperpage{1000}
  \item \texttt  {IsConstantTimeAccessGeneralMapping}, \hyperpage{438}
  \item \texttt  {IsConstantTimeAccessList}, \hyperpage{251}
  \item \texttt  {IsContainedInSpan}, \hyperpage{910}
  \item \texttt  {IsCopyable}, \hyperpage{159}
  \item \texttt  {IsCyc}, \hyperpage{224}
  \item \texttt  {IsCyclic}, \hyperpage{522}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsCyclicTom}, \hyperpage{1057}
  \item \texttt  {IsCyclotomic}, \hyperpage{224}
  \item \texttt  {IsCyclotomicField}, \hyperpage{894}
  \item \texttt  {IsCyclotomicMatrixGroup}, \hyperpage{625}
  \item \texttt  {IsDenseList}, \hyperpage{250}
  \item \texttt  {IsDiagonalMat}, \hyperpage{319}
  \item \texttt  {IsDictionary}, \hyperpage{374}
  \item \texttt  {IsDigitChar}, \hyperpage{358}
  \item \texttt  {IsDirectory}, \hyperpage{131}
  \item \texttt  {IsDirectoryPath}, \hyperpage{135}
  \item \texttt  {IsDirectProductElement}, \hyperpage{424}
  \item \texttt  {IsDisjoint}, \hyperpage{241}
  \item \texttt  {IsDistributive}, \hyperpage{857}
  \item \texttt  {IsDivisionRing}, \hyperpage{874}
  \item \texttt  {IsDomain}, \hyperpage{407}
  \item \texttt  {IsDoneIterator}, \hyperpage{398}
  \item \texttt  {IsDoubleCoset}
    \subitem operation, \hyperpage{510}
  \item \texttt  {IsDuplicateFree}, \hyperpage{276}
  \item \texttt  {IsDuplicateFreeList}, \hyperpage{276}
  \item \texttt  {IsDxLargeGroup}, \hyperpage{1108}
  \item \texttt  {IsElementaryAbelian}, \hyperpage{522}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsElementOfFpMonoid}, \hyperpage{786}
  \item \texttt  {IsElementOfFpSemigroup}, \hyperpage{786}
  \item \texttt  {IsElementOfFreeMagmaRing}, \hyperpage{989}
  \item \texttt  {IsElementOfFreeMagmaRingCollection}, \hyperpage{989}
  \item \texttt  {IsElementOfFreeMagmaRingFamily}, \hyperpage{989}
  \item \texttt  {IsElementOfMagmaRingModuloRelations}, \hyperpage{990}
  \item \texttt  {IsElement}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Modulo}\discretionary {-}{}{}\texttt  {Relations}\discretionary {-}{}{}\texttt  {Collection}, 
		\hyperpage{990}
  \item \texttt  {IsElement}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Modulo}\discretionary {-}{}{}\texttt  {Relations}\discretionary {-}{}{}\texttt  {Family}, 
		\hyperpage{990}
  \item \texttt  {IsElement}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Modulo}\discretionary {-}{}{}\texttt  {Span}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Zero}\discretionary {-}{}{}\texttt  {Family}, 
		\hyperpage{991}
  \item \texttt  {IsEmpty}, \hyperpage{391}
  \item \texttt  {IsEmptyString}, \hyperpage{357}
  \item \texttt  {IsEndOfStream}, \hyperpage{143}
  \item \texttt  {IsEndoGeneralMapping}, \hyperpage{439}
  \item \texttt{IsEndoGeneralMapping}
    \subitem same as IsBinaryRelation, \hyperpage{442}
  \item \texttt  {IsEqualSet}, \hyperpage{280}
  \item \texttt  {IsEquivalenceClass}, \hyperpage{448}
  \item \texttt  {IsEquivalenceRelation}, \hyperpage{444}
  \item \texttt  {IsEuclideanRing}, \hyperpage{860}
  \item \texttt  {IsEvenInt}, \hyperpage{179}
  \item \texttt  {IsExecutableFile}, \hyperpage{135}
  \item \texttt  {IsExistingFile}, \hyperpage{134}
  \item \texttt  {IsExtAElement}, \hyperpage{418}
  \item \texttt  {IsExternalOrbit}, \hyperpage{590}
  \item \texttt  {IsExternalSet}, \hyperpage{589}
  \item \texttt  {IsExternalSubset}, \hyperpage{590}
  \item \texttt  {IsExtLElement}, \hyperpage{419}
  \item \texttt  {IsExtRElement}, \hyperpage{419}
  \item \texttt  {IsFamilyPcgs}, \hyperpage{652}
  \item \texttt  {IsFFE}, \hyperpage{882}
  \item \texttt  {IsFFECollColl}, \hyperpage{882}
  \item \texttt  {IsFFECollCollColl}, \hyperpage{882}
  \item \texttt  {IsFFECollection}, \hyperpage{882}
  \item \texttt  {IsFFEMatrixGroup}, \hyperpage{620}
  \item \texttt  {IsField}, \hyperpage{874}
  \item \texttt{IsFieldControlledByGaloisGroup}, \hyperpage{878}
  \item \texttt  {IsFieldHomomorphism}, \hyperpage{438}
  \item \texttt  {IsFinite}, \hyperpage{391}
    \subitem float, \hyperpage{242}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsFiniteDimensional}, \hyperpage{872}
    \subitem for matrix algebras, \hyperpage{932}
  \item \texttt  {IsFiniteFieldPolynomialRing}, \hyperpage{1012}
  \item \texttt  {IsFinitelyGeneratedGroup}, \hyperpage{527}
  \item \texttt  {IsFiniteOrderElement}, \hyperpage{422}
  \item \texttt  {IsFiniteOrderElementCollColl}, \hyperpage{422}
  \item \texttt  {IsFiniteOrderElementCollection}, \hyperpage{422}
  \item \texttt  {IsFiniteOrdersPcgs}, \hyperpage{630}
  \item \texttt  {IsFixedStabilizer}, \hyperpage{615}
  \item \texttt  {IsFLMLOR}, \hyperpage{930}
  \item \texttt  {IsFLMLORWithOne}, \hyperpage{930}
  \item \texttt  {IsFpGroup}, \hyperpage{665}
  \item \texttt  {IsFpMonoid}, \hyperpage{786}
  \item \texttt  {IsFpSemigroup}, \hyperpage{786}
  \item \texttt  {IsFreeGroup}, \hyperpage{474}
  \item \texttt  {IsFreeLeftModule}, \hyperpage{871}
  \item \texttt  {IsFreeMagmaRing}, \hyperpage{987}
  \item \texttt  {IsFreeMagmaRingWithOne}, \hyperpage{988}
  \item \texttt  {IsFromFpGroupGeneralMappingByImages}, \hyperpage{570}
  \item \texttt  {IsFromFpGroupHomomorphismByImages}, \hyperpage{570}
  \item \texttt  {IsFrom}\discretionary {-}{}{}\texttt  {Fp}\discretionary {-}{}{}\texttt  {Group}\discretionary {-}{}{}\texttt  {Std}\discretionary {-}{}{}\texttt  {Gens}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Images}, 
		\hyperpage{570}
  \item \texttt  {IsFrom}\discretionary {-}{}{}\texttt  {Fp}\discretionary {-}{}{}\texttt  {Group}\discretionary {-}{}{}\texttt  {Std}\discretionary {-}{}{}\texttt  {Gens}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Images}, 
		\hyperpage{570}
  \item \texttt  {IsFullHomModule}, \hyperpage{916}
  \item \texttt  {IsFullMatrixModule}, \hyperpage{873}
  \item \texttt  {IsFullRowModule}, \hyperpage{873}
  \item \texttt  {IsFull}\discretionary {-}{}{}\texttt  {Subgroup}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {Lor}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {Respecting}\discretionary {-}{}{}\texttt  {Bilinear}\discretionary {-}{}{}\texttt  {Form}, 
		\hyperpage{623}
  \item \texttt  {IsFull}\discretionary {-}{}{}\texttt  {Subgroup}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {Lor}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {Respecting}\discretionary {-}{}{}\texttt  {Quadratic}\discretionary {-}{}{}\texttt  {Form}, 
		\hyperpage{624}
  \item \texttt  {IsFull}\discretionary {-}{}{}\texttt  {Subgroup}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {Lor}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {Respecting}\discretionary {-}{}{}\texttt  {Sesquilinear}\discretionary {-}{}{}\texttt  {Form}, 
		\hyperpage{623}
  \item \texttt  {IsFullTransformationMonoid}, \hyperpage{814}
  \item \texttt  {IsFullTransformationSemigroup}, \hyperpage{814}
  \item \texttt  {IsFunction}, \hyperpage{76}
  \item \texttt  {IsFunctionField}, \hyperpage{1013}
  \item \texttt  {IsGAPRandomSource}, \hyperpage{193}
  \item \texttt  {IsGaussianIntegers}, \hyperpage{899}
  \item \texttt  {IsGaussianRationals}, \hyperpage{893}
  \item \texttt  {IsGaussianSpace}, \hyperpage{911}
  \item \texttt  {IsGaussInt}, \hyperpage{227}
  \item \texttt  {IsGaussRat}, \hyperpage{228}
  \item \texttt  {IsGeneralizedDomain}, \hyperpage{407}
  \item \texttt  {IsGeneralizedRowVector}, \hyperpage{264}
  \item \texttt  {IsGeneralLinearGroup}, \hyperpage{622}
  \item \texttt  {IsGeneralMapping}, \hyperpage{438}
  \item \texttt  {IsGeneralMappingFamily}, \hyperpage{440}
  \item \texttt  {IsGeneratorsOfSemigroup}, \hyperpage{764}
  \item \texttt{IsGeneratorsOf\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{403}
  \item \texttt  {IsGL}, \hyperpage{622}
  \item \texttt  {IsGlobalRandomSource}, \hyperpage{193}
  \item \texttt  {IsGreensClass}, \hyperpage{774}
  \item \texttt  {IsGreensDClass}, \hyperpage{774}
  \item \texttt  {IsGreensDRelation}, \hyperpage{774}
  \item \texttt  {IsGreensHClass}, \hyperpage{774}
  \item \texttt  {IsGreensHRelation}, \hyperpage{774}
  \item \texttt  {IsGreensJClass}, \hyperpage{774}
  \item \texttt  {IsGreensJRelation}, \hyperpage{774}
  \item \texttt  {IsGreensLClass}, \hyperpage{774}
  \item \texttt  {IsGreensLessThanOrEqual}, \hyperpage{774}
  \item \texttt  {IsGreensLRelation}, \hyperpage{774}
  \item \texttt  {IsGreensRClass}, \hyperpage{774}
  \item \texttt  {IsGreensRelation}, \hyperpage{774}
  \item \texttt  {IsGreensRRelation}, \hyperpage{774}
  \item \texttt  {IsGroup}, \hyperpage{498}
  \item \texttt  {IsGroupGeneralMapping}, \hyperpage{435}
  \item \texttt  {IsGroup}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {As}\discretionary {-}{}{}\texttt  {Group}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Images}, 
		\hyperpage{569}
  \item \texttt  {IsGroupGeneralMappingByImages}, \hyperpage{569}
  \item \texttt  {IsGroupGeneralMappingByPcgs}, \hyperpage{570}
  \item \texttt  {IsGroupHClass}, \hyperpage{776}
  \item \texttt  {IsGroupHomomorphism}, \hyperpage{435}
  \item \texttt  {IsGroupOfAutomorphisms}, \hyperpage{563}
  \item \texttt  {IsGroupRing}, \hyperpage{988}
  \item \texttt  {IsHandledByNiceBasis}, \hyperpage{919}
  \item \texttt  {IsHandledByNiceMonomorphism}, \hyperpage{560}
  \item \texttt  {IsHasseDiagram}, \hyperpage{444}
  \item \texttt  {IsHomogeneousList}, \hyperpage{250}
  \item \texttt  {IsIdempotent}, \hyperpage{411}
  \item \texttt  {IsIdenticalObj}, \hyperpage{157}
  \item \texttt  {IsIncomparableUnder}, \hyperpage{451}
  \item \texttt  {IsInducedFromNormalSubgroup}, \hyperpage{1198}
  \item \texttt  {IsInducedPcgs}, \hyperpage{635}
  \item \texttt  {IsInducedPcgsWrtSpecialPcgs}, \hyperpage{647}
  \item \texttt  {IsInfBitsFamily}, \hyperpage{481}
  \item \texttt  {IsInfiniteAbelianizationGroup}, \hyperpage{688}
  \item \texttt{IsInfiniteAbelianizationGroup}
    \subitem for groups, \hyperpage{688}
  \item \texttt  {IsInfinity}, \hyperpage{228}
  \item \texttt  {IsInjective}, \hyperpage{428}
  \item \texttt  {IsInjectiveListTrans}, \hyperpage{802}
  \item \texttt  {IsInnerAutomorphism}, \hyperpage{562}
  \item \texttt  {IsInputOutputStream}, \hyperpage{149}
  \item \texttt  {IsInputStream}, \hyperpage{140}
  \item \texttt  {IsInputTextNone}, \hyperpage{140}
  \item \texttt  {IsInputTextStream}, \hyperpage{140}
  \item \texttt  {IsInt}, \hyperpage{178}
  \item \texttt  {IsIntegerMatrixGroup}, \hyperpage{625}
  \item \texttt  {IsIntegers}, \hyperpage{178}
  \item \texttt  {IsIntegralBasis}, \hyperpage{908}
  \item \texttt  {IsIntegralCyclotomic}, \hyperpage{224}
  \item \texttt  {IsIntegralRing}, \hyperpage{856}
  \item \texttt  {IsInternallyConsistent}, \hyperpage{163}
    \subitem for character tables, \hyperpage{1095}
    \subitem for tables of marks, \hyperpage{1057}
  \item \texttt  {IsInverseMonoid}, \hyperpage{771}
  \item \texttt  {IsInverseSemigroup}, \hyperpage{771}
  \item \texttt  {IsInverseSubsemigroup}, \hyperpage{769}
  \item \texttt  {IsIrreducibleCharacter}, \hyperpage{1134}
  \item \texttt  {IsIrreducibleRingElement}, \hyperpage{859}
  \item \texttt  {IsIterator}, \hyperpage{398}
  \item \texttt  {IsJacobianElement}, \hyperpage{422}
  \item \texttt  {IsJacobianElementCollColl}, \hyperpage{422}
  \item \texttt  {IsJacobianElementCollection}, \hyperpage{422}
  \item \texttt  {IsJacobianRing}, \hyperpage{857}
  \item \texttt  {IsLaurentPolynomial}, \hyperpage{1000}
  \item \texttt  {IsLaurentPolynomialDefaultRep}, \hyperpage{1023}
  \item \texttt  {IsLDistributive}, \hyperpage{856}
  \item \texttt  {IsLeftAlgebraModuleElement}, \hyperpage{948}
  \item \texttt  {IsLeft}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Collection}, 
		\hyperpage{948}
  \item \texttt  {IsLeftIdeal}, \hyperpage{852}
  \item \texttt  {IsLeftIdealInParent}, \hyperpage{852}
  \item \texttt  {IsLeftModule}, \hyperpage{868}
  \item \texttt  {IsLeftModuleGeneralMapping}, \hyperpage{437}
  \item \texttt  {IsLeftModuleHomomorphism}, \hyperpage{437}
  \item \texttt  {IsLeftOperatorAdditiveGroup}, \hyperpage{868}
  \item \texttt  {IsLeftSemigroupIdeal}, \hyperpage{772}
  \item \texttt  {IsLeftVectorSpace}, \hyperpage{900}
  \item \texttt  {IsLessThanOrEqualUnder}, \hyperpage{452}
  \item \texttt  {IsLessThanUnder}, \hyperpage{452}
  \item \texttt  {IsLetterAssocWordRep}, \hyperpage{480}
  \item \texttt  {IsLetterWordsFamily}, \hyperpage{480}
  \item \texttt  {IsLexicographicallyLess}, \hyperpage{285}
  \item \texttt  {IsLexOrderedFFE}, \hyperpage{884}
  \item \texttt  {IsLieAbelian}, \hyperpage{964}
  \item \texttt  {IsLieAlgebra}, \hyperpage{931}
  \item \texttt  {IsLieMatrix}, \hyperpage{315}
  \item \texttt  {IsLieNilpotent}, \hyperpage{964}
  \item \texttt  {IsLieObject}, \hyperpage{957}
  \item \texttt  {IsLieObjectCollection}, \hyperpage{957}
  \item \texttt  {IsLieSolvable}, \hyperpage{965}
  \item \texttt  {IsLinearMapping}, \hyperpage{437}
  \item \texttt  {IsLinearMappingsModule}, \hyperpage{917}
  \item \texttt  {IsLineByLineProfileActive}, \hyperpage{118}
  \item \texttt  {IsList}, \hyperpage{249}
  \item \texttt  {IsListDefault}, \hyperpage{264}
  \item \texttt  {IsListOrCollection}, \hyperpage{386}
  \item \texttt  {IsLogOrderedFFE}, \hyperpage{884}
  \item \texttt  {IsLookupDictionary}, \hyperpage{374}
  \item \texttt  {IsLowerAlphaChar}, \hyperpage{358}
  \item \texttt  {IsLowerTriangularMat}, \hyperpage{319}
  \item \texttt  {IsMagma}, \hyperpage{457}
  \item \texttt  {IsMagmaHomomorphism}, \hyperpage{434}
  \item \texttt  {IsMagmaRingModuloRelations}, \hyperpage{991}
  \item \texttt  {IsMagmaRingModuloSpanOfZero}, \hyperpage{991}
  \item \texttt  {IsMagmaRingObjDefaultRep}, \hyperpage{988}
  \item \texttt  {IsMagmaWithInverses}, \hyperpage{458}
  \item \texttt  {IsMagmaWithInversesIfNonzero}, \hyperpage{457}
  \item \texttt  {IsMagmaWithOne}, \hyperpage{457}
  \item \texttt  {IsMagmaWithZeroAdjoined}, \hyperpage{460}
  \item \texttt  {IsMapping}, \hyperpage{428}
  \item \texttt  {IsMatchingSublist}, \hyperpage{276}
  \item \texttt  {IsMatrix}, \hyperpage{314}
  \item \texttt  {IsMatrixGroup}, \hyperpage{619}
  \item \texttt  {IsMatrixModule}, \hyperpage{873}
  \item \texttt  {IsMatrixSpace}, \hyperpage{911}
  \item \texttt  {IsMersenneTwister}, \hyperpage{193}
  \item \texttt  {IsMinimalNonmonomial}, \hyperpage{1202}
  \item \texttt  {IsModuloPcgs}, \hyperpage{637}
  \item \texttt  {IsMonoid}, \hyperpage{766}
  \item \texttt  {IsMonomial}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt{IsMonomial}
    \subitem for positive integers, \hyperpage{1199}
  \item \texttt  {IsMonomialGroup}, \hyperpage{523}
  \item \texttt  {IsMonomialMatrix}, \hyperpage{319}
  \item \texttt  {IsMonomialNumber}, \hyperpage{1199}
  \item \texttt  {IsMonomialOrdering}, \hyperpage{1014}
  \item \texttt  {IsMultiplicativeElement}, \hyperpage{419}
  \item \texttt  {IsMultiplicativeElementWithInverse}, \hyperpage{420}
  \item \texttt  {IsMultiplicativeElementWithOne}, \hyperpage{419}
  \item \texttt  {IsMultiplicativeElementWithZero}, \hyperpage{419}
  \item \texttt  {IsMultiplicative}\discretionary {-}{}{}\texttt  {Generalized}\discretionary {-}{}{}\texttt  {Row}\discretionary {-}{}{}\texttt  {Vector}, 
		\hyperpage{264}
  \item \texttt  {IsMultiplicativeZero}, \hyperpage{465}
  \item \texttt  {IsMutable}, \hyperpage{159}
  \item \texttt  {IsMutableBasis}, \hyperpage{909}
  \item \texttt  {IsNaN}, \hyperpage{242}
  \item \texttt  {IsNaturalAlternatingGroup}, \hyperpage{602}
  \item \texttt  {IsNaturalGL}, \hyperpage{622}
  \item \texttt  {IsNaturalGLnZ}, \hyperpage{625}
  \item \texttt  {IsNaturalSL}, \hyperpage{622}
  \item \texttt  {IsNaturalSLnZ}, \hyperpage{625}
  \item \texttt  {IsNaturalSymmetricGroup}, \hyperpage{602}
  \item \texttt  {IsNearAdditiveElement}, \hyperpage{418}
  \item \texttt  {IsNearAdditiveElementWithInverse}, \hyperpage{418}
  \item \texttt  {IsNearAdditiveElementWithZero}, \hyperpage{418}
  \item \texttt  {IsNearAdditiveGroup}, \hyperpage{842}
  \item \texttt  {IsNearAdditiveMagma}, \hyperpage{842}
  \item \texttt  {IsNearAdditiveMagmaWithInverses}, \hyperpage{842}
  \item \texttt  {IsNearAdditiveMagmaWithZero}, \hyperpage{842}
  \item \texttt  {IsNearlyCharacterTable}, \hyperpage{1074}
  \item \texttt  {IsNearRingElement}, \hyperpage{420}
  \item \texttt  {IsNearRingElementWithInverse}, \hyperpage{421}
  \item \texttt  {IsNearRingElementWithOne}, \hyperpage{420}
  \item \texttt  {IsNegInfinity}, \hyperpage{228}
  \item \texttt  {IsNegRat}, \hyperpage{221}
  \item \texttt  {IsNilpotent}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt{IsNilpotent}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {IsNilpotentElement}, \hyperpage{974}
  \item \texttt  {IsNilpotentGroup}, \hyperpage{522}
  \item \texttt  {IsNilpotentTom}, \hyperpage{1057}
  \item \texttt  {IsNInfinity}, \hyperpage{242}
  \item \texttt  {IsNonassocWord}, \hyperpage{468}
  \item \texttt  {IsNonassocWordCollection}, \hyperpage{469}
  \item \texttt  {IsNonassocWordWithOne}, \hyperpage{468}
  \item \texttt  {IsNonassocWordWithOneCollection}, \hyperpage{469}
  \item \texttt  {IsNonnegativeIntegers}, \hyperpage{178}
  \item \texttt  {IsNonSPGeneralMapping}, \hyperpage{440}
  \item \texttt  {IsNonTrivial}, \hyperpage{391}
  \item \texttt  {IsNormal}, \hyperpage{500}
  \item \texttt  {IsNormalBasis}, \hyperpage{908}
  \item \texttt  {IsNotIdenticalObj}, \hyperpage{158}
  \item \texttt  {IsNumberField}, \hyperpage{894}
  \item \texttt  {IsObject}, \hyperpage{156}
  \item \texttt  {IsOddInt}, \hyperpage{179}
  \item isomorphic
    \subitem pc group, \hyperpage{656, 657}
  \item \texttt  {IsomorphicSubgroups}, \hyperpage{567}
  \item \texttt  {IsomorphismFpAlgebra}, \hyperpage{944}
  \item \texttt  {IsomorphismFpGroup}, \hyperpage{678}
  \item \texttt{IsomorphismFpGroup}
    \subitem for subgroups of fp groups, \hyperpage{681}
  \item \texttt  {IsomorphismFpGroupByGenerators}, \hyperpage{679}
  \item \texttt  {IsomorphismFpGroupByGeneratorsNC}, \hyperpage{679}
  \item \texttt  {IsomorphismFpGroupByPcgs}, \hyperpage{654}
  \item \texttt  {IsomorphismFpSemigroup}, \hyperpage{788}
  \item \texttt  {IsomorphismGroups}, \hyperpage{565}
  \item \texttt  {IsomorphismMatrixAlgebra}, \hyperpage{944}
  \item \texttt  {IsomorphismPartialPermMonoid}, \hyperpage{840}
  \item \texttt  {IsomorphismPartialPermSemigroup}, \hyperpage{840}
  \item \texttt  {IsomorphismPcGroup}, \hyperpage{657}
  \item \texttt  {IsomorphismPermGroup}, \hyperpage{601}
    \subitem for Imf matrix groups, \hyperpage{760}
  \item \texttt  {IsomorphismPermGroupImfGroup}, \hyperpage{761}
  \item \texttt  {IsomorphismReesMatrixSemigroup}, \hyperpage{778}
  \item \texttt  {IsomorphismReesZeroMatrixSemigroup}, \hyperpage{778}
  \item \texttt  {IsomorphismRefinedPcGroup}, \hyperpage{656}
  \item \texttt{Isomorphism\mbox{\texttt{\mdseries\slshape Rep}}\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{404}
  \item isomorphisms
    \subitem find all, \hyperpage{565}
  \item \texttt  {IsomorphismSCAlgebra}
    \subitem for an algebra, \hyperpage{945}
    \subitem w.r.t. a given basis, \hyperpage{945}
  \item \texttt  {IsomorphismSimplifiedFpGroup}, \hyperpage{682}
  \item \texttt  {IsomorphismSpecialPcGroup}, \hyperpage{658}
  \item \texttt  {IsomorphismTransformationMonoid}, \hyperpage{815}
  \item \texttt  {IsomorphismTransformationSemigroup}, \hyperpage{815}
  \item \texttt  {Isomorphism}\discretionary {-}{}{}\texttt  {Type}\discretionary {-}{}{}\texttt  {Info}\discretionary {-}{}{}\texttt  {Finite}\discretionary {-}{}{}\texttt  {Simple}\discretionary {-}{}{}\texttt  {Group}
    \subitem for a character table, \hyperpage{1082}
    \subitem for a group, \hyperpage{524}
    \subitem for a group order, \hyperpage{524}
  \item \texttt  {IsOne}, \hyperpage{410}
  \item \texttt  {IsOperation}, \hyperpage{77}
  \item \texttt  {IsOrdering}, \hyperpage{450}
  \item \texttt  {IsOrderingOnFamilyOfAssocWords}, \hyperpage{453}
  \item \texttt  {IsOrdinaryMatrix}, \hyperpage{315}
  \item \texttt  {IsOrdinaryTable}, \hyperpage{1074}
  \item \texttt  {IsOutputStream}, \hyperpage{140}
  \item \texttt  {IsOutputTextNone}, \hyperpage{140}
  \item \texttt  {IsOutputTextStream}, \hyperpage{140}
  \item \texttt  {IsPackageMarkedForLoading}, \hyperpage{1210}
  \item \texttt  {IsPadicExtensionNumber}, \hyperpage{1032}
  \item \texttt  {IsPadicExtensionNumberFamily}, \hyperpage{1032}
  \item \texttt  {IsParentPcgsFamilyPcgs}, \hyperpage{652}
  \item \texttt  {IsPartialOrderBinaryRelation}, \hyperpage{444}
  \item \texttt  {IsPartialPerm}, \hyperpage{819}
  \item \texttt  {IsPartialPermCollection}, \hyperpage{819}
  \item \texttt  {IsPartialPermMonoid}, \hyperpage{838}
  \item \texttt  {IsPartialPermSemigroup}, \hyperpage{838}
  \item \texttt  {IsPcGroup}, \hyperpage{653}
  \item \texttt  {IsPcGroupGeneralMappingByImages}, \hyperpage{570}
  \item \texttt  {IsPcGroupHomomorphismByImages}, \hyperpage{570}
  \item \texttt  {IsPcgs}, \hyperpage{629}
  \item \texttt  {IsPcgsCentralSeries}, \hyperpage{641}
  \item \texttt  {IsPcgsChiefSeries}, \hyperpage{643}
  \item \texttt  {IsPcgsElementaryAbelianSeries}, \hyperpage{640}
  \item \texttt  {IsPcgsPCentralSeriesPGroup}, \hyperpage{642}
  \item \texttt  {IsPerfect}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsPerfectGroup}, \hyperpage{522}
  \item \texttt  {IsPerfectTom}, \hyperpage{1057}
  \item \texttt  {IsPerm}, \hyperpage{595}
  \item \texttt  {IsPermCollColl}, \hyperpage{595}
  \item \texttt  {IsPermCollection}, \hyperpage{595}
  \item \texttt  {IsPermGroup}, \hyperpage{600}
  \item \texttt  {IsPermGroupGeneralMapping}, \hyperpage{569}
  \item \texttt  {IsPermGroupGeneralMappingByImages}, \hyperpage{569}
  \item \texttt  {IsPermGroupHomomorphism}, \hyperpage{569}
  \item \texttt  {IsPermGroupHomomorphismByImages}, \hyperpage{569}
  \item \texttt  {IsPGroup}, \hyperpage{527}
  \item \texttt  {IsPInfinity}, \hyperpage{242}
  \item \texttt  {IsPNilpotent}, \hyperpage{528}
  \item \texttt  {IsPolycyclicGroup}, \hyperpage{523}
  \item \texttt  {IsPolynomial}, \hyperpage{999}
  \item \texttt  {IsPolynomialDefaultRep}, \hyperpage{1022}
  \item \texttt  {IsPolynomialFunction}, \hyperpage{998}
  \item \texttt  {IsPolynomialFunctionsFamily}, \hyperpage{1020}
  \item \texttt  {IsPolynomialRing}, \hyperpage{1012}
  \item \texttt  {IsPosInt}, \hyperpage{178}
  \item \texttt  {IsPositiveIntegers}, \hyperpage{178}
  \item \texttt  {IsPosRat}, \hyperpage{221}
  \item \texttt  {IsPreimages}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {As}\discretionary {-}{}{}\texttt  {Group}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Images}, 
		\hyperpage{569}
  \item \texttt  {IsPreOrderBinaryRelation}, \hyperpage{444}
  \item \texttt  {IsPrime}, \hyperpage{859}
  \item \texttt  {IsPrimeField}, \hyperpage{877}
  \item \texttt  {IsPrimeInt}, \hyperpage{184}
  \item \texttt  {IsPrimeOrdersPcgs}, \hyperpage{630}
  \item \texttt  {IsPrimePowerInt}, \hyperpage{185}
  \item \texttt  {IsPrimitive}
    \subitem for a group, an action domain, etc., \hyperpage{587}
    \subitem for an external set, \hyperpage{587}
  \item \texttt  {IsPrimitiveCharacter}, \hyperpage{1197}
  \item \texttt  {IsPrimitivePolynomial}, \hyperpage{1000}
  \item \texttt  {IsPrimitiveRootMod}, \hyperpage{198}
  \item \texttt  {IsProbablyPrimeInt}, \hyperpage{184}
  \item \texttt  {IsPseudoCanonicalBasisFullHomModule}, \hyperpage{917}
  \item \texttt  {IsPSolubleCharacterTable}, \hyperpage{1095}
  \item \texttt  {IsPSolubleCharacterTableOp}, \hyperpage{1095}
  \item \texttt  {IsPSolvable}, \hyperpage{528}
  \item \texttt  {IsPSolvableCharacterTable}, \hyperpage{1095}
  \item \texttt  {IsPSolvableCharacterTableOp}, \hyperpage{1095}
  \item \texttt  {IsPurePadicNumber}, \hyperpage{1030}
  \item \texttt  {IsPurePadicNumberFamily}, \hyperpage{1030}
  \item \texttt  {IsQuasiPrimitive}, \hyperpage{1197}
  \item \texttt  {IsQuaternion}, \hyperpage{932}
  \item \texttt  {IsQuaternionCollColl}, \hyperpage{932}
  \item \texttt  {IsQuaternionCollection}, \hyperpage{932}
  \item \texttt  {IsQuickPositionList}, \hyperpage{297}
  \item \texttt  {IsQuotientSemigroup}, \hyperpage{773}
  \item \texttt  {IsRandomSource}, \hyperpage{192}
  \item \texttt  {IsRange}, \hyperpage{295}
  \item \texttt  {IsRat}, \hyperpage{221}
  \item \texttt  {IsRationalFunction}, \hyperpage{998}
  \item \texttt  {IsRationalFunctionDefaultRep}, \hyperpage{1022}
  \item \texttt  {IsRationalFunctionsFamily}, \hyperpage{1020}
  \item \texttt  {IsRationalMatrixGroup}, \hyperpage{625}
  \item \texttt  {IsRationals}, \hyperpage{220}
  \item \texttt  {IsRationalsPolynomialRing}, \hyperpage{1012}
  \item \texttt  {IsRDistributive}, \hyperpage{856}
  \item \texttt  {IsReadableFile}, \hyperpage{134}
  \item \texttt  {IsReadOnlyGlobal}, \hyperpage{51}
  \item \texttt  {IsRecord}, \hyperpage{377}
  \item \texttt  {IsRecordCollColl}, \hyperpage{377}
  \item \texttt  {IsRecordCollection}, \hyperpage{377}
  \item \texttt  {IsRectangularTable}, \hyperpage{251}
  \item \texttt  {IsReduced}, \hyperpage{491}
  \item \texttt  {IsReductionOrdering}, \hyperpage{453}
  \item \texttt  {IsReesCongruence}, \hyperpage{772}
  \item \texttt  {IsReesCongruenceSemigroup}, \hyperpage{771}
  \item \texttt  {IsReesMatrixSemigroup}, \hyperpage{781}
  \item \texttt  {IsReesMatrixSemigroupElement}, \hyperpage{779}
  \item \texttt  {IsReesMatrixSubsemigroup}, \hyperpage{780}
  \item \texttt  {IsReesZeroMatrixSemigroup}, \hyperpage{781}
  \item \texttt  {IsReesZeroMatrixSemigroupElement}, \hyperpage{779}
  \item \texttt  {IsReesZeroMatrixSubsemigroup}, \hyperpage{780}
  \item \texttt  {IsReflexiveBinaryRelation}, \hyperpage{443}
  \item \texttt  {IsRegular}
    \subitem for a group, an action domain, etc., \hyperpage{586}
    \subitem for an external set, \hyperpage{586}
  \item \texttt  {IsRegularDClass}, \hyperpage{776}
  \item \texttt  {IsRegularSemigroup}, \hyperpage{770}
  \item \texttt  {IsRegularSemigroupElement}, \hyperpage{770}
  \item \texttt  {IsRelativelySM}
    \subitem for a character, \hyperpage{1201}
    \subitem for a group, \hyperpage{1201}
  \item \texttt  {IsRestrictedJacobianElement}, \hyperpage{422}
  \item \texttt  {IsRestrictedJacobianElementCollColl}, \hyperpage{422}
  \item \texttt  {IsRestricted}\discretionary {-}{}{}\texttt  {Jacobian}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Collection}, 
		\hyperpage{422}
  \item \texttt  {IsRestrictedLieAlgebra}, \hyperpage{971}
  \item \texttt  {IsRestrictedLieObject}, \hyperpage{957}
  \item \texttt  {IsRestrictedLieObjectCollection}, \hyperpage{957}
  \item \texttt  {IsRewritingSystem}, \hyperpage{490}
  \item \texttt  {IsRightAlgebraModuleElement}, \hyperpage{948}
  \item \texttt  {IsRight}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Collection}, 
		\hyperpage{948}
  \item \texttt  {IsRightCoset}, \hyperpage{508}
  \item \texttt  {IsRightIdeal}, \hyperpage{852}
  \item \texttt  {IsRightIdealInParent}, \hyperpage{852}
  \item \texttt  {IsRightModule}, \hyperpage{869}
  \item \texttt  {IsRightOperatorAdditiveGroup}, \hyperpage{869}
  \item \texttt  {IsRightSemigroupIdeal}, \hyperpage{772}
  \item \texttt  {IsRing}, \hyperpage{848}
  \item \texttt  {IsRingElement}, \hyperpage{420}
  \item \texttt  {IsRingElementWithInverse}, \hyperpage{421}
  \item \texttt  {IsRingElementWithOne}, \hyperpage{421}
  \item \texttt  {IsRingGeneralMapping}, \hyperpage{437}
  \item \texttt  {IsRingHomomorphism}, \hyperpage{437}
  \item \texttt  {IsRingWithOne}, \hyperpage{854}
  \item \texttt  {IsRingWithOneGeneralMapping}, \hyperpage{438}
  \item \texttt  {IsRingWithOneHomomorphism}, \hyperpage{438}
  \item \texttt  {IsRootSystem}, \hyperpage{966}
  \item \texttt  {IsRootSystemFromLieAlgebra}, \hyperpage{966}
  \item \texttt  {IsRowModule}, \hyperpage{872}
  \item \texttt  {IsRowSpace}, \hyperpage{910}
  \item \texttt  {IsRowVector}, \hyperpage{304}
  \item \texttt  {IsScalar}, \hyperpage{421}
  \item \texttt  {IsSemiEchelonized}, \hyperpage{912}
  \item \texttt  {IsSemigroup}, \hyperpage{762}
  \item \texttt  {IsSemigroupCongruence}, \hyperpage{772}
  \item \texttt  {IsSemigroupIdeal}, \hyperpage{772}
  \item \texttt  {IsSemilatticeAsSemigroup}, \hyperpage{1217}
  \item \texttt  {IsSemiRegular}
    \subitem for a group, an action domain, etc., \hyperpage{586}
    \subitem for an external set, \hyperpage{586}
  \item \texttt  {IsSet}, \hyperpage{277}
  \item \texttt  {IsShortLexLessThanOrEqual}, \hyperpage{476}
  \item \texttt  {IsShortLexOrdering}, \hyperpage{454}
  \item \texttt  {IsSimple}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsSimpleAlgebra}, \hyperpage{931}
  \item \texttt  {IsSimpleGroup}, \hyperpage{523}
  \item \texttt  {IsSimpleSemigroup}, \hyperpage{771}
  \item \texttt  {IsSingleValued}, \hyperpage{428}
  \item \texttt  {IsSL}, \hyperpage{622}
  \item \texttt  {IsSolvable}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsSolvableGroup}, \hyperpage{522}
  \item \texttt  {IsSolvableTom}, \hyperpage{1057}
  \item \texttt  {IsSortedList}, \hyperpage{276}
  \item \texttt  {IsSpecialLinearGroup}, \hyperpage{622}
  \item \texttt  {IsSpecialPcgs}, \hyperpage{645}
  \item \texttt  {IsSPGeneralMapping}, \hyperpage{440}
  \item \texttt  {IsSporadicSimple}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {IsSSortedList}, \hyperpage{277}
  \item \texttt  {IsStandardIterator}, \hyperpage{397}
  \item \texttt  {IsStraightLineProgElm}, \hyperpage{488}
  \item \texttt  {IsStraightLineProgram}, \hyperpage{483}
  \item \texttt  {IsStream}, \hyperpage{139}
  \item \texttt  {IsString}, \hyperpage{352}
  \item \texttt  {IsStringRep}, \hyperpage{356}
  \item \texttt{Is\mbox{\texttt{\mdseries\slshape Struct}}}, 
		\hyperpage{405}
  \item \texttt  {IsSubgroup}, \hyperpage{500}
  \item \texttt  {IsSubgroupFpGroup}, \hyperpage{665}
  \item \texttt  {IsSubgroupOfWholeGroupByQuotientRep}, \hyperpage{682}
  \item \texttt  {IsSubgroupSL}, \hyperpage{622}
  \item \texttt  {IsSubmonoidFpMonoid}, \hyperpage{786}
  \item \texttt  {IsSubnormal}, \hyperpage{501}
  \item \texttt  {IsSubnormallyMonomial}
    \subitem for a character, \hyperpage{1200}
    \subitem for a group, \hyperpage{1200}
  \item \texttt  {IsSubsemigroup}, \hyperpage{763}
  \item \texttt  {IsSubsemigroupFpSemigroup}, \hyperpage{786}
  \item \texttt  {IsSubset}, \hyperpage{393}
  \item \texttt  {IsSubsetBlist}, \hyperpage{300}
  \item \texttt  {IsSubsetLocallyFiniteGroup}, \hyperpage{527}
  \item \texttt  {IsSubsetSet}, \hyperpage{280}
  \item \texttt  {IsSubspacesVectorSpace}, \hyperpage{902}
  \item \texttt{IsSub\mbox{\texttt{\mdseries\slshape struct}}}, 
		\hyperpage{407}
  \item \texttt  {IsSupersolvable}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt{IsSupersolvable}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {IsSupersolvableGroup}, \hyperpage{523}
  \item \texttt  {IsSurjective}, \hyperpage{428}
  \item \texttt  {IsSyllableAssocWordRep}, \hyperpage{481}
  \item \texttt  {IsSyllableWordsFamily}, \hyperpage{481}
  \item \texttt  {IsSymmetricBinaryRelation}, \hyperpage{443}
  \item \texttt  {IsSymmetricGroup}, \hyperpage{603}
  \item \texttt  {IsSymmetricInverseMonoid}, \hyperpage{839}
  \item \texttt  {IsSymmetricInverseSemigroup}, \hyperpage{839}
  \item \texttt  {IsTable}, \hyperpage{250}
  \item \texttt  {IsTableOfMarks}, \hyperpage{1051}
  \item \texttt  {IsTableOfMarksWithGens}, \hyperpage{1063}
  \item \texttt  {IsToPcGroupGeneralMappingByImages}, \hyperpage{570}
  \item \texttt  {IsToPcGroupHomomorphismByImages}, \hyperpage{570}
  \item \texttt  {IsToPermGroupGeneralMappingByImages}, \hyperpage{569}
  \item \texttt  {IsToPermGroupHomomorphismByImages}, \hyperpage{569}
  \item \texttt  {IsTotal}, \hyperpage{427}
  \item \texttt  {IsTotalOrdering}, \hyperpage{451}
  \item \texttt  {IsTransformation}, \hyperpage{795}
  \item \texttt  {IsTransformationCollection}, \hyperpage{795}
  \item \texttt  {IsTransformationMonoid}, \hyperpage{813}
  \item \texttt  {IsTransformationSemigroup}, \hyperpage{813}
  \item \texttt  {IsTransitive}
    \subitem for a character, \hyperpage{1138}
    \subitem for a group, an action domain, etc., \hyperpage{585}
    \subitem for a permutation group, \hyperpage{585}
    \subitem for an external set, \hyperpage{585}
  \item \texttt  {IsTransitiveBinaryRelation}, \hyperpage{443}
  \item \texttt  {IsTranslationInvariantOrdering}, \hyperpage{453}
  \item \texttt  {IsTrivial}, \hyperpage{391}
  \item \texttt  {IsTwoSidedIdeal}, \hyperpage{852}
  \item \texttt  {IsTwoSidedIdealInParent}, \hyperpage{852}
  \item \texttt  {IsUEALatticeElement}, \hyperpage{982}
  \item \texttt  {IsUEALatticeElementCollection}, \hyperpage{982}
  \item \texttt  {IsUEALatticeElementFamily}, \hyperpage{982}
  \item \texttt  {IsUniqueFactorizationRing}, \hyperpage{856}
  \item \texttt  {IsUnit}, \hyperpage{857}
  \item \texttt  {IsUnivariatePolynomial}, \hyperpage{1000}
  \item \texttt  {IsUnivariatePolynomialRing}, \hyperpage{1013}
  \item \texttt  {IsUnivariateRationalFunction}, \hyperpage{999}
  \item \texttt  {IsUnknown}, \hyperpage{1192}
  \item \texttt  {IsUpperAlphaChar}, \hyperpage{358}
  \item \texttt  {IsUpperTriangularMat}, \hyperpage{319}
  \item \texttt  {IsValidIdentifier}, \hyperpage{49}
  \item \texttt  {IsVector}, \hyperpage{420}
  \item \texttt  {IsVectorSpace}, \hyperpage{900}
  \item \texttt  {IsVirtualCharacter}, \hyperpage{1134}
  \item \texttt  {IsWeightLexOrdering}, \hyperpage{455}
  \item \texttt  {IsWeightRepElement}, \hyperpage{983}
  \item \texttt  {IsWeightRepElementCollection}, \hyperpage{983}
  \item \texttt  {IsWeightRepElementFamily}, \hyperpage{983}
  \item \texttt  {IsWellFoundedOrdering}, \hyperpage{451}
  \item \texttt  {IsWeylGroup}, \hyperpage{968}
  \item \texttt  {IsWholeFamily}, \hyperpage{392}
  \item \texttt  {IsWLetterAssocWordRep}, \hyperpage{480}
  \item \texttt  {IsWLetterWordsFamily}, \hyperpage{480}
  \item \texttt  {IsWord}, \hyperpage{467}
  \item \texttt  {IsWordCollection}, \hyperpage{468}
  \item \texttt  {IsWordWithInverse}, \hyperpage{467}
  \item \texttt  {IsWordWithOne}, \hyperpage{467}
  \item \texttt  {IsWreathProductOrdering}, \hyperpage{456}
  \item \texttt  {IsWritableFile}, \hyperpage{135}
  \item \texttt  {IsXInfinity}, \hyperpage{242}
  \item \texttt  {IsZero}, \hyperpage{411}
  \item \texttt  {IsZeroGroup}, \hyperpage{771}
  \item \texttt  {IsZeroSimpleSemigroup}, \hyperpage{771}
  \item \texttt  {IsZeroSquaredElement}, \hyperpage{423}
  \item \texttt  {IsZeroSquaredElementCollColl}, \hyperpage{423}
  \item \texttt  {IsZeroSquaredElementCollection}, \hyperpage{423}
  \item \texttt  {IsZeroSquaredRing}, \hyperpage{857}
  \item \texttt  {IsZmodnZObj}, \hyperpage{190}
  \item \texttt  {IsZmodnZObjNonprime}, \hyperpage{190}
  \item \texttt  {IsZmodpZObj}, \hyperpage{190}
  \item \texttt  {IsZmodpZObjLarge}, \hyperpage{190}
  \item \texttt  {IsZmodpZObjSmall}, \hyperpage{190}
  \item \texttt  {Iterated}, \hyperpage{292}
  \item \texttt  {Iterator}, \hyperpage{397}
  \item iterator
    \subitem for low index subgroups, \hyperpage{677}
  \item \texttt  {IteratorByBasis}, \hyperpage{907}
  \item \texttt  {IteratorByFunctions}, \hyperpage{399}
  \item \texttt  {IteratorList}, \hyperpage{399}
  \item \texttt  {IteratorOfCartesianProduct}
    \subitem for a list of lists, \hyperpage{288}
    \subitem for several lists, \hyperpage{288}
  \item \texttt  {IteratorOfCombinations}, \hyperpage{208}
  \item \texttt  {IteratorOfPartitions}, \hyperpage{214}
  \item \texttt  {IteratorOfTuples}, \hyperpage{211}
  \item \texttt  {IteratorSorted}, \hyperpage{398}
  \item \texttt  {IteratorStabChain}, \hyperpage{613}

  \indexspace

  \item $j_N$ (irrational value), \hyperpage{231}
  \item \texttt  {Jacobi}, \hyperpage{198}
  \item \texttt  {JenningsLieAlgebra}, \hyperpage{972}
  \item \texttt  {JenningsSeries}, \hyperpage{533}
  \item \texttt  {JoinEquivalenceRelations}, \hyperpage{448}
  \item \texttt  {JoinOfIdempotentPartialPermsNC}, \hyperpage{821}
  \item \texttt  {JoinOfPartialPerms}, \hyperpage{821}
  \item \texttt  {JoinStringsWithSeparator}, \hyperpage{363}
  \item \texttt  {JordanDecomposition}, \hyperpage{333}

  \indexspace

  \item $k_N$ (irrational value), \hyperpage{231}
  \item \texttt  {KappaPerp}, \hyperpage{974}
  \item \texttt  {KB{\textunderscore }REW}, \hyperpage{791}
  \item kernel
    \subitem group homomorphism, \hyperpage{557}
    \subitem of a matrix, \hyperpage{324}
  \item \texttt  {KernelOfAdditiveGeneralMapping}, \hyperpage{436}
  \item \texttt  {KernelOfCharacter}, \hyperpage{1136}
  \item \texttt  {Kernel}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Multiplicative}\discretionary {-}{}{}\texttt  {General}\discretionary {-}{}{}\texttt  {Mapping}, 
		\hyperpage{435}
  \item \texttt  {KernelOfTransformation}, \hyperpage{807}
  \item \texttt  {KeyDependentOperation}, \hyperpage{1294}
  \item \texttt  {KillingMatrix}, \hyperpage{974}
  \item \texttt  {KnownAttributesOfObject}, \hyperpage{170}
  \item \texttt  {KnownPropertiesOfObject}, \hyperpage{174}
  \item \texttt  {KnownTruePropertiesOfObject}, \hyperpage{174}
  \item \texttt  {KnowsDictionary}, \hyperpage{374}
  \item \texttt  {KnowsHowToDecompose}, \hyperpage{553}
  \item \texttt  {KnuthBendixRewritingSystem}
    \subitem for a monoid and a reduction ordering, \hyperpage{792}
    \subitem for a semigroup and a reduction ordering, \hyperpage{792}
  \item Krasner-Kaloujnine theorem, \hyperpage{723}
  \item \texttt  {KroneckerProduct}, \hyperpage{322}
  \item \texttt  {KuKGenerators}, \hyperpage{723}

  \indexspace

  \item $l_N$ (irrational value), \hyperpage{231}
  \item \texttt  {Lambda}, \hyperpage{196}
  \item larger or equal, \hyperpage{56}
  \item larger test, \hyperpage{56}
  \item \texttt  {Larger}\discretionary {-}{}{}\texttt  {Quotient}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Subgroup}\discretionary {-}{}{}\texttt  {Abelianization}, 
		\hyperpage{686}
  \item \texttt  {LargestElementGroup}, \hyperpage{545}
  \item \texttt  {LargestElementStabChain}, \hyperpage{613}
  \item \texttt  {LargestImageOfMovedPoint}
    \subitem for a partial permutation, \hyperpage{828}
    \subitem for a partial permutation coll, \hyperpage{828}
    \subitem for a transformation, \hyperpage{807}
    \subitem for a transformation coll, \hyperpage{807}
  \item \texttt  {LargestMovedPoint}
    \subitem for a list or collection of permutations, \hyperpage{596}
    \subitem for a partial perm, \hyperpage{827}
    \subitem for a partial perm coll, \hyperpage{827}
    \subitem for a permutation, \hyperpage{596}
    \subitem for a transformation, \hyperpage{806}
    \subitem for a transformation coll, \hyperpage{806}
  \item \texttt  {LargestUnknown}, \hyperpage{1192}
  \item \texttt{last}, \hyperpage{79}
  \item \texttt{last2}, \hyperpage{79}
  \item \texttt{last3}, \hyperpage{79}
  \item \texttt  {LastSystemError}, \hyperpage{130}
  \item LaTeX
    \subitem for a decomposition matrix, \hyperpage{1093}
    \subitem for GAP objects, \hyperpage{370}
    \subitem for permutation characters, \hyperpage{1154}
    \subitem for the result of a straight line program, \hyperpage{485}
  \item \texttt  {LaTeXStringDecompositionMatrix}, \hyperpage{1093}
  \item lattice base reduction, \hyperpage{346, 347}
  \item lattice basis reduction
    \subitem for virtual characters, \hyperpage{1143}
  \item \texttt  {LatticeByCyclicExtension}, \hyperpage{541}
  \item \texttt  {LatticeGeneratorsInUEA}, \hyperpage{982}
  \item \texttt  {LatticeSubgroups}, \hyperpage{538}
  \item \texttt  {LatticeSubgroupsByTom}, \hyperpage{1048}
  \item \texttt  {LaurentPolynomialByCoefficients}, \hyperpage{1009}
  \item \texttt  {LaurentPolynomialByExtRep}, \hyperpage{1024}
  \item \texttt  {LaurentPolynomialByExtRepNC}, \hyperpage{1024}
  \item \texttt  {LClassOfHClass}, \hyperpage{774}
  \item \texttt  {Lcm}
    \subitem for (a ring and) a list of elements, \hyperpage{863}
    \subitem for (a ring and) several elements, \hyperpage{863}
  \item \texttt  {LcmInt}, \hyperpage{183}
  \item \texttt  {LcmOp}, \hyperpage{863}
  \item \texttt  {LeadCoeffsIGS}, \hyperpage{636}
  \item \texttt  {LeadingCoefficient}, \hyperpage{1004}
  \item \texttt  {LeadingCoefficientOfPolynomial}, \hyperpage{1015}
  \item \texttt  {LeadingExponentOfPcElement}, \hyperpage{632}
  \item \texttt  {LeadingMonomial}, \hyperpage{1004}
  \item \texttt  {LeadingMonomialOfPolynomial}, \hyperpage{1014}
  \item \texttt  {LeadingTermOfPolynomial}, \hyperpage{1015}
  \item left cosets, \hyperpage{508}
  \item \texttt  {LeftActingAlgebra}, \hyperpage{949}
  \item \texttt  {LeftActingDomain}, \hyperpage{870}
  \item \texttt  {LeftActingRingOfIdeal}, \hyperpage{854}
  \item \texttt  {LeftAlgebraModule}, \hyperpage{947}
  \item \texttt  {LeftAlgebraModuleByGenerators}, \hyperpage{946}
  \item \texttt  {LeftDerivations}, \hyperpage{960}
  \item \texttt  {LeftIdeal}, \hyperpage{851}
  \item \texttt  {LeftIdealByGenerators}, \hyperpage{853}
  \item \texttt  {LeftIdealNC}, \hyperpage{852}
  \item \texttt  {LeftModuleByGenerators}, \hyperpage{870}
  \item \texttt  {LeftModuleByHomomorphismToMatAlg}, \hyperpage{950}
  \item \texttt  {LeftModuleGeneralMappingByImages}, \hyperpage{914}
  \item \texttt  {LeftModuleHomomorphismByImages}, \hyperpage{915}
  \item \texttt  {LeftModuleHomomorphismByImagesNC}, \hyperpage{915}
  \item \texttt  {LeftModuleHomomorphismByMatrix}, \hyperpage{915}
  \item \texttt  {LeftOne}
    \subitem for a partial perm, \hyperpage{830}
    \subitem for a transformation, \hyperpage{811}
  \item \texttt  {LeftQuotient}, \hyperpage{414}
  \item \texttt{LeftQuotient}
    \subitem for words, \hyperpage{476}
  \item \texttt  {LeftShiftRowVector}, \hyperpage{309}
  \item legacy, \hyperpage{1215}
  \item \texttt  {Legendre}, \hyperpage{199}
  \item \texttt  {Length}, \hyperpage{277}
    \subitem for a associative word, \hyperpage{477}
  \item length
    \subitem of a word, \hyperpage{477}
  \item \texttt  {LengthsTom}, \hyperpage{1053}
  \item \texttt  {LengthWPObj}, \hyperpage{1301}
  \item \texttt  {LenstraBase}, \hyperpage{897}
  \item \texttt  {LessThanFunction}, \hyperpage{452}
  \item \texttt  {LessThanOrEqualFunction}, \hyperpage{452}
  \item \texttt  {LetterRepAssocWord}, \hyperpage{481}
  \item \texttt  {LevelsOfGenerators}, \hyperpage{456}
  \item \texttt  {LeviMalcevDecomposition}
    \subitem for Lie algebras, \hyperpage{939}
  \item \texttt  {LexicographicOrdering}, \hyperpage{453}
  \item \texttt  {LGFirst}, \hyperpage{646}
  \item \texttt  {LGLayers}, \hyperpage{646}
  \item \texttt  {LGLength}, \hyperpage{646}
  \item \texttt  {LGWeights}, \hyperpage{646}
  \item library tables, \hyperpage{1071}
  \item \texttt  {LieAlgebra}
    \subitem for an associative algebra, \hyperpage{959}
    \subitem for field and generators, \hyperpage{959}
  \item \texttt  {LieAlgebraByStructureConstants}, \hyperpage{958}
  \item \texttt  {LieBracket}, \hyperpage{414}
  \item \texttt  {LieCenter}, \hyperpage{961}
  \item \texttt  {LieCentralizer}, \hyperpage{962}
  \item \texttt  {LieCentre}, \hyperpage{961}
  \item \texttt  {LieCoboundaryOperator}, \hyperpage{979}
  \item \texttt  {LieDerivedSeries}, \hyperpage{963}
  \item \texttt  {LieDerivedSubalgebra}, \hyperpage{962}
  \item \texttt  {LieFamily}, \hyperpage{957}
  \item \texttt  {LieLowerCentralSeries}, \hyperpage{964}
  \item \texttt  {LieNilRadical}, \hyperpage{963}
  \item \texttt  {LieNormalizer}, \hyperpage{962}
  \item \texttt  {LieObject}, \hyperpage{957}
  \item \texttt  {LieSolvableRadical}, \hyperpage{963}
  \item \texttt  {LieUpperCentralSeries}, \hyperpage{964}
  \item \texttt  {LiftedInducedPcgs}, \hyperpage{640}
  \item \texttt  {LiftedPcElement}, \hyperpage{640}
  \item \texttt  {LinearAction}, \hyperpage{647}
  \item \texttt  {LinearActionLayer}, \hyperpage{648}
  \item \texttt  {LinearCharacters}
    \subitem for a character table, \hyperpage{1081}
    \subitem for a group, \hyperpage{1081}
  \item \texttt  {LinearCombination}, \hyperpage{906}
  \item \texttt  {LinearCombinationPcgs}, \hyperpage{632}
  \item \texttt  {LinearIndependentColumns}, \hyperpage{345}
  \item \texttt  {LinearOperation}, \hyperpage{647}
  \item \texttt  {LinearOperationLayer}, \hyperpage{648}
  \item \texttt  {LinesOfStraightLineProgram}, \hyperpage{483}
  \item \texttt  {List}
    \subitem for a collection, \hyperpage{388}
    \subitem for a list (and a function), \hyperpage{288}
  \item list
    \subitem sorted, \hyperpage{276}
  \item list and non-list
    \subitem difference, \hyperpage{267}
    \subitem left quotient, \hyperpage{270}
    \subitem mod, \hyperpage{269}
    \subitem product, \hyperpage{268}
    \subitem quotient, \hyperpage{269}
  \item list assignment
    \subitem operation, \hyperpage{251}
  \item list boundedness test
    \subitem operation, \hyperpage{251}
  \item list element
    \subitem access, \hyperpage{252}
    \subitem assignment, \hyperpage{254}
    \subitem operation, \hyperpage{251}
  \item list equal
    \subitem comparison, \hyperpage{262}
  \item list of available books, \hyperpage{29}
  \item list smaller
    \subitem comparison, \hyperpage{262}
  \item list unbind
    \subitem operation, \hyperpage{251}
  \item \texttt  {ListBlist}, \hyperpage{299}
  \item \texttt  {ListN}, \hyperpage{292}
  \item \texttt  {ListOfDigits}, \hyperpage{181}
  \item \texttt  {ListPerm}, \hyperpage{598}
  \item \texttt  {ListStabChain}, \hyperpage{612}
  \item \texttt  {ListTransformation}, \hyperpage{804}
  \item \texttt  {ListWithIdenticalEntries}, \hyperpage{271}
  \item \texttt  {ListX}, \hyperpage{292}
  \item \texttt  {LLL}, \hyperpage{1143}
  \item LLL algorithm
    \subitem for Gram matrices, \hyperpage{347}
    \subitem for vectors, \hyperpage{346}
    \subitem for virtual characters, \hyperpage{1143}
  \item \texttt  {LLLReducedBasis}, \hyperpage{346}
  \item \texttt  {LLLReducedGramMat}, \hyperpage{347}
  \item \texttt  {LoadDynamicModule}, \hyperpage{1210}
  \item \texttt  {LoadPackage}, \hyperpage{1204}
  \item \texttt{local}, \hyperpage{66}
  \item \texttt  {Log}, \hyperpage{240}
  \item \texttt  {Log10}, \hyperpage{240}
  \item \texttt  {Log1p}, \hyperpage{240}
  \item \texttt  {Log2}, \hyperpage{240}
  \item logarithm
    \subitem discrete, \hyperpage{197}
    \subitem of a root of unity, \hyperpage{227}
  \item \texttt  {LogFFE}, \hyperpage{885}
  \item logical, \hyperpage{245}
  \item Logical conjunction, \hyperpage{247}
  \item Logical disjunction, \hyperpage{246}
  \item Logical negation, \hyperpage{247}
  \item logical operations, \hyperpage{246}
  \item \texttt  {LogInt}, \hyperpage{179}
  \item \texttt  {LogMod}, \hyperpage{197}
  \item \texttt  {LogModShanks}, \hyperpage{197}
  \item \texttt  {LogPackageLoadingMessage}, \hyperpage{1206}
  \item \texttt  {LogTo}
    \subitem for a filename, \hyperpage{137}
    \subitem for streams, \hyperpage{145}
    \subitem stop logging, \hyperpage{137}
  \item \texttt  {LongestWeylWordPerm}, \hyperpage{969}
  \item \texttt  {LookupDictionary}, \hyperpage{374}
  \item loop
    \subitem for, \hyperpage{63}
    \subitem read eval print, \hyperpage{79}
    \subitem repeat, \hyperpage{62}
    \subitem while, \hyperpage{62}
  \item loop over iterator, \hyperpage{64}
  \item loop over object, \hyperpage{64}
  \item loop over range, \hyperpage{63}
  \item loops
    \subitem leaving, \hyperpage{65}
    \subitem restarting, \hyperpage{65}
  \item \texttt  {LowercaseString}, \hyperpage{361}
  \item \texttt  {LowerCentralSeriesOfGroup}, \hyperpage{532}
  \item \texttt  {LowIndexSubgroupsFpGroup}, \hyperpage{677}
  \item \texttt  {LowIndexSubgroupsFpGroupIterator}, \hyperpage{677}
  \item \texttt{LQUO}
    \subitem for a permutation and transformation, \hyperpage{801}
    \subitem for a permutation or partial permutation         and partial permutation, 
		\hyperpage{833}
  \item \texttt  {Lucas}, \hyperpage{218}

  \indexspace

  \item $m_N$ (irrational value), \hyperpage{231}
  \item \texttt  {Magma}, \hyperpage{458}
  \item \texttt  {MagmaByGenerators}, \hyperpage{459}
  \item \texttt  {MagmaByMultiplicationTable}, \hyperpage{461}
  \item \texttt  {MagmaElement}, \hyperpage{462}
  \item \texttt  {MagmaHomomorphismByFunctionNC}, \hyperpage{434}
  \item \texttt  {MagmaRingModuloSpanOfZero}, \hyperpage{991}
  \item \texttt  {MagmaWithInverses}, \hyperpage{459}
  \item \texttt  {MagmaWithInversesByGenerators}, \hyperpage{459}
  \item \texttt  {Magma}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Inverses}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Multiplication}\discretionary {-}{}{}\texttt  {Table}, 
		\hyperpage{462}
  \item \texttt  {MagmaWithOne}, \hyperpage{458}
  \item \texttt  {MagmaWithOneByGenerators}, \hyperpage{459}
  \item \texttt  {MagmaWithOneByMultiplicationTable}, \hyperpage{462}
  \item \texttt  {MagmaWithZeroAdjoined}, \hyperpage{460}
  \item \texttt  {MakeConfluent}, \hyperpage{492}
  \item \texttt  {MakeFloat}, \hyperpage{243}
  \item \texttt  {MakeImmutable}, \hyperpage{160}
  \item \texttt  {MakeReadOnlyGlobal}, \hyperpage{52}
  \item \texttt  {MakeReadWriteGlobal}, \hyperpage{52}
  \item map
    \subitem parametrized, \hyperpage{1175}
  \item \texttt  {MappedWord}, \hyperpage{470}
  \item \texttt  {MappingByFunction}
    \subitem by function (and inverse function) between two domains, 
		\hyperpage{425}
    \subitem by function and function that computes one preimage, 
		\hyperpage{425}
  \item \texttt  {MappingGeneratorsImages}, \hyperpage{569}
  \item \texttt  {MappingPermListList}, \hyperpage{598}
  \item maps, \hyperpage{1164}
  \item \texttt  {MarksTom}, \hyperpage{1052}
  \item \texttt  {MatAlgebra}, \hyperpage{927}
  \item \texttt  {MatClassMultCoeffsCharTable}, \hyperpage{1098}
  \item \texttt  {MathieuGroup}, \hyperpage{729}
  \item \texttt  {MatLieAlgebra}, \hyperpage{960}
  \item matrices
    \subitem commutator, \hyperpage{317}
  \item \texttt  {Matrix}, \hyperpage{782}
  \item matrix automorphisms, \hyperpage{1168}
  \item matrix spaces, \hyperpage{910}
  \item \texttt  {MatrixAlgebra}, \hyperpage{927}
  \item \texttt  {MatrixAutomorphisms}, \hyperpage{1117}
  \item \texttt  {MatrixByBlockMatrix}, \hyperpage{338}
  \item \texttt  {MatrixLieAlgebra}, \hyperpage{960}
  \item \texttt  {MatrixOfAction}, \hyperpage{950}
  \item \texttt  {MatScalarProducts}, \hyperpage{1135}
  \item \texttt  {MatTom}, \hyperpage{1055}
  \item \texttt  {MaximalAbelianQuotient}, \hyperpage{535}
  \item \texttt  {MaximalBlocks}
    \subitem for a group, an action domain, etc., \hyperpage{587}
    \subitem for an external set, \hyperpage{587}
  \item \texttt  {MaximalNormalSubgroups}, \hyperpage{538}
  \item \texttt  {MaximalSubgroupClassReps}, \hyperpage{537}
  \item \texttt  {MaximalSubgroups}, \hyperpage{537}
  \item \texttt{MaximalSubgroups}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {MaximalSubgroupsLattice}, \hyperpage{539}
  \item \texttt  {MaximalSubgroupsTom}, \hyperpage{1061}
  \item \texttt  {Maximum}
    \subitem for a list, \hyperpage{286}
    \subitem for various objects, \hyperpage{286}
  \item \texttt  {MaximumList}, \hyperpage{287}
  \item meet strategy, \hyperpage{1311}
  \item \texttt  {MeetEquivalenceRelations}, \hyperpage{448}
  \item \texttt  {MeetMaps}, \hyperpage{1179}
  \item \texttt  {MeetOfPartialPerms}, \hyperpage{822}
  \item \texttt  {MemoryUsage}, \hyperpage{163}
  \item method, \hyperpage{1219}
  \item \texttt  {Mid}, \hyperpage{241}
  \item \texttt  {MinimalElementCosetStabChain}, \hyperpage{613}
  \item \texttt  {MinimalGeneratingSet}, \hyperpage{545}
  \item \texttt{MinimalGeneratingSet}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {MinimalNonmonomialGroup}, \hyperpage{1202}
  \item \texttt  {MinimalNormalSubgroups}, \hyperpage{538}
  \item \texttt  {MinimalPolynomial}, \hyperpage{1006}
    \subitem over a field, \hyperpage{879}
  \item \texttt{MinimalPolynomial}
    \subitem over a ring, \hyperpage{1006}
  \item \texttt  {MinimalStabChain}, \hyperpage{610}
  \item \texttt  {MinimalSupergroupsLattice}, \hyperpage{540}
  \item \texttt  {MinimalSupergroupsTom}, \hyperpage{1061}
  \item \texttt  {MinimizedBombieriNorm}, \hyperpage{1009}
  \item \texttt  {Minimum}
    \subitem for a list, \hyperpage{286}
    \subitem for various objects, \hyperpage{286}
  \item \texttt  {MinimumList}, \hyperpage{287}
  \item \texttt  {MinusCharacter}, \hyperpage{1186}
  \item mod
    \subitem Integers, \hyperpage{190}
    \subitem Laurent polynomials, \hyperpage{996}
    \subitem lists, \hyperpage{269}
    \subitem rationals, \hyperpage{58}
  \item \texttt  {\texttt  {\char 92\relax }mod}, \hyperpage{413}
    \subitem for residue class rings, \hyperpage{189}
    \subitem for two pcgs, \hyperpage{638}
  \item \texttt{mod}, \hyperpage{57}
    \subitem arithmetic operators, \hyperpage{57}
    \subitem for character tables, \hyperpage{1079}
    \subitem residue class rings, \hyperpage{189}
  \item modular inverse, \hyperpage{58}
  \item modular remainder, \hyperpage{58}
  \item modular roots, \hyperpage{200}
  \item \texttt  {ModuleByRestriction}, \hyperpage{952}
  \item \texttt  {ModuleOfExtension}, \hyperpage{660}
  \item modulo, \hyperpage{57}
    \subitem arithmetic operators, \hyperpage{57}
    \subitem residue class rings, \hyperpage{189}
  \item \texttt  {ModuloPcgs}, \hyperpage{637}
  \item \texttt  {MoebiusMu}, \hyperpage{202}
  \item \texttt  {MoebiusTom}, \hyperpage{1056}
  \item \texttt  {MolienSeries}, \hyperpage{1152}
  \item \texttt  {MolienSeriesInfo}, \hyperpage{1152}
  \item \texttt  {MolienSeriesWithGivenDenominator}, \hyperpage{1154}
  \item \texttt  {Monoid}
    \subitem for a list, \hyperpage{766}
    \subitem for various generators, \hyperpage{766}
  \item \texttt  {MonoidByGenerators}, \hyperpage{766}
  \item \texttt  {MonoidByMultiplicationTable}, \hyperpage{767}
  \item \texttt  {MonoidOfRewritingSystem}, \hyperpage{792}
  \item \texttt  {MonomialComparisonFunction}, \hyperpage{1015}
  \item \texttt  {MonomialExtGrlexLess}, \hyperpage{1018}
  \item \texttt  {MonomialExtrepComparisonFun}, \hyperpage{1015}
  \item \texttt  {MonomialGrevlexOrdering}, \hyperpage{1016}
  \item \texttt  {MonomialGrlexOrdering}, \hyperpage{1016}
  \item \texttt  {MonomialLexOrdering}, \hyperpage{1015}
  \item \texttt{MonomialTotalDegreeLess}, \hyperpage{1216}
  \item monomorphisms
    \subitem find all, \hyperpage{567}
  \item \texttt  {MorClassLoop}, \hyperpage{567}
  \item \texttt  {MostFrequentGeneratorFpGroup}, \hyperpage{674}
  \item \texttt  {MovedPoints}
    \subitem for a list or collection of permutations, \hyperpage{596}
    \subitem for a partial perm, \hyperpage{825}
    \subitem for a partial perm coll, \hyperpage{825}
    \subitem for a permutation, \hyperpage{596}
    \subitem for a transformation, \hyperpage{805}
    \subitem for a transformation coll, \hyperpage{805}
  \item \texttt  {MTX}, \hyperpage{1034}
  \item \texttt  {MTX.BasesCompositionSeries}, \hyperpage{1037}
  \item \texttt  {MTX.BasesMaximalSubmodules}, \hyperpage{1037}
  \item \texttt  {MTX.BasesMinimalSubmodules}, \hyperpage{1037}
  \item \texttt  {MTX.BasesMinimalSupermodules}, \hyperpage{1037}
  \item \texttt  {MTX.BasesSubmodules}, \hyperpage{1036}
  \item \texttt  {MTX.BasisInOrbit}, \hyperpage{1041}
  \item \texttt  {MTX.BasisModuleEndomorphisms}, \hyperpage{1039}
  \item \texttt  {MTX.BasisModuleHomomorphisms}, \hyperpage{1039}
  \item \texttt  {MTX.BasisRadical}, \hyperpage{1037}
  \item \texttt  {MTX.BasisSocle}, \hyperpage{1037}
  \item \texttt  {MTX.CollectedFactors}, \hyperpage{1037}
  \item \texttt  {MTX.CompositionFactors}, \hyperpage{1037}
  \item \texttt  {MTX.DegreeSplittingField}, \hyperpage{1035}
  \item \texttt  {MTX.Dimension}, \hyperpage{1035}
  \item \texttt  {MTX.Distinguish}, \hyperpage{1040}
  \item \texttt  {MTX.Field}, \hyperpage{1035}
  \item \texttt  {MTX.Generators}, \hyperpage{1034}
  \item \texttt  {MTX.HomogeneousComponents}, \hyperpage{1036}
  \item \texttt  {MTX.Homomorphism}, \hyperpage{1040}
  \item \texttt  {MTX.Homomorphisms}, \hyperpage{1040}
  \item \texttt  {MTX.Indecomposition}, \hyperpage{1036}
  \item \texttt  {MTX.InducedAction}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionFactorMatrix}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionFactorModule}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionMatrix}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionMatrixNB}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionSubmodule}, \hyperpage{1038}
  \item \texttt  {MTX.InducedActionSubmoduleNB}, \hyperpage{1038}
  \item \texttt  {MTX.InvariantBilinearForm}, \hyperpage{1040}
  \item \texttt  {MTX.InvariantQuadraticForm}, \hyperpage{1041}
  \item \texttt  {MTX.InvariantSesquilinearForm}, \hyperpage{1040}
  \item \texttt  {MTX.IsAbsolutelyIrreducible}, \hyperpage{1035}
  \item \texttt  {MTX.IsEquivalent}, \hyperpage{1039}
  \item \texttt  {MTX.IsIndecomposable}, \hyperpage{1035}
  \item \texttt  {MTX.IsIrreducible}, \hyperpage{1035}
  \item \texttt  {MTX.IsomorphismIrred}, \hyperpage{1039}
  \item \texttt  {MTX.IsomorphismModules}, \hyperpage{1039}
  \item \texttt  {MTX.ModuleAutomorphisms}, \hyperpage{1039}
  \item \texttt  {MTX.NormedBasisAndBaseChange}, \hyperpage{1038}
  \item \texttt  {MTX.OrthogonalSign}, \hyperpage{1041}
  \item \texttt  {MTX.ProperSubmoduleBasis}, \hyperpage{1036}
  \item \texttt  {MTX.SubGModule}, \hyperpage{1036}
  \item \texttt  {MTX.SubmoduleGModule}, \hyperpage{1036}
  \item multiple indices, \hyperpage{252}
    \subitem assignment, \hyperpage{254}
  \item multiplication, \hyperpage{57}
    \subitem matrices, \hyperpage{316}
    \subitem matrix and matrix list, \hyperpage{317}
    \subitem matrix and scalar, \hyperpage{316}
    \subitem matrix and vector, \hyperpage{316}
    \subitem operation, \hyperpage{413}
    \subitem scalar and matrix, \hyperpage{316}
    \subitem scalar and matrix list, \hyperpage{317}
    \subitem scalar and vector, \hyperpage{305}
    \subitem vector and matrix, \hyperpage{316}
    \subitem vector and matrix list, \hyperpage{317}
    \subitem vector and scalar, \hyperpage{305}
    \subitem vectors, \hyperpage{306}
  \item \texttt  {MultiplicationTable}
    \subitem for a list of elements, \hyperpage{462}
    \subitem for a magma, \hyperpage{462}
  \item multiplicative order of an integer, \hyperpage{197}
  \item \texttt  {MultiplicativeNeutralElement}, \hyperpage{465}
  \item \texttt  {MultiplicativeZero}, \hyperpage{465}
  \item \texttt  {MultiplicativeZeroOp}, \hyperpage{410}
  \item multiplicity
    \subitem of constituents of a group character, \hyperpage{1135}
  \item Multiplier, \hyperpage{549}
  \item multisets, \hyperpage{279}
  \item \texttt  {MultRowVector}, \hyperpage{309}
  \item Murnaghan components, \hyperpage{1150, 1151}
  \item \texttt  {MutableBasis}, \hyperpage{909}
  \item \texttt  {MutableBasisOfClosureUnderAction}, \hyperpage{935}
  \item \texttt  {Mutable}\discretionary {-}{}{}\texttt  {Basis}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Nonassociative}\discretionary {-}{}{}\texttt  {Algebra}, 
		\hyperpage{936}
  \item \texttt  {MutableBasisOfNonassociativeAlgebra}, \hyperpage{936}
  \item \texttt{MutableIdentityMat}, \hyperpage{1216}
  \item \texttt{MutableNullMat}, \hyperpage{1216}

  \indexspace

  \item \texttt  {Name}, \hyperpage{162}
  \item \texttt  {NameFunction}, \hyperpage{70}
  \item \texttt  {NameRNam}, \hyperpage{383}
  \item \texttt  {NamesFilter}, \hyperpage{166}
  \item \texttt  {NamesGVars}, \hyperpage{53}
  \item \texttt  {NamesLocalVariablesFunction}, \hyperpage{71}
  \item \texttt  {NamesOfComponents}, \hyperpage{1232}
  \item \texttt  {NamesOfFusionSources}, \hyperpage{1172}
  \item namespace, \hyperpage{49}, \hyperpage{51}
  \item \texttt  {NamesSystemGVars}, \hyperpage{54}
  \item \texttt  {NamesUserGVars}, \hyperpage{54}
  \item \texttt  {NaturalCharacter}
    \subitem for a group, \hyperpage{1132}
    \subitem for a homomorphism, \hyperpage{1132}
  \item \texttt  {NaturalHomomorphismByGenerators}, \hyperpage{434}
  \item \texttt  {NaturalHomomorphismByIdeal}, \hyperpage{865}
    \subitem for an algebra and an ideal, \hyperpage{943}
  \item \texttt  {NaturalHomomorphismByNormalSubgroup}, \hyperpage{534}
  \item \texttt  {Natural}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Normal}\discretionary {-}{}{}\texttt  {SubgroupNC}, 
		\hyperpage{534}
  \item \texttt  {Natural}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {Module}, 
		\hyperpage{953}
  \item \texttt  {NaturalHomomorphismBySubspace}, \hyperpage{916}
  \item \texttt  {Natural}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Lie}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {From}\discretionary {-}{}{}\texttt  {Nilpotent}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{973}
  \item \texttt  {NaturalLeqPartialPerm}, \hyperpage{834}
  \item \texttt  {NaturalPartialOrder}, \hyperpage{839}
  \item \texttt  {NearAdditiveGroup}, \hyperpage{844}
  \item \texttt  {NearAdditiveGroupByGenerators}, \hyperpage{845}
  \item \texttt  {NearAdditiveMagma}, \hyperpage{844}
  \item \texttt  {NearAdditiveMagmaByGenerators}, \hyperpage{844}
  \item \texttt  {NearAdditiveMagmaWithZero}, \hyperpage{844}
  \item \texttt  {Near}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Zero}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Generators}, 
		\hyperpage{844}
  \item \texttt  {NearlyCharacterTablesFamily}, \hyperpage{1075}
  \item negative number, \hyperpage{57}
  \item \texttt  {NegativeRoots}, \hyperpage{967}
  \item \texttt  {NegativeRootVectors}, \hyperpage{967}
  \item \texttt  {NestingDepthA}, \hyperpage{265}
  \item \texttt  {NestingDepthM}, \hyperpage{265}
  \item \texttt  {NewAttribute}, \hyperpage{1226}
  \item \texttt{NewAttribute}
    \subitem example, \hyperpage{1250}
  \item \texttt  {NewCategory}, \hyperpage{1225}
  \item \texttt  {NewConstructor}, \hyperpage{1228}
  \item \texttt  {NewDictionary}, \hyperpage{373}
  \item \texttt  {NewFamily}, \hyperpage{1229}
  \item \texttt  {NewFilter}, \hyperpage{1227}
  \item \texttt  {NewFloat}, \hyperpage{243}
  \item \texttt  {NewInfoClass}, \hyperpage{106}
  \item newline, \hyperpage{47}
  \item \texttt  {NewmanInfinityCriterion}, \hyperpage{688}
  \item \texttt  {NewOperation}, \hyperpage{1228}
  \item \texttt  {NewProperty}, \hyperpage{1227}
  \item \texttt  {NewRepresentation}, \hyperpage{1226}
  \item \texttt{NewRepresentation}
    \subitem example, \hyperpage{1251}
  \item \texttt  {NewType}, \hyperpage{1230}
  \item \texttt  {NextIterator}, \hyperpage{398}
  \item \texttt  {NextPrimeInt}, \hyperpage{186}
  \item \texttt  {NF}, \hyperpage{893}
  \item \texttt  {NiceAlgebraMonomorphism}, \hyperpage{944}
  \item \texttt  {NiceBasis}, \hyperpage{918}
  \item \texttt  {NiceBasisFiltersInfo}, \hyperpage{920}
  \item \texttt  {NiceFreeLeftModule}, \hyperpage{918}
  \item \texttt  {NiceFreeLeftModuleInfo}, \hyperpage{918}
  \item \texttt  {NiceMonomorphism}, \hyperpage{560}
  \item \texttt  {NiceMonomorphismAutomGroup}, \hyperpage{565}
  \item \texttt  {NiceObject}, \hyperpage{560}
  \item \texttt  {NiceVector}, \hyperpage{918}
  \item \texttt  {NilpotencyClassOfGroup}, \hyperpage{522}
  \item \texttt  {NilpotentQuotientOfFpLieAlgebra}, \hyperpage{976}
  \item \texttt  {NK}, \hyperpage{231}
  \item \texttt{NOAUTO}, \hyperpage{1205}
  \item \texttt  {NonabelianExteriorSquare}, \hyperpage{550}
  \item \texttt  {NonnegativeIntegers}, \hyperpage{177}
  \item \texttt  {NonnegIntScalarProducts}, \hyperpage{1182}
  \item \texttt  {NonNilpotentElement}, \hyperpage{974}
  \item \texttt  {Norm}, \hyperpage{880}
    \subitem for a class function, \hyperpage{1135}
  \item \texttt{Norm}
    \subitem of character, \hyperpage{1135}
  \item \texttt  {NormalBase}, \hyperpage{881}
  \item \texttt  {NormalClosure}, \hyperpage{515}
  \item \texttt  {NormalFormIntMat}, \hyperpage{343}
  \item \texttt  {NormalIntersection}, \hyperpage{515}
  \item \texttt  {Normalized}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Magma}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Modulo}\discretionary {-}{}{}\texttt  {Relations}, 
		\hyperpage{991}
  \item \texttt  {NormalizedWhitespace}, \hyperpage{363}
  \item \texttt  {Normalizer}
    \subitem for a group and a group element, \hyperpage{514}
    \subitem for two groups, \hyperpage{514}
  \item normalizer, \hyperpage{514}
  \item \texttt  {NormalizerInGLnZ}, \hyperpage{626}
  \item \texttt  {NormalizerInGLnZBravaisGroup}, \hyperpage{627}
  \item \texttt  {NormalizersTom}, \hyperpage{1058}
  \item \texttt  {NormalizerTom}, \hyperpage{1058}
  \item \texttt  {NormalizeWhitespace}, \hyperpage{362}
  \item \texttt  {NormalSeriesByPcgs}, \hyperpage{644}
  \item \texttt  {NormalSubgroupClasses}, \hyperpage{1120}
  \item \texttt  {NormalSubgroupClassesInfo}, \hyperpage{1119}
  \item \texttt  {NormalSubgroups}, \hyperpage{537}
  \item \texttt  {NormedRowVector}, \hyperpage{306}
  \item \texttt  {NormedRowVectors}, \hyperpage{914}
  \item \texttt{NormedVectors}, \hyperpage{1216}
  \item \texttt{not}, \hyperpage{247}
  \item \texttt  {NrArrangements}, \hyperpage{209}
  \item \texttt  {NrBasisVectors}, \hyperpage{909}
  \item \texttt  {NrCombinations}, \hyperpage{209}
  \item \texttt  {NrComponentsOfPartialPerm}, \hyperpage{829}
  \item \texttt  {NrComponentsOfTransformation}, \hyperpage{809}
  \item \texttt  {NrConjugacyClasses}, \hyperpage{513}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt  {NrConjugacyClassesGL}, \hyperpage{735}
  \item \texttt  {NrConjugacyClassesGU}, \hyperpage{735}
  \item \texttt  {NrConjugacyClassesPGL}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesPGU}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesPSL}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesPSU}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesSL}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesSLIsogeneous}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesSU}, \hyperpage{736}
  \item \texttt  {NrConjugacyClassesSUIsogeneous}, \hyperpage{736}
  \item \texttt  {NrDerangements}, \hyperpage{212}
  \item \texttt  {NrFixedPoints}
    \subitem for a partial perm, \hyperpage{826}
    \subitem for a partial perm coll, \hyperpage{826}
  \item \texttt  {NrInputsOfStraightLineProgram}, \hyperpage{483}
  \item \texttt  {NrMovedPoints}
    \subitem for a list or collection of permutations, \hyperpage{597}
    \subitem for a partial perm, \hyperpage{826}
    \subitem for a partial perm coll, \hyperpage{826}
    \subitem for a permutation, \hyperpage{597}
    \subitem for a transformation, \hyperpage{805}
    \subitem for a transformation coll, \hyperpage{805}
  \item \texttt  {NrOrderedPartitions}, \hyperpage{215}
  \item \texttt  {NrPartitions}, \hyperpage{214}
  \item \texttt  {NrPartitionsSet}, \hyperpage{213}
  \item \texttt  {NrPartitionTuples}, \hyperpage{217}
  \item \texttt  {NrPermutationsList}, \hyperpage{212}
  \item \texttt  {NrPolyhedralSubgroups}, \hyperpage{1096}
  \item \texttt  {NrPrimitiveGroups}, \hyperpage{750}
  \item \texttt  {NrRestrictedPartitions}, \hyperpage{216}
  \item \texttt  {NrSubsTom}, \hyperpage{1053}
  \item \texttt  {NrTransitiveGroups}, \hyperpage{738}
  \item \texttt  {NrTuples}, \hyperpage{211}
  \item \texttt  {NrUnorderedTuples}, \hyperpage{210}
  \item \texttt  {NthRootsInGroup}, \hyperpage{514}
  \item \texttt  {NullAlgebra}, \hyperpage{928}
  \item \texttt  {NullMat}, \hyperpage{320}
  \item \texttt  {NullspaceIntMat}, \hyperpage{339}
  \item \texttt  {NullspaceMat}, \hyperpage{324}
  \item \texttt  {NullspaceMatDestructive}, \hyperpage{324}
  \item \texttt  {NullspaceModQ}, \hyperpage{337}
  \item \texttt  {Number}, \hyperpage{289}
  \item number
    \subitem Bell, \hyperpage{206}
    \subitem binomial, \hyperpage{205}
    \subitem Stirling, of the first kind, \hyperpage{207}
    \subitem Stirling, of the second kind, \hyperpage{207}
  \item number field, \hyperpage{894}
  \item number fields
    \subitem Galois group, \hyperpage{897}
  \item \texttt  {NumberArgumentsFunction}, \hyperpage{70}
  \item \texttt  {NumberFFVector}, \hyperpage{308}
  \item \texttt  {NumberIrreducibleSolvableGroups}, \hyperpage{752}
  \item \texttt  {NumberPerfectGroups}, \hyperpage{745}
  \item \texttt  {NumberPerfectLibraryGroups}, \hyperpage{745}
  \item \texttt  {NumberSmallGroups}, \hyperpage{741}
  \item \texttt  {NumberSmallRings}, \hyperpage{866}
  \item \texttt  {NumbersString}, \hyperpage{364}
  \item \texttt  {NumberSyllables}, \hyperpage{479}
  \item \texttt  {NumberTransformation}, \hyperpage{798}
  \item numerator
    \subitem of a rational, \hyperpage{221}
  \item \texttt  {NumeratorOfModuloPcgs}, \hyperpage{638}
  \item \texttt  {NumeratorOfRationalFunction}, \hyperpage{998}
  \item \texttt  {NumeratorRat}, \hyperpage{221}

  \indexspace

  \item \texttt  {ObjByExtRep}, \hyperpage{1240}
    \subitem for creating a UEALattice element, \hyperpage{982}
  \item \texttt  {Objectify}, \hyperpage{1230}
  \item \texttt  {ObjectifyWithAttributes}, \hyperpage{1230}
  \item obsolete, \hyperpage{1215}
  \item \texttt  {OCOneCocycles}, \hyperpage{548}
  \item octal character codes, \hyperpage{355}
  \item \texttt  {OctaveAlgebra}, \hyperpage{927}
  \item \texttt{od}, \hyperpage{63}
  \item \texttt  {OldGeneratorsOfPresentation}, \hyperpage{710}
  \item \texttt  {Omega}, \hyperpage{521}
    \subitem construct an orthogonal group, \hyperpage{733}
  \item OmniGraffle, \hyperpage{539}
  \item \texttt  {ONanScottType}, \hyperpage{603}
  \item \texttt  {OnBreak}, \hyperpage{86}
  \item \texttt  {OnBreakMessage}, \hyperpage{88}
  \item \texttt  {One}, \hyperpage{409}
    \subitem for a partial perm, \hyperpage{830}
  \item one cohomology, \hyperpage{546}
  \item \texttt  {OneAttr}, \hyperpage{408}
  \item \texttt  {OneCoboundaries}, \hyperpage{547}
  \item \texttt  {OneCocycles}
    \subitem for a group and a pcgs, \hyperpage{546}
    \subitem for generators and a group, \hyperpage{546}
    \subitem for generators and a pcgs, \hyperpage{546}
    \subitem for two groups, \hyperpage{546}
  \item \texttt  {OneFactorBound}, \hyperpage{1009}
  \item \texttt  {OneImmutable}, \hyperpage{408}
  \item \texttt  {OneIrreducibleSolvableGroup}, \hyperpage{752}
  \item \texttt{One\mbox{\texttt{\mdseries\slshape Library}}Group}, 
		\hyperpage{738}
  \item \texttt  {OneMutable}, \hyperpage{409}
  \item \texttt  {OneOfPcgs}, \hyperpage{631}
  \item \texttt  {OneOp}, \hyperpage{409}
  \item \texttt{OnePrimitiveGroup}, \hyperpage{738}
  \item \texttt  {OneSameMutability}, \hyperpage{409}
  \item \texttt  {OneSM}, \hyperpage{409}
  \item \texttt  {OneSmallGroup}, \hyperpage{741}
  \item \texttt{OneTransitiveGroup}, \hyperpage{738}
  \item \texttt  {OnIndeterminates}
    \subitem as a permutation action, \hyperpage{575}
  \item \texttt  {OnLeftInverse}, \hyperpage{573}
  \item \texttt  {OnLines}, \hyperpage{575}
  \item \texttt{OnLines}
    \subitem example, \hyperpage{730}
  \item \texttt  {OnPairs}, \hyperpage{573}
  \item \texttt  {OnPoints}, \hyperpage{572}
  \item \texttt  {OnQuit}, \hyperpage{128}
  \item \texttt  {OnRight}, \hyperpage{572}
  \item \texttt  {OnSets}, \hyperpage{573}
  \item \texttt  {OnSetsDisjointSets}, \hyperpage{574}
  \item \texttt  {OnSetsSets}, \hyperpage{573}
  \item \texttt  {OnSetsTuples}, \hyperpage{574}
  \item \texttt  {OnSubspacesByCanonicalBasis}, \hyperpage{576}
  \item \texttt  {OnSubspaces}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Canonical}\discretionary {-}{}{}\texttt  {Basis}\discretionary {-}{}{}\texttt  {Concatenations}, 
		\hyperpage{576}
  \item \texttt  {OnTuples}, \hyperpage{573}
  \item \texttt  {OnTuplesSets}, \hyperpage{574}
  \item \texttt  {OnTuplesTuples}, \hyperpage{574}
  \item \texttt{PCore}
    \subitem see PCore, \hyperpage{515}
  \item \texttt{Operation}, \hyperpage{1215}
  \item operation, \hyperpage{1219}
  \item \texttt  {OperationAlgebraHomomorphism}
    \subitem action on a free left module, \hyperpage{943}
    \subitem action w.r.t. a basis of the module, \hyperpage{943}
  \item \texttt{OperationHomomorphism}, \hyperpage{1215}
  \item operations
    \subitem for booleans, \hyperpage{246}
  \item Operations for algebraic elements, \hyperpage{1027}
  \item operators, \hyperpage{49}
    \subitem arithmetic, \hyperpage{57}
    \subitem associativity, \hyperpage{58}
    \subitem for cyclotomics, \hyperpage{229}
    \subitem for lists, \hyperpage{263}
    \subitem precedence, \hyperpage{57}
  \item options, \hyperpage{33}
    \subitem command line, filenames, \hyperpage{37}
    \subitem command line, internal, \hyperpage{38}
    \subitem under UNIX, \hyperpage{33}
  \item \texttt{or}, \hyperpage{246}
  \item \texttt  {Orbit}, \hyperpage{576}
  \item \texttt  {OrbitFusions}, \hyperpage{1175}
  \item \texttt  {OrbitishFO}, \hyperpage{1298}
  \item \texttt  {OrbitLength}, \hyperpage{578}
  \item \texttt  {OrbitLengths}
    \subitem for a group, a set of seeds, etc., \hyperpage{578}
    \subitem for an external set, \hyperpage{578}
  \item \texttt  {OrbitLengthsDomain}
    \subitem for a group and a set of seeds, \hyperpage{578}
    \subitem of an external set, \hyperpage{578}
  \item \texttt  {OrbitPerms}, \hyperpage{601}
  \item \texttt  {OrbitPowerMaps}, \hyperpage{1168}
  \item \texttt  {Orbits}
    \subitem attribute, \hyperpage{577}
    \subitem operation, \hyperpage{577}
  \item \texttt{Orbits}
    \subitem as attributes for external sets, \hyperpage{1296}
  \item \texttt  {OrbitsDomain}
    \subitem for a group and an action domain, \hyperpage{577}
    \subitem of an external set, \hyperpage{577}
  \item \texttt  {OrbitsishOperation}, \hyperpage{1297}
  \item \texttt  {OrbitsPerms}, \hyperpage{601}
  \item \texttt  {OrbitStabChain}, \hyperpage{612}
  \item \texttt  {OrbitStabilizer}, \hyperpage{578}
  \item \texttt  {OrbitStabilizerAlgorithm}, \hyperpage{579}
  \item \texttt  {Order}, \hyperpage{412}
    \subitem for a class function, \hyperpage{1130}
  \item order
    \subitem of a group, \hyperpage{496}
    \subitem of a list, collection or domain, \hyperpage{392}
    \subitem of the prime residue group, \hyperpage{196}
  \item ordered partitions
    \subitem internal representation, \hyperpage{1305}
  \item \texttt  {OrderedPartitions}, \hyperpage{214}
  \item ordering
    \subitem booleans, \hyperpage{246}
    \subitem of records, \hyperpage{381}
  \item \texttt  {OrderingByLessThanFunctionNC}, \hyperpage{450}
  \item \texttt  {OrderingByLessThanOrEqualFunctionNC}, \hyperpage{450}
  \item \texttt  {OrderingOfRewritingSystem}, \hyperpage{491}
  \item \texttt  {OrderingOnGenerators}, \hyperpage{453}
  \item \texttt  {OrderingsFamily}, \hyperpage{450}
  \item \texttt  {OrderMod}, \hyperpage{197}
  \item \texttt  {OrderOfRewritingSystem}, \hyperpage{491}
  \item \texttt  {OrdersClassRepresentatives}, \hyperpage{1083}
  \item \texttt  {OrdersTom}, \hyperpage{1053}
  \item \texttt  {Ordinal}, \hyperpage{367}
  \item ordinary character, \hyperpage{1134}
  \item \texttt  {OrdinaryCharacterTable}
    \subitem for a character table, \hyperpage{1081}
    \subitem for a group, \hyperpage{1081}
  \item \texttt  {OrthogonalComponents}, \hyperpage{1150}
  \item \texttt  {OrthogonalEmbeddings}, \hyperpage{348}
  \item \texttt  {Orthogonal}\discretionary {-}{}{}\texttt  {Embeddings}\discretionary {-}{}{}\texttt  {Special}\discretionary {-}{}{}\texttt  {Dimension}, 
		\hyperpage{1145}
  \item output
    \subitem suppressing, \hyperpage{79}
  \item \texttt  {OutputLogTo}
    \subitem for a filename, \hyperpage{137}
    \subitem for streams, \hyperpage{146}
    \subitem stop logging output, \hyperpage{137}
  \item \texttt  {OutputTextFile}, \hyperpage{147}
  \item \texttt  {OutputTextNone}, \hyperpage{151}
  \item \texttt  {OutputTextString}, \hyperpage{149}
  \item \texttt  {OutputTextUser}, \hyperpage{148}
  \item \texttt  {Overlaps}, \hyperpage{241}
  \item overload, \hyperpage{1223}

  \indexspace

  \item $p$-group, \hyperpage{527}
  \item package, \hyperpage{1203}
  \item \texttt  {PACKAGE{\textunderscore }DEBUG}, \hyperpage{1206}
  \item \texttt  {PACKAGE{\textunderscore }ERROR}, \hyperpage{1206}
  \item \texttt  {PACKAGE{\textunderscore }INFO}, \hyperpage{1206}
  \item \texttt  {PackageVariablesInfo}, \hyperpage{1211}
  \item \texttt  {PACKAGE{\textunderscore }WARNING}, \hyperpage{1206}
  \item \texttt  {PadicCoefficients}, \hyperpage{346}
  \item \texttt  {PadicExtensionNumberFamily}, \hyperpage{1031}
  \item \texttt  {PadicNumber}
    \subitem for a p-adic extension family and a list, \hyperpage{1031}
    \subitem for a p-adic extension family and a rational, 
		\hyperpage{1031}
    \subitem for a pure p-adic numbers family and a list, 
		\hyperpage{1031}
    \subitem for pure padics, \hyperpage{1029}
  \item \texttt  {PadicValuation}, \hyperpage{860}
  \item \texttt  {Pager}, \hyperpage{31}
  \item \texttt  {PageSource}, \hyperpage{72}
  \item \texttt  {Parametrized}, \hyperpage{1177}
  \item parametrized maps, \hyperpage{1164}
  \item \texttt  {Parent}, \hyperpage{406}
  \item \texttt  {ParentPcgs}, \hyperpage{635}
  \item \texttt  {ParseRelators}, \hyperpage{666}
  \item partial order, \hyperpage{444}
  \item \texttt  {PartialFactorization}, \hyperpage{187}
  \item \texttt  {PartialOrderByOrderingFunction}, \hyperpage{446}
  \item \texttt  {PartialOrderOfHasseDiagram}, \hyperpage{445}
  \item \texttt  {PartialPerm}
    \subitem for a dense image, \hyperpage{819}
    \subitem for a domain and image, \hyperpage{819}
  \item \texttt  {PartialPermFamily}, \hyperpage{819}
  \item \texttt  {PartialPermOp}, \hyperpage{820}
  \item \texttt  {PartialPermOpNC}, \hyperpage{820}
  \item \texttt  {Partitions}, \hyperpage{213}
  \item partitions
    \subitem improper, of an integer, \hyperpage{214}
    \subitem ordered, of an integer, \hyperpage{214}
    \subitem restricted, of an integer, \hyperpage{215}
  \item \texttt  {PartitionsGreatestEQ}, \hyperpage{215}
  \item \texttt  {PartitionsGreatestLE}, \hyperpage{215}
  \item \texttt  {PartitionsSet}, \hyperpage{213}
  \item \texttt  {PartitionTuples}, \hyperpage{217}
  \item \texttt  {PcElementByExponents}, \hyperpage{632}
  \item \texttt  {PcElementByExponentsNC}, \hyperpage{632}
  \item \texttt  {PCentralLieAlgebra}, \hyperpage{972}
  \item \texttt  {PCentralNormalSeriesByPcgsPGroup}, \hyperpage{642}
  \item \texttt  {PCentralSeries}, \hyperpage{532}
  \item \texttt  {PcGroupCode}, \hyperpage{663}
  \item \texttt  {PcGroupFpGroup}, \hyperpage{654}
  \item \texttt  {PcGroupWithPcgs}, \hyperpage{657}
  \item \texttt  {Pcgs}, \hyperpage{629}
  \item \texttt  {PcgsByPcSequence}, \hyperpage{630}
  \item \texttt  {PcgsByPcSequenceNC}, \hyperpage{630}
  \item \texttt  {PcgsCentralSeries}, \hyperpage{641}
  \item \texttt  {PcgsChiefSeries}, \hyperpage{643}
  \item \texttt  {PcgsElementaryAbelianSeries}
    \subitem for a group, \hyperpage{640}
    \subitem for a list of normal subgroups, \hyperpage{640}
  \item \texttt  {Pcgs{\textunderscore }}\discretionary {-}{}{}\texttt  {Orbit}\discretionary {-}{}{}\texttt  {Stabilizer}, 
		\hyperpage{649}
  \item \texttt  {PcgsPCentralSeriesPGroup}, \hyperpage{642}
  \item \texttt  {PClassPGroup}, \hyperpage{528}
  \item \texttt  {PCore}, \hyperpage{515}
  \item \texttt  {PcSeries}, \hyperpage{631}
  \item perfect groups, \hyperpage{743}
  \item \texttt  {PerfectGroup}
    \subitem for a pair [ order, index ], \hyperpage{744}
    \subitem for group order (and index), \hyperpage{744}
  \item \texttt  {PerfectIdentification}, \hyperpage{745}
  \item \texttt  {PerfectResiduum}, \hyperpage{518}
  \item \texttt  {Perform}, \hyperpage{285}
  \item \texttt  {Permanent}, \hyperpage{218}
  \item \texttt  {PermBounds}, \hyperpage{1160}
  \item \texttt  {PermCharInfo}, \hyperpage{1155}
  \item \texttt  {PermCharInfoRelative}, \hyperpage{1156}
  \item \texttt  {PermChars}, \hyperpage{1157}
  \item \texttt  {PermCharsTom}
    \subitem from a character table, \hyperpage{1065}
    \subitem via fusion map, \hyperpage{1065}
  \item \texttt  {PermComb}, \hyperpage{1160}
  \item \texttt  {PermLeftQuoPartialPerm}, \hyperpage{833}
  \item \texttt  {PermLeftQuoPartialPermNC}, \hyperpage{833}
  \item \texttt  {PermLeftQuoTransformation}, \hyperpage{802}
  \item \texttt  {PermLeftQuoTransformationNC}, \hyperpage{802}
  \item \texttt  {PermList}, \hyperpage{598}
  \item \texttt  {PermListList}, \hyperpage{286}
  \item \texttt  {Permutation}
    \subitem for a group, an action domain, etc., \hyperpage{583}
    \subitem for an external set, \hyperpage{583}
  \item permutation character, \hyperpage{1188}
  \item permutation characters
    \subitem possible, \hyperpage{1154}
  \item \texttt  {PermutationCharacter}
    \subitem for a group, an action domain, and a function, 
		\hyperpage{1133}
    \subitem for two groups, \hyperpage{1133}
  \item \texttt  {PermutationCycle}, \hyperpage{584}
  \item \texttt  {PermutationGModule}, \hyperpage{1034}
  \item \texttt  {PermutationMat}, \hyperpage{321}
  \item \texttt  {PermutationOfImage}, \hyperpage{801}
  \item \texttt  {PermutationsFamily}, \hyperpage{595}
  \item \texttt  {PermutationsList}, \hyperpage{211}
  \item \texttt  {PermutationTom}, \hyperpage{1051}
  \item \texttt  {Permuted}, \hyperpage{288}
    \subitem as a permutation action, \hyperpage{575}
    \subitem for a class function, \hyperpage{1129}
  \item \texttt  {PGL}, \hyperpage{734}
  \item \texttt  {PGU}, \hyperpage{734}
  \item \texttt  {Phi}, \hyperpage{196}
  \item point stabilizer, \hyperpage{578}
  \item \texttt  {PolynomialByExtRep}, \hyperpage{1023}
  \item \texttt  {PolynomialByExtRepNC}, \hyperpage{1023}
  \item \texttt  {PolynomialCoefficientsOfPolynomial}, \hyperpage{1003}
  \item \texttt  {PolynomialDivisionAlgorithm}, \hyperpage{1017}
  \item \texttt  {PolynomialModP}, \hyperpage{1007}
  \item \texttt  {PolynomialReducedRemainder}, \hyperpage{1017}
  \item \texttt  {PolynomialReduction}, \hyperpage{1017}
  \item \texttt  {PolynomialRing}
    \subitem for a ring and a list of indeterminate numbers, 
		\hyperpage{1011}
    \subitem for a ring and a list of indeterminates, \hyperpage{1011}
    \subitem for a ring and a list of names (and an exclusion list), 
		\hyperpage{1011}
    \subitem for a ring and a rank (and an exclusion list), 
		\hyperpage{1011}
  \item \texttt  {POmega}, \hyperpage{735}
  \item \texttt  {PopOptions}, \hyperpage{128}
  \item \texttt  {Position}, \hyperpage{271}
  \item \texttt  {PositionBound}, \hyperpage{274}
  \item \texttt  {PositionCanonical}, \hyperpage{272}
  \item \texttt{PositionFirstComponent}, \hyperpage{1216}
  \item \texttt  {PositionNonZero}, \hyperpage{275}
  \item \texttt  {PositionNot}, \hyperpage{274}
  \item \texttt  {PositionNthOccurrence}, \hyperpage{272}
  \item \texttt  {PositionProperty}, \hyperpage{274}
  \item \texttt  {Positions}, \hyperpage{272}
  \item \texttt  {PositionSet}, \hyperpage{273}
  \item \texttt  {PositionsOp}, \hyperpage{272}
  \item \texttt  {PositionSorted}, \hyperpage{273}
  \item \texttt{PositionSortedOp}, \hyperpage{273}
  \item \texttt  {PositionsProperty}, \hyperpage{274}
  \item \texttt  {PositionStream}, \hyperpage{144}
  \item \texttt  {PositionSublist}, \hyperpage{275}
  \item \texttt  {PositionWord}, \hyperpage{477}
  \item positive number, \hyperpage{57}
  \item \texttt  {PositiveIntegers}, \hyperpage{177}
  \item \texttt  {PositiveRoots}, \hyperpage{966}
  \item \texttt  {PositiveRootVectors}, \hyperpage{967}
  \item possible permutation characters, \hyperpage{1154}
  \item \texttt  {PossibleClassFusions}, \hyperpage{1173}
  \item \texttt  {PossibleFusionsCharTableTom}, \hyperpage{1064}
  \item \texttt  {PossiblePowerMaps}, \hyperpage{1166}
  \item power, \hyperpage{57}
    \subitem matrix, \hyperpage{317}
    \subitem meaning for class functions, \hyperpage{1128}
    \subitem of words, \hyperpage{476}
  \item power set, \hyperpage{208}
  \item \texttt  {PowerMap}, \hyperpage{1165}
  \item \texttt  {PowerMapByComposition}, \hyperpage{1168}
  \item \texttt  {PowerMapOp}, \hyperpage{1165}
  \item \texttt  {PowerMapsAllowedBySymmetrizations}, \hyperpage{1187}
  \item \texttt  {PowerMod}, \hyperpage{864}
  \item \texttt  {PowerModCoeffs}, \hyperpage{313}
  \item \texttt  {PowerModInt}, \hyperpage{184}
  \item \texttt  {PowerPartition}, \hyperpage{217}
  \item \texttt  {PowerSubalgebraSeries}, \hyperpage{933}
  \item \texttt  {PQuotient}, \hyperpage{683}
  \item precedence, \hyperpage{57}
  \item precedence test
    \subitem for permutations, \hyperpage{595}
  \item \texttt  {PrecisionFloat}, \hyperpage{241}
  \item Prefix, \hyperpage{364}
  \item \texttt  {PrefrattiniSubgroup}, \hyperpage{517}
  \item \texttt{PrefrattiniSubgroup}
    \subitem for groups with pcgs, \hyperpage{649}
  \item \texttt  {PreImage}
    \subitem set of preimages of a collection under a general mapping, 
		\hyperpage{432}
    \subitem set of preimages of the range of a general mapping, 
		\hyperpage{432}
    \subitem unique preimage of an element under a general mapping, 
		\hyperpage{432}
  \item \texttt  {PreImageElm}, \hyperpage{431}
  \item \texttt  {PreImagePartialPerm}, \hyperpage{834}
  \item \texttt  {PreImages}
    \subitem set of preimages of a collection under a general mapping, 
		\hyperpage{432}
    \subitem set of preimages of an elm under a general mapping, 
		\hyperpage{432}
    \subitem set of preimages of the range of a general mapping, 
		\hyperpage{432}
  \item \texttt  {PreImagesElm}, \hyperpage{431}
  \item \texttt  {PreImagesOfTransformation}, \hyperpage{803}
  \item \texttt  {PreImagesRange}, \hyperpage{431}
  \item \texttt  {PreImagesRepresentative}, \hyperpage{431}
  \item \texttt  {PreImagesSet}, \hyperpage{432}
  \item preorder, \hyperpage{444}
  \item \texttt  {PresentationFpGroup}, \hyperpage{690}
  \item \texttt  {PresentationNormalClosure}, \hyperpage{697}
  \item \texttt  {PresentationNormalClosureRrs}, \hyperpage{697}
  \item \texttt  {PresentationSubgroup}, \hyperpage{693}
  \item \texttt  {PresentationSubgroupMtc}, \hyperpage{695}
  \item \texttt  {PresentationSubgroupRrs}
    \subitem for a group and a coset table (and a string), 
		\hyperpage{693}
    \subitem for two groups (and a string), \hyperpage{693}
  \item \texttt  {PresentationViaCosetTable}, \hyperpage{691}
  \item previous result, \hyperpage{79}
  \item \texttt  {PrevPrimeInt}, \hyperpage{186}
  \item \texttt  {PrimalityProof}, \hyperpage{185}
  \item primary subgroup generators, \hyperpage{712}
  \item \texttt  {PrimaryGeneratorWords}, \hyperpage{695}
  \item prime residue group, \hyperpage{195}
    \subitem exponent, \hyperpage{196}
    \subitem generator, \hyperpage{198}
    \subitem order, \hyperpage{196}
  \item \texttt  {PrimeBlocks}, \hyperpage{1091}
  \item \texttt  {PrimeBlocksOp}, \hyperpage{1091}
  \item \texttt  {PrimeDivisors}, \hyperpage{187}
  \item \texttt  {PrimeField}, \hyperpage{877}
  \item \texttt  {PrimePGroup}, \hyperpage{527}
  \item \texttt  {PrimePowersInt}, \hyperpage{189}
  \item \texttt  {PrimeResidues}, \hyperpage{195}
  \item \texttt  {Primes}, \hyperpage{184}
  \item primitive, \hyperpage{587}
  \item primitive root modulo an integer, \hyperpage{198}
  \item \texttt  {PrimitiveElement}, \hyperpage{877}
  \item \texttt  {PrimitiveGroup}, \hyperpage{750}
  \item \texttt  {PrimitiveGroupsIterator}, \hyperpage{750}
  \item \texttt  {PrimitiveIdentification}, \hyperpage{751}
  \item \texttt  {Primitive}\discretionary {-}{}{}\texttt  {Index}\discretionary {-}{}{}\texttt  {Irreducible}\discretionary {-}{}{}\texttt  {Solvable}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{753}
  \item \texttt  {PRI}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {V}\discretionary {-}{}{}\texttt  {E{\textunderscore }}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {N}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {C}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {S{\textunderscore }}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {AGMA}, 
		\hyperpage{751}
  \item \texttt  {PrimitivePolynomial}, \hyperpage{1007}
  \item \texttt  {PrimitiveRoot}, \hyperpage{888}
  \item \texttt  {PrimitiveRootMod}, \hyperpage{198}
  \item \texttt  {Print}, \hyperpage{83}
  \item \texttt  {PrintAmbiguity}, \hyperpage{1182}
  \item \texttt  {PrintArray}, \hyperpage{322}
  \item \texttt  {PrintCharacterTable}, \hyperpage{1101}
  \item \texttt  {PrintCSV}, \hyperpage{152}
  \item \texttt  {PrintFactorsInt}, \hyperpage{188}
  \item \texttt  {PrintFormattingStatus}, \hyperpage{146}
  \item \texttt  {PrintObj}, \hyperpage{84}
    \subitem for a character table, \hyperpage{1098}
    \subitem for a ffe, \hyperpage{890}
    \subitem for a string, \hyperpage{353}
    \subitem for a table of marks, \hyperpage{1049}
    \subitem for class functions, \hyperpage{1130}
  \item \texttt  {PrintString}, \hyperpage{360}
  \item \texttt  {PrintTo}, \hyperpage{136}
    \subitem for streams, \hyperpage{145}
  \item \texttt  {ProbabilityShapes}, \hyperpage{1008}
  \item procedure call, \hyperpage{60}
  \item procedure call with arguments, \hyperpage{60}
  \item \texttt  {Process}, \hyperpage{153}
  \item \texttt  {PRO}\discretionary {-}{}{}\texttt  {D{\textunderscore }}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {F2}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {T{\textunderscore }}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {F2}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {T{\textunderscore }}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {V}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {NCED}, 
		\hyperpage{337}
  \item \texttt  {PRO}\discretionary {-}{}{}\texttt  {D{\textunderscore }}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {F2}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {T{\textunderscore }}\discretionary {-}{}{}\texttt  {G}\discretionary {-}{}{}\texttt  {F2}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {T{\textunderscore }}\discretionary {-}{}{}\texttt  {S}\discretionary {-}{}{}\texttt  {I}\discretionary {-}{}{}\texttt  {MPLE}, 
		\hyperpage{337}
  \item \texttt  {Product}, \hyperpage{291}
  \item product
    \subitem of words, \hyperpage{476}
    \subitem rational functions, \hyperpage{996}
  \item \texttt  {ProductCoeffs}, \hyperpage{312}
  \item \texttt  {ProductOfStraightLinePrograms}, \hyperpage{487}
  \item \texttt  {ProductSpace}, \hyperpage{933}
  \item \texttt  {ProductX}, \hyperpage{294}
  \item \texttt  {ProfileFunctions}, \hyperpage{111}
  \item \texttt  {ProfileGlobalFunctions}, \hyperpage{111}
  \item \texttt  {ProfileLineByLine}, \hyperpage{117}
  \item \texttt  {ProfileMethods}, \hyperpage{112}
  \item \texttt  {ProfileOperations}, \hyperpage{111}
  \item \texttt  {ProfileOperationsAndMethods}, \hyperpage{111}
  \item \texttt  {ProjectedInducedPcgs}, \hyperpage{639}
  \item \texttt  {ProjectedPcElement}, \hyperpage{639}
  \item \texttt  {Projection}
    \subitem for a domain, \hyperpage{427}
    \subitem for a domain and a positive integer, \hyperpage{427}
    \subitem for group products, \hyperpage{724}
    \subitem for two domains, \hyperpage{427}
  \item \texttt{Projection}
    \subitem example for direct products, \hyperpage{719}
    \subitem example for semidirect products, \hyperpage{720}
    \subitem example for subdirect products, \hyperpage{721}
    \subitem example for wreath products, \hyperpage{722}
  \item \texttt  {ProjectionMap}, \hyperpage{1177}
  \item projections
    \subitem find all, \hyperpage{566}
  \item \texttt  {Projective}\discretionary {-}{}{}\texttt  {Action}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {Matrix}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{621}
  \item \texttt  {ProjectiveActionOnFullSpace}, \hyperpage{621}
  \item \texttt  {ProjectiveGeneralLinearGroup}, \hyperpage{734}
  \item \texttt  {ProjectiveGeneralUnitaryGroup}, \hyperpage{734}
  \item \texttt  {ProjectiveOmega}, \hyperpage{735}
  \item \texttt  {ProjectiveOrder}, \hyperpage{336}
  \item \texttt  {ProjectiveSpecialLinearGroup}, \hyperpage{734}
  \item \texttt  {ProjectiveSpecialUnitaryGroup}, \hyperpage{734}
  \item \texttt  {ProjectiveSymplecticGroup}, \hyperpage{735}
  \item prompt, \hyperpage{79}
    \subitem partial, \hyperpage{79}
  \item \texttt  {PRump}, \hyperpage{519}
  \item \texttt  {PseudoRandom}, \hyperpage{396}
    \subitem for finitely presented groups, \hyperpage{670}
  \item \texttt  {PSL}, \hyperpage{734}
  \item \texttt  {PSP}, \hyperpage{735}
  \item \texttt  {PSp}, \hyperpage{735}
  \item \texttt  {PSU}, \hyperpage{734}
  \item \texttt  {PthPowerImage}
    \subitem for basis and element, \hyperpage{971}
    \subitem for element, \hyperpage{971}
    \subitem for element and integer, \hyperpage{972}
  \item \texttt  {PthPowerImages}, \hyperpage{971}
  \item \texttt  {PurePadicNumberFamily}, \hyperpage{1029}
  \item \texttt  {PushOptions}, \hyperpage{127}

  \indexspace

  \item \texttt  {Quadratic}, \hyperpage{234}
  \item quadratic residue, \hyperpage{198, 199}
  \item \texttt  {QuaternionAlgebra}, \hyperpage{926}
  \item \texttt  {QuaternionGroup}, \hyperpage{727}
  \item \texttt{QUIET}, \hyperpage{1216}
  \item \texttt  {QUIT}, \hyperpage{92}
  \item \texttt{QUIT}
    \subitem emergency quit, \hyperpage{92}
  \item quit
    \subitem in emergency, \hyperpage{92}
  \item \texttt  {QUIT{\textunderscore }GAP}, \hyperpage{92}
  \item \texttt  {QUITTING}, \hyperpage{93}
  \item \texttt  {QuoInt}, \hyperpage{181}
  \item \texttt  {Quotient}, \hyperpage{850}
  \item quotient
    \subitem for finitely presented groups, \hyperpage{666}
    \subitem matrices, \hyperpage{317}
    \subitem matrix and matrix list, \hyperpage{317}
    \subitem matrix and scalar, \hyperpage{317}
    \subitem of free monoid, \hyperpage{790}
    \subitem of free semigroup, \hyperpage{787}
    \subitem of words, \hyperpage{476}
    \subitem rational functions, \hyperpage{996}
    \subitem scalar and matrix, \hyperpage{317}
    \subitem scalar and matrix list, \hyperpage{317}
    \subitem vector and matrix, \hyperpage{317}
  \item \texttt  {QuotientFromSCTable}, \hyperpage{926}
  \item \texttt  {QuotientMod}, \hyperpage{863}
  \item \texttt  {QuotientPolynomialsExtRep}, \hyperpage{1024}
  \item \texttt  {QuotientRemainder}, \hyperpage{861}
  \item \texttt  {QuotientSemigroupCongruence}, \hyperpage{773}
  \item \texttt  {QuotientSemigroupHomomorphism}, \hyperpage{773}
  \item \texttt  {QuotientSemigroupPreimage}, \hyperpage{773}
  \item \texttt  {QuotRemLaurpols}, \hyperpage{1002}

  \indexspace

  \item $r_N$ (irrational value), \hyperpage{230}
  \item \texttt  {RadicalGroup}, \hyperpage{518}
  \item \texttt  {RadicalOfAlgebra}, \hyperpage{938}
  \item \texttt  {Random}
    \subitem for a list or collection, \hyperpage{396}
    \subitem for integers, \hyperpage{181}
    \subitem for lower and upper bound, \hyperpage{396}
    \subitem for random source and list, \hyperpage{192}
    \subitem for random source and two integers, \hyperpage{192}
    \subitem for rationals, \hyperpage{222}
  \item \texttt{Random}, \hyperpage{396}
  \item random seed, \hyperpage{397}
  \item \texttt  {RandomBinaryRelationOnPoints}, \hyperpage{445}
  \item \texttt  {RandomInvertibleMat}, \hyperpage{323}
  \item \texttt  {RandomIsomorphismTest}, \hyperpage{663}
  \item \texttt  {RandomList}, \hyperpage{397}
  \item \texttt  {RandomMat}, \hyperpage{322}
  \item \texttt  {RandomPartialPerm}
    \subitem for a positive integer, \hyperpage{823}
    \subitem for a set of positive integers, \hyperpage{823}
    \subitem for domain and image, \hyperpage{823}
  \item \texttt  {RandomPrimitivePolynomial}, \hyperpage{890}
  \item \texttt  {RandomSource}, \hyperpage{194}
  \item \texttt  {RandomTransformation}, \hyperpage{798}
  \item \texttt  {RandomUnimodularMat}, \hyperpage{323}
  \item \texttt  {Range}
    \subitem of a general mapping, \hyperpage{428}
  \item range, \hyperpage{294}
  \item \texttt  {RankAction}
    \subitem for a group, an action domain, etc., \hyperpage{586}
    \subitem for an external set, \hyperpage{586}
  \item \texttt  {RankFilter}, \hyperpage{166}
  \item \texttt  {RankMat}, \hyperpage{323}
  \item \texttt  {RankOfPartialPerm}, \hyperpage{824}
  \item \texttt  {RankOfPartialPermCollection}, \hyperpage{824}
  \item \texttt  {RankOfPartialPermSemigroup}, \hyperpage{838}
  \item \texttt  {RankOfTransformation}
    \subitem for a transformation and a list, \hyperpage{804}
    \subitem for a transformation and a positive integer, 
		\hyperpage{804}
  \item \texttt  {RankPGroup}, \hyperpage{528}
  \item \texttt  {Rat}, \hyperpage{222}
    \subitem for floats, \hyperpage{243}
    \subitem for strings, \hyperpage{366}
  \item \texttt  {RationalClass}, \hyperpage{513}
  \item \texttt  {RationalClasses}, \hyperpage{513}
  \item \texttt  {RationalFunctionByExtRep}, \hyperpage{1023}
  \item \texttt  {RationalFunctionByExtRepNC}, \hyperpage{1023}
  \item \texttt  {Rational}\discretionary {-}{}{}\texttt  {Function}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Ext}\discretionary {-}{}{}\texttt  {Rep}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Cancellation}, 
		\hyperpage{1025}
  \item \texttt  {RationalFunctionsFamily}, \hyperpage{1020}
  \item \texttt  {RationalizedMat}, \hyperpage{235}
  \item \texttt  {Rationals}, \hyperpage{220}
  \item \texttt  {RClassOfHClass}, \hyperpage{774}
  \item \texttt  {Read}, \hyperpage{135}
    \subitem for streams, \hyperpage{142}
  \item read eval print loop, \hyperpage{79}
  \item \texttt  {ReadAll}, \hyperpage{143}
  \item \texttt  {ReadAllLine}, \hyperpage{150}
  \item \texttt  {ReadAsFunction}, \hyperpage{136}
    \subitem for streams, \hyperpage{142}
  \item \texttt  {ReadByte}, \hyperpage{142}
  \item \texttt  {ReadCommandLineHistory}, \hyperpage{97}
  \item \texttt  {ReadCSV}, \hyperpage{152}
  \item \texttt  {ReadLine}, \hyperpage{142}
  \item \texttt{ReadlineInitLine}, \hyperpage{96}
  \item \texttt  {ReadPackage}, \hyperpage{1207}
  \item \texttt{ReadPkg}, \hyperpage{1216}
  \item \texttt  {RealClasses}, \hyperpage{1087}
  \item \texttt  {RealizableBrauerCharacters}, \hyperpage{1163}
  \item \texttt  {RealPart}, \hyperpage{233}
  \item \texttt  {RecNames}, \hyperpage{378}
  \item record
    \subitem component access, \hyperpage{378}
    \subitem component assignment, \hyperpage{379}
    \subitem component variable, \hyperpage{378}
    \subitem component variable assignment, \hyperpage{379}
  \item record assignment
    \subitem operation, \hyperpage{383}
  \item record boundness test
    \subitem operation, \hyperpage{383}
  \item record component
    \subitem operation, \hyperpage{383}
  \item record unbind
    \subitem operation, \hyperpage{383}
  \item recursion, \hyperpage{66}
  \item \texttt  {RedispatchOnCondition}, \hyperpage{1222}
  \item redisplay a help section, \hyperpage{29}
  \item redisplay with next help viewer, \hyperpage{29}
  \item \texttt  {ReduceCoeffs}, \hyperpage{312}
  \item \texttt  {ReduceCoeffsMod}, \hyperpage{312}
  \item \texttt  {ReducedAdditiveInverse}, \hyperpage{492}
  \item \texttt  {ReducedCharacters}, \hyperpage{1143}
  \item \texttt  {ReducedClassFunctions}, \hyperpage{1142}
  \item \texttt  {ReducedComm}, \hyperpage{492}
  \item \texttt  {ReducedConfluentRewritingSystem}, \hyperpage{790}
  \item \texttt  {ReducedConjugate}, \hyperpage{492}
  \item \texttt  {ReducedDifference}, \hyperpage{492}
  \item \texttt  {ReducedForm}, \hyperpage{491}
  \item \texttt  {ReducedGroebnerBasis}
    \subitem for a list and a monomial ordering, \hyperpage{1019}
    \subitem for an ideal and a monomial ordering, \hyperpage{1019}
  \item \texttt  {ReducedInverse}, \hyperpage{492}
  \item \texttt  {ReducedLeftQuotient}, \hyperpage{492}
  \item \texttt  {ReducedOne}, \hyperpage{492}
  \item \texttt  {ReducedPcElement}, \hyperpage{633}
  \item \texttt  {ReducedPower}, \hyperpage{492}
  \item \texttt  {ReducedProduct}, \hyperpage{492}
  \item \texttt  {ReducedQuotient}, \hyperpage{492}
  \item \texttt  {ReducedScalarProduct}, \hyperpage{492}
  \item \texttt  {ReducedSum}, \hyperpage{492}
  \item \texttt  {ReducedZero}, \hyperpage{492}
  \item \texttt  {ReduceRules}, \hyperpage{491}
  \item \texttt  {ReduceStabChain}, \hyperpage{614}
  \item \texttt  {Ree}, \hyperpage{729}
  \item \texttt  {ReeGroup}, \hyperpage{729}
  \item \texttt  {ReesCongruenceOfSemigroupIdeal}, \hyperpage{772}
  \item \texttt  {ReesMatrixSemigroup}, \hyperpage{777}
  \item \texttt  {ReesMatrixSemigroupElement}, \hyperpage{780}
  \item \texttt  {ReesMatrixSubsemigroup}, \hyperpage{778}
  \item \texttt  {ReesZeroMatrixSemigroup}, \hyperpage{777}
  \item \texttt  {ReesZeroMatrixSemigroupElement}, \hyperpage{780}
  \item \texttt  {ReesZeroMatrixSubsemigroup}, \hyperpage{778}
  \item \texttt  {RefinedPcGroup}, \hyperpage{656}
  \item \texttt  {ReflectionMat}, \hyperpage{322}
  \item reflexive relation, \hyperpage{443}
  \item \texttt  {ReflexiveClosureBinaryRelation}, \hyperpage{445}
  \item regular, \hyperpage{586}
  \item regular action, \hyperpage{581}
  \item \texttt  {RegularActionHomomorphism}, \hyperpage{582}
  \item \texttt  {RegularModule}, \hyperpage{1106}
  \item relations, \hyperpage{424}
  \item \texttt  {RelationsOfFpSemigroup}, \hyperpage{789}
  \item \texttt  {RelativeBasis}, \hyperpage{905}
  \item \texttt  {RelativeBasisNC}, \hyperpage{905}
  \item \texttt  {RelativeDiameter}, \hyperpage{241}
  \item relatively prime, \hyperpage{58}
  \item \texttt  {RelativeOrderOfPcElement}, \hyperpage{631}
  \item \texttt  {RelativeOrders}, \hyperpage{630}
  \item \texttt{RelativeOrders}
    \subitem of a pcgs, \hyperpage{630}
  \item \texttt  {RelatorsOfFpGroup}, \hyperpage{668}
  \item remainder
    \subitem operation, \hyperpage{413}
  \item remainder of a quotient, \hyperpage{182}
  \item \texttt  {RemInt}, \hyperpage{182}
  \item \texttt  {Remove}, \hyperpage{256}
  \item remove
    \subitem an element from a set, \hyperpage{281}
  \item \texttt  {RemoveCharacters}, \hyperpage{363}
  \item \texttt  {RemoveFile}, \hyperpage{138}
  \item \texttt  {RemoveOuterCoeffs}, \hyperpage{310}
  \item \texttt  {RemoveRelator}, \hyperpage{701}
  \item \texttt  {RemoveSet}, \hyperpage{281}
  \item \texttt  {RemoveStabChain}, \hyperpage{615}
  \item \texttt{repeat} loop, \hyperpage{62}
  \item \texttt  {ReplacedString}, \hyperpage{362}
  \item representation
    \subitem as a sum of two squares, \hyperpage{203}
  \item \texttt  {RepresentationsOfObject}, \hyperpage{170}
  \item \texttt  {Representative}, \hyperpage{393}
  \item representative
    \subitem of a list or collection, \hyperpage{393}
  \item \texttt  {RepresentativeAction}, \hyperpage{580}
  \item \texttt  {RepresentativeLinearOperation}, \hyperpage{945}
  \item \texttt{RepresentativeOperation}, \hyperpage{1215}
  \item \texttt  {RepresentativesContainedRightCosets}, \hyperpage{510}
  \item \texttt  {RepresentativesFusions}, \hyperpage{1175}
  \item \texttt  {RepresentativeSmallest}, \hyperpage{393}
  \item \texttt  {RepresentativesMinimalBlocks}
    \subitem for a group, an action domain, etc., \hyperpage{588}
    \subitem for an external set, \hyperpage{588}
  \item \texttt  {RepresentativesPerfectSubgroups}, \hyperpage{540}
  \item \texttt  {RepresentativesPowerMaps}, \hyperpage{1168}
  \item \texttt  {RepresentativesSimpleSubgroups}, \hyperpage{540}
  \item \texttt  {RepresentativeTom}, \hyperpage{1064}
  \item \texttt  {RepresentativeTomByGenerators}, \hyperpage{1064}
  \item \texttt  {RepresentativeTomByGeneratorsNC}, \hyperpage{1064}
  \item \texttt{RequirePackage}, \hyperpage{1216}
  \item \texttt  {Reread}, \hyperpage{138}
  \item \texttt  {REREADING}, \hyperpage{138}
  \item \texttt  {RereadPackage}, \hyperpage{1207}
  \item \texttt{RereadPkg}, \hyperpage{1216}
  \item \texttt  {Reset}, \hyperpage{193}
  \item \texttt  {ResetFilterObj}, \hyperpage{1228}
  \item \texttt  {ResetOptionsStack}, \hyperpage{128}
  \item residue
    \subitem quadratic, \hyperpage{198, 199}
  \item \texttt  {RespectsAddition}, \hyperpage{435}
  \item \texttt  {RespectsAdditiveInverses}, \hyperpage{435}
  \item \texttt  {RespectsInverses}, \hyperpage{434}
  \item \texttt  {RespectsMultiplication}, \hyperpage{434}
  \item \texttt  {RespectsOne}, \hyperpage{434}
  \item \texttt  {RespectsScalarMultiplication}, \hyperpage{437}
  \item \texttt  {RespectsZero}, \hyperpage{436}
  \item \texttt  {RestrictedClassFunction}, \hyperpage{1140}
  \item \texttt  {RestrictedClassFunctions}, \hyperpage{1140}
  \item \texttt  {Restricted}\discretionary {-}{}{}\texttt  {Lie}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Structure}\discretionary {-}{}{}\texttt  {Constants}, 
		\hyperpage{959}
  \item \texttt  {RestrictedMapping}, \hyperpage{427}
  \item \texttt  {RestrictedPartialPerm}, \hyperpage{821}
  \item \texttt  {RestrictedPartitions}, \hyperpage{215}
  \item \texttt  {RestrictedPerm}, \hyperpage{598}
  \item \texttt  {RestrictedPermNC}, \hyperpage{598}
  \item \texttt  {RestrictedTransformation}, \hyperpage{800}
  \item \texttt  {RestrictedTransformationNC}, \hyperpage{800}
  \item \texttt  {RestrictOutputsOfSLP}, \hyperpage{486}
  \item \texttt  {Resultant}, \hyperpage{1005}
  \item \texttt  {ResultOfStraightLineProgram}, \hyperpage{484}
  \item \texttt{return}, \hyperpage{86}
    \subitem no value, \hyperpage{69}
    \subitem with value, \hyperpage{69}
  \item return from break loop, \hyperpage{86}
  \item \texttt  {ReturnFail}, \hyperpage{75}
  \item \texttt  {ReturnFalse}, \hyperpage{75}
  \item \texttt  {ReturnFirst}, \hyperpage{75}
  \item \texttt  {ReturnNothing}, \hyperpage{75}
  \item \texttt  {ReturnTrue}, \hyperpage{74}
  \item \texttt  {Reversed}, \hyperpage{284}
  \item \texttt  {ReverseNaturalPartialOrder}, \hyperpage{839}
  \item \texttt  {RewindStream}, \hyperpage{144}
  \item \texttt  {RewriteWord}, \hyperpage{677}
  \item right cosets, \hyperpage{507}
  \item \texttt  {RightActingAlgebra}, \hyperpage{949}
  \item \texttt  {RightActingRingOfIdeal}, \hyperpage{854}
  \item \texttt  {RightAlgebraModule}, \hyperpage{947}
  \item \texttt  {RightAlgebraModuleByGenerators}, \hyperpage{946}
  \item \texttt  {RightCoset}, \hyperpage{507}
  \item \texttt  {RightCosets}, \hyperpage{508}
  \item \texttt  {RightCosetsNC}, \hyperpage{508}
  \item \texttt  {RightDerivations}, \hyperpage{960}
  \item \texttt  {RightIdeal}, \hyperpage{851}
  \item \texttt  {RightIdealByGenerators}, \hyperpage{853}
  \item \texttt  {RightIdealNC}, \hyperpage{852}
  \item \texttt  {RightModuleByHomomorphismToMatAlg}, \hyperpage{950}
  \item \texttt  {RightOne}
    \subitem for a partial perm, \hyperpage{830}
    \subitem for a transformation, \hyperpage{811}
  \item \texttt  {RightShiftRowVector}, \hyperpage{309}
  \item \texttt  {RightTransversal}, \hyperpage{509}
  \item \texttt  {Ring}
    \subitem for a collection, \hyperpage{848}
    \subitem for ring elements, \hyperpage{848}
  \item \texttt  {RingByGenerators}, \hyperpage{849}
  \item \texttt  {RingByStructureConstants}, \hyperpage{867}
  \item \texttt  {RingGeneralMappingByImages}, \hyperpage{864}
  \item \texttt  {RingHomomorphismByImages}, \hyperpage{865}
  \item \texttt  {RingHomomorphismByImagesNC}, \hyperpage{865}
  \item \texttt  {RingWithOne}
    \subitem for a collection, \hyperpage{855}
    \subitem for ring elements, \hyperpage{855}
  \item \texttt  {RingWithOneByGenerators}, \hyperpage{855}
  \item \texttt  {RNamObj}
    \subitem for a positive integer, \hyperpage{383}
    \subitem for a string, \hyperpage{383}
  \item root
    \subitem of 1 modulo an integer, \hyperpage{200}
    \subitem of an integer, \hyperpage{180}
    \subitem of an integer modulo another, \hyperpage{199}
    \subitem of an integer, smallest, \hyperpage{180}
  \item \texttt  {RootInt}, \hyperpage{180}
  \item \texttt  {RootMod}, \hyperpage{199}
  \item \texttt  {RootOfDefiningPolynomial}, \hyperpage{877}
  \item roots of unity, \hyperpage{223}
  \item \texttt  {RootsMod}, \hyperpage{200}
  \item \texttt  {RootsOfPolynomial}, \hyperpage{1001}
  \item \texttt  {RootsOfUPol}, \hyperpage{1002}
  \item \texttt  {RootsUnityMod}, \hyperpage{200}
  \item \texttt  {RootSystem}, \hyperpage{966}
  \item \texttt  {Round}, \hyperpage{241}
  \item \texttt  {RoundCyc}, \hyperpage{226}
  \item row spaces, \hyperpage{910}
  \item \texttt  {Rows}, \hyperpage{782}
  \item \texttt  {RREF}, \hyperpage{323}
  \item \texttt  {Rules}, \hyperpage{490}
  \item \texttt  {Runtime}, \hyperpage{110}
  \item \texttt  {Runtimes}, \hyperpage{109}

  \indexspace

  \item $s_N$ (irrational value), \hyperpage{230}
  \item \texttt  {SameBlock}, \hyperpage{1092}
  \item save, \hyperpage{42}
  \item \texttt  {SaveCommandLineHistory}, \hyperpage{97}
  \item \texttt  {SaveOnExitFile}, \hyperpage{93}
  \item \texttt  {SaveWorkspace}, \hyperpage{42}
  \item saving on exit, \hyperpage{92}
  \item \texttt  {ScalarProduct}
    \subitem for characters, \hyperpage{1135}
  \item Schreier, \hyperpage{693}
  \item Schreier-Sims
    \subitem random, \hyperpage{605}
  \item Schur multiplier, \hyperpage{549}
  \item \texttt  {SchurCover}, \hyperpage{549}
  \item \texttt  {SchurCoverOfSymmetricGroup}, \hyperpage{552}
  \item scope, \hyperpage{50}
  \item \texttt  {Sec}, \hyperpage{240}
  \item \texttt  {Sech}, \hyperpage{240}
  \item \texttt  {SecHMSM}, \hyperpage{369}
  \item secondary subgroup generators, \hyperpage{712}
  \item \texttt  {SecondsDMYhms}, \hyperpage{370}
  \item \texttt  {SeekPositionStream}, \hyperpage{144}
  \item \texttt  {SemidirectProduct}
    \subitem for a group of automorphisms and a group, \hyperpage{719}
    \subitem for acting group, action, and a group, \hyperpage{719}
  \item \texttt  {SemiEchelonBasis}, \hyperpage{912}
  \item \texttt  {SemiEchelonBasisNC}, \hyperpage{912}
  \item \texttt  {SemiEchelonMat}, \hyperpage{328}
  \item \texttt  {SemiEchelonMatDestructive}, \hyperpage{328}
  \item \texttt  {SemiEchelonMats}, \hyperpage{329}
  \item \texttt  {SemiEchelonMatsDestructive}, \hyperpage{329}
  \item \texttt  {SemiEchelonMatTransformation}, \hyperpage{329}
  \item \texttt  {Semigroup}
    \subitem for a list, \hyperpage{762}
    \subitem for various generators, \hyperpage{762}
  \item semigroup, \hyperpage{762}
  \item \texttt  {SemigroupByGenerators}, \hyperpage{763}
  \item \texttt  {SemigroupByMultiplicationTable}, \hyperpage{765}
  \item \texttt  {SemigroupIdealByGenerators}, \hyperpage{772}
  \item \texttt  {SemigroupOfRewritingSystem}, \hyperpage{792}
  \item semiregular, \hyperpage{586}
  \item \texttt  {SemiSimpleType}, \hyperpage{965}
  \item sequence
    \subitem Bernoulli, \hyperpage{206}
    \subitem Fibonacci, \hyperpage{217}
    \subitem Lucas, \hyperpage{218}
  \item \texttt  {Set}, \hyperpage{389}
  \item set difference
    \subitem of collections, \hyperpage{395}
  \item set stabilizer, \hyperpage{578}
  \item \texttt  {SetAssertionLevel}, \hyperpage{108}
  \item \texttt  {SetCommutator}, \hyperpage{655}
  \item \texttt  {SetConjugate}, \hyperpage{655}
  \item \texttt  {SetCrystGroupDefaultAction}, \hyperpage{627}
  \item \texttt  {SetCyclotomicsLimit}, \hyperpage{236}
  \item \texttt  {SetDefaultInfoOutput}, \hyperpage{108}
  \item \texttt  {SetElmWPObj}, \hyperpage{1301}
  \item \texttt  {SetEntrySCTable}, \hyperpage{925}
  \item \texttt  {SetFilterObj}, \hyperpage{1227}
  \item \texttt  {SetFloats}, \hyperpage{243}
  \item \texttt  {SetGasmanMessageStatus}, \hyperpage{125}
  \item \texttt  {SetHelpViewer}, \hyperpage{30}
  \item \texttt  {SetIndeterminateName}, \hyperpage{995}
  \item \texttt  {SetInfoHandler}, \hyperpage{107}
  \item \texttt  {SetInfoLevel}, \hyperpage{106}
  \item \texttt  {SetInfoOutput}, \hyperpage{107}
  \item \texttt  {SetName}, \hyperpage{162}
  \item \texttt  {SetNameObject}, \hyperpage{85}
  \item \texttt  {SetPackagePath}, \hyperpage{1205}
  \item \texttt  {SetParent}, \hyperpage{406}
  \item \texttt  {SetPower}, \hyperpage{655}
  \item \texttt  {SetPrintFormattingStatus}, \hyperpage{146}
  \item \texttt  {SetRecursionTrapInterval}, \hyperpage{124}
  \item \texttt  {SetReducedMultiplication}, \hyperpage{668}
  \item Sets, \hyperpage{249}
  \item sets, \hyperpage{279}
  \item \texttt  {Setter}, \hyperpage{171}
  \item setter, \hyperpage{171}
  \item \texttt  {SetUserPreference}, \hyperpage{39}
  \item \texttt  {SetX}, \hyperpage{294}
  \item \texttt  {ShallowCopy}, \hyperpage{161}
  \item \texttt{ShallowCopy}
    \subitem for lists, \hyperpage{259}
  \item \texttt  {ShiftedCoeffs}, \hyperpage{313}
  \item \texttt  {ShiftedPadicNumber}, \hyperpage{1030}
  \item short vectors spanning a lattice, \hyperpage{346}, 
		\hyperpage{1143}
  \item \texttt  {ShortestVectors}, \hyperpage{348}
  \item \texttt  {ShortLexLeqPartialPerm}, \hyperpage{835}
  \item \texttt  {ShortLexOrdering}, \hyperpage{454}
  \item \texttt  {ShowAdditionTable}, \hyperpage{847}
  \item \texttt  {ShowArgument}, \hyperpage{103}
  \item \texttt  {ShowArguments}, \hyperpage{102}
  \item \texttt  {ShowDetails}, \hyperpage{103}
  \item \texttt  {ShowGcd}, \hyperpage{862}
  \item \texttt  {ShowImpliedFilters}, \hyperpage{166}
  \item \texttt  {ShowMethods}, \hyperpage{103}
  \item \texttt  {ShowMultiplicationTable}, \hyperpage{847}
  \item \texttt  {ShowOtherMethods}, \hyperpage{103}
  \item \texttt  {ShowPackageVariables}, \hyperpage{1211}
  \item \texttt  {ShowUserPreferences}, \hyperpage{39}
  \item \texttt  {ShrinkAllocationPlist}, \hyperpage{262}
  \item \texttt  {ShrinkAllocationString}, \hyperpage{357}
  \item \texttt  {ShrinkRowVector}, \hyperpage{309}
  \item \texttt  {Shuffle}, \hyperpage{285}
  \item \texttt  {SiftedPcElement}, \hyperpage{632}
  \item \texttt  {SiftedPermutation}, \hyperpage{613}
  \item \texttt  {SiftedVector}, \hyperpage{914}
  \item \texttt  {Sigma}, \hyperpage{201}
  \item \texttt  {SigmaL}, \hyperpage{734}
  \item sign
    \subitem of an integer, \hyperpage{179}
  \item \texttt  {SignFloat}, \hyperpage{241}
  \item \texttt  {SignInt}, \hyperpage{179}
  \item \texttt  {SignPartition}, \hyperpage{216}
  \item \texttt  {SignPerm}, \hyperpage{597}
  \item \texttt  {SimpleGroup}, \hyperpage{525}
  \item \texttt  {SimpleGroupsIterator}, \hyperpage{526}
  \item \texttt  {SimpleLieAlgebra}, \hyperpage{961}
  \item \texttt  {SimpleSystem}, \hyperpage{967}
  \item \texttt  {SimplifiedFpGroup}, \hyperpage{693}
  \item \texttt  {SimplifyPresentation}, \hyperpage{702}
  \item \texttt  {SimsNo}, \hyperpage{751}
  \item \texttt  {SimultaneousEigenvalues}, \hyperpage{336}
  \item \texttt  {Sin}, \hyperpage{240}
  \item \texttt  {SinCos}, \hyperpage{240}
  \item \texttt  {SingleCollector}, \hyperpage{655}
  \item singlequote character, \hyperpage{355}
  \item singlequotes, \hyperpage{352}
  \item \texttt  {Sinh}, \hyperpage{240}
  \item \texttt  {SIntChar}, \hyperpage{365}
  \item \texttt  {Size}, \hyperpage{392}
    \subitem for a character table, \hyperpage{1082}
  \item \texttt{Size}
    \subitem for groups with pcgs, \hyperpage{649}
  \item size
    \subitem of a list or collection, \hyperpage{392}
  \item \texttt  {SizeBlist}, \hyperpage{299}
  \item \texttt  {SizeConsiderFunction}, \hyperpage{543}
  \item \texttt  {SizeNumbersPerfectGroups}, \hyperpage{745}
  \item \texttt  {SizeOfFieldOfDefinition}, \hyperpage{1162}
  \item \texttt  {SizesCentralisers}, \hyperpage{1084}
  \item \texttt  {SizesCentralizers}, \hyperpage{1084}
  \item \texttt  {SizesConjugacyClasses}, \hyperpage{1084}
  \item \texttt  {SizeScreen}, \hyperpage{100}
  \item \texttt  {SizesPerfectGroups}, \hyperpage{744}
  \item \texttt  {SizeStabChain}, \hyperpage{612}
  \item \texttt  {SL}
    \subitem for dimension and a field size, \hyperpage{731}
    \subitem for dimension and a ring, \hyperpage{731}
  \item \texttt  {SlotUsagePattern}, \hyperpage{487}
  \item smaller
    \subitem associative words, \hyperpage{476}
    \subitem elements of finitely presented groups, \hyperpage{667}
    \subitem for pcwords, \hyperpage{653}
    \subitem for transformations, \hyperpage{802}
    \subitem nonassociative words, \hyperpage{469}
    \subitem rational functions, \hyperpage{997}
  \item smaller or equal, \hyperpage{56}
  \item smaller test, \hyperpage{56}
  \item \texttt  {Smaller}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Permutation}\discretionary {-}{}{}\texttt  {Representation}, 
		\hyperpage{601}
  \item \texttt  {SmallestGeneratorPerm}, \hyperpage{596}
  \item \texttt  {SmallestIdempotentPower}
    \subitem for a partial perm, \hyperpage{829}
    \subitem for a transformation, \hyperpage{809}
  \item \texttt  {SmallestImageOfMovedPoint}
    \subitem for a partial permutation, \hyperpage{827}
    \subitem for a partial permutation coll, \hyperpage{827}
    \subitem for a transformation, \hyperpage{806}
    \subitem for a transformation coll, \hyperpage{806}
  \item \texttt  {SmallestMovedPoint}
    \subitem for a list or collection of permutations, \hyperpage{596}
    \subitem for a partial perm, \hyperpage{827}
    \subitem for a partial perm coll, \hyperpage{827}
    \subitem for a permutation, \hyperpage{596}
    \subitem for a transformation, \hyperpage{805}
    \subitem for a transformation coll, \hyperpage{805}
  \item \texttt  {SmallestRootInt}, \hyperpage{180}
  \item \texttt  {SmallGeneratingSet}, \hyperpage{545}
  \item \texttt  {SmallGroup}
    \subitem for a pair [ order, index ], \hyperpage{741}
    \subitem for group order and index, \hyperpage{741}
  \item \texttt  {SmallGroupsInformation}, \hyperpage{742}
  \item \texttt  {SmallRing}, \hyperpage{865}
  \item \texttt  {SmallSimpleGroup}, \hyperpage{526}
  \item Smith normal form, \hyperpage{1216}
  \item \texttt  {SmithNormalFormIntegerMat}, \hyperpage{342}
  \item \texttt  {SmithNormalFormIntegerMatTransforms}, \hyperpage{342}
  \item \texttt  {SMTX.AbsoluteIrreducibilityTest}, \hyperpage{1042}
  \item \texttt  {SMTX.AlgEl}, \hyperpage{1043}
  \item \texttt  {SMTX.AlgElCharPol}, \hyperpage{1043}
  \item \texttt  {SMTX.AlgElCharPolFac}, \hyperpage{1043}
  \item \texttt  {SMTX.AlgElMat}, \hyperpage{1043}
  \item \texttt  {SMTX.AlgElNullspaceDimension}, \hyperpage{1044}
  \item \texttt  {SMTX.AlgElNullspaceVec}, \hyperpage{1043}
  \item \texttt  {SMTX.CentMat}, \hyperpage{1044}
  \item \texttt  {SMTX.CentMatMinPoly}, \hyperpage{1044}
  \item \texttt  {SMTX.CompleteBasis}, \hyperpage{1043}
  \item \texttt  {SMTX.Getter}, \hyperpage{1042}
  \item \texttt  {SMTX.GoodElementGModule}, \hyperpage{1041}
  \item \texttt  {SMTX.IrreducibilityTest}, \hyperpage{1042}
  \item \texttt  {SMTX.MatrixSum}, \hyperpage{1042}
  \item \texttt  {SMTX.MinimalSubGModule}, \hyperpage{1042}
  \item \texttt  {SMTX.MinimalSubGModules}, \hyperpage{1042}
  \item \texttt  {SMTX.RandomIrreducibleSubGModule}, \hyperpage{1041}
  \item \texttt  {SMTX.Setter}, \hyperpage{1042}
  \item \texttt  {SMTX.SortHomGModule}, \hyperpage{1041}
  \item \texttt  {SMTX.Subbasis}, \hyperpage{1043}
  \item \texttt  {SO}, \hyperpage{732}
  \item \texttt  {Socle}, \hyperpage{518}
  \item \texttt  {SocleTypePrimitiveGroup}, \hyperpage{604}
  \item \texttt  {SolutionIntMat}, \hyperpage{339}
  \item \texttt  {SolutionMat}, \hyperpage{325}
  \item \texttt  {SolutionMatDestructive}, \hyperpage{325}
  \item \texttt  {SolutionNullspaceIntMat}, \hyperpage{339}
  \item \texttt  {SolvableQuotient}
    \subitem for a f.p. group and a list of primes, \hyperpage{685}
    \subitem for a f.p. group and a list of tuples, \hyperpage{685}
    \subitem for a f.p. group and a size, \hyperpage{685}
  \item \texttt  {Sort}, \hyperpage{277}
  \item \texttt  {SortBy}, \hyperpage{277}
  \item Sorted Lists as Collections, \hyperpage{385}
  \item \texttt  {SortedCharacters}, \hyperpage{1115}
  \item \texttt  {SortedCharacterTable}
    \subitem relative to the table of a factor group, \hyperpage{1115}
    \subitem w.r.t. a normal subgroup, \hyperpage{1115}
    \subitem w.r.t. a series of normal subgroups, \hyperpage{1115}
  \item \texttt  {SortedList}, \hyperpage{388}
  \item \texttt  {SortedSparseActionHomomorphism}, \hyperpage{581}
  \item \texttt  {SortedTom}, \hyperpage{1050}
  \item \texttt  {Sortex}, \hyperpage{278}
  \item \texttt  {SortingPerm}, \hyperpage{279}
  \item \texttt  {SortParallel}, \hyperpage{278}
  \item \texttt  {Source}, \hyperpage{429}
  \item \texttt  {SourceOfIsoclinicTable}, \hyperpage{1113}
  \item \texttt  {SP}
    \subitem for dimension and a ring, \hyperpage{732}
    \subitem for dimension and field size, \hyperpage{732}
  \item \texttt  {Sp}
    \subitem for dimension and a ring, \hyperpage{732}
    \subitem for dimension and field size, \hyperpage{732}
  \item space, \hyperpage{47}
  \item \texttt  {SparseActionHomomorphism}, \hyperpage{581}
  \item \texttt  {SparseCartanMatrix}, \hyperpage{968}
  \item \texttt  {SparseHashTable}, \hyperpage{376}
  \item \texttt  {SparseIntKey}, \hyperpage{375}
  \item special character sequences, \hyperpage{354}
  \item \texttt  {SpecialLinearGroup}
    \subitem for dimension and a field size, \hyperpage{731}
    \subitem for dimension and a ring, \hyperpage{731}
  \item \texttt  {SpecialOrthogonalGroup}, \hyperpage{732}
  \item \texttt  {SpecialPcgs}
    \subitem for a group, \hyperpage{646}
    \subitem for a pcgs, \hyperpage{646}
  \item \texttt  {SpecialSemilinearGroup}, \hyperpage{734}
  \item \texttt  {SpecialUnitaryGroup}, \hyperpage{731}
  \item \texttt  {SplitCharacters}, \hyperpage{1108}
  \item \texttt  {SplitExtension}, \hyperpage{660}
    \subitem with specified homomorphism, \hyperpage{662}
  \item \texttt  {SplitString}, \hyperpage{362}
  \item \texttt  {SplittingField}, \hyperpage{1000}
  \item Spreadsheet, \hyperpage{152}
  \item \texttt  {SQ}
    \subitem synonym of SolvableQuotient, \hyperpage{685}
  \item \texttt  {Sqrt}, \hyperpage{414}
  \item \texttt  {Square}, \hyperpage{241}
  \item square root
    \subitem of an integer, \hyperpage{180}
  \item \texttt  {SquareRoots}, \hyperpage{466}
  \item \texttt  {SSortedList}, \hyperpage{389}
  \item \texttt  {StabChain}
    \subitem for a group (and a record), \hyperpage{608}
    \subitem for a group and a base, \hyperpage{608}
  \item \texttt  {StabChainBaseStrongGenerators}, \hyperpage{609}
  \item \texttt  {StabChainImmutable}, \hyperpage{608}
  \item \texttt  {StabChainMutable}
    \subitem for a group, \hyperpage{608}
    \subitem for a homomorphism, \hyperpage{608}
  \item \texttt  {StabChainOp}, \hyperpage{608}
  \item \texttt  {StabChainOptions}, \hyperpage{609}
  \item \texttt  {Stabilizer}, \hyperpage{578}
  \item \texttt  {StabilizerOfExternalSet}, \hyperpage{591}
  \item \texttt  {StabilizerPcgs}, \hyperpage{649}
  \item Stack trace, \hyperpage{89}
  \item \texttt  {StandardAssociate}, \hyperpage{858}
  \item \texttt  {StandardAssociateUnit}, \hyperpage{859}
  \item \texttt  {StandardizeTable}, \hyperpage{675}
  \item \texttt  {StandardWreathProduct}, \hyperpage{722}
  \item \texttt  {StarCyc}, \hyperpage{233}
  \item \texttt  {StartlineFunc}, \hyperpage{71}
  \item \texttt  {StartsWith}, \hyperpage{364}
  \item \texttt  {START{\textunderscore }TEST}, \hyperpage{118}
  \item \texttt  {State}, \hyperpage{193}
  \item Stirling number of the first kind, \hyperpage{207}
  \item Stirling number of the second kind, \hyperpage{207}
  \item \texttt  {Stirling1}, \hyperpage{207}
  \item \texttt  {Stirling2}, \hyperpage{207}
  \item \texttt  {STOP{\textunderscore }TEST}, \hyperpage{118}
  \item \texttt  {StoredGroebnerBasis}, \hyperpage{1019}
  \item \texttt  {StoreFusion}, \hyperpage{1172}
  \item \texttt  {StraightLineProgElm}, \hyperpage{488}
  \item \texttt  {StraightLineProgGens}, \hyperpage{488}
  \item \texttt  {StraightLineProgram}
    \subitem for a list of lines (and the number of generators), 
		\hyperpage{483}
    \subitem for a string and a list of generators names, 
		\hyperpage{483}
  \item \texttt  {StraightLineProgramNC}
    \subitem for a list of lines (and the number of generators), 
		\hyperpage{483}
    \subitem for a string and a list of generators names, 
		\hyperpage{483}
  \item \texttt  {StraightLineProgramsTom}, \hyperpage{1062}
  \item \texttt  {StreamsFamily}, \hyperpage{140}
  \item \texttt  {StretchImportantSLPElement}, \hyperpage{489}
  \item strictly sorted list, \hyperpage{277}
  \item \texttt  {String}, \hyperpage{360}
    \subitem for a cyclotomic, \hyperpage{225}
  \item \texttt  {StringDate}, \hyperpage{369}
  \item \texttt  {StringFactorizationWord}, \hyperpage{667}
  \item \texttt  {StringNumbers}, \hyperpage{365}
  \item \texttt  {StringOfResultOfStraightLineProgram}, \hyperpage{485}
  \item \texttt  {StringPP}, \hyperpage{361}
  \item strings
    \subitem equality of, \hyperpage{358}
    \subitem inequality of, \hyperpage{358}
    \subitem lexicographic ordering of, \hyperpage{359}
  \item \texttt  {StringTime}, \hyperpage{369}
  \item \texttt  {StripLineBreakCharacters}, \hyperpage{361}
  \item \texttt  {StrongGeneratorsStabChain}, \hyperpage{612}
  \item \texttt  {StronglyConnectedComponents}, \hyperpage{446}
  \item \mbox{\texttt{\mdseries\slshape Struct}}, \hyperpage{403}
  \item \texttt{\mbox{\texttt{\mdseries\slshape Struct}}ByGenerators}, 
		\hyperpage{403}
  \item \texttt  {StructuralCopy}, \hyperpage{161}
  \item \texttt{StructuralCopy}
    \subitem for lists, \hyperpage{260}
  \item structure constant, \hyperpage{1097, 1098}
  \item \texttt  {StructureConstantsTable}, \hyperpage{924}
  \item \texttt  {StructureDescription}, \hyperpage{505}
  \item \texttt{\mbox{\texttt{\mdseries\slshape Struct}}WithGenerators}, 
		\hyperpage{403}
  \item \texttt  {SU}, \hyperpage{731}
  \item \texttt  {SubadditiveGroup}, \hyperpage{845}
  \item \texttt  {SubadditiveGroupNC}, \hyperpage{845}
  \item \texttt  {SubadditiveMagma}, \hyperpage{845}
  \item \texttt  {SubadditiveMagmaNC}, \hyperpage{845}
  \item \texttt  {SubadditiveMagmaWithZero}, \hyperpage{845}
  \item \texttt  {SubadditiveMagmaWithZeroNC}, \hyperpage{845}
  \item \texttt  {Subalgebra}, \hyperpage{928}
  \item \texttt  {SubAlgebraModule}, \hyperpage{950}
  \item \texttt  {SubalgebraNC}, \hyperpage{928}
  \item \texttt  {SubalgebraWithOne}, \hyperpage{929}
  \item \texttt  {SubalgebraWithOneNC}, \hyperpage{929}
  \item \texttt  {SubdirectProduct}, \hyperpage{721}
  \item \texttt  {SubdirectProducts}, \hyperpage{721}
  \item Subdomains, \hyperpage{407}
  \item \texttt  {Subfield}, \hyperpage{876}
  \item \texttt  {SubfieldNC}, \hyperpage{876}
  \item \texttt  {Subfields}, \hyperpage{878}
  \item \texttt  {Subgroup}, \hyperpage{499}
    \subitem for a group, \hyperpage{499}
  \item subgroup fusions, \hyperpage{1169}
  \item subgroup generators tree, \hyperpage{712}
  \item \texttt  {SubgroupByPcgs}, \hyperpage{636}
  \item \texttt  {SubgroupByProperty}, \hyperpage{501}
  \item \texttt  {SubgroupNC}, \hyperpage{499}
  \item \texttt  {SubgroupOfWholeGroupByCosetTable}, \hyperpage{676}
  \item \texttt  {Subgroup}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Whole}\discretionary {-}{}{}\texttt  {Group}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Quotient}\discretionary {-}{}{}\texttt  {Subgroup}, 
		\hyperpage{682}
  \item \texttt  {SubgroupProperty}, \hyperpage{616}
  \item subgroups
    \subitem polyhedral, \hyperpage{1096}
  \item \texttt  {SubgroupShell}, \hyperpage{502}
  \item \texttt  {SubgroupsSolvableGroup}, \hyperpage{542}
  \item sublist, \hyperpage{252}
    \subitem access, \hyperpage{252}
    \subitem assignment, \hyperpage{254}
    \subitem operation, \hyperpage{253}
  \item sublist assignment
    \subitem operation, \hyperpage{255}
  \item \texttt  {Submagma}, \hyperpage{459}
  \item \texttt  {SubmagmaNC}, \hyperpage{459}
  \item \texttt  {SubmagmaWithInverses}, \hyperpage{459}
  \item \texttt  {SubmagmaWithInversesNC}, \hyperpage{459}
  \item \texttt  {SubmagmaWithOne}, \hyperpage{459}
  \item \texttt  {SubmagmaWithOneNC}, \hyperpage{459}
  \item \texttt  {Submodule}, \hyperpage{870}
  \item \texttt  {SubmoduleNC}, \hyperpage{870}
  \item \texttt  {Submonoid}, \hyperpage{766}
  \item \texttt  {SubmonoidNC}, \hyperpage{766}
  \item \texttt  {SubnearAdditiveGroup}, \hyperpage{845}
  \item \texttt  {SubnearAdditiveGroupNC}, \hyperpage{845}
  \item \texttt  {SubnearAdditiveMagma}, \hyperpage{845}
  \item \texttt  {SubnearAdditiveMagmaNC}, \hyperpage{845}
  \item \texttt  {SubnearAdditiveMagmaWithZero}, \hyperpage{845}
  \item \texttt  {SubnearAdditiveMagmaWithZeroNC}, \hyperpage{845}
  \item \texttt  {SubnormalSeries}, \hyperpage{530}
  \item \texttt  {Subring}, \hyperpage{850}
  \item \texttt  {SubringNC}, \hyperpage{850}
  \item \texttt  {Subrings}, \hyperpage{866}
  \item \texttt  {SubringWithOne}, \hyperpage{855}
  \item \texttt  {SubringWithOneNC}, \hyperpage{855}
  \item \texttt  {Subsemigroup}, \hyperpage{762}
  \item \texttt  {SubsemigroupNC}, \hyperpage{762}
  \item subset test
    \subitem for collections, \hyperpage{393}
  \item subsets, \hyperpage{208}
  \item \texttt  {Subspace}, \hyperpage{901}
  \item \texttt  {SubspaceNC}, \hyperpage{901}
  \item \texttt  {Subspaces}, \hyperpage{902}
  \item \texttt  {SubstitutedWord}
    \subitem replace a subword by a given word, \hyperpage{478}
    \subitem replace an interval by a given word, \hyperpage{478}
  \item \texttt  {SubsTom}, \hyperpage{1052}
  \item \texttt{Sub\mbox{\texttt{\mdseries\slshape struct}}}, 
		\hyperpage{407}
  \item \texttt{Sub\mbox{\texttt{\mdseries\slshape struct}}NC}, 
		\hyperpage{407}
  \item \texttt  {SubSyllables}, \hyperpage{479}
  \item subtract
    \subitem a set from another, \hyperpage{282}
  \item \texttt  {SubtractBlist}, \hyperpage{302}
  \item subtraction, \hyperpage{57}
    \subitem matrices, \hyperpage{316}
    \subitem matrix and scalar, \hyperpage{316}
    \subitem rational functions, \hyperpage{996}
    \subitem scalar and matrix, \hyperpage{316}
    \subitem scalar and matrix list, \hyperpage{317}
    \subitem scalar and vector, \hyperpage{305}
    \subitem vector and scalar, \hyperpage{305}
    \subitem vectors, \hyperpage{305}
  \item \texttt  {SubtractSet}, \hyperpage{282}
  \item \texttt  {Subword}, \hyperpage{477}
  \item \texttt  {Successors}, \hyperpage{444}
  \item Suffix, \hyperpage{364}
  \item \texttt  {Sum}, \hyperpage{291}
  \item \texttt  {SumFactorizationFunctionPcgs}, \hyperpage{644}
  \item \texttt  {SumIntersectionMat}, \hyperpage{330}
  \item \texttt  {SumX}, \hyperpage{294}
  \item \texttt  {Sup}, \hyperpage{241}
  \item \texttt  {SupersolvableResiduum}, \hyperpage{518}
  \item support
    \subitem email address, \hyperpage{27}
  \item \texttt  {SupportedCharacterTableInfo}, \hyperpage{1073}
  \item \texttt  {SurjectiveActionHomomorphismAttr}, \hyperpage{592}
  \item \texttt  {SuzukiGroup}, \hyperpage{729}
  \item \texttt  {SylowComplement}, \hyperpage{519}
  \item \texttt  {SylowSubgroup}, \hyperpage{519}
  \item \texttt  {SylowSystem}, \hyperpage{520}
  \item symmetric group
    \subitem power map, \hyperpage{217}
  \item symmetric power, \hyperpage{1150}
  \item symmetric relation, \hyperpage{443}
  \item \texttt  {SymmetricClosureBinaryRelation}, \hyperpage{446}
  \item \texttt  {SymmetricGroup}
    \subitem for a degree, \hyperpage{728}
    \subitem for a domain, \hyperpage{728}
  \item \texttt  {SymmetricInverseMonoid}, \hyperpage{839}
  \item \texttt  {SymmetricInverseSemigroup}, \hyperpage{839}
  \item \texttt  {SymmetricParentGroup}, \hyperpage{603}
  \item \texttt  {SymmetricParts}, \hyperpage{1150}
  \item \texttt  {SymmetricPowerOfAlgebraModule}, \hyperpage{985}
  \item \texttt  {Symmetrizations}, \hyperpage{1149}
  \item symmetrizations
    \subitem orthogonal, \hyperpage{1150}
    \subitem symplectic, \hyperpage{1151}
  \item \texttt  {SymplecticComponents}, \hyperpage{1151}
  \item \texttt  {SymplecticGroup}
    \subitem for dimension and a ring, \hyperpage{732}
    \subitem for dimension and field size, \hyperpage{732}
  \item syntax errors, \hyperpage{79}
  \item system getter, \hyperpage{170}
  \item system setter, \hyperpage{170}
  \item \texttt  {Sz}, \hyperpage{729}

  \indexspace

  \item $t_N$ (irrational value), \hyperpage{230}
  \item table automorphisms, \hyperpage{1175}, \hyperpage{1189}
  \item table of chapters for help books, \hyperpage{29}
  \item table of sections for help books, \hyperpage{29}
  \item \texttt  {TableAutomorphisms}, \hyperpage{1117}
  \item \texttt  {TableOfMarks}
    \subitem for a group, \hyperpage{1047}
    \subitem for a matrix, \hyperpage{1047}
    \subitem for a string, \hyperpage{1047}
  \item \texttt  {TableOfMarksByLattice}, \hyperpage{1048}
  \item \texttt  {TableOfMarksComponents}, \hyperpage{1052}
  \item \texttt  {TableOfMarksCyclic}, \hyperpage{1066}
  \item \texttt  {TableOfMarksDihedral}, \hyperpage{1066}
  \item \texttt  {TableOfMarksFamily}, \hyperpage{1051}
  \item \texttt  {TableOfMarksFrobenius}, \hyperpage{1067}
  \item tables, \hyperpage{1068}, \hyperpage{1071}
  \item tabulator, \hyperpage{47}
  \item \texttt  {Tan}, \hyperpage{240}
  \item \texttt  {Tanh}, \hyperpage{240}
  \item \texttt  {Tau}, \hyperpage{201}
  \item \texttt{TCENUM}, \hyperpage{672}
  \item \texttt  {TeachingMode}, \hyperpage{100}
  \item \texttt  {TemporaryGlobalVarName}, \hyperpage{54}
  \item \texttt  {Tensored}, \hyperpage{1139}
  \item \texttt  {TensorProductGModule}, \hyperpage{1034}
  \item \texttt  {TensorProductOfAlgebraModules}
    \subitem for a list of algebra modules, \hyperpage{984}
    \subitem for two algebra modules, \hyperpage{984}
  \item \texttt  {Test}, \hyperpage{120}
  \item test
    \subitem for a primitive root, \hyperpage{198}
    \subitem for a rational, \hyperpage{221}
    \subitem for records, \hyperpage{377}
    \subitem for set equality, \hyperpage{280}
  \item \texttt  {TestConsistencyMaps}, \hyperpage{1181}
  \item \texttt  {TestDirectory}, \hyperpage{122}
  \item \texttt  {Tester}, \hyperpage{171}
  \item tester, \hyperpage{171}
  \item \texttt  {TestHomogeneous}, \hyperpage{1196}
  \item \texttt  {TestInducedFromNormalSubgroup}, \hyperpage{1198}
  \item \texttt  {TestJacobi}, \hyperpage{925}
  \item \texttt  {TestMonomial}
    \subitem for a character, \hyperpage{1198}
    \subitem for a character and a Boolean, \hyperpage{1198}
    \subitem for a group, \hyperpage{1198}
    \subitem for a group and a Boolean, \hyperpage{1198}
  \item \texttt  {TestMonomialQuick}
    \subitem for a character, \hyperpage{1200}
    \subitem for a group, \hyperpage{1200}
  \item \texttt  {TestMonomialUseLattice}, \hyperpage{1199}
  \item \texttt  {TestPackage}, \hyperpage{1208}
  \item \texttt  {TestPackageAvailability}, \hyperpage{1207}
  \item \texttt  {TestPerm1}, \hyperpage{1159}
  \item \texttt  {TestPerm2}, \hyperpage{1159}
  \item \texttt  {TestPerm3}, \hyperpage{1159}
  \item \texttt  {TestPerm4}, \hyperpage{1159}
  \item \texttt  {TestPerm5}, \hyperpage{1159}
  \item \texttt  {TestQuasiPrimitive}, \hyperpage{1197}
  \item \texttt  {TestRelativelySM}
    \subitem for a character, \hyperpage{1201}
    \subitem for a character and a normal subgroup, \hyperpage{1201}
    \subitem for a group, \hyperpage{1201}
    \subitem for a group and a normal subgroup, \hyperpage{1201}
  \item \texttt  {TestSubnormallyMonomial}
    \subitem for a character, \hyperpage{1200}
    \subitem for a group, \hyperpage{1200}
  \item \texttt{then}, \hyperpage{60}
  \item \texttt{ThreeGroup} library, \hyperpage{740}
  \item \texttt  {TietzeWordAbstractWord}, \hyperpage{697}
  \item \texttt  {time}, \hyperpage{110}
  \item Timeouts, \hyperpage{73}
  \item \texttt  {Trace}
    \subitem for a field element, \hyperpage{880}
    \subitem for a matrix, \hyperpage{880}
    \subitem of a matrix, \hyperpage{318}
  \item \texttt  {TraceAllMethods}, \hyperpage{105}
  \item \texttt  {TracedCosetFpGroup}, \hyperpage{671}
  \item \texttt  {TraceImmediateMethods}, \hyperpage{105}
  \item \texttt  {TraceMat}, \hyperpage{318}
  \item \texttt  {TraceMethods}
    \subitem for a list of operations, \hyperpage{104}
    \subitem for operations, \hyperpage{104}
  \item \texttt  {TracePolynomial}, \hyperpage{879}
  \item \texttt  {TransferDiagram}, \hyperpage{1180}
  \item \texttt  {Transformation}
    \subitem for a list and function, \hyperpage{796}
    \subitem for a source and destination, \hyperpage{796}
    \subitem for an image list, \hyperpage{796}
  \item \texttt  {TransformationByImageAndKernel}
    \subitem for an image and kernel, \hyperpage{797}
  \item \texttt  {TransformationFamily}, \hyperpage{795}
  \item \texttt  {TransformationList}
    \subitem for an image list, \hyperpage{796}
  \item \texttt  {TransformationListList}
    \subitem for a source and destination, \hyperpage{796}
  \item \texttt  {TransformationNumber}, \hyperpage{798}
  \item \texttt  {TransformationOp}, \hyperpage{797}
  \item \texttt  {TransformationOpNC}, \hyperpage{797}
  \item \texttt  {TransformingPermutations}, \hyperpage{1118}
  \item \texttt  {Transforming}\discretionary {-}{}{}\texttt  {Permutations}\discretionary {-}{}{}\texttt  {Character}\discretionary {-}{}{}\texttt  {Tables}, 
		\hyperpage{1118}
  \item transitive, \hyperpage{585}
  \item transitive relation, \hyperpage{443}
  \item \texttt  {TransitiveClosureBinaryRelation}, \hyperpage{446}
  \item \texttt  {TransitiveGroup}, \hyperpage{738}
  \item \texttt  {TransitiveIdentification}, \hyperpage{739}
  \item \texttt  {Transitivity}
    \subitem for a character, \hyperpage{1138}
    \subitem for a group and an action domain, \hyperpage{585}
    \subitem for an external set, \hyperpage{585}
  \item \texttt  {TranslatorSubalgebra}, \hyperpage{954}
  \item transporter, \hyperpage{580}
  \item \texttt  {TransposedMat}, \hyperpage{321}
  \item \texttt  {TransposedMatAttr}, \hyperpage{321}
  \item \texttt  {TransposedMatDestructive}, \hyperpage{321}
  \item \texttt  {TransposedMatImmutable}, \hyperpage{321}
  \item \texttt  {TransposedMatMutable}, \hyperpage{321}
  \item \texttt  {TransposedMatOp}, \hyperpage{321}
  \item \texttt  {TransposedMatrixGroup}, \hyperpage{620}
  \item \texttt  {TriangulizedIntegerMat}, \hyperpage{341}
  \item \texttt  {TriangulizedIntegerMatTransform}, \hyperpage{341}
  \item \texttt  {TriangulizedMat}, \hyperpage{323}
  \item \texttt  {TriangulizedNullspaceMat}, \hyperpage{324}
  \item \texttt  {TriangulizedNullspaceMatDestructive}, \hyperpage{324}
  \item \texttt  {TriangulizeIntegerMat}, \hyperpage{341}
  \item \texttt  {TriangulizeMat}, \hyperpage{324}
  \item \texttt  {TrimPartialPerm}, \hyperpage{835}
  \item \texttt  {TrimTransformation}, \hyperpage{811}
  \item \texttt  {TrivialCharacter}
    \subitem for a character table, \hyperpage{1132}
    \subitem for a group, \hyperpage{1132}
  \item \texttt  {TrivialGroup}, \hyperpage{726}
  \item \texttt  {TrivialIterator}, \hyperpage{399}
  \item \texttt  {TrivialSubalgebra}, \hyperpage{929}
  \item \texttt  {TrivialSubgroup}, \hyperpage{516}
  \item \texttt  {TrivialSubmagmaWithOne}, \hyperpage{466}
  \item \texttt  {TrivialSubmodule}, \hyperpage{871}
  \item \texttt  {TrivialSubmonoid}, \hyperpage{767}
  \item \texttt  {TrivialSubnearAdditiveMagmaWithZero}, \hyperpage{847}
  \item \texttt  {TrivialSubspace}, \hyperpage{902}
  \item \texttt  {Trunc}, \hyperpage{241}
  \item \texttt  {TryCosetTableInWholeGroup}, \hyperpage{675}
  \item \texttt  {TryGcdCancelExtRepPolynomials}, \hyperpage{1025}
  \item \texttt  {TryNextMethod}, \hyperpage{1221}
  \item tuple stabilizer, \hyperpage{578}
  \item \texttt  {Tuples}, \hyperpage{210}
  \item \texttt  {TwoClosure}, \hyperpage{616}
  \item \texttt  {TwoCoboundaries}, \hyperpage{659}
  \item \texttt  {TwoCocycles}, \hyperpage{659}
  \item \texttt  {TwoCohomology}, \hyperpage{659}
  \item \texttt{TwoGroup} library, \hyperpage{740}
  \item \texttt  {TwoSidedIdeal}, \hyperpage{851}
  \item \texttt  {TwoSidedIdealByGenerators}, \hyperpage{852}
  \item \texttt  {TwoSidedIdealNC}, \hyperpage{852}
  \item \texttt  {TwoSquares}, \hyperpage{203}
  \item type
    \subitem boolean, \hyperpage{245}
    \subitem cyclotomic, \hyperpage{223}
    \subitem records, \hyperpage{377}
    \subitem strings, \hyperpage{352}
  \item \texttt  {TypeObj}, \hyperpage{176}
  \item \texttt  {TypeOfDefaultGeneralMapping}, \hyperpage{441}
  \item \texttt  {TzEliminate}
    \subitem for a presentation (and a generator), \hyperpage{704}
    \subitem for a presentation (and an integer), \hyperpage{704}
  \item \texttt  {TzFindCyclicJoins}, \hyperpage{706}
  \item \texttt  {TzGo}, \hyperpage{701}
  \item \texttt  {TzGoGo}, \hyperpage{703}
  \item \texttt  {TzImagesOldGens}, \hyperpage{710}
  \item \texttt  {TzInitGeneratorImages}, \hyperpage{710}
  \item \texttt  {TzNewGenerator}, \hyperpage{701}
  \item \texttt  {TzOptions}, \hyperpage{716}
  \item \texttt  {TzPreImagesNewGens}, \hyperpage{711}
  \item \texttt  {TzPrint}, \hyperpage{699}
  \item \texttt  {TzPrintGeneratorImages}, \hyperpage{711}
  \item \texttt  {TzPrintGenerators}, \hyperpage{698}
  \item \texttt  {TzPrintLengths}, \hyperpage{699}
  \item \texttt  {TzPrintOptions}, \hyperpage{717}
  \item \texttt  {TzPrintPairs}, \hyperpage{700}
  \item \texttt  {TzPrintPresentation}, \hyperpage{699}
  \item \texttt  {TzPrintRelators}, \hyperpage{698}
  \item \texttt  {TzPrintStatus}, \hyperpage{699}
  \item \texttt  {TzSearch}, \hyperpage{704}
  \item \texttt  {TzSearchEqual}, \hyperpage{705}
  \item \texttt  {TzSort}, \hyperpage{691}
  \item \texttt  {TzSubstitute}
    \subitem for a presentation (and an integer and 0/1/2), 
		\hyperpage{706}
    \subitem for a presentation and a word, \hyperpage{706}
  \item \texttt  {TzSubstituteCyclicJoins}, \hyperpage{710}

  \indexspace

  \item $u_N$ (irrational value), \hyperpage{230}
  \item \texttt  {UglyVector}, \hyperpage{918}
  \item \texttt  {Unbind}
    \subitem for multiple indices, \hyperpage{257}
    \subitem unbind a list entry, \hyperpage{257}
    \subitem unbind a record component, \hyperpage{382}
    \subitem unbind a variable, \hyperpage{51}
  \item \texttt  {Unbind\texttt  {\char 92\relax }.}, \hyperpage{383}
  \item \texttt  {Unbind\texttt  {\char 92\relax }[\texttt  {\char 92\relax }]}, 
		\hyperpage{252}
  \item \texttt  {UnbindElmWPObj}, \hyperpage{1301}
  \item \texttt  {UnbindGlobal}, \hyperpage{53}
  \item \texttt  {UncoverageLineByLine}, \hyperpage{117}
  \item \texttt  {UnderlyingCharacteristic}
    \subitem for a character, \hyperpage{1084}
    \subitem for a character table, \hyperpage{1084}
  \item \texttt  {UnderlyingCharacterTable}, \hyperpage{1125}
  \item \texttt  {UnderlyingElement}
    \subitem fp group elements, \hyperpage{669}
    \subitem fp semigroup elements, \hyperpage{788}
  \item \texttt  {UnderlyingExternalSet}, \hyperpage{592}
  \item \texttt  {UnderlyingFamily}, \hyperpage{958}
  \item \texttt  {UnderlyingGeneralMapping}, \hyperpage{429}
  \item \texttt  {UnderlyingGroup}
    \subitem for character tables, \hyperpage{1076}
    \subitem for tables of marks, \hyperpage{1054}
  \item \texttt  {UnderlyingInjectionZeroMagma}, \hyperpage{461}
  \item \texttt  {UnderlyingLeftModule}, \hyperpage{906}
  \item \texttt  {UnderlyingLieAlgebra}, \hyperpage{966}
  \item \texttt  {UnderlyingMagma}, \hyperpage{988}
  \item \texttt  {UnderlyingRelation}, \hyperpage{429}
  \item \texttt  {UnderlyingRingElement}, \hyperpage{958}
  \item \texttt  {UnderlyingSemigroup}
    \subitem for a Rees 0-matrix semigroup, \hyperpage{783}
    \subitem for a Rees matrix semigroup, \hyperpage{783}
  \item \texttt  {UnInstallCharReadHookFunc}, \hyperpage{152}
  \item \texttt  {Union}
    \subitem for a list, \hyperpage{394}
    \subitem for various collections, \hyperpage{394}
  \item union
    \subitem of collections, \hyperpage{394}
    \subitem of sets, \hyperpage{281}
  \item \texttt  {Union2}, \hyperpage{394}
  \item \texttt  {UnionBlist}
    \subitem for a list, \hyperpage{300}
    \subitem for various boolean lists, \hyperpage{300}
  \item \texttt  {Unique}, \hyperpage{283}
  \item \texttt  {UniteBlist}, \hyperpage{301}
  \item \texttt  {UniteBlistList}, \hyperpage{301}
  \item \texttt  {UniteSet}, \hyperpage{281}
  \item \texttt  {Units}, \hyperpage{858}
  \item \texttt  {UnivariatenessTestRationalFunction}, \hyperpage{1002}
  \item \texttt  {UnivariatePolynomial}, \hyperpage{1001}
  \item \texttt  {UnivariatePolynomialByCoefficients}, \hyperpage{1001}
  \item \texttt  {UnivariatePolynomialRing}
    \subitem for a ring (and a name and an exclusion list), 
		\hyperpage{1013}
    \subitem for a ring (and an indeterminate number), \hyperpage{1013}
  \item \texttt  {Univariate}\discretionary {-}{}{}\texttt  {Rational}\discretionary {-}{}{}\texttt  {Function}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Coefficients}, 
		\hyperpage{1010}
  \item \texttt  {UniversalEnvelopingAlgebra}, \hyperpage{975}
  \item UNIX
    \subitem features, \hyperpage{33}
    \subitem options, \hyperpage{33}
  \item \texttt  {UNIXSelect}, \hyperpage{141}
  \item \texttt  {Unknown}, \hyperpage{1191}
  \item \texttt  {UnloadSmallGroupsData}, \hyperpage{742}
  \item \texttt  {UnorderedTuples}, \hyperpage{210}
  \item \texttt  {UnprofileFunctions}, \hyperpage{111}
  \item \texttt  {UnprofileLineByLine}, \hyperpage{117}
  \item \texttt  {UnprofileMethods}, \hyperpage{112}
  \item \texttt{until}, \hyperpage{62}
  \item \texttt  {UntraceAllMethods}, \hyperpage{105}
  \item \texttt  {UntraceImmediateMethods}, \hyperpage{105}
  \item \texttt  {UntraceMethods}
    \subitem for a list of operations, \hyperpage{105}
    \subitem for operations, \hyperpage{105}
  \item \texttt  {UpdateMap}, \hyperpage{1178}
  \item \texttt  {UpEnv}, \hyperpage{90}
  \item \texttt  {UpperCentralSeriesOfGroup}, \hyperpage{532}
  \item \texttt  {UpperSubdiagonal}, \hyperpage{331}
  \item \texttt  {UseBasis}, \hyperpage{872}
  \item \texttt  {UseFactorRelation}, \hyperpage{415}
  \item \texttt  {UseIsomorphismRelation}, \hyperpage{416}
  \item \texttt  {UserPreference}, \hyperpage{39}
  \item \texttt  {UseSubsetRelation}, \hyperpage{415}
  \item utilities for editing GAP files, \hyperpage{99}

  \indexspace

  \item $v_N$ (irrational value), \hyperpage{230}
  \item \texttt  {ValidatePackageInfo}, \hyperpage{1211}
  \item \texttt  {Valuation}, \hyperpage{1030}
  \item \texttt  {Value}
    \subitem for a univariate rat. function, a value (and a one), 
		\hyperpage{1005}
    \subitem for rat. function, a list of indeterminates, a value (and a one), 
		\hyperpage{1005}
  \item \texttt  {ValueCochain}, \hyperpage{978}
  \item \texttt  {ValueGlobal}, \hyperpage{52}
  \item \texttt  {ValueMolienSeries}, \hyperpage{1153}
  \item \texttt  {ValueOption}, \hyperpage{128}
  \item \texttt  {ValuePol}, \hyperpage{311}
  \item \texttt  {ValuesOfClassFunction}, \hyperpage{1125}
  \item \texttt  {VectorSpace}, \hyperpage{900}
  \item \texttt  {Vector}\discretionary {-}{}{}\texttt  {Space}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Pcgs}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Elementary}\discretionary {-}{}{}\texttt  {Abelian}\discretionary {-}{}{}\texttt  {Group}, 
		\hyperpage{647}
  \item \texttt{vi}, \hyperpage{99}
  \item \texttt  {View}, \hyperpage{83}
  \item \texttt  {ViewObj}, \hyperpage{84}
    \subitem for a character table, \hyperpage{1098}
    \subitem for a ffe, \hyperpage{890}
    \subitem for a string, \hyperpage{353}
    \subitem for a table of marks, \hyperpage{1048}
    \subitem for class functions, \hyperpage{1130}
  \item \texttt  {ViewString}, \hyperpage{360}
  \item \texttt{vim}, \hyperpage{99}
  \item virtual character, \hyperpage{1134}
  \item virtual characters, \hyperpage{1122}
  \item \texttt  {VirtualCharacter}
    \subitem for a character table and a list, \hyperpage{1131}
    \subitem for a group and a list, \hyperpage{1131}

  \indexspace

  \item $w_N$ (irrational value), \hyperpage{230}
  \item \texttt  {WeakPointerObj}, \hyperpage{1300}
  \item web sites
    \subitem for GAP, \hyperpage{27}
  \item \texttt  {WedgeGModule}, \hyperpage{1034}
  \item \texttt  {WeekDay}, \hyperpage{369}
  \item \texttt  {WeightLexOrdering}, \hyperpage{454}
  \item \texttt  {WeightOfGenerators}, \hyperpage{455}
  \item \texttt  {WeightsTom}, \hyperpage{1056}
  \item \texttt  {WeightVecFFE}, \hyperpage{310}
  \item \texttt  {WeylGroup}, \hyperpage{969}
  \item \texttt  {WeylOrbitIterator}, \hyperpage{970}
  \item \texttt  {Where}, \hyperpage{89}
  \item \texttt{while} loop, \hyperpage{62}
  \item \texttt  {WordAlp}, \hyperpage{361}
  \item words
    \subitem in generators, \hyperpage{503}
  \item Wreath product embedding, \hyperpage{723}
  \item \texttt  {WreathProduct}, \hyperpage{722}
  \item \texttt  {WreathProductImprimitiveAction}, \hyperpage{722}
  \item \texttt  {WreathProductOrdering}, \hyperpage{456}
  \item \texttt  {WreathProductProductAction}, \hyperpage{723}
  \item \texttt  {WriteAll}, \hyperpage{145}
  \item \texttt  {WriteByte}, \hyperpage{144}
  \item \texttt  {WriteGapIniFile}, \hyperpage{39}
  \item \texttt  {WriteLine}, \hyperpage{144}

  \indexspace

  \item \texttt  {X}
    \subitem for a family and a number, \hyperpage{994}
    \subitem for a ring (and a name, and an exclusion list), 
		\hyperpage{994}
    \subitem for a ring (and a number), \hyperpage{994}
  \item $x_N$ (irrational value), \hyperpage{230}

  \indexspace

  \item $y_N$ (irrational value), \hyperpage{230}

  \indexspace

  \item \texttt  {Z}
    \subitem for field size, \hyperpage{882}
    \subitem for prime and degree, \hyperpage{882}
  \item \texttt  {ZClassRepsQClass}, \hyperpage{626}
  \item \texttt  {Zero}, \hyperpage{409}
    \subitem for a partial perm, \hyperpage{830}
  \item \texttt  {ZeroAttr}, \hyperpage{409}
  \item \texttt  {ZeroCoefficient}, \hyperpage{989}
  \item \texttt  {ZeroCoefficientRatFun}, \hyperpage{1022}
  \item \texttt  {ZeroImmutable}, \hyperpage{409}
  \item \texttt  {ZeroMapping}, \hyperpage{426}
  \item \texttt  {ZeroMutable}, \hyperpage{409}
  \item \texttt  {ZeroOp}, \hyperpage{409}
  \item \texttt  {ZeroSameMutability}, \hyperpage{409}
  \item \texttt  {ZeroSM}, \hyperpage{409}
  \item \texttt  {Zeta}, \hyperpage{241}
  \item \texttt  {ZippedProduct}, \hyperpage{1024}
  \item \texttt  {ZippedSum}, \hyperpage{1024}
  \item \texttt  {ZmodnZ}, \hyperpage{189}
  \item \texttt  {ZmodnZObj}
    \subitem for a residue class family and integer, \hyperpage{190}
    \subitem for two integers, \hyperpage{190}
  \item \texttt  {ZmodpZ}, \hyperpage{189}
  \item \texttt  {ZmodpZNC}, \hyperpage{189}
  \item \texttt  {ZumbroichBase}, \hyperpage{896}
  \item \texttt  {Zuppos}, \hyperpage{541}

\end{theindex}
