\letter {}
(Near-)Additive Magma Categories, \indexit{558}
(Near-)Additive Magma Generation, \indexit{559}
`+', 48
`-', 48
`-A', 30
`-B', 30
`-C', 31
`-D', 30
`-K', 29
`-L', 29
`-M', 30
`-N', 30
`-O', 30
`-P', 31
\sub on Macintosh, 31
`-R', 29
`-T', 31
`-U', 31
`-W', 31
\sub on Macintosh, 32
`-X', 31
`-Y', 31
`-a', 30
\sub on Macintosh, 32
`-b', 27
`-e', 27
\sub on Macintosh, 32
`-f', 27
\sub on Macintosh, 32
`-g', 28
`-g -g', 28
`-h', 27
`-i', 31
`-l', 29
`-m', 28
`-n', 28
\sub on Macintosh, 32
`-o', 28
\sub on Macintosh, 32
`-p', 31
`-q', 27
`-r', 29
`-x', 28
`-y', 28
`-z', 31
\sub on Macintosh, 31
`.gaprc', 33
`/', 48
\sub for character tables, 734
`\*', 48
\sub for character tables, 734
`\\\char 39', 252
`\\XYZ', 252
`\\\"', 252
`\\\\', 252
`\\b', 252
`\\c', 252
`\\in', operation for testing membership, 277
`\\n', 252
`\\r', 252
`{\accent 94 }', 48
\sub for class functions, 773
1-Cohomology, \indexit{380}
2-Cohomology and Extensions, \indexit{459}
\letter A
`AbelianGroup', 512
`AbelianInvariants', for character tables, 736
\sub for groups, 369
Abelian Invariants for Subgroups, \indexit{479}
`AbelianInvariantsMultiplier', 383
`AbelianInvariantsNormalClosureFpGroup', 479
`Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 479
`AbelianInvariantsOfList', 244
`AbelianInvariantsSubgroupFpGroup', 479
`AbelianInvariantsSubgroupFpGroupMtc', 479
`AbelianInvariantsSubgroupFpGroupRrs', 479
`AbelianNumberField', 592
abelian number field, 594
abelian number fields, canonicalbasis, 595
abelian number fields, Galois group, 597
`AbelianSubfactorAction', 405
About Group Actions, \indexit{397}
`AbsInt', 127
`AbsoluteIrreducibleModules', 754
`AbsoluteValue', 159
absolute value of an integer, 127
`AbsolutIrreducibleModules', 754
abstract word, 326
`AbstractWordTietzeWord', 488
accessing, list elements, 175
\sub record elements, 263
Accessing a Module, \indexit{698}
Accessing Record Elements, \indexit{263}
Accessing Subgroups via Tables of Marks, \indexit{719}
`AClosestVectorCombinationsMatFFEVecFFE', 220
`AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 220
`ActingAlgebra', 635
`ActingDomain', 409
Acting OnRight and OnLeft, \indexit{435}
`Action', 404
action, by conjugation, 398
\sub on blocks, 398
\sub on sets, 398
`ActionHomomorphism', 403
Action of a group on itself, \indexit{405}
Action on Subfactors Defined by a Pcgs, \indexit{450}
actions, 398
Actions of Matrix Groups, \indexit{431}
`ActorOfExternalSet', 411
`Add', 178
add, an element to a set, 198
`AddCoeffs', 218
`AddGenerator', 490
`AddGenerators', 346
`AddGeneratorsExtendSchreierTree', 427
addition, 48
\sub list and non-list, 187
\sub matrices, 224
\sub matrix and scalar, 224
\sub operation, 297
\sub rational functions, 671
\sub scalar and matrix, 224
\sub scalar and matrix list, 226
\sub scalar and vector, 216
\sub vector and scalar, 216
\sub vectors, 216
Additive Arithmetic for Lists, \indexit{187}
`AdditiveInverse', 295
`AdditiveInverseAttr', 295
`AdditiveInverseImmutable', 295
`AdditiveInverseMutable', 295
`AdditiveInverseOp', 295
`AdditiveInverseSameMutability', 295
`AdditiveInverseSM', 295
`AdditiveNeutralElement', 560
`AddRelator', 490
`AddRowVector', 218
`AddRule', 346
`AddRuleReduced', 346
`AddSet', 198
`AdjointAssociativeAlgebra', 652
`AdjointBasis', 624
`AdjointMatrix', 652
`AdjointModule', 637
Advanced Features of GAP, \indexit{30}
Advanced List Manipulations, \indexit{206}
Advanced Methods for Dixon-Schneider Calculations, \indexit{755}
`AffineAction', 450
`AffineActionLayer', 450
`AffineOperation', 450
`AffineOperationLayer', 450
`Agemo', 366
`Algebra', 615
`AlgebraByStructureConstants', 618
`AlgebraGeneralMappingByImages', 629
`AlgebraHomomorphismByImages', 629
`AlgebraHomomorphismByImagesNC', 629
`AlgebraicExtension', 692
`AlgebraWithOne', 615
`AlgebraWithOneGeneralMappingByImages', 630
`AlgebraWithOneHomomorphismByImages', 630
`AlgebraWithOneHomomorphismByImagesNC', 630
`AllBlocks', 408
`AllIrreducibleSolvableGroups', 530
`All<Library>Groups', 518
`AllPrimitiveGroups', 518
`AllSmallGroups', 521
`AllTransitiveGroups', 518
`Alpha', 825
`AlternatingGroup', 512
`and', 171
\sub for filters, 117, 172
An Example of Advanced Dixon-Schneider Calculations, \indexit{756}
`ANFAutomorphism', 597
`AntiSymmetricParts', 790
antisymmetric relation, 316
`Append', 179
`AppendTo', 95
\sub for streams, 101
Apple, 841, 842
`ApplicableMethod', 78
ApplicableMethod, \indexit{78}
`ApplicableMethodTypes', 78
`Apply', 201
`ApplySimpleReflection', 649
`ApproximateSuborbitsStabilizerPermGroup', 425
`ARCH_IS_MAC', 35
`ARCH_IS_UNIX', 35
`ARCH_IS_WINDOWS', 35
`arg', special function argument, 46, 56
Arithmetic for External Representations of Polynomials, \indexit{691}
Arithmetic for Lists, \indexit{185}
Arithmetic Operations for Class Functions, \indexit{772}
Arithmetic Operations for Elements, \indexit{297}
Arithmetic Operations for General Mappings, \indexit{310}
Arithmetic Operators, \indexit{48}
`Arrangements', 149
arrow notation for functions, 57
`AsAlgebra', 624
`AsAlgebraWithOne', 625
`AsBinaryRelationOnPoints', 317
`AsBlockMatrix', 240
`AscendingChain', 372
`AsDivisionRing', 579
`AsDuplicateFreeList', 200
`AsField', 579
`AsFreeLeftModule', 576
`AsGroup', 351
`AsGroupGeneralMappingByImages', 387
`AsLeftIdeal', 566
`AsLeftModule', 574
`AsList', 272
`AsMagma', 321
`AsMonoid', 546
`AsPolynomial', 673
`AsRightIdeal', 566
`AsRing', 563
`AsSemigroup', 539
`Assert', 81
`AssertionLevel', 81
Assertions, \indexit{81}
`AsSet', 272
`AssignGeneratorVariables', 333
assignment, to a list, 177
\sub to a record, 263
\sub variable, 50
Assignments, \indexit{50}
`AssignNiceMonomorphismAutomorphismGroup', 393
`AssociatedPartition', 154
`AssociatedReesMatrixSemigroupOfDClass', 545
`Associates', 569
associativity, 48
`AssocWordByLetterRep', 338
`AsSortedList', 272
`AsSSortedList', 272
`As<Struct>', 289
`AsSubalgebra', 625
`AsSubalgebraWithOne', 625
`AsSubgroup', 352
`AsSubgroupOfWholeGroupByQuotient', 477
`AsSubmagma', 322
`AsSubmonoid', 546
`AsSubsemigroup', 539
`AsSubspace', 600
`AsSub<struct>', 292
`AsTransformation', 556
`AsTransformationNC', 556
`AsTwoSidedIdeal', 566
`AsVectorSpace', 599
at exit functions, 73
ATLAS Irrationalities, \indexit{161}
`AtlasIrrationality', 163
atomic irrationalities, 161
Attributes, \indexit{121}
Attributes and Operations for Algebras, \indexit{623}
Attributes and Properties for (Near-)Additive Magmas, \indexit{560}
Attributes and Properties for Collections, \indexit{273}
Attributes and Properties for Magmas, \indexit{323}
Attributes and Properties for Matrix Groups, \indexit{430}
Attributes and Properties of Character Tables, \indexit{734}
Attributes and Properties of Elements, \indexit{293}
Attributes of and Operations on Equivalence Relations, \indexit{318}
Attributes of Tables of Marks, \indexit{709}
`AttributeValueNotSet', 122
`AugmentationIdeal', 664
`AugmentedCosetTableInWholeGroup', 471
`AugmentedCosetTableMtc', 471
`AugmentedCosetTableRrs', 471
Augmented Coset Tables and Rewriting, \indexit{471}
automatic loading of gap packages, 846
`AutomorphismDomain', 392
`AutomorphismGroup', 392
\sub for groups with pcgs, 451
automorphism group, of number fields, 597
Automorphisms and Equivalence of Character Tables, \indexit{763}
`AutomorphismsOfTable', 738
\letter B
$b_N$, 161
backslash character, 252
backspace character, 252
`Backtrace', GAP3 name for `Where', 70
Backtrack, \indexit{427}
`BANNER', 851
`BaseFixedSpace', 231
`BaseIntersectionIntMats', 241
`BaseIntMat', 241
`BaseMat', 234
`BaseMatDestructive', 234
`BaseOfGroup', 424
`BaseOrthogonalSpaceMat', 234
Bases of Vector Spaces, \indexit{601}
`BaseStabChain', 424
`BaseSteinitzVectors', 234
Basic Actions, \indexit{398}
Basic Groups, \indexit{511}
Basic Operations for Class Functions, \indexit{770}
Basic Operations for Lists, \indexit{175}
`BasicWreathProductOrdering', 285
`Basis', 602
`BasisNC', 602
`BasisVectors', 603
`Bell', 148
`Bernoulli', 148
`BestQuoInt', 129
`BestSplittingMatrix', 755
`BiAlgebraModule', 633
`BiAlgebraModuleByGenerators', 633
`BilinearFormMat', 648
binary relation, 315
`BinaryRelationByElements', 315
`BinaryRelationOnPoints', 317
`BinaryRelationOnPointsNC', 317
Binary Relations on Points, \indexit{317}
`BinaryRelationTransformation', 557
`BindGlobal', 45
`Binomial', 147
blank, 41
`BlistList', 211
Block Matrices, \indexit{240}
`BlockMatrix', 240
`Blocks', 408
`BlocksInfo', 743
Block Systems, \indexit{408}
`BlownUpMat', 236
`BlownUpVector', 236
`BlowUpIsomorphism', 431
BNF, 59
body, 55
`BombieriNorm', 679
Boolean Lists Representing Subsets, \indexit{211}
bound, 43
Brauer character, 777
`BrauerCharacterValue', 800
`BrauerTable', 728
`BrauerTableOp', 728
`BravaisGroup', 434
`BravaisSubgroups', 434
`BravaisSupergroups', 434
Break, \indexit{55}
break loop message, 70
Break Loops, \indexit{67}
`break' statement, 55
browsing backwards, 22
browsing backwards one chapter, 23
browsing forward, 22
browsing forward one chapter, 23
browsing the next section browsed, 23
browsing the previous section browsed, 23
Browsing through the Sections, \indexit{22}
bug reports, see If Things Go Wrong, 838
Building new orderings, \indexit{281}
\letter C
$c_N$, 161
Calculating with Group Automorphisms, \indexit{393}
Calendar Arithmetic, \indexit{259}
`CallFuncList', 62
Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
Cancellation Tests for Rational Functions, \indexit{691}
`CanComputeIndex', 384
`CanComputeIsSubset', 384
`CanComputeSize', 384
`CanComputeSizeAnySubgroup', 384
candidates, for permutation characters, 793, 796
`CanEasilyCompareElements', 296
`CanEasilyCompareElementsFamily', 296
`CanEasilyComputePcgs', 437
`CanEasilySortElements', 296
`CanEasilySortElementsFamily', 296
`CanEasilyTestMembership', 384
`CanonicalBasis', 602
canonical basis, for matrix spaces, 609
\sub for row spaces, 609
`CanonicalGenerators', 648
`CanonicalPcElement', 439
`CanonicalPcgs', 442
`CanonicalPcgsByGeneratorsWithImages', 444
`Canonical\-Representative\-Determinator\-Of\-External\-Set', 411
`CanonicalRepresentativeOfExternalSet', 411
`CanonicalRightCosetElement', 358
Carmichael's lambda function, 139
carriage return character, 252
`CartanMatrix', 647
`CartanSubalgebra', 644
`Cartesian', 202
Categories, \indexit{118}
Categories and Properties of Algebras, \indexit{622}
Categories for Streams and the StreamsFamily, \indexit{97}
Categories of Associative Words, \indexit{331}
Categories of Matrices, \indexit{223}
`CategoriesOfObject', 120
Categories of Words and Nonassociative Words, \indexit{326}
`CategoryCollections', 269
`Center', 324
center, 323
`CentralCharacter', 781
central character, 781
`CentralIdempotentsOfAlgebra', 627
centraliser, 323
`Centralizer', 323
\sub for groups with pcgs, 451
`CentralizerInGLnZ', 434
`CentralizerModulo', 373
`CentralizerSizeLimitConsiderFunction', 452
`CentralNormalSeriesByPcgs', 446
`Centre', 324
\sub for groups with pcgs, 451
centre, of a character, 780
`CentreOfCharacter', 780
`CF', 592
`ChangeStabChain', 426
Changing Presentations, \indexit{490}
Changing the Help Viewer, \indexit{23}
Changing the Representation, \indexit{290}
Changing the Structure, \indexit{289}
`CHAR_INT', 258
`CHAR_SINT', 258
`Character', 775
Character Conversion, \indexit{258}
`CharacterDegrees', 734
Character Degrees and Derived Length, \indexit{825}
`Characteristic', 293
characteristic, for class functions, 774
`CharacteristicPolynomial', 235
characteristic polynomial, for field elements, 581
`CharacterNames', 738
`CharacterParameters', 739
characters, 768
\sub permutation, 793, 796
\sub symmetrizations of, 790
`CharacterTable', 728
Character Table Categories, \indexit{730}
`CharacterTableDirectProduct', 758
`CharacterTableFactorGroup', 759
`CharacterTableIsoclinic', 760
`CharacterTableRegular', 729
character tables, 727
\sub access to, 727
\sub calculate, 727
\sub infix operators, 734
\sub of groups, 727
`CharacterTableWithSortedCharacters', 761
`CharacterTableWithSortedClasses', 761
`CharacterTableWreathSymmetric', 760
character value, of group element using powering operator, 773
`CharsFamily', 254
`CheapFactorsInt', 134
`CheckFixedPoints', 814
`CheckForHandlingByNiceBasis', 614
`CheckPermChar', 821
`ChevalleyBasis', 646
`ChiefNormalSeriesByPcgs', 447
`ChiefSeries', 370
`ChiefSeriesThrough', 370
`ChiefSeriesUnderAction', 370
`ChineseRem', 130
Chinese remainder, 131
`Chomp', 257
`CIUnivPols', 671
`ClassElementLattice', 375
classes, real, 740
`ClassesSolvableGroup', 451
`ClassFunction', 775
class function, 768
class function objects, 768
class functions, 811
\sub as ring elements, 772
`ClassFunctionSameType', 776
Class Fusions between Character Tables, \indexit{806}
Classical Groups, \indexit{513}
`ClassMultiplicationCoefficient', for character tables, 747
class multiplication coefficient, 747, 748
`ClassNames', 738
`ClassNamesTom', 710
`ClassOrbit', 740
`ClassParameters', 739
`ClassPermutation', 762
`ClassPositionsOfAgemo', 740
`ClassPositionsOfCentre', for characters, 780
\sub for character tables, 740
`ClassPositionsOfDerivedSubgroup', 741
`Class\-Positions\-Of\-Direct\-Product\-Decompositions', 741
`ClassPositionsOfElementaryAbelianSeries', 741
`ClassPositionsOfFittingSubgroup', 741
`ClassPositionsOfKernel', 779
`ClassPositionsOfLowerCentralSeries', 741
`ClassPositionsOfMaximalNormalSubgroups', 740
`ClassPositionsOfMinimalNormalSubgroups', 740
`ClassPositionsOfNormalClosure', 741
`ClassPositionsOfNormalSubgroup', 766
`ClassPositionsOfNormalSubgroups', 740
`ClassPositionsOfSupersolvableResiduum', 741
`ClassPositionsOfUpperCentralSeries', 741
`ClassRoots', 740
`ClassStructureCharTable', 747
`ClassTypesTom', 709
`CleanedTailPcElement', 440
`ClearCacheStats', 84
`ClearProfile', 83
clone, an object, 113
`CloseMutableBasis', 607
`CloseStream', 98
`ClosureGroup', 354
`ClosureGroupAddElm', 354
`ClosureGroupCompare', 354
`ClosureGroupDefault', 354
`ClosureGroupIntest', 354
`ClosureLeftModule', 575
`ClosureNearAdditiveGroup', 561
Closure Operations and Other Constructors, \indexit{317}
`ClosureRing', 563
Closures of (Sub)groups, \indexit{354}
`Closure<Struct>', 289
`ClosureSubgroup', 354
`ClosureSubgroupNC', 354
`Coboundaries', 657
`Cochain', 656
`CochainSpace', 656
`Cocycles', 657
cocycles, 380
`CodePcGroup', 462
`CodePcgs', 462
Coding a Pc Presentation, \indexit{462}
coefficient, binomial, 147
Coefficient List Arithmetic, \indexit{218}
`Coefficients', 603
coefficients, for cyclotomics, 159
`CoefficientsAndMagmaElements', 665
`CoefficientsFamily', 688
`CoefficientsMultiadic', 130
`CoefficientsOfLaurentPolynomial', 680
`CoefficientsOfUnivariatePolynomial', 673
`Coefficients\-Of\-Univariate\-Rational\-Function', 673
`CoefficientsQadic', 130
`CoefficientsRing', 681
`CoeffsCyc', 159
`CoeffsMod', 219
cohomology, 380
`COHORTS_PRIMITIVE_GROUPS', 528
`CoKernelOfAdditiveGeneralMapping', 312
`CoKernelOfMultiplicativeGeneralMapping', 311
`CollapsedMat', 817
`Collected', 200
Collection Families, \indexit{268}
`CollectionsFamily', 268
Coloring the Prompt and Input, \indexit{38}
`ColorPrompt', 38
`ColumnIndexOfReesMatrixSemigroupElement', 545
`Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
`Combinations', 149
Combinations, Arrangements and Tuples, \indexit{149}
`CombinatorialCollector', 456
Combinatorial Numbers, \indexit{147}
`Comm', 297
\sub for words, 335
Command Line Options, \indexit{27}
comments, 41
`CommutativeDiagram', 814
`CommutatorFactorGroup', 373
`CommutatorLength', 364
\sub for character tables, 736
`CommutatorSubgroup', 363
`Compacted', 199
`CompanionMat', 237
`CompareVersionNumbers', 849
comparison, fp semigroup elements, 551
\sub operation, 296
\sub rational functions, 671
Comparison of Associative Words, \indexit{334}
Comparison of Class Functions, \indexit{771}
Comparison of Elements of Finitely Presented Groups, \indexit{465}
Comparison of Elements of Finitely Presented Semigroups, \indexit{551}
Comparison of Permutations, \indexit{413}
Comparison of Rational Functions, \indexit{671}
Comparison of Words, \indexit{328}
Comparison Operations for Elements, \indexit{296}
Comparisons, \indexit{47}
comparisons, of booleans, 170
\sub of lists, 184
Comparisons of Booleans, \indexit{170}
Comparisons of Cyclotomics, \indexit{161}
Comparisons of Lists, \indexit{184}
Comparisons of Records, \indexit{265}
Comparisons of Strings, \indexit{254}
`CompatibleConjugacyClasses', 733
`CompatiblePairs', 460
Compilation, \indexit{833}
Compiling Library Code, \indexit{36}
`Complementclasses', 363
`ComplementclassesEA', 382
`ComplementIntMat', 242
`ComplementSystem', 366
Completion Files, \indexit{34}
`ComplexConjugate', 164
\sub for class functions, 774
`ComplexificationQuat', 619
Components of a Dixon Record, \indexit{756}
`CompositionMapping', 305
\sub for Frobenius automorphisms, 589
`CompositionMapping2', 305
`CompositionMaps', 811
`CompositionOfStraightLinePrograms', 342
`CompositionSeries', 370
\sub for groups with pcgs, 451
`ComputedBrauerTables', 728
`ComputedClassFusions', 807
`ComputedIndicators', 746
`ComputedIsPSolvableCharacterTables', 746
`ComputedPowerMaps', 803
`ComputedPrimeBlockss', 742
Computing a Pcgs, \indexit{437}
Computing a Permutation Representation, \indexit{417}
Computing Pc Groups, \indexit{457}
Computing Possible Permutation Characters, \indexit{796}
Computing the Irreducible Characters of a Group, \indexit{751}
`Concatenation', 199
concatenation, of lists, 199
`Conductor', 159
`ConfluentRws', 346
`Congruences', for character tables, 819
Congruences for semigroups, \indexit{542}
`ConjugacyClass', 360
Conjugacy Classes, \indexit{360}
`ConjugacyClasses', attribute, 360
\sub for character tables, 732
\sub for groups with pcgs, 451
\sub for linear groups, 517
`ConjugacyClassesByOrbits', 361
`ConjugacyClassesByRandomSearch', 361
Conjugacy Classes in Classical Groups, \indexit{517}
Conjugacy Classes in Solvable Groups, \indexit{451}
`ConjugacyClassesMaximalSubgroups', 374
`ConjugacyClassesPerfectSubgroups', 377
`ConjugacyClassesSubgroups', 374
`ConjugacyClassSubgroups', 374
conjugate, matrix, 225
\sub of a word, 335
`ConjugateDominantWeight', 649
`ConjugateDominantWeightWithWord', 649
`ConjugateGroup', 351
`Conjugates', 582
`ConjugateSubgroup', 353
`ConjugateSubgroups', 353
conjugation, 398
`ConjugatorAutomorphism', 391
`ConjugatorAutomorphismNC', 391
`ConjugatorIsomorphism', 390
`ConjugatorOfConjugatorIsomorphism', 391
`ConnectGroupAndCharacterTable', 732
`ConsiderKernels', 819
`ConsiderSmallerPowerMaps', 820
`ConsiderStructureConstants', 811
`ConsiderTableAutomorphisms', 822
`ConstantTimeAccessList', 195
constituent, of a group character, 778
`ConstituentsCompositionMapping', 306
`ConstituentsOfCharacter', 779
Constructing Algebras as Free Algebras, \indexit{616}
Constructing Algebras by Generators, \indexit{615}
Constructing Algebras by Structure Constants, \indexit{617}
Constructing Character Tables from Others, \indexit{758}
Constructing Domains, \indexit{288}
Constructing Lie algebras, \indexit{641}
Constructing Pc Groups, \indexit{455}
Constructing Subdomains, \indexit{292}
Constructing Tables of Marks, \indexit{704}
Constructing Vector Spaces, \indexit{599}
Construction of Abelian Number Fields, \indexit{592}
Construction of Stabilizer Chains, \indexit{422}
Constructors for Basic Groups, \indexit{517}
`ContainedCharacters', 818
`ContainedDecomposables', 818
`ContainedMaps', 813
`ContainedPossibleCharacters', 816, 817
`ContainedPossibleVirtualCharacters', 816, 817
`ContainedSpecialVectors', 816, 817
`ContainedTom', 714
`ContainingTom', 714
`ContinuedFractionApproximationOfRoot', 143
`ContinuedFractionExpansionOfRoot', 143
Continued Fractions, \indexit{143}
`continue' statement, 55
Conventions for Character Tables, \indexit{731}
convert, to a string, 253
Converting Groups to Finitely Presented Groups, \indexit{473}
`ConvertToCharacterTable', 730
`ConvertToCharacterTableNC', 730
`ConvertToMatrixRep', 237
`ConvertToMatrixRepNC', 237
`ConvertToRangeRep', 209
`ConvertToStringRep', 253
`ConvertToTableOfMarks', 708
`ConvertToVectorRep', 217
`ConvertToVectorRepNC', 217
`ConwayPolynomial', 589
Conway Polynomials, \indexit{589}
coprime, 48
copy, 113
\sub an object, 113
`COPY_LIST_ENTRIES', 179
`CopyOptionsDefaults', 426
Copyrights, \indexit{845}
`CopyStabChain', 426
`Core', 362
`CorrespondingGeneratorsByModuloPcgs', 444
coset, 357
`CosetLeadersMatFFE', 220
Cosets, \indexit{357}
`CosetTable', 467
`CosetTableBySubgroup', 468
`CosetTableDefaultLimit', 469
`CosetTableDefaultMaxLimit', 469
`CosetTableFromGensAndRels', 468
`CosetTableInWholeGroup', 471
`CosetTableOfFpSemigroup', 554
Coset Tables and Coset Enumeration, \indexit{467}
Coset tables for subgroups in the whole group, \indexit{471}
`CosetTableStandard', 470
CRC, 37
`CrcFile', 95
\sub example, 37
CRC Numbers, \indexit{37}
`CreateCompletionFiles', 34
`CreateCompletionFilesPkg', 850
Creating Character Tables, \indexit{727}
Creating Class Functions from Values Lists, \indexit{775}
Creating Class Functions using Groups, \indexit{776}
Creating Finite Fields, \indexit{587}
Creating Finitely Presented Groups, \indexit{464}
Creating Finitely Presented Semigroups, \indexit{550}
Creating Group Homomorphisms, \indexit{385}
Creating Groups, \indexit{350}
Creating Mappings, \indexit{305}
Creating Permutations, \indexit{415}
Creating Presentations, \indexit{482}
Creation of Algebraic Extensions, \indexit{692}
Creation of Rational Functions, \indexit{690}
Credit, \indexit{21}
`CrystGroupDefaultAction', 435
`Cycle', 406
`CycleLength', 406
`CycleLengths', 406
`Cycles', 406
`CycleStructureClass', 780
`CycleStructurePerm', 414
`CyclicExtensionsTom', 714
`CyclicGroup', 511
`CyclotomicField', 592
cyclotomic field elements, 157
cyclotomic fields, canonicalbasis, 595
`CyclotomicPolynomial', 677
Cyclotomic Polynomials, \indexit{677}
`Cyclotomics', 157
cyclotomics, defaultfield, 593
\letter D
$d_N$, 161
Darstellungsgruppe, see `EpimorphismSchurCover', 383
`DataType', 125
data type, unknown, 168
`DayDMY', 260
`DaysInMonth', 259
`DaysInYear', 259
Debugging Recursion, \indexit{85}
DEC, 245
`DeclareAutoPackage', 850
`DeclareHandlingByNiceBasis', 613
`DeclareInfoClass', 80
`DeclarePackage', 850
`DeclarePackageAutoDocumentation', 850
`DeclarePackageDocumentation', 850
`DecodeTree', 500
DecodeTree, \indexit{500}
decompose, a group character, 778
`DecomposedFixedPointVector', 714
`DecomposeTensorProduct', 658
`Decomposition', 245
`DecompositionInt', 246
`DecompositionMatrix', 744
decomposition matrix, 245
Decompositions, \indexit{245}
`Decreased', 787
`DefaultField', 579
\sub for cyclotomics, 160
\sub for finite field elements, 587
`DefaultFieldByGenerators', 579
`DefaultFieldOfMatrix', 226
`DefaultFieldOfMatrixGroup', 430
`DefaultRing', 562
\sub for finite field elements, 587
`DefaultRingByGenerators', 563
`DefaultStabChainOptions', 423
Defining a Pcgs Yourself, \indexit{437}
`DefiningPolynomial', 580
`DefiningQuotientHomomorphism', 477
`DegreeFFE', 586
`DegreeIndeterminate', 675
`DegreeOfBinaryRelation', 316
`DegreeOfCharacter', 778
`DegreeOfLaurentPolynomial', 674
`DegreeOfTransformation', 555
`DegreeOfTransformationSemigroup', 541
`DegreeOverPrimeField', 580
`Delta', 825
denominator, of a rational, 146
`DenominatorCyc', 160
`DenominatorOfModuloPcgs', 443
`DenominatorOfRationalFunction', 673
`DenominatorRat', 146
deprecated, 850
`DepthOfPcElement', 439
`DepthOfUpperTriangularMatrix', 235
`Derangements', 151
`Derivations', 642
`Derivative', 676
`DerivedLength', 371
`DerivedSeriesOfGroup', 371
`DerivedSubgroup', 363
`DerivedSubgroupsTom', 713
`DerivedSubgroupsTomPossible', 713
`DerivedSubgroupsTomUnique', 713
`DerivedSubgroupTom', 713
`DescriptionOfRootOfUnity', 160
`Determinant', 227
determinant character, 781
`DeterminantIntMat', 245
`DeterminantMat', 227
`DeterminantMatDestructive', 227
`DeterminantMatDivFree', 227
Determinant of an integer matrix, \indexit{245}
`DeterminantOfCharacter', 781
Developing rewriting systems, \indexit{348}
`DiagonalizeIntMat', 243
`DiagonalizeMat', 232
`DiagonalMat', 228
`DiagonalOfMat', 235
`Difference', 276
`DifferenceBlist', 212
`DihedralGroup', 512
`Dimension', 576
`DimensionOfHighestWeightModule', 658
`DimensionOfMatrixGroup', 430
`DimensionOfVectors', 608
`DimensionsLoewyFactors', 372
`DimensionsMat', 226
Directories, \indexit{91}
`DirectoriesLibrary', 91
`DirectoriesPackageLibrary', 848
`DirectoriesPackagePrograms', 849
`DirectoriesSystemPrograms', 92
`Directory', 91
`DirectoryContents', 92
`DirectoryCurrent', 91
`DirectoryTemporary', 91
`DirectProduct', 505
`DirectProductOp', 505
Direct Products, \indexit{505}
`DirectSumDecomposition', 627
\sub for Lie algebras, 646
Direct Sum Decompositions, \indexit{646}
`DirectSumOfAlgebraModules', 638
\sub for Lie algebras, 661
`DirectSumOfAlgebras', 626
`DisableAttributeValueStoring', 123
disable automatic loading, 846
`Discriminant', 676
`Display', 67
\sub for character tables, 748, 775
\sub for tables of marks, 706
`DisplayCacheStats', 84
`DisplayCompositionSeries', 370
`DisplayEggBoxOfDClass', 543
`DisplayImfInvariants', 532
`DisplayInformationPerfectGroups', 525
`DisplayOptions', 750
`DisplayOptionsStack', 89
`DisplayProfile', 83
`DisplayRevision', 84
`DistancesDistributionMatFFEVecFFE', 220
`DistancesDistributionVecFFEsVecFFE', 220
`DistanceVecFFE', 220
Distinguished Subalgebras, \indexit{643}
division, 48
\sub operation, 297
`DivisionRingByGenerators', 579
division rings, 578
divisors, of an integer, 134
`DivisorsInt', 134
Dixon-Schneider algorithm, 754
`DixonInit', 755
`DixonRecord', 755
`DixonSplit', 755
`DixontinI', 755
`DMYDay', 260
`DMYhmsSeconds', 261
`DnLattice', 788
`DnLatticeIterative', 789
`do', 53
document formats (text, dvi, ps, pdf, html), 23
`Domain', 293
`DomainByGenerators', 293
Domain Categories, \indexit{290}
Domains, \indexit{110}
Domains Generated by Class Functions, \indexit{801}
Domains of Subspaces of Vector Spaces, \indexit{601}
`DominantCharacter', 657
`DominantWeights', 657
`DoubleCoset', 359
`DoubleCosetRepsAndSizes', 360
Double Cosets, \indexit{359}
`DoubleCosets', operation, 359
`DoubleCosetsNC', operation, 359
doublequote character, 252
doublequotes, 250
`DownEnv', 71
Dummy Streams, \indexit{106}
duplicate free, 195
`DuplicateFreeList', 200
Duplication of Lists, \indexit{181}
Duplication of Objects, \indexit{113}
`DxIncludeIrreducibles', 755
\letter E
`E', 157
$e_N$, 161
`EANormalSeriesByPcgs', 445
`Earns', 407
`EB', 161
`EC', 161
Echelonized Matrices, \indexit{232}
`ED', 161
`Edit', 75
Editing Files, \indexit{75}
Editor Support, \indexit{75}
`EE', 161
`EF', 161
Efficiency of Homomorphisms, \indexit{388}
`EG', 161
`EggBoxOfDClass', 543
`EH', 161
`EI', 162
`Eigenspaces', 231
`Eigenvalues', 231
`EigenvaluesChar', 781
`Eigenvectors', 231
Eigenvectors and eigenvalues, \indexit{231}
`EJ', 162
`EK', 162
`EL', 162
`ElementaryAbelianGroup', 512
`ElementaryAbelianSeries', 371
`ElementaryAbelianSeriesLargeSteps', 371
Elementary Divisors, \indexit{232}
`ElementaryDivisorsMat', 232
`ElementaryDivisorsMatDestructive', 232
Elementary Operations for a Pcgs, \indexit{438}
Elementary Operations for a Pcgs and an Element, \indexit{439}
Elementary Operations for Integers, \indexit{127}
Elementary Operations for Rationals, \indexit{145}
Elementary Tietze Transformations, \indexit{493}
`ElementOfFpGroup', 466
`ElementOfFpSemigroup', 552
`ElementOfMagmaRing', 665
`ElementOrdersPowerMap', 804
`ElementProperty', 427
`Elements', 273
elements, definition, 109
\sub of a list or collection, 273
Elements as equivalence classes, \indexit{109}
`ElementsFamily', 268
Elements in Algebraic Extensions, \indexit{692}
Elements of Free Magma Rings, \indexit{665}
Elements of pc groups, \indexit{454}
`ElementsStabChain', 425
Elements with Prescribed Images, \indexit{403}
element test, for lists, 183
`elif', 51
`EliminatedWord', 336
`EliminationOrdering', 685
`else', 51
`EM', 162
`emacs', 75
`Embedding', 306
\sub example for direct products, 505
\sub example for semidirect products, 507
\sub example for wreath products, 508
\sub for group products, 510
\sub for Lie algebras, 641
\sub for magma rings, 665
embeddings, find all, 394
Embeddings and Projections for Group Products, \indexit{510}
`EmptyBinaryRelation', 315
`EmptyMatrix', 228
`EmptyPlist', 183
`EmptySCTable', 617
`EmptyStabChain', 426
`EmptyString', 253
`EnableAttributeValueStoring', 123
`End', 611
`end', 55
Enlarging Internally Represented Lists, \indexit{183}
`Enumerator', 269
`EnumeratorByBasis', 604
`EnumeratorByFunctions', 270
Enumerators, \indexit{209}
`EnumeratorSorted', 269
environment, 55
`Epicentre', 383
`EpimorphismFromFreeGroup', 354
`EpimorphismNilpotentQuotient', 478
`EpimorphismNonabelianExteriorSquare', 383
`EpimorphismPGroup', 478
`EpimorphismQuotientSystem', 478
epimorphisms, find all, 394
`EpimorphismSchurCover', 383
equality, associative words, 334
\sub elements of finitely presented groups, 465
\sub nonassociative words, 328
\sub of records, 265
\sub operation, 296
\sub pcwords, 454
Equality and Comparison of Domains, \indexit{288}
equality test, 47
\sub for permutations, 413
equivalence class, 319
Equivalence Classes, \indexit{319}
`EquivalenceClasses', attribute, 319
`EquivalenceClassOfElement', 319
`EquivalenceClassOfElementNC', 319
`EquivalenceClassRelation', 319
equivalence relation, 316, 318
`EquivalenceRelationByPairs', 318
`EquivalenceRelationByPairsNC', 318
`EquivalenceRelationByPartition', 318
`EquivalenceRelationByPartitionNC', 318
`EquivalenceRelationByProperty', 318
`EquivalenceRelationByRelation', 318
`EquivalenceRelationPartition', 318
Equivalence Relations, \indexit{318}
`ER', 162
`Error', 73
Error, \indexit{73}
`ErrorCount', 73
ErrorCount, \indexit{73}
`ErrorNoTraceBack', 69
errors, syntax, 64
`ES', 162
escaped characters, 252
escaping non-special characters, 252
`ET', 162
`EU', 162
`EuclideanDegree', 570
`EuclideanQuotient', 570
`EuclideanRemainder', 571
Euclidean Rings, \indexit{570}
Euler's totient function, 138
`EulerianFunction', 369
`EulerianFunctionByTom', 715
`EV', 162
`EvalStraightLineProgElm', 344
`EvalString', 259
evaluation, 42
\sub strings, 258
`EW', 162
`EX', 162
`ExactSizeConsiderFunction', 379
`Exec', 108
Exec, \indexit{108}
execution, 49
exit, 73
expanded form of monomials, 689
Expert Windows installation, \indexit{844}
`Exponent', 369
\sub for character tables, 736
exponent, of the prime residue group, 139
exponentiation, operation, 297
`ExponentOfPcElement', 439
`ExponentsConjugateLayer', 440
`ExponentsOfCommutator', 440
`ExponentsOfConjugate', 440
`ExponentsOfPcElement', 439
`ExponentsOfRelativePower', 440
Exponents of Special Products, \indexit{440}
`ExponentSumWord', 335
`ExponentSyllable', 337
Expressing Group Elements as Words in Generators, \indexit{354}
Expressions, \indexit{42}
`ExtendedPcgs', 442
`ExtendStabChain', 426
`Extension', 459
`ExtensionNC', 459
`ExtensionRepresentatives', 460
`Extensions', 459
Extensions of the p-adic Numbers, \indexit{695}
`ExteriorCentre', 383
`ExteriorPowerOfAlgebraModule', 661
`ExternalOrbit', 410
`ExternalOrbits', 410
`ExternalOrbitsStabilizers', 410
External Representation for Nonassociative Words, \indexit{330}
external representation of polynomials, 689
`ExternalSet', 409
External Sets, \indexit{409}
`ExternalSubset', 410
`Extract', 785
`ExtraspecialGroup', 512
`ExtRepDenominatorRatFun', 689
`ExtRepNumeratorRatFun', 689
`ExtRepOfObj', external representation, for cyclotomics, 160
`ExtRepPolynomialRatFun', 689
`EY', 162
\letter F
$f_N$, 161
`FactorCosetAction', 405
\sub for fp groups, 468
`FactorCosetOperation', 468
`FactorFreeSemigroupByRelations', 550
`FactorGroup', 373
`FactorGroupFpGroupByRels', 464
`FactorGroupNC', 373
`FactorGroupNormalSubgroupClasses', 766
Factor Groups, \indexit{373}
Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{443}
Factor Groups of Polycyclic Groups in their Own Representation, \indexit{444}
`FactorGroupTom', 715
`Factorial', 147
`Factorization', 355
factorization, 354
`Factors', 570
\sub of univariate polynomial, 678
`FactorsInt', 132
`FactorsOfDirectProduct', 759
`FactorsSquarefree', 678
Fail, \indexit{170}
`fail', 170
`FaithfulModule', 637
\sub for Lie algebras, 655
Families, \indexit{116}
`FamiliesOfGeneralMappingsAndRanges', 314
`FamiliesOfRows', 765
`FamilyForOrdering', 282
`FamilyObj', 116
`FamilyPcgs', 454
`FamilyRange', 314
`FamilySource', 314
FAQ, 837
features, under UNIX, 27
`fi', 51
`Fibonacci', 155
Fibonacci and Lucas Sequences, \indexit{155}
`Field', 578
`FieldExtension', 580
field homomorphisms, Frobenius, 589
`FieldOfMatrixGroup', 430
`FieldOverItselfByGenerators', 580
fields, 578
File Access, \indexit{93}
`FileDescriptorOfStream', 98
`Filename', 92
Filename, \indexit{92}
File Operations, \indexit{94}
File Streams, \indexit{103}
`Filtered', 203
Filters, \indexit{117}
Filters Controlling the Arithmetic Behaviour of Lists, \indexit{185}
Finding Positions in Lists, \indexit{191}
Finding Submodules, \indexit{698}
`FindSl2', 653
Finish Installation and Cleanup, \indexit{835}
Finite Field Elements, \indexit{584}
Finitely Presented Lie Algebras, \indexit{653}
Finitely presented monoids, \indexit{552}
finiteness test, for a list or collection, 273
Finite Perfect Groups, \indexit{523}
`First', 204
`FittingSubgroup', 364
`Flat', 200
flush character, 252
For, \indexit{53}
`ForAll', 204
`ForAny', 204
`for' loop, 53
`FpElmComparisonMethod', 465
`FpGroupPresentation', 483
`FpGrpMonSmgOfFpGrpMonSmgElement', 550
`FpLieAlgebraByCartanMatrix', 654
frame, 790, 791
`FrattiniSubgroup', 364
\sub for groups with pcgs, 451
`FreeAlgebra', 616
`FreeAlgebraWithOne', 616
`FreeAssociativeAlgebra', 616
`FreeAssociativeAlgebraWithOne', 616
`FreeGeneratorsOfFpGroup', 465
`FreeGeneratorsOfFpSemigroup', 551
`FreeGeneratorsOfWholeGroup', 465
`FreeGroup', 332
`FreeGroupOfFpGroup', 465
Free Groups, Monoids and Semigroups, \indexit{332}
`FreeLeftModule', 576
`FreeLieAlgebra', 642
`FreeMagma', 329
`FreeMagmaRing', 664
Free Magma Rings, \indexit{664}
Free Magmas, \indexit{329}
`FreeMagmaWithOne', 329
Free Modules, \indexit{576}
`FreeMonoid', 547
\sub with example, 332
`FreeMonoidOfRewritingSystem', 554
`FreeProduct', 510
Free Products, \indexit{510}
`FreeSemigroup', 332
\sub with examples, 540
`FreeSemigroupOfFpSemigroup', 551
`FreeSemigroupOfRewritingSystem', 554
Frobenius automorphism, 589
`FrobeniusAutomorphism', 589
FrobeniusAutomorphism, \indexit{589}
`FrobeniusCharacterValue', 800
`FullMatrixAlgebra', 619
`FullMatrixAlgebraCentralizer', 627
`FullMatrixLieAlgebra', 642
`FullMatrixModule', 577
`FullMatrixSpace', 608
`FullRowModule', 577
`FullRowSpace', 608
`FullTransformationSemigroup', 541
Function, \indexit{55}
`function', 55
`FunctionAction', 409
function call, 46
\sub with arguments, 46
\sub with options, 47
Function Calls, \indexit{46}
`FunctionOperation', 850
functions, 61, 304
\sub definition by arrow notation, 57
\sub definition of, 55
\sub recursive, 55
\sub with a variable number of arguments, 46, 56
`FunctionsFamily', 63
Functions for Coding Theory, \indexit{220}
Functions for GAP Packages, \indexit{847}
Functions that do nothing, \indexit{63}
Function that Modify Boolean Lists, \indexit{213}
Function Types, \indexit{63}
`FusionCharTableTom', 721
`FusionConjugacyClasses', 807
`FusionConjugacyClassesOp', 807
fusions, 806
`FusionsAllowedByRestrictions', 822
`FusionsTom', 710
\letter G
$G$-sets, 397, 409
$g_N$, 161
`gac', 35
Galois Action, \indexit{580}
Galois Conjugacy of Cyclotomics, \indexit{164}
`GaloisCyc', 164
\sub for class functions, 774
`GaloisField', 588
`GaloisGroup', of field, 581
\sub of rational class of a group, 362
Galois Groups of Abelian Number Fields, \indexit{597}
`GaloisMat', 165
`GaloisStabilizer', 594
`GaloisType', 679
`gap.rc', 32, 33
GAP3, 34
`Gap3CatalogueIdGroup', 521
GAP for Macintosh OS X, \indexit{841}
GAP for MacOS, \indexit{842}
`GAPInfo', 851
`GAPInfo.RootPaths', 29
`GapInputPcGroup', 458
`GapInputSCTable', 617
`GAPKB_REW', 553
GAP Root Directory, \indexit{90}
`GasmanLimits', 87
`GasmanMessageStatus', 87
`GasmanStatistics', 87
Gaussian algorithm, 230
`GaussianIntegers', 598
`GaussianRationals', 593
Gaussians, \indexit{598}
`Gcd', 571
Gcd and Lcm, \indexit{571}
`Gcdex', 130
`GcdInt', 129
`GcdOp', 571
`GcdRepresentation', 571
`GcdRepresentationOp', 572
General Binary Relations, \indexit{315}
`GeneralisedEigenspaces', 231
`GeneralisedEigenvalues', 231
generalized characters, 768
`GeneralizedEigenspaces', 231
`GeneralizedEigenvalues', 231
`GeneralLinearGroup', 514
`GeneralMappingByElements', 305
General Mappings, \indexit{313}
`GeneralMappingsFamily', 314
`GeneralOrthogonalGroup', 515
`GeneralUnitaryGroup', 514
Generating Fields, \indexit{578}
Generating modules, \indexit{574}
Generating Rings, \indexit{562}
generator, of the prime residue group, 140
`GeneratorsOfAdditiveGroup', 560
`GeneratorsOfAdditiveMagma', 560
`GeneratorsOfAdditiveMagmaWithZero', 560
`GeneratorsOfAlgebra', 623
`GeneratorsOfAlgebraModule', 634
`GeneratorsOfAlgebraWithOne', 623
`GeneratorsOfDivisionRing', 579
`GeneratorsOfDomain', 293
`Generators\-Of\-Equivalence\-Relation\-Partition', 318
`GeneratorsOfField', 579
`GeneratorsOfGroup', 351
`GeneratorsOfIdeal', 565
`GeneratorsOfLeftIdeal', 566
`GeneratorsOfLeftModule', 574
`GeneratorsOfLeftOperatorAdditiveGroup', 574
`GeneratorsOfLeftVectorSpace', 600
`GeneratorsOfMagma', 323
`GeneratorsOfMagmaWithInverses', 323
`GeneratorsOfMagmaWithOne', 323
`GeneratorsOfMonoid', 546
`GeneratorsOfNearAdditiveGroup', 560
`GeneratorsOfNearAdditiveMagma', 560
`GeneratorsOfNearAdditiveMagmaWithZero', 560
`GeneratorsOfPresentation', 482
`GeneratorsOfRightIdeal', 566
`GeneratorsOfRightModule', 575
`GeneratorsOfRightOperatorAdditiveGroup', 575
`GeneratorsOfRing', 563
`GeneratorsOfRingWithOne', 567
`GeneratorsOfRws', 346
`GeneratorsOfSemigroup', 540
`GeneratorsOf<Struct>', 289
`GeneratorsOfTwoSidedIdeal', 565
`GeneratorsOfVectorSpace', 600
`GeneratorsPrimeResidues', 139
`GeneratorsSmallest', 380
`GeneratorsSubgroupsTom', 719
`GeneratorSyllable', 337
Generic Construction of Tables of Marks, \indexit{723}
`GetFusionMap', 808
Get the Archives, \indexit{832}
getting help, 22
`GF', 588
`GL', 514
GL and SL, \indexit{431}
Global Memory Information, \indexit{87}
`GlobalMersenneTwister', 136
`GlobalRandomSource', 136
`GModuleByMats', 697
`GO', 515
`GQuotients', 394
`Grading', 628
Green's Relations, \indexit{542}
`GreensDClasses', 544
`GreensDClassOfElement', 543
`GreensDRelation', 543
`GreensHClasses', 544
`GreensHClassOfElement', 543
`GreensHRelation', 543
`GreensJClasses', 544
`GreensJClassOfElement', 543
`GreensJRelation', 543
`GreensLClasses', 544
`GreensLClassOfElement', 543
`GreensLRelation', 543
`GreensRClasses', 544
`GreensRClassOfElement', 543
`GreensRRelation', 543
Groebner Bases, \indexit{686}
`GroebnerBasis', 686
`GroebnerBasisNC', 686
`Group', 350
group actions, 397, 398
\sub operations syntax, 397
Group Actions - Name Changes, \indexit{850}
group algebra, 663
Group Automorphisms, \indexit{390}
`GroupByRws', 456
`GroupByRwsNC', 456
group characters, 768
Group Elements, \indexit{350}
`GroupGeneralMappingByImages', 386
`GroupHClassOfGreensDClass', 544
`GroupHomomorphismByFunction', 386
`GroupHomomorphismByImages', 385
`GroupHomomorphismByImagesNC', 385
`GroupOfPcgs', 438
group operations, 398, 850
Group Properties, \indexit{367}
`GroupRing', 664
group ring, 663
Groups of Automorphisms, \indexit{392}
`GroupStabChain', 425
`GroupWithGenerators', 351
`GU', 514
\letter H
$h_N$, 161
`HallSubgroup', 365
`HallSystem', 366
\sub for groups with pcgs, 451
Handling of Streams in the Background, \indexit{106}
`HasAbelianFactorGroup', 373
`HasElementaryAbelianFactorGroup', 373
`HasIndeterminateName', 670
`HasParent', 291
`HasseDiagramBinaryRelation', 317
`HeadPcElementByNumber', 440
`HenselBound', 679
hermite normal form, 851
`HermiteNormalFormIntegerMat', 243
`HermiteNormalFormIntegerMatTransform', 243
`HeuristicCancelPolynomials', 691
`HexStringInt', 255
`HighestWeightModule', 660
History of Character Theory Stuff in GAP, \indexit{726}
`HMSMSec', 260
`Hom', 611
`HomeEnumerator', 409
Homomorphism for very large groups, \indexit{389}
`HomomorphismQuotientSemigroup', 542
homomorphisms, find all, 394
homomorphisms, Frobenius, field, 589
Homomorphisms of Algebras, \indexit{629}
`HomomorphismTransformationSemigroup', 541
How to Implement New Kinds of Vector Spaces, \indexit{613}
`HumanReadableDefinition', 717
\letter I
$i_N$, 162
`Ideal', 564
`IdealByGenerators', 565
`IdealNC', 565
Ideals, \indexit{621}
Ideals in Rings, \indexit{564}
Ideals of semigroups, \indexit{541}
`Idempotents', 324
`IdempotentsTom', 710
`IdempotentsTomInfo', 710
Identical Lists, \indexit{180}
Identical Objects, \indexit{110}
Identical Records, \indexit{264}
`IdentificationOfConjugacyClasses', 732
`Identifier', for character tables, 739
\sub for tables of marks, 711
Identifiers, \indexit{42}
`Identity', 293
`IdentityBinaryRelation', 315
`IdentityFromSCTable', 618
`IdentityMapping', 306
`IdentityMat', 228
`IdentityTransformation', 555
`IdFunc', 63
`IdGap3SolvableGroup', 521
`IdGroup', 521
`IdSmallGroup', 521
`IdsOfAllSmallGroups', 521
If, \indexit{51}
`if' statement, 51
If Things Go Wrong, \indexit{837}
`Image', 308
\sub for Frobenius automorphisms, 589
image, vector under matrix, 225
`ImageElm', 308
`ImageListOfTransformation', 556
`Images', 308
`ImagesElm', 307
`ImageSetOfTransformation', 556
`ImagesRepresentative', 307
`ImagesSet', 307
`ImagesSmallestGenerators', 389
`ImagesSource', 307
Images under Mappings, \indexit{307}
`ImaginaryPart', 164
`ImfInvariants', 534
`ImfMatrixGroup', 535
`ImfNumberQClasses', 532
`ImfNumberQQClasses', 532
`ImfNumberZClasses', 532
`Immutable', 112
`ImmutableBasis', 607
`ImmutableMatrix', 237
`in', for collections, 277
\sub for lists, 183
\sub for strictly sorted lists, 197
\sub operation for, 277
`IndependentGeneratorsOfAbelianGroup', 380
`Indeterminate', 669
`IndeterminateName', 670
`Indeterminateness', 816
`IndeterminateNumberOfLaurentPolynomial', 680
`Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 670
`Indeterminate\-Of\-Univariate\-Rational\-Function', 670
Indeterminates, \indexit{669}
`IndeterminatesOfPolynomialRing', 681
`Index', 352
`IndexInWholeGroup', 352
`IndexNC', 352
Index numbers of primitive groups, \indexit{529}
`Indicator', 746
`IndicatorOp', 746
`IndicesCentralNormalSteps', 445
`IndicesChiefNormalSteps', 446
`IndicesEANormalSteps', 445
`IndicesInvolutaryGenerators', 470
`IndicesNormalSteps', 447
`IndicesOfAdjointBasis', 624
`IndicesPCentralNormalStepsPGroup', 446
`IndicesStabChain', 425
`Indirected', 812
Induced Actions, \indexit{699}
`InducedAutomorphism', 393
`InducedClassFunction', 782
`InducedClassFunctions', 783
`InducedClassFunctionsByFusionMap', 783
`InducedCyclic', 783
`InducedPcgs', 441
`InducedPcgsByGenerators', 441
`InducedPcgsByGeneratorsNC', 441
`InducedPcgsByPcSequence', 441
`InducedPcgsByPcSequenceAndGenerators', 442
`InducedPcgsByPcSequenceNC', 441
`InducedPcgsWrtFamilyPcgs', 454
`InducedPcgsWrtSpecialPcgs', 449
`Inequalities', 799
inequality, of records, 265
inequality test, 47
`InertiaSubgroup', 780
Infinity, \indexit{160}
`infinity', 160
inflated class functions, 782
`Info', 80
`InfoAlgebra', 615
`InfoAttributes', 123
`InfoBckt', 427
`InfoCharacterTable', 731
`InfoCoh', 382
`InfoComplement', 363
`InfoCoset', 360
`InfoFpGroup', 464
Info Functions, \indexit{80}
`InfoGroebner', 687
`InfoGroup', 351
`InfoLattice', 377
`InfoLevel', 80
`InfoMatrix', 223
`InfoMonomial', 824
`InfoNumtheor', 138
`InfoOptions', 89
`InfoPcSubgroup', 380
Information about a function, \indexit{61}
Information about the version used, \indexit{84}
`InfoText', 739
`InfoTom', 708
`InfoWarning', 81
`Init', 136
`InitFusion', 821
`InitPowerMap', 819
`InjectionZeroMagma', 322
`InnerAutomorphism', 391
`InnerAutomorphismNC', 391
`InnerAutomorphismsAutomorphismGroup', 392
inner product, of group characters, 778
Input-Output Streams, \indexit{104}
`InputLogTo', 95
\sub for streams, 102
\sub stop logging input, 95
`InputOutputLocalProcess', 105
`InputTextFile', 103
`InputTextNone', 106
`InputTextString', 104
`InputTextUser', 103
`InsertTrivialStabilizer', 426
`InstallAtExit', 73
installation, 831
Installation of GAP for MacOS, \indexit{842}
Installation Overview, \indexit{831}
`InstallCharReadHookFunc', 106
`InstalledPackageVersion', 848
`InstallFactorMaintenance', 299
`InstallHandlingByNiceBasis', 613
Installing a GAP Package, \indexit{846}
`InstallIsomorphismMaintenance', 299
`InstallSubsetMaintenance', 299
`Int', 127
\sub for cyclotomics, 158
\sub for strings, 258
`INT_CHAR', 258
integer part of a quotient, 129
`Integers', 126
Integral Bases of Abelian Number Fields, \indexit{595}
`IntegralizedMat', 246
`IntegratedStraightLineProgram', 342
`IntermediateGroup', 372
`IntermediateResultOfSLP', 343
`IntermediateResultOfSLPWithoutOverwrite', 343
`Intermediate\-Results\-Of\-SLPWithout\-Overwrite', 343
`IntermediateSubgroups', 372
Internally Represented Cyclotomics, \indexit{166}
Internally Represented Strings, \indexit{253}
`InterpolatedPolynomial', 573
`IntersectBlist', 213
`Intersection', 275
\sub for groups with pcgs, 451
intersection, of collections, 275
\sub of sets, 198
`Intersection2', 275
`IntersectionBlist', 212
`IntersectionsTom', 715
`IntersectSet', 198
`IntFFE', 587
`IntFFESymm', 587
`IntHexString', 258
`IntScalarProducts', 816, 817
`IntVecFFE', 587
`InvariantBilinearForm', 432
`InvariantElementaryAbelianSeries', 371
Invariant Forms, \indexit{432}, \indexit{700}
`InvariantLattice', 434
`InvariantQuadraticForm', 432
`InvariantSesquilinearForm', 432
`Invariant\-Subgroups\-Elementary\-Abelian\-Group', 378
`Inverse', 295
inverse, group homomorphism, 387
\sub matrix, 225
\sub of class function, 773
`InverseAttr', 295
`InverseClasses', 739
`InverseGeneralMapping', 305
`InverseImmutable', 295
`InverseMap', 812
`InverseMatMod', 239
`InverseMutable', 295
`InverseOp', 295
`InverseRepresentative', 425
`InverseSameMutability', 295
`InverseSM', 295
Invoking the Help, \indexit{22}
`Irr', 735
irrationalities, 157
`IrrBaumClausen', 752
`IrrConlon', 752
`IrrDixonSchneider', 752
Irreducibility Tests, \indexit{698}
irreducible character, 777
irreducible characters, computation, 755
`IrreducibleDifferences', 784
Irreducible Maximal Finite Integral Matrix Groups, \indexit{531}
`IrreducibleModules', 754
\sub for groups with pcgs, 451
`IrreducibleRepresentations', 752
`IrreducibleRepresentationsDixon', 753
`IrreducibleSolvableGroup', 530
`IrreducibleSolvableGroupMS', 530
Irreducible Solvable Matrix Groups, \indexit{530}
`Is16BitsFamily', 338
`Is32BitsFamily', 338
`Is8BitsFamily', 338
`IsAbelian', 324
\sub for character tables, 736
`IsAbelianNumberField', 594
`IsAbelianNumberFieldPolynomialRing', 682
`IsAbelianTom', 712
`IsAdditiveElement', 300
`IsAdditiveElementWithInverse', 300
`IsAdditiveElementWithZero', 300
`IsAdditiveGroup', 559
`IsAdditiveGroupGeneralMapping', 312
`IsAdditiveGroupHomomorphism', 312
`IsAdditivelyCommutative', 560
`IsAdditivelyCommutativeElement', 302
`IsAdditivelyCommutativeElementCollColl', 302
`Is\-Additively\-Commutative\-Element\-Collection', 302
`IsAdditivelyCommutativeElementFamily', 302
`IsAdditiveMagma', 558
`IsAdditiveMagmaWithInverses', 559
`IsAdditiveMagmaWithZero', 558
`IsAlgebra', 622
`IsAlgebraGeneralMapping', 313
`IsAlgebraHomomorphism', 313
`IsAlgebraicElement', 693
`IsAlgebraicExtension', 692
`IsAlgebraModuleElement', 634
`IsAlgebraModuleElementCollection', 634
`IsAlgebraModuleElementFamily', 634
`IsAlgebraWithOne', 622
`IsAlgebraWithOneGeneralMapping', 313
`IsAlgebraWithOneHomomorphism', 313
`IsAlphaChar', 254
`IsAlternatingGroup', 418
`IsAnticommutative', 568
`IsAntisymmetricBinaryRelation', 316
`IsAssociated', 569
`IsAssociative', 324
`IsAssociativeElement', 302
`IsAssociativeElementCollColl', 302
`IsAssociativeElementCollection', 302
`IsAssocWord', 331
`IsAssocWordWithInverse', 331
`IsAssocWordWithOne', 331
`IsAutomorphismGroup', 392
`IsBasicWreathLessThanOrEqual', 334
`IsBasicWreathProductOrdering', 286
`IsBasis', 602
`IsBasisByNiceBasis', 613
`IsBasisOfAlgebraModuleElementSpace', 635
`IsBergerCondition', 825
`IsBijective', 307
`IsBinaryRelation', 315
\sub same as `IsEndoGeneralMapping', 315
`IsBLetterAssocWordRep', 338
`IsBLetterWordsFamily', 338
`IsBlist', 211
`IsBlockMatrixRep', 240
`IsBool', 170
`IsBound', for lists, 179
IsBound and Unbind for Lists, \indexit{179}
IsBound and Unbind for Records, \indexit{266}
`IsBoundGlobal', 45
`IsBrauerTable', 730
`IsBravaisGroup', 434
`IsBuiltFromAdditiveMagmaWithInverses', 347
`IsBuiltFromGroup', 347
`IsBuiltFromMagma', 347
`IsBuiltFromMagmaWithInverses', 347
`IsBuiltFromMagmaWithOne', 347
`IsBuiltFromSemigroup', 347
`IsCanonicalBasis', 605
`IsCanonicalBasisFullMatrixModule', 609
`IsCanonicalBasisFullRowModule', 609
`IsCanonicalNiceMonomorphism', 390
`IsCanonicalPcgs', 442
`IsCentral', 324
`IsCentralFactor', 383
`IsChar', 250
`IsCharacter', 777
`IsCharacteristicSubgroup', 353
`IsCharacterTable', 730
`IsCharacterTableInProgress', 730
`IsCharCollection', 250
`IsCheapConwayPolynomial', 590
`IsClassFunction', 768
`IsClassFusionOfNormalSubgroup', 746
`IsClosedStream', 97
`IsCochain', 656
`IsCochainCollection', 656
`IsCollection', 268
`IsCollectionFamily', 268
`IsCommutative', 324
`IsCommutativeElement', 302
`IsCommutativeElementCollColl', 302
`IsCommutativeElementCollection', 302
`IsCompositionMappingRep', 305
`IsConfluent', 345
\sub for pc groups, 456
`Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 374
`IsConjugacyClassSubgroupsRep', 374
`IsConjugate', 362
`IsConjugatorAutomorphism', 391
`IsConjugatorIsomorphism', 391
`IsConstantRationalFunction', 674
`IsConstantTimeAccessGeneralMapping', 313
`IsConstantTimeAccessList', 174
`IsContainedInSpan', 607
`IsCopyable', 112
`IsCyc', 158
`IsCyclic', 367
\sub for character tables, 736
`IsCyclicTom', 712
`IsCyclotomic', 158
`IsCyclotomicField', 594
`IsCyclotomicMatrixGroup', 433
`IsDenseList', 173
`IsDiagonalMat', 227
`IsDigitChar', 254
`IsDirectoryPath', 93
`IsDistributive', 568
`IsDivisionRing', 578
`IsDomain', 292
`IsDoneIterator', 279
`IsDoubleCoset', 360
`IsDuplicateFree', 195
`IsDuplicateFreeList', 195
`IsDxLargeGroup', 756
`IsElementaryAbelian', 367
\sub for character tables, 736
`IsElementOfFpMonoid', 550
`IsElementOfFpSemigroup', 550
`IsElementOfFreeMagmaRing', 665
`IsElementOfFreeMagmaRingCollection', 665
`IsElementOfFreeMagmaRingFamily', 665
`IsElementOfMagmaRingModuloRelations', 666
`Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 666
`Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 666
`Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 667
`IsEmpty', 273
`IsEmptyString', 253
`IsEndOfStream', 100
`IsEndoGeneralMapping', 313
\sub same as `IsBinaryRelation', 315
`IsEqualSet', 197
`IsEquivalenceClass', 319
`IsEquivalenceRelation', 316
`IsEuclideanRing', 570
`IsEvenInt', 127
`IsExecutableFile', 93
`IsExistingFile', 93
`IsExtAElement', 300
`IsExternalOrbit', 410
`IsExternalSet', 409
`IsExternalSubset', 410
`IsExtLElement', 300
`IsExtRElement', 300
`IsFamilyPcgs', 454
`IsFFE', 584
`IsFFECollColl', 584
`IsFFECollection', 584
`IsField', 578
`IsFieldControlledByGaloisGroup', 581
`IsFieldHomomorphism', 313
`IsFinite', 273
\sub for character tables, 736
`IsFiniteDimensional', 576
\sub for matrix algebras, 623
`IsFiniteFieldPolynomialRing', 682
`IsFinitelyGeneratedGroup', 368
`IsFiniteOrderElement', 302
`IsFiniteOrderElementCollColl', 302
`IsFiniteOrderElementCollection', 302
`IsFiniteOrdersPcgs', 438
`IsFixedStabilizer', 427
`IsFLMLOR', 622
`IsFLMLORWithOne', 622
`IsFpGroup', 464
`IsFpMonoid', 550
`IsFpSemigroup', 550
`IsFreeGroup', 332
`IsFreeLeftModule', 576
`IsFreeMagmaRing', 664
`IsFreeMagmaRingWithOne', 664
`IsFromFpGroupGeneralMappingByImages', 396
`IsFromFpGroupHomomorphismByImages', 396
`Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 396
`Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 396
`IsFullHomModule', 612
`IsFullMatrixModule', 577
`IsFullRowModule', 577
`Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 432
`Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 433
`Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 432
`IsFullTransformationSemigroup', 541
`IsFunction', 63
`IsGAPRandomSource', 136
`IsGaussianIntegers', 598
`IsGaussianRationals', 593
`IsGaussianSpace', 607
`IsGaussInt', 160
`IsGaussRat', 160
`IsGeneralizedDomain', 292
`IsGeneralizedRowVector', 185
`IsGeneralLinearGroup', 431
`IsGeneralMapping', 313
`IsGeneralMappingFamily', 314
`IsGeneratorsOf<Struct>', 289
`IsGL', 431
`IsGlobalRandomSource', 136
`IsGreensClass', 543
`IsGreensDClass', 543
`IsGreensDRelation', 543
`IsGreensHClass', 543
`IsGreensHRelation', 543
`IsGreensJClass', 543
`IsGreensJRelation', 543
`IsGreensLClass', 543
`IsGreensLessThanOrEqual', 543
`IsGreensLRelation', 543
`IsGreensRClass', 543
`IsGreensRelation', 543
`IsGreensRRelation', 543
`IsGroup', 351
`IsGroupGeneralMapping', 311
`Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 396
`IsGroupGeneralMappingByImages', 396
`IsGroupGeneralMappingByPcgs', 396
`IsGroupHClass', 544
`IsGroupHomomorphism', 311
`IsGroupOfAutomorphisms', 392
`IsGroupRing', 664
`IsHandledByNiceBasis', 577
\sub for vector spaces, 613
`IsHandledByNiceMonomorphism', 390
`IsHasseDiagram', 316
`IsHomogeneousList', 174
`IsIdempotent', 295
`IsIdenticalObj', 110
`IsIncomparableUnder', 282
`IsInducedFromNormalSubgroup', 827
`IsInducedPcgs', 441
`IsInducedPcgsWrtSpecialPcgs', 449
`IsInfBitsFamily', 338
`IsInfinity', 160
`IsInjective', 307
`IsInnerAutomorphism', 391
`IsInputOutputStream', 104
`IsInputStream', 97
`IsInputTextNone', 97
`IsInputTextStream', 97
`IsInt', 127
`IsIntegerMatrixGroup', 434
`IsIntegers', 126
`IsIntegralBasis', 605
`IsIntegralCyclotomic', 158
`IsIntegralRing', 567
`IsInternallyConsistent', 114
\sub for character tables, 745
\sub for tables of marks, 713
`IsIrreducibleCharacter', 777
`IsIrreducibleRingElement', 569
`IsIterator', 279
`IsJacobianElement', 302
`IsJacobianElementCollColl', 302
`IsJacobianElementCollection', 302
`IsJacobianRing', 568
`IsLaurentPolynomial', 673
`IsLaurentPolynomialDefaultRep', 689
`IsLDistributive', 568
`IsLeftAlgebraModuleElement', 634
`IsLeftAlgebraModuleElementCollection', 634
`IsLeftIdeal', 565
`IsLeftIdealInParent', 565
`IsLeftModule', 574
`IsLeftModuleGeneralMapping', 312
`IsLeftModuleHomomorphism', 312
`IsLeftOperatorAdditiveGroup', 574
`IsLeftSemigroupIdeal', 541
`IsLeftVectorSpace', 599
`IsLessThanOrEqualUnder', 282
`IsLessThanUnder', 282
`IsLetterAssocWordRep', 337
`IsLetterWordsFamily', 337
`IsLexicographicallyLess', 201
`IsLexOrderedFFE', 585
`IsLieAbelian', 645
`IsLieAlgebra', 622
`IsLieMatrix', 224
`IsLieNilpotent', 645
`IsLieObject', 640
`IsLieObjectCollection', 640
`IsLieSolvable', 645
`IsLinearMapping', 312
`IsLinearMappingsModule', 612
`IsList', 173
`IsListDefault', 186
`IsListOrCollection', 269
`IsLogOrderedFFE', 585
`IsLowerAlphaChar', 254
`IsLowerTriangularMat', 227
`IsMagma', 320
`IsMagmaHomomorphism', 310
`IsMagmaRingModuloRelations', 666
`IsMagmaRingModuloSpanOfZero', 667
`IsMagmaWithInverses', 320
`IsMagmaWithInversesIfNonzero', 320
`IsMagmaWithOne', 320
`IsMapping', 306
`IsMatchingSublist', 194
`IsMatrix', 223
`IsMatrixGroup', 430
`IsMatrixModule', 577
`IsMatrixSpace', 607
`IsMersenneTwister', 136
`IsMinimalNonmonomial', 830
`IsModuloPcgs', 443
`IsMonoid', 546
`IsMonomial', for characters, 827
\sub for character tables, 736
\sub for groups, 827
\sub for positive integers, 828
`IsMonomialGroup', 367
`IsMonomialMatrix', 227
`IsMonomialNumber', 828
`IsMonomialOrdering', 683
`IsMultiplicativeElement', 300
`IsMultiplicativeElementWithInverse', 301
`IsMultiplicativeElementWithOne', 301
`IsMultiplicativeElementWithZero', 301
`IsMultiplicativeGeneralizedRowVector', 185
`IsMultiplicativeZero', 324
`IsMutable', 112
`IsMutableBasis', 606
`IsNaturalAlternatingGroup', 417
`IsNaturalGL', 432
`IsNaturalGLnZ', 434
`IsNaturalSL', 432
`IsNaturalSLnZ', 434
`IsNaturalSymmetricGroup', 417
`IsNearAdditiveElement', 300
`IsNearAdditiveElementWithInverse', 300
`IsNearAdditiveElementWithZero', 300
`IsNearAdditiveGroup', 558
`IsNearAdditiveMagma', 558
`IsNearAdditiveMagmaWithInverses', 558
`IsNearAdditiveMagmaWithZero', 558
`IsNearlyCharacterTable', 730
`IsNearRingElement', 301
`IsNearRingElementWithInverse', 301
`IsNearRingElementWithOne', 301
`IsNegRat', 146
`IsNilpotent', for character tables, 736
\sub for groups with pcgs, 451
`IsNilpotentElement', 652
`IsNilpotentGroup', 367
`IsNilpotentTom', 712
`IsNonassocWord', 327
`IsNonassocWordCollection', 327
`IsNonassocWordWithOne', 327
`IsNonassocWordWithOneCollection', 327
`IsNonnegativeIntegers', 126
`IsNonSPGeneralMapping', 314
`IsNonTrivial', 273
`IsNormal', 352
`IsNormalBasis', 605
`IsNotIdenticalObj', 111
`IsNumberField', 594
`IsObject', 109
`IsOddInt', 127
isomorphic, pc group, 457, 458
`IsomorphicSubgroups', 394
`IsomorphismFpAlgebra', 631
`IsomorphismFpGroup', 473
\sub for subgroups of fp groups, 475
`IsomorphismFpGroupByGenerators', 473
`IsomorphismFpGroupByGeneratorsNC', 473
`IsomorphismFpGroupByPcgs', 455
`IsomorphismFpSemigroup', 551
`IsomorphismGroups', 394
`IsomorphismMatrixAlgebra', 631
`IsomorphismPcGroup', 458
`IsomorphismPermGroup', 417
\sub for Imf matrix groups, 537
`IsomorphismPermGroupImfGroup', 538
`IsomorphismReesMatrixSemigroup', 545
`IsomorphismRefinedPcGroup', 457
`Isomorphism<Rep><Struct>', 290
isomorphisms, find all, 394
`IsomorphismSCAlgebra', 632
`IsomorphismSimplifiedFpGroup', 476
`IsomorphismSpecialPcGroup', 458
`IsomorphismTransformationSemigroup', 541
`IsomorphismTypeInfoFiniteSimpleGroup', 368
`IsOne', 295
`IsOperation', 63
`IsOrdering', 281
`IsOrderingOnFamilyOfAssocWords', 283
`IsOrdinaryMatrix', 223
`IsOrdinaryTable', 730
`IsOutputStream', 97
`IsOutputTextNone', 98
`IsOutputTextStream', 98
`IsPadicExtensionNumber', 696
`IsPadicExtensionNumberFamily', 696
`IsParentPcgsFamilyPcgs', 454
`IsPartialOrderBinaryRelation', 316
`IsPcGroup', 455
`IsPcGroupGeneralMappingByImages', 396
`IsPcGroupHomomorphismByImages', 396
`IsPcgs', 437
`IsPcgsCentralSeries', 445
`IsPcgsChiefSeries', 446
`IsPcgsElementaryAbelianSeries', 445
`IsPcgsPCentralSeriesPGroup', 446
`IsPerfect', for character tables, 736
`IsPerfectGroup', 367
`IsPerfectTom', 712
`IsPerm', 412
`IsPermCollColl', 412
`IsPermCollection', 412
`IsPermGroup', 416
`IsPermGroupGeneralMappingByImages', 396
`IsPermGroupHomomorphismByImages', 396
`IsPGroup', 368
`IsPNilpotent', 369
`IsPolycyclicGroup', 367
`IsPolynomial', 673
`IsPolynomialDefaultRep', 689
`IsPolynomialFunction', 672
`IsPolynomialFunctionsFamily', 687
`IsPolynomialRing', 682
`IsPosInt', 127
`IsPositiveIntegers', 126
`IsPosRat', 146
`Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 396
`IsPreOrderBinaryRelation', 316
`IsPrime', 569
`IsPrimeField', 580
`IsPrimeInt', 131
`IsPrimeOrdersPcgs', 438
`IsPrimePowerInt', 132
`IsPrimitive', 408
`IsPrimitiveCharacter', 826
`IsPrimitivePolynomial', 674
`IsPrimitiveRootMod', 140
`IsProbablyPrimeInt', 131
`IsPseudoCanonicalBasisFullHomModule', 612
`IsPSolvable', 369
`IsPSolvableCharacterTable', 746
`IsPSolvableCharacterTableOp', 746
`IsPurePadicNumber', 695
`IsPurePadicNumberFamily', 695
`IsQuasiPrimitive', 826
`IsQuaternion', 623
`IsQuaternionCollColl', 623
`IsQuaternionCollection', 623
`IsQuickPositionList', 209
`IsQuotientSemigroup', 542
`IsRandomSource', 136
`IsRange', 208
`IsRat', 145
`IsRationalFunction', 672
`IsRationalFunctionDefaultRep', 689
`IsRationalFunctionsFamily', 687
`IsRationalMatrixGroup', 433
`IsRationals', 145
`IsRationalsPolynomialRing', 682
`IsRDistributive', 568
`IsReadableFile', 93
`IsReadOnlyGlobal', 44
`IsRecord', 262
`IsRecordCollColl', 262
`IsRecordCollection', 262
`IsReduced', 346
`IsReductionOrdering', 283
`IsReesCongruence', 542
`IsReesCongruenceSemigroup', 541
`IsReesMatrixSemigroup', 544
`IsReesMatrixSemigroupElement', 545
`IsReesZeroMatrixSemigroup', 544
`IsReesZeroMatrixSemigroupElement', 545
`IsReflexiveBinaryRelation', 315
`IsRegular', 407
`IsRegularDClass', 544
`IsRegularSemigroup', 540
`IsRegularSemigroupElement', 540
`IsRelativelySM', 829
`IsRestrictedLieAlgebra', 650
`IsRewritingSystem', 345
`IsRightAlgebraModuleElement', 634
`IsRightAlgebraModuleElementCollection', 634
`IsRightCoset', 358
`IsRightIdeal', 565
`IsRightIdealInParent', 565
`IsRightModule', 575
`IsRightOperatorAdditiveGroup', 574
`IsRightSemigroupIdeal', 541
`IsRing', 562
`IsRingElement', 301
`IsRingElementWithInverse', 301
`IsRingElementWithOne', 301
`IsRingGeneralMapping', 313
`IsRingHomomorphism', 313
`IsRingWithOne', 566
`IsRingWithOneGeneralMapping', 313
`IsRingWithOneHomomorphism', 313
`IsRootSystem', 647
`IsRootSystemFromLieAlgebra', 647
`IsRowModule', 577
`IsRowSpace', 607
`IsRowVector', 215
`IsScalar', 301
`IsSemiEchelonized', 608
`IsSemigroup', 539
`IsSemigroupCongruence', 542
`IsSemigroupIdeal', 541
`IsSemiRegular', 407
`IsSet', 195
`IsShortLexLessThanOrEqual', 334
`IsShortLexOrdering', 284
`IsSimple', for character tables, 736
`IsSimpleAlgebra', 623
`IsSimpleGroup', 367
`IsSimpleSemigroup', 540
`IsSingleValued', 306
`IsSL', 432
`IsSolvable', for character tables, 736
`IsSolvableGroup', 367
`IsSolvableTom', 712
`IsSortedList', 195
`IsSpecialLinearGroup', 432
`IsSpecialPcgs', 448
`IsSPGeneralMapping', 314
`IsSporadicSimple', for character tables, 736
`IsSSortedList', 195
`IsStandardGeneratorsOfGroup', 718
`IsStraightLineProgElm', 343
`IsStraightLineProgram', 339
`IsStream', 97
`IsString', 250
`IsStringRep', 253
`Is<Struct>', 290
`IsSubgroup', 352
`IsSubgroupFpGroup', 464
`IsSubgroupOfWholeGroupByQuotientRep', 477
`IsSubgroupSL', 432
`IsSubmonoidFpMonoid', 549
`IsSubnormal', 353
`IsSubnormallyMonomial', 829
`IsSubsemigroupFpSemigroup', 549
`IsSubset', 275
`IsSubsetBlist', 212
`IsSubsetLocallyFiniteGroup', 368
`IsSubsetSet', 198
`IsSubspacesVectorSpace', 601
`IsSub<struct>', 292
`IsSupersolvable', for character tables, 736
\sub for groups with pcgs, 451
`IsSupersolvableGroup', 367
`IsSurjective', 307
`IsSyllableAssocWordRep', 338
`IsSyllableWordsFamily', 338
`IsSymmetricBinaryRelation', 316
`IsSymmetricGroup', 418
`IsTable', 174
`IsTableOfMarks', 708
`IsTableOfMarksWithGens', 719
`IsToPcGroupGeneralMappingByImages', 396
`IsToPcGroupHomomorphismByImages', 396
`IsToPermGroupGeneralMappingByImages', 396
`IsToPermGroupHomomorphismByImages', 396
`IsTotal', 306
`IsTotalOrdering', 282
`IsTransformation', 555
`IsTransformationCollection', 555
`IsTransformationMonoid', 541
`IsTransformationSemigroup', 541
`IsTransitive', for characters, 780
\sub for class functions, 780
\sub for group actions, 407
`IsTransitiveBinaryRelation', 316
`IsTranslationInvariantOrdering', 283
`IsTrivial', 273
`IsTuple', 304
`IsTwoSidedIdeal', 565
`IsTwoSidedIdealInParent', 565
`IsUEALatticeElement', 659
`IsUEALatticeElementCollection', 659
`IsUEALatticeElementFamily', 659
`IsUniqueFactorizationRing', 567
`IsUnit', 568
`IsUnivariatePolynomial', 673
`IsUnivariatePolynomialRing', 683
`IsUnivariateRationalFunction', 673
`IsUnknown', 168
`IsUpperAlphaChar', 254
`IsUpperTriangularMat', 227
`IsValidIdentifier', 42
`IsVector', 301
`IsVectorSpace', 599
`IsVirtualCharacter', 777
`IsWeightLexOrdering', 285
`IsWeightRepElement', 660
`IsWeightRepElementCollection', 660
`IsWeightRepElementFamily', 660
`IsWellFoundedOrdering', 282
`IsWeylGroup', 648
`IsWholeFamily', 274
`IsWLetterAssocWordRep', 338
`IsWLetterWordsFamily', 338
`IsWord', 326
`IsWordCollection', 327
`IsWordWithInverse', 326
`IsWordWithOne', 326
`IsWreathProductOrdering', 286
`IsWritableFile', 93
`IsZero', 295
`IsZeroGroup', 541
`IsZeroSimpleSemigroup', 540
`IsZeroSquaredElement', 303
`IsZeroSquaredElementCollColl', 303
`IsZeroSquaredElementCollection', 303
`IsZeroSquaredRing', 568
`IsZmodnZObj', 135
`IsZmodnZObjNonprime', 135
`IsZmodpZObj', 135
`IsZmodpZObjLarge', 135
`IsZmodpZObjSmall', 135
`Iterated', 206
`Iterator', 278
iterator, for low index subgroups, 472
`IteratorByBasis', 604
`IteratorByFunctions', 280
`IteratorList', 280
Iterators, \indexit{278}
`IteratorSorted', 279
\letter J
$j_N$, 162
`Jacobi', 140
`JenningsLieAlgebra', 651
`JenningsSeries', 372
`JoinEquivalenceRelations', 318
`JoinStringsWithSeparator', 257
`JordanDecomposition', 236
\letter K
$k_N$, 162
`KappaPerp', 652
`KB_REW', 553
`KernelOfAdditiveGeneralMapping', 312
`KernelOfCharacter', 779
`KernelOfMultiplicativeGeneralMapping', 311
`KernelOfTransformation', 556
Keywords, \indexit{41}
`KillingMatrix', 652
`KnownAttributesOfObject', 121
Known Problems of the Configure Process, \indexit{838}
`KnownPropertiesOfObject', 124
`KnownTruePropertiesOfObject', 124
`KnowsHowToDecompose', 384
`KnuthBendixRewritingSystem', 554
Krasner-Kaloujnine theorem, 509
`KroneckerProduct', 229
`KuKGenerators', 509
\letter L
$l_N$, 162
`Lambda', 138
Language Overview, \indexit{39}
larger or equal, 47
larger test, 47
`LargestElementGroup', 380
`LargestElementStabChain', 425
`LargestMovedPoint', 413
`LargestUnknown', 168
`last', 64
`LastSystemError', 90
`LaTeXStringDecompositionMatrix', 744
lattice base reduction, 246, 247
lattice basis reduction, for virtual characters, 785
`LatticeByCyclicExtension', 377
`LatticeGeneratorsInUEA', 659
Lattice Reduction, \indexit{246}
`LatticeSubgroups', 375
`LatticeSubgroupsByTom', 706
`LaurentPolynomialByCoefficients', 680
`LaurentPolynomialByExtRep', 690
`LaurentPolynomialByExtRepNC', 690
Laurent Polynomials, \indexit{680}
`LClassOfHClass', 543
`Lcm', 572
`LcmInt', 130
`LcmOp', 572
`LeadCoeffsIGS', 442
`LeadingCoefficient', 675
`LeadingCoefficientOfPolynomial', 684
`LeadingExponentOfPcElement', 439
`LeadingMonomial', 676
`LeadingMonomialOfPolynomial', 683
`LeadingTermOfPolynomial', 683
Leaving GAP, \indexit{73}
`LeftActingAlgebra', 635
`LeftActingDomain', 575
`LeftActingRingOfIdeal', 566
`LeftAlgebraModule', 633
`LeftAlgebraModuleByGenerators', 633
left cosets, 358
`LeftDerivations', 642
`LeftIdeal', 564
`LeftIdealByGenerators', 565
`LeftIdealNC', 565
`LeftModuleByGenerators', 575
`LeftModuleByHomomorphismToMatAlg', 636
`LeftModuleGeneralMappingByImages', 610
`LeftModuleHomomorphismByImages', 610
`LeftModuleHomomorphismByImagesNC', 610
`LeftModuleHomomorphismByMatrix', 611
`LeftQuotient', 297
\sub for words, 335
`LeftShiftRowVector', 219
legacy, 850
`Legendre', 141
`Length', 195
\sub of an associative word, 335
length, of a word, 335
`LengthsTom', 709
`LenstraBase', 596
`LessThanFunction', 282
`LessThanOrEqualFunction', 282
`LetterRepAssocWord', 338
`LevelsOfGenerators', 286
`LeviMalcevDecomposition', 628
\sub for Lie algebras, 646
Lexical Structure, \indexit{40}
`LexicographicOrdering', 283
`LGFirst', 449
`LGLayers', 449
`LGLength', 449
`LGWeights', 448
library tables, 727
`LieAlgebra', 641
`LieAlgebraByStructureConstants', 641
`LieBracket', 297
`LieCenter', 643
`LieCentralizer', 643
`LieCentre', 643
`LieCoboundaryOperator', 656
`LieDerivedSeries', 644
`LieDerivedSubalgebra', 644
`LieFamily', 641
`LieLowerCentralSeries', 645
`LieNilRadical', 644
`LieNormalizer', 643
`LieObject', 640
Lie objects, \indexit{640}
`LieSolvableRadical', 644
`LieUpperCentralSeries', 645
`LiftedInducedPcgs', 444
`LiftedPcElement', 444
`LinearAction', 450
`LinearActionLayer', 450
`LinearCharacters', 736
`LinearCombination', 604
`LinearCombinationPcgs', 439
Linear equations over the integers and Integral Matrices, \indexit{241}
`LinearIndependentColumns', 246
Linear Mappings, \indexit{312}
`LinearOperation', 450
`LinearOperationLayer', 450
Line Editing, \indexit{74}
`LinesOfStraightLineProgram', 340
`List', 203
list and non-list, difference, 188
\sub left quotient, 190
\sub mod, 190
\sub product, 189
\sub quotient, 190
List Assignment, \indexit{177}
list assignment, operation, 175
`ListBlist', 212
list boundedness test, operation, 175
List Categories, \indexit{173}
list element, access, 175
\sub assignment, 177
\sub operation, 175
List Elements, \indexit{175}
list equal, comparison, 184
`ListN', 206
list of available books, 23
`ListPerm', 415
Lists and Collections, \indexit{269}
list smaller, comparison, 184
`ListStabChain', 425
list unbind, operation, 175
`ListWithIdenticalEntries', 191
`ListX', 206
`LLL', 785
LLL algorithm, for Gram matrices, 247
\sub for vectors, 246
\sub for virtual characters, 785
`LLLReducedBasis', 246
`LLLReducedGramMat', 247
`LoadDynamicModule', 35
Loading a GAP Package, \indexit{846}
loading a saved workspace, 37
`LoadPackage', 846
`local', 55
logarithm, discrete, 140
\sub of a root of unity, 160
`LogFFE', 586
logical, 170
logical operations, 171
`LogInt', 128
`LogMod', 139
`LogModShanks', 139
`LogTo', 95
\sub for streams, 101
\sub stop logging, 95
`LongestWeylWordPerm', 649
loop, read eval print, 64
loop, `for', 53
\sub `repeat', 52
\sub `while', 52
loop over iterator, 54
loop over object, 54
loop over range, 53
loops, leaving, 55
\sub restarting, 55
`LowercaseString', 255
`LowerCentralSeriesOfGroup', 371
Low Index Subgroups, \indexit{472}
`LowIndexSubgroupsFpGroup', 472
`LowIndexSubgroupsFpGroupIterator', 472
Low Level Routines to Modify and Create Stabilizer Chains, \indexit{426}
`Lucas', 155
\letter M
$m_N$, 162
Macintosh, 841, 842
MacOS, 842
`Magma', 321
`MagmaByGenerators', 321
`MagmaByMultiplicationTable', 322
Magma Categories, \indexit{320}
`MagmaElement', 322
Magma Generation, \indexit{321}
`MagmaHomomorphismByFunctionNC', 310
Magma Homomorphisms, \indexit{310}
`MagmaRingModuloSpanOfZero', 667
Magma Rings modulo Relations, \indexit{666}
Magma Rings modulo the Span of a Zero Element, \indexit{667}
Magmas Defined by Multiplication Tables, \indexit{322}
`MagmaWithInverses', 321
`MagmaWithInversesByGenerators', 321
`MagmaWithInversesByMultiplicationTable', 322
`MagmaWithOne', 321
`MagmaWithOneByGenerators', 321
`MagmaWithOneByMultiplicationTable', 322
Main Loop, \indexit{64}
`MakeConfluent', 346
`MakeImmutable', 112
`MakeReadOnlyGlobal', 44
`MakeReadWriteGlobal', 44
Making transformation semigroups, \indexit{541}
Manual Conventions, \indexit{20}
map, parametrized, 811
`MappedWord', 328
`MappingByFunction', 305
`MappingPermListList', 415
Mappings that Respect Addition, \indexit{312}
Mappings that Respect Multiplication, \indexit{311}
Mappings which are Compatible with Algebraic Structures, \indexit{310}
maps, 802
`MarksTom', 709
`MatAlgebra', 619
`MatClassMultCoeffsCharTable', 748
`MathieuGroup', 513
`MatLieAlgebra', 642
matrices, commutator, 226
Matrices as Basis of a Row Space, \indexit{234}
Matrices as Linear Mappings, \indexit{235}
Matrices over Finite Fields, \indexit{237}
Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{230}
`MatrixAlgebra', 619
`MatrixAutomorphisms', 763
matrix automorphisms, 805
`MatrixByBlockMatrix', 240
Matrix Constructions, \indexit{228}
Matrix Groups in Characteristic 0, \indexit{433}
`MatrixLieAlgebra', 642
`MatrixOfAction', 635
matrix spaces, 607
`MatScalarProducts', 778
`MatTom', 711
`MaximalAbelianQuotient', 373
`MaximalBlocks', 408
`MaximalNormalSubgroups', 375
`MaximalSubgroupClassReps', 374
`MaximalSubgroups', 374
\sub for groups with pcgs, 451
`MaximalSubgroupsLattice', 376
`MaximalSubgroupsTom', 715
`Maximum', 201
`MaximumList', 202
MeatAxe Modules, \indexit{697}
`MeetEquivalenceRelations', 318
`MeetMaps', 814
Membership Test for Collections, \indexit{277}
Membership Test for Lists, \indexit{183}
`MemoryUsage', 114
`MinimalElementCosetStabChain', 425
`MinimalGeneratingSet', 380
\sub for groups with pcgs, 451
`MinimalNonmonomialGroup', 830
Minimal Nonmonomial Groups, \indexit{830}
`MinimalNormalSubgroups', 375
`MinimalPolynomial', 677
\sub over a field, 581
\sub over a ring, 677
Minimal Polynomials, \indexit{677}
`MinimalStabChain', 423
`MinimalSupergroupsLattice', 376
`MinimalSupergroupsTom', 716
`MinimizedBombieriNorm', 679
`Minimum', 201
`MinimumList', 202
`MinusCharacter', 820
Miscellaneous, \indexit{144}
Miscellaneous Name Changes or Removed Names, \indexit{851}
mod, integers, 135
\sub laurent polynomials, 671
\sub lists, 190
\sub rationals, 48
`mod', 48
\sub arithmetic operators, 48
\sub for character tables, 734
\sub residue class rings, 134
modular inverse, 48
modular remainder, 48
modular roots, 142
`ModuleByRestriction', 637
Module Constructions, \indexit{697}
Module Homomorphisms, \indexit{700}
`ModuleOfExtension', 460
Modules over Lie Algebras and Their Cohomology, \indexit{655}
Modules over Semisimple Lie Algebras, \indexit{657}
modulo, 48
\sub arithmetic operators, 48
\sub for pcgs, 443
\sub residue class rings, 134
`ModuloPcgs', 443
`MoebiusMu', 143
`MoebiusTom', 711
Molien Series, \indexit{792}
`MolienSeries', 792
`MolienSeriesInfo', 792
`MolienSeriesWithGivenDenominator', 793
`Monoid', 546
`MonoidByGenerators', 546
`MonoidByMultiplicationTable', 547
`MonoidOfRewritingSystem', 554
`MonomialComparisonFunction', 684
`MonomialExtGrlexLess', 686
`MonomialExtrepComparisonFun', 684
`MonomialGrevlexOrdering', 685
`MonomialGrlexOrdering', 685
`MonomialLexOrdering', 684
Monomial Orderings, \indexit{683}
`MonomialTotalDegreeLess', 851
monomorphisms, find all, 394
`MorClassLoop', 394
More about Boolean Lists, \indexit{214}
More About Global Variables, \indexit{44}
More about Tables of Marks, \indexit{703}
`MostFrequentGeneratorFpGroup', 470
`MovedPoints', 414
Moved Points of Permutations, \indexit{413}
`MTX.BasesCompositionSeries', 699
`MTX.BasesMaximalSubmodules', 699
`MTX.BasesMinimalSubmodules', 698
`MTX.BasesMinimalSupermodules', 699
`MTX.BasesSubmodules', 698
`MTX.BasisInOrbit', 700
`MTX.BasisRadical', 699
`MTX.BasisSocle', 699
`MTX.CollectedFactors', 699
`MTX.CompositionFactors', 699
`MTX.DegreeSplittingField', 698
`MTX.Dimension', 698
`MTX.Distinguish', 700
`MTX.Field', 698
`MTX.Generators', 698
`MTX.Homomorphism', 700
`MTX.Homomorphisms', 700
`MTX.InducedAction', 699
`MTX.InducedActionFactorMatrix', 699
`MTX.InducedActionFactorModule', 699
`MTX.InducedActionMatrix', 699
`MTX.InducedActionMatrixNB', 699
`MTX.InducedActionSubmodule', 699
`MTX.InducedActionSubmoduleNB', 699
`MTX.InvariantBilinearForm', 700
`MTX.InvariantQuadraticForm', 700
`MTX.InvariantSesquilinearForm', 700
`MTX.IsAbsolutelyIrreducible', 698
`MTX.IsEquivalent', 700
`MTX.IsIrreducible', 698
`MTX.Isomorphism', 700
`MTX.NormedBasisAndBaseChange', 699
`MTX.OrthogonalSign', 700
`MTX.ProperSubmoduleBasis', 698
`MTX.SubGModule', 698
`MTX.SubmoduleGModule', 698
multiplication, 48
\sub matrices, 225
\sub matrix and matrix list, 226
\sub matrix and scalar, 224
\sub matrix and vector, 225
\sub operation, 297
\sub scalar and matrix, 224
\sub scalar and matrix list, 226
\sub scalar and vector, 216
\sub vector and matrix, 225
\sub vector and matrix list, 226
\sub vector and scalar, 216
\sub vectors, 216
`MultiplicationTable', 322
Multiplicative Arithmetic for Lists, \indexit{188}
Multiplicative Arithmetic Functions, \indexit{142}
`MultiplicativeNeutralElement', 324
multiplicative order of an integer, 139
`MultiplicativeZero', 324
`MultiplicativeZeroOp', 294
multiplicity, of constituents of a group character, 778
multiplier, 383
multisets, 197
Multivariate Polynomials, \indexit{677}
`MultRowVector', 219
Murnaghan components, 790, 791
Mutability and Copyability, \indexit{111}
Mutability Status and List Arithmetic, \indexit{190}
Mutable Bases, \indexit{606}
`MutableBasis', 606
`MutableBasisOfClosureUnderAction', 625
`Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 626
`MutableBasisOfNonassociativeAlgebra', 626
`MutableCopyMat', 229
`MutableIdentityMat', 229
`MutableNullMat', 229
\letter N
$n_k$, 163
`Name', 114
`NameFunction', 61
`NameRNam', 267
`NamesFilter', 118
`NamesGVars', 45
`NamesLocalVariablesFunction', 61
`NamesOfFusionSources', 809
`NamesSystemGVars', 45
`NamesUserGVars', 45
`NaturalCharacter', 776
Natural Embeddings related to Magma Rings, \indexit{665}
`NaturalHomomorphismByGenerators', 310
`NaturalHomomorphismByIdeal', 631
`NaturalHomomorphismByNormalSubgroup', 373
`NaturalHomomorphismByNormalSubgroupNC', 373
`NaturalHomomorphismBySubAlgebraModule', 638
`NaturalHomomorphismBySubspace', 611
`NearAdditiveGroup', 559
`NearAdditiveGroupByGenerators', 559
`NearAdditiveMagma', 559
`NearAdditiveMagmaByGenerators', 559
`NearAdditiveMagmaWithZero', 559
`NearAdditiveMagmaWithZeroByGenerators', 559
`NearlyCharacterTablesFamily', 731
negative number, 48
`NegativeRoots', 647
`NegativeRootVectors', 647
`NestingDepthA', 186
`NestingDepthM', 186
`NewInfoClass', 80
newline, 41
newline character, 252
`NewmanInfinityCriterion', 480
New Presentations and Presentations for Subgroups, \indexit{475}
`NextIterator', 279
`NextPrimeInt', 132
`NF', 593
`NiceBasis', 613
`NiceBasisFiltersInfo', 614
`NiceFreeLeftModule', 613
`NiceFreeLeftModuleInfo', 613
`NiceMonomorphism', 390
`NiceMonomorphismAutomGroup', 393
Nice Monomorphisms, \indexit{390}
`NiceObject', 390
`NiceVector', 613
`NilpotencyClassOfGroup', 367
`NilpotentQuotientOfFpLieAlgebra', 654
`NK', 163
`NOAUTO', 847
`NonabelianExteriorSquare', 383
`NonnegativeIntegers', 126
`NonnegIntScalarProducts', 816, 817
`NonNilpotentElement', 652
`Norm', 581
\sub of character, 778
`NormalBase', 583
`NormalClosure', 363
`NormalFormIntMat', 244
Normal Forms of Integer Matrices - Name Changes, \indexit{851}
Normal Forms over the Integers, \indexit{242}
`NormalIntersection', 363
`Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 666
`NormalizedWhitespace', 256
`Normalizer', 362
normalizer, 362
`NormalizerInGLnZ', 434
`NormalizerInGLnZBravaisGroup', 434
`NormalizersTom', 713
`NormalizerTom', 713
`NormalizeWhitespace', 256
`NormalSeriesByPcgs', 447
Normal Structure, \indexit{362}
`NormalSubgroupClasses', 766
`NormalSubgroupClassesInfo', 765
`NormalSubgroups', 375
`NormedRowVector', 217
`NormedRowVectors', 610
`NormedVectors', 851
`not', 172
`NrArrangements', 150
`NrBasisVectors', 606
`NrCombinations', 149
`NrConjugacyClasses', 361
\sub for character tables, 736
`NrConjugacyClassesGL', 517
`NrConjugacyClassesGU', 517
`NrConjugacyClassesPGL', 517
`NrConjugacyClassesPGU', 517
`NrConjugacyClassesPSL', 517
`NrConjugacyClassesPSU', 517
`NrConjugacyClassesSL', 517
`NrConjugacyClassesSLIsogeneous', 517
`NrConjugacyClassesSU', 517
`NrConjugacyClassesSUIsogeneous', 517
`NrDerangements', 152
`NrInputsOfStraightLineProgram', 340
`NrMovedPoints', 414
`NrOrderedPartitions', 154
`NrPartitions', 153
`NrPartitionsSet', 152
`NrPartitionTuples', 155
`NrPermutationsList', 151
`NrPolyhedralSubgroups', 747
`NrPrimitiveGroups', 528
`NrRestrictedPartitions', 154
`NrSubsTom', 709
`NrTransitiveGroups', 519
`NrTuples', 151
`NrUnorderedTuples', 150
`NullAlgebra', 620
`NullMat', 228
`NullspaceIntMat', 241
`NullspaceMat', 230
`NullspaceMatDestructive', 230
`NullspaceModQ', 239
`Number', 203
number, Bell, 148
\sub binomial, 147
\sub Stirling, of the first kind, 148
\sub Stirling, of the second kind, 149
`NumberArgumentsFunction', 61
`NumberFFVector', 218
number field, 594
number fields, Galois group, 597
`NumberIrreducibleSolvableGroups', 530
`NumberPerfectGroups', 524
`NumberPerfectLibraryGroups', 524
`NumberSmallGroups', 521
`NumberSyllables', 336
numerator, of a rational, 146
`NumeratorOfModuloPcgs', 443
`NumeratorOfRationalFunction', 672
`NumeratorRat', 146
Numerical Group Attributes, \indexit{369}
\letter O
$O_p(G)$, see `PCore', 362
`ObjByExtRep', 659
Objects, \indexit{109}
obsolete, 850
`OCOneCocycles', 382
octal character codes, 252
`OctaveAlgebra', 619
`od', 53
`OldGeneratorsOfPresentation', 498
`Omega', 366
`ONanScottType', 418
`OnBreak', 68
`OnBreakMessage', 70
`One', 293
`OneAttr', 293
`OneCoboundaries', 381
`OneCocycles', 381
one cohomology, 380
`OneFactorBound', 679
`OneImmutable', 293
`OneIrreducibleSolvableGroup', 530
`One<Library>Group', 519
`OneMutable', 293
`OneOfPcgs', 438
`OneOp', 293
`OnePrimitiveGroup', 519
`OneSameMutability', 293
`OneSM', 293
`OneSmallGroup', 521
`OneTransitiveGroup', 519
`OnIndeterminates', 677
\sub as a permutation action, 399
`OnLeftInverse', 398
`OnLines', 399
\sub example, 514
`OnPairs', 398
`OnPoints', 398
`OnRight', 398
`OnSets', 398
`OnSetsDisjointSets', 399
`OnSetsSets', 398
`OnSetsTuples', 399
`OnSubspacesByCanonicalBasis', 400
`OnTuples', 398
`OnTuplesSets', 399
`OnTuplesTuples', 399
`Operation', 850
`OperationAlgebraHomomorphism', 631
Operational Structure of Domains, \indexit{287}
`OperationHomomorphism', 850
operations, for booleans, 171
Operations and Attributes for Vector Spaces, \indexit{600}
Operations applicable to All Streams, \indexit{98}
Operations Concerning Blocks, \indexit{742}
Operations for (Near-)Additive Magmas, \indexit{561}
Operations for Abelian Number Fields, \indexit{593}
operations for algebraic elements, 692
Operations for Associative Words, \indexit{335}
Operations for Associative Words by their Syllables, \indexit{336}
Operations for Booleans, \indexit{171}
Operations for Brauer Characters, \indexit{800}
Operations for Class Functions, \indexit{777}
Operations for Collections, \indexit{275}
Operations for Cyclotomics, \indexit{157}
Operations for Domains, \indexit{292}
Operations for Finite Field Elements, \indexit{586}
Operations for Finitely Presented Groups, \indexit{466}
Operations for Group Homomorphisms, \indexit{387}
Operations for Input Streams, \indexit{98}
Operations for Lists, \indexit{199}
Operations for Output Streams, \indexit{101}
Operations for Pc Groups, \indexit{458}
Operations for Rational Functions, \indexit{671}
Operations for Special Kinds of Bases, \indexit{605}
Operations for Stabilizer Chains, \indexit{424}
Operations for Vector Space Bases, \indexit{603}
Operations for Words, \indexit{328}
Operations on elements of the algebra, \indexit{346}
Operations on rewriting systems, \indexit{345}
Operations to Evaluate Strings, \indexit{258}
Operations to Produce or Manipulate Strings, \indexit{255}
Operations which have Special Methods for Groups with Pcgs, \indexit{451}
operators, 42
\sub arithmetic, 48
\sub associativity, 49
\sub for cyclotomics, 161
\sub for lists, 185
\sub precedence, 48, 49
Operators for Character Tables, \indexit{734}
Operators for Matrices, \indexit{224}
Operators for Row Vectors, \indexit{215}
Optimization and Compiler Options, \indexit{839}
options, 27, 831
\sub command line, filenames, 29
\sub command line, internal, 31
options, under UNIX, 27
`or', 171
`Orbit', 400
`OrbitFusions', 810
`OrbitLength', 401
`OrbitLengths', 401
`OrbitLengthsDomain', 401
`OrbitPerms', 416
`OrbitPowerMaps', 805
`Orbits', operation/attribute, 401
Orbits, \indexit{400}
`OrbitsDomain', 401
`OrbitsPerms', 416
`OrbitStabChain', 425
`OrbitStabilizer', 402
`OrbitStabilizerAlgorithm', 402
Orbit Stabilizer Methods for Polycyclic Groups, \indexit{451}
`Order', 296
\sub of a class function, 774
order, of a group, 350
\sub of a list, collection or domain, 274
\sub of the prime residue group, 138
`OrderedPartitions', 153
ordering, booleans, 171
\sub of records, 266
`OrderingByLessThanFunctionNC', 281
`OrderingByLessThanOrEqualFunctionNC', 281
`OrderingOfRewritingSystem', 345
`OrderingOnGenerators', 283
`OrderingsFamily', 281
Orderings on families of associative words, \indexit{283}
`OrderMod', 139
`OrderOfRewritingSystem', 345
`OrdersClassRepresentatives', 737
`OrdersTom', 709
`Ordinal', 259
ordinary character, 777
`OrdinaryCharacterTable', 736
`OrthogonalComponents', 790
Orthogonal Embeddings, \indexit{248}
`OrthogonalEmbeddings', 248
`OrthogonalEmbeddingsSpecialDimension', 786
OSX, 841
Other Filters, \indexit{125}
Other Operations Applicable to any Object, \indexit{114}
Other Operations for Character Tables, \indexit{745}
Other Operations for Tables of Marks, \indexit{713}
output, suppressing, 64
`OutputLogTo', 95
\sub for streams, 102
\sub stop logging output, 95
`OutputTextFile', 103
`OutputTextNone', 106
`OutputTextString', 104
`OutputTextUser', 104
\letter P
$p$-group, 368
package, 846
Package Interface - Obsolete Functions and Name Changes, \indexit{850}
Packages, \indexit{835}
`PadicCoefficients', 246
`PadicExtensionNumberFamily', 695
`PadicNumber', 695
\sub for pure padics, 694
`PadicValuation', 570
`Pager', 25
`Parametrized', 813
Parametrized Maps, \indexit{811}
parametrized maps, 802
`Parent', 291
`ParentPcgs', 441
Parents, \indexit{291}
`PartialFactorization', 133
partial order, 316
`PartialOrderByOrderingFunction', 317
`PartialOrderOfHasseDiagram', 316
`Partitions', 153
partitions, improper, of an integer, 154
\sub ordered, of an integer, 154
\sub restricted, of an integer, 154
`PartitionsGreatestEQ', 154
`PartitionsGreatestLE', 154
`PartitionsSet', 152
`PartitionTuples', 155
`PcElementByExponents', 439
`PcElementByExponentsNC', 439
`PCentralLieAlgebra', 651
`PCentralNormalSeriesByPcgsPGroup', 446
`PCentralSeries', 372
`PcGroupCode', 462
`PcGroupCodeRec', 462
`PcGroupFpGroup', 455
Pc groups versus fp groups, \indexit{455}
`PcGroupWithPcgs', 457
`Pcgs', 437
`Pcgs_OrbitStabilizer', 451
Pcgs and Normal Series, \indexit{445}
`PcgsByPcSequence', 437
`PcgsByPcSequenceNC', 437
`PcgsCentralSeries', 445
`PcgsChiefSeries', 446
`PcgsElementaryAbelianSeries', 445
`PcgsPCentralSeriesPGroup', 446
`PClassPGroup', 369
`PCore', 362
`PcSeries', 438
`PerfectGroup', 523
perfect groups, 523
`PerfectIdentification', 524
`PerfectResiduum', 364
`Perform', 201
`Permanent', 156
Permanent of a Matrix, \indexit{156}
`PermBounds', 799
`PermCharInfo', 794
`PermCharInfoRelative', 795
`PermChars', 796
`PermCharsTom', 722
`PermComb', 799
`PermLeftQuoTransformation', 557
`PermList', 415
`PermListList', 201
`Permutation', 406
`PermutationCharacter', 777
permutation character, 822
permutation characters, possible, 793, 796
`PermutationCycle', 406
`PermutationCycleOp', 406
`PermutationGModule', 697
`PermutationMat', 228
`PermutationsFamily', 412
Permutations Induced by Elements and Cycles, \indexit{406}
`PermutationsList', 151
`PermutationTom', 708
`Permuted', 202
\sub as a permutation action, 400
\sub for class functions, 774
`PGL', 516
`PGU', 516
`Phi', 138
point stabilizer, 402
Polycyclic Generating Systems, \indexit{436}
`PolynomialByExtRep', 690
`PolynomialByExtRepNC', 690
`PolynomialCoefficientsOfPolynomial', 675
`PolynomialDivisionAlgorithm', 686
Polynomial Factorization, \indexit{678}
`PolynomialModP', 678
`PolynomialReducedRemainder', 686
`PolynomialReduction', 685
`PolynomialRing', 681
Polynomial Rings, \indexit{681}
Polynomials as Univariate Polynomials in one Indeterminate, \indexit{675}
polynomials over abelian number fields, factors, 593
Polynomials over the Rationals, \indexit{678}
`PopOptions', 88
Portability, \indexit{90}
Porting GAP, \indexit{840}
`Position', 191
`PositionBound', 193
`PositionCanonical', 192
`PositionFirstComponent', 194
`PositionNonZero', 194
`PositionNot', 194
`PositionNthOccurrence', 192
`PositionProperty', 193
`Positions', 192
`PositionSet', 193
`PositionsOp', 192
`PositionSorted', 192
`PositionStream', 100
`PositionSublist', 194
`PositionWord', 335
`PositiveIntegers', 126
positive number, 48
`PositiveRoots', 647
`PositiveRootVectors', 647
`PossibleClassFusions', 809
`PossibleFusionsCharTableTom', 721
Possible Permutation Characters, \indexit{793}
possible permutation characters, 793, 796
`PossiblePowerMaps', 803
power, 48
\sub matrix, 225
\sub meaning for class functions, 773
\sub of words, 335
`PowerMap', 803
`PowerMapByComposition', 805
`PowerMapOp', 803
Power Maps, \indexit{802}
`PowerMapsAllowedBySymmetrizations', 820
`PowerMod', 572
`PowerModCoeffs', 221
`PowerModInt', 131
`PowerPartition', 155
powerset, 149
`PowerSubalgebraSeries', 624
`PQuotient', 477
precedence, 48
precedence test, for permutations, 413
`PrefrattiniSubgroup', 364
\sub for groups with pcgs, 451
`PreImage', 309
`PreImageElm', 309
`PreImages', 309
`PreImagesElm', 308
Preimages in the Free Group, \indexit{465}
Preimages in the Free Semigroup, \indexit{551}
`PreimagesOfTransformation', 556
`PreImagesRange', 308
`PreImagesRepresentative', 309
`PreImagesSet', 309
Preimages under Homomorphisms from an FpGroup, \indexit{476}
Preimages under Mappings, \indexit{308}
preorder, 316
`PresentationFpGroup', 482
`PresentationNormalClosure', 487
`PresentationNormalClosureRrs', 487
`PresentationSubgroup', 485
`PresentationSubgroupMtc', 486
`PresentationSubgroupRrs', 485
`PresentationViaCosetTable', 483
previous result, 64
`PrevPrimeInt', 132
`PrimaryGeneratorWords', 486
primary subgroup generators, 500
`PrimeBlocks', 742
`PrimeBlocksOp', 742
`PrimeField', 580
Prime Integers and Factorization, \indexit{131}
`PrimePGroup', 369
`PrimePowersInt', 134
prime residue group, 138
\sub exponent, 139
\sub generator, 140
\sub order, 138
Prime Residues, \indexit{138}
`PrimeResidues', function, 138
`Primes', 131
primitive, 408
`PRIMITIVE_INDICES_MAGMA', 529
`PrimitiveElement', 580
`PrimitiveGroup', 528
Primitive Groups, \indexit{418}
`PrimitiveGroupsIterator', 528
`PrimitiveIdentification', 529
`PrimitiveIndexIrreducibleSolvableGroup', 530
Primitive Permutation Groups, \indexit{527}
`PrimitivePolynomial', 678
`PrimitiveRoot', 588
`PrimitiveRootMod', 140
primitive root modulo an integer, 140
Primitive Roots and Discrete Logarithms, \indexit{139}
Primitivity of Characters, \indexit{825}
`Print', 66
`PrintAmbiguity', 816
`PrintArray', 229
`PrintCharacterTable', 751
`PrintFactorsInt', 134
`PrintFormattingStatus', 102
Printing, Viewing and Displaying Finite Field Elements, \indexit{590}
Printing Character Tables, \indexit{748}
Printing Class Functions, \indexit{774}
Printing Presentations, \indexit{488}
Printing Tables of Marks, \indexit{706}
`PrintObj', 67
\sub for character tables, 748, 774
\sub for tables of marks, 706
`PrintTo', 95
\sub for streams, 101
`ProbabilityShapes', 679
problems, 837
Problems on Particular Systems, \indexit{839}
procedure call, 50
Procedure Calls, \indexit{50}
procedure call with arguments, 50
`Process', 107
Process, \indexit{107}
`PROD_GF2MAT_GF2MAT_ADVANCED', 239
`PROD_GF2MAT_GF2MAT_SIMPLE', 239
`Product', 205
product, of words, 335
\sub rational functions, 671
`ProductCoeffs', 221
`ProductOfStraightLinePrograms', 343
`ProductSpace', 624
`ProductX', 207
`ProfileFunctions', 83
`ProfileGlobalFunctions', 83
`ProfileMethods', 82
`ProfileOperations', 82
`ProfileOperationsAndMethods', 82
`PROFILETHRESHOLD', 83
Profiling, \indexit{82}
`ProjectedInducedPcgs', 444
`ProjectedPcElement', 444
`Projection', 306
\sub example for direct products, 505
\sub example for semidirect products, 507
\sub example for subdirect products, 508
\sub example for wreath products, 508
\sub for group products, 510
`ProjectionMap', 812
projections, find all, 394
`ProjectiveActionHomomorphismMatrixGroup', 431
`ProjectiveActionOnFullSpace', 431
`ProjectiveGeneralLinearGroup', 516
`ProjectiveGeneralUnitaryGroup', 516
`ProjectiveOrder', 238
`ProjectiveSpecialLinearGroup', 516
`ProjectiveSpecialUnitaryGroup', 516
`ProjectiveSymplecticGroup', 516
prompt, 64
\sub partial, 64
Properties, \indexit{124}
Properties and Attributes for Lists, \indexit{194}
Properties and Attributes of (General) Mappings, \indexit{306}
Properties and Attributes of Binary Relations, \indexit{315}
Properties and Attributes of Matrices, \indexit{226}
Properties and Attributes of Rational Functions, \indexit{672}
Properties and basic functionality, \indexit{282}
Properties of a Lie Algebra, \indexit{645}
Properties of rewriting systems, \indexit{347}
Properties of Rings, \indexit{567}
Properties of Tables of Marks, \indexit{712}
`PRump', 365
`PseudoRandom', 278
`PSL', 516
`PSP', 516
`PSp', 516
`PSU', 516
`PthPowerImage', 651
`PthPowerImages', 651
Pure p-adic Numbers, \indexit{694}
`PurePadicNumberFamily', 694
`PushOptions', 88
\letter Q
`Quadratic', 164
quadratic residue, 141
`QuaternionAlgebra', 619
`QUIET', 851
`QUIT', emergency quit, 73
quit, in emergency, 73
`quit', 68
`QUITTING', 73
`QuoInt', 129
`Quotient', 563
quotient, for finitely presented groups, 464
\sub matrices, 225
\sub matrix and matrix list, 226
\sub matrix and scalar, 225
\sub of free monoid, 552
\sub of free semigroup, 550
\sub of words, 335
\sub rational functions, 671
\sub scalar and matrix, 225
\sub scalar and matrix list, 226
\sub vector and matrix, 225
`QuotientFromSCTable', 618
Quotient Methods, \indexit{477}
`QuotientMod', 572
`QuotientPolynomialsExtRep', 691
`QuotientRemainder', 571
Quotients, \indexit{542}
Quotients and Remainders, \indexit{129}
`QuotientSemigroupCongruence', 542
`QuotientSemigroupHomomorphism', 542
`QuotientSemigroupPreimage', 542
`QuotRemLaurpols', 680
\letter R
$r_N$, 162
`RadicalGroup', 364
`RadicalOfAlgebra', 627
`Random', 136
\sub `[coll]', 277
\sub for integers, 129
\sub for rationals, 146
`RandomBinaryRelationOnPoints', 317
random element, of a list or collection, 277
Random Elements, \indexit{277}
`RandomInvertibleMat', 230
`RandomIsomorphismTest', 462
Random Isomorphism Testing, \indexit{462}
Randomized Methods for Permutation Groups, \indexit{420}
`RandomList', 278
`RandomMat', 230
Random Matrices, \indexit{230}
`RandomPrimitivePolynomial', 590
random seed, 278
`RandomSource', 137
Random Sources, \indexit{136}
`RandomTransformation', 555
`RandomUnimodularMat', 230
`Range', 307
range, 207
Ranges, \indexit{207}
`RankAction', 407
`RankFilter', 117
`RankMat', 230
`RankOfTransformation', 556
`RankPGroup', 369
`Rat', 146
\sub for strings, 258
`RationalClass', 361
`RationalClasses', 362
`RationalFunctionByExtRep', 690
`RationalFunctionByExtRepNC', 690
`Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 691
Rational Function Families, \indexit{687}
`RationalFunctionsFamily', 687
`RationalizedMat', 166
`Rationals', 145
`RClassOfHClass', 543
`Read', 94
\sub for streams, 99
`ReadAll', 99
`ReadAllLine', 105
`ReadAsFunction', 94
\sub for streams, 99
`ReadByte', 99
read eval print loop, 64
`ReadLine', 99
`ReadPackage', 847
`ReadPkg', 850
`ReadTest', 84
\sub for streams, 99
`RealClasses', 740
`RealizableBrauerCharacters', 800
`RealPart', 164
`RecNames', 262
Recognizing Characters, \indexit{254}
record, component access, 263
\sub component assignment, 263
\sub component variable, 263
\sub component variable assignment, 264
Record Access Operations, \indexit{267}
Record Assignment, \indexit{263}
record assignment, operation, 267
record boundness test, operation, 267
record component, operation, 267
record unbind, operation, 267
Recovery from NoMethodFound-Errors, \indexit{77}
recursion, 55
redisplay a help section, 23
redisplay with next help viewer, 23
`ReduceCoeffs', 221
`ReduceCoeffsMod', 221
`ReducedAdditiveInverse', 346
`ReducedCharacters', 784
`ReducedClassFunctions', 784
`ReducedComm', 346
`ReducedConfluentRewritingSystem', 553
`ReducedConjugate', 346
`ReducedDifference', 346
`ReducedForm', 345
`ReducedGroebnerBasis', 687
`ReducedInverse', 346
`ReducedLeftQuotient', 346
`ReducedOne', 346
`ReducedPcElement', 439
`ReducedPower', 346
`ReducedProduct', 346
`ReducedQuotient', 346
`ReducedScalarProduct', 346
`ReducedSum', 346
`ReducedZero', 346
`ReduceRules', 346
`ReduceStabChain', 426
Reducing Virtual Characters, \indexit{784}
`Ree', 513
`ReeGroup', 513
`ReesCongruenceOfSemigroupIdeal', 541
`ReesMatrixSemigroup', 544
`ReesMatrixSemigroupElement', 545
Rees Matrix Semigroups, \indexit{544}
`ReesZeroMatrixSemigroup', 544
`ReesZeroMatrixSemigroupElement', 545
`ReesZeroMatrixSemigroupElementIsZero', 545
`RefinedPcGroup', 457
`ReflectionMat', 229
`ReflexiveClosureBinaryRelation', 317
reflexive relation, 315
regular, 407
regular action, 404
`RegularActionHomomorphism', 405
`RegularModule', 754
relations, 304
Relations Between Domains, \indexit{298}
`RelationsOfFpSemigroup', 551
`RelativeBasis', 603
`RelativeBasisNC', 603
relatively prime, 48
`RelativeOrderOfPcElement', 439
`RelativeOrders', of a pcgs, 438
Relators in a Presentation, \indexit{488}
`RelatorsOfFpGroup', 465
remainder, operation, 297
remainder of a quotient, 129
`RemInt', 129
`Remove', 178
remove, an element from a set, 198
`RemoveCharacters', 256
`RemoveFile', 96
`RemoveOuterCoeffs', 219
`RemoveRelator', 490
`RemoveSet', 198
`RemoveStabChain', 426
Repeat, \indexit{52}
`repeat' loop, 52
`ReplacedString', 256
Representation, \indexit{120}
representation, as a sum of two squares, 144
Representations for Associative Words, \indexit{337}
Representations for Group Homomorphisms, \indexit{396}
Representations given by modules, \indexit{754}
Representations of Algebras, \indexit{632}
`RepresentationsOfObject', 121
`Representative', 274
representative, of a list or collection, 275
`RepresentativeAction', 403
`RepresentativeLinearOperation', 632
`RepresentativeOperation', 850
`RepresentativesContainedRightCosets', 359
`RepresentativesFusions', 810
`RepresentativeSmallest', 275
`RepresentativesMinimalBlocks', 408
`RepresentativesPerfectSubgroups', 377
`RepresentativesPowerMaps', 805
`RepresentativesSimpleSubgroups', 377
`RepresentativeTom', 720
`RepresentativeTomByGenerators', 720
`RepresentativeTomByGeneratorsNC', 720
`RequirePackage', 850
`Reread', 96
`REREADING', 96
`RereadPackage', 847
`RereadPkg', 850
`Reset', 136
`ResetOptionsStack', 88
residue, quadratic, 141
Residue Class Rings, \indexit{134}
`RespectsAddition', 312
`RespectsAdditiveInverses', 312
`RespectsInverses', 311
`RespectsMultiplication', 311
`RespectsOne', 311
`RespectsScalarMultiplication', 312
`RespectsZero', 312
`RestoreStateRandom', 277
Restricted and Induced Class Functions, \indexit{782}
`RestrictedClassFunction', 782
`RestrictedClassFunctions', 782
Restricted Lie algebras, \indexit{650}
`RestrictedMapping', 306
`RestrictedPartitions', 154
`RestrictedPerm', 415
`RestrictedPermNC', 415
`RestrictedTransformation', 556
`RestrictOutputsOfSLP', 342
`Resultant', 676
`ResultOfStraightLineProgram', 340
Return, \indexit{58}
`return', 68
\sub no value, 58
\sub with value, 58
`ReturnFail', 63
`ReturnFalse', 63
return from break loop, 68
`ReturnTrue', 63
`Reversed', 200
`RewindStream', 100
`RewriteWord', 471
Rewriting in Groups and Monoids, \indexit{347}
Rewriting Systems and the Knuth-Bendix Procedure, \indexit{553}
`RightActingAlgebra', 635
`RightActingRingOfIdeal', 566
`RightAlgebraModule', 633
`RightAlgebraModuleByGenerators', 633
`RightCoset', 357
`RightCosets', 358
right cosets, 357
`RightCosetsNC', 358
`RightDerivations', 642
`RightIdeal', 564
`RightIdealByGenerators', 565
`RightIdealNC', 565
`RightModuleByHomomorphismToMatAlg', 636
`RightShiftRowVector', 219
`RightTransversal', 358
`Ring', 562
`RingByGenerators', 563
Ring Homomorphisms, \indexit{313}
Rings With One, \indexit{566}
`RingWithOne', 566
`RingWithOneByGenerators', 567
`RNamObj', 267
root, of 1 modulo an integer, 142
\sub of an integer, 128
\sub of an integer, smallest, 128
\sub of an integer modulo another, 141
`RootInt', 128
`RootMod', 141
`RootOfDefiningPolynomial', 580
`RootsMod', 141
Roots Modulo Integers, \indexit{140}
roots of unity, 157
`RootsOfUPol', 675
`RootsUnityMod', 142
`RootSystem', 647
`RoundCyc', 159
Row and Matrix Spaces, \indexit{607}
`RowIndexOfReesMatrixSemigroupElement', 545
`Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
row spaces, 607
Row Vectors over Finite Fields, \indexit{217}
`Rules', 345
Running GAP under MacOS, \indexit{31}
`Runtime', 82
`Runtimes', 81
\letter S
$s_N$, 162
`SameBlock', 743
`SandwichMatrixOfReesMatrixSemigroup', 545
`SandwichMatrixOfReesZeroMatrixSemigroup', 545
save, 37
`SaveOnExitFile', 73
`SaveWorkspace', 37
Saving and Loading a Workspace, \indexit{37}
Saving a Pc Group, \indexit{458}
saving on exit, 73
`ScalarProduct', for characters, 778
Schreier, 485
Schreier-Sims, random, 420
`SchurCover', 383
Schur Covers and Multipliers, \indexit{383}
Schur multiplier, 383
scope, 43
`ScriptFromString', 717
Searching for Homomorphisms, \indexit{394}
`SecHMSM', 260
secondary subgroup generators, 500
`SecondsDMYhms', 260
`SeekPositionStream', 100
Selecting a Different MeatAxe, \indexit{698}
Selection Functions, \indexit{518}
`SemidirectProduct', 506
Semidirect Products, \indexit{506}
`SemiEchelonBasis', 609
`SemiEchelonBasisNC', 609
`SemiEchelonMat', 232
`SemiEchelonMatDestructive', 233
`SemiEchelonMats', 233
`SemiEchelonMatsDestructive', 233
`SemiEchelonMatTransformation', 233
`Semigroup', 539
semigroup, 539
`SemigroupByGenerators', 539
`SemigroupByMultiplicationTable', 540
`SemigroupIdealByGenerators', 541
`SemigroupOfRewritingSystem', 554
semiregular, 407
Semisimple Lie Algebras and Root Systems, \indexit{646}
`SemiSimpleType', 646
sequence, Bernoulli, 148
\sub Fibonacci, 155
\sub Lucas, 156
Series of Ideals, \indexit{644}
`Set', 271
`SetAssertionLevel', 81
`SetCommutator', 456
`SetConjugate', 456
`SetCrystGroupDefaultAction', 435
set difference, of collections, 276
`SetEntrySCTable', 617
`SetGasmanMessageStatus', 87
`SetHelpViewer', 24
`SetIndeterminateName', 670
`SetInfoLevel', 80
`SetName', 114
Set Operations via Boolean Lists, \indexit{212}
`SetParent', 291
`SetPower', 456
`SetPrintFormattingStatus', 102
`SetRecursionTrapInterval', 86
`SetReducedMultiplication', 465
Sets, \indexit{110}
sets, 173, 197
Sets of Subgroups, \indexit{374}
set stabilizer, 402
`Setter', 122
setter, 122
Setter and Tester for Attributes, \indexit{122}
`SetX', 207
`ShallowCopy', 113
\sub for lists, 181
`ShiftedCoeffs', 221
`ShiftedPadicNumber', 694
Shifting and Trimming Coefficient Lists, \indexit{219}
`ShortestVectors', 248
`ShortLexOrdering', 284
short vectors spanning a lattice, 246, 785
`ShowArgument', 77
`ShowArguments', 77
`ShowDetails', 77
`ShowImpliedFilters', 118
`ShowMethods', 78
`ShowOtherMethods', 78
`ShrinkAllocationPlist', 183
`ShrinkAllocationString', 253
`ShrinkCoeffs', 222
`ShrinkRowVector', 219
`SiftedPcElement', 439
`SiftedPermutation', 425
`SiftedVector', 610
`Sigma', 142
sign, of an integer, 127
Sign and Cycle Structure, \indexit{414}
`SignInt', 127
`SignPartition', 154
`SignPerm', 414
`SimpleLieAlgebra', 642
`SimpleSystem', 647
`SimplifiedFpGroup', 484
SimplifiedFpGroup, \indexit{484}
`SimplifyPresentation', 491
`SimsNo', 529
`SimultaneousEigenvalues', 239
`SingleCollector', 456
singlequote character, 252
singlequotes, 250
`SINT_CHAR', 258
`Size', 274
\sub for character tables, 736
\sub for groups with pcgs, 451
size, of a list or collection, 274
`SizeBlist', 212
`SizeConsiderFunction', 379
`SizeNumbersPerfectGroups', 524
`SizeOfFieldOfDefinition', 800
`SizesCentralizers', 737
`SizesConjugacyClasses', 737
`SizeScreen', 76
SizeScreen, \indexit{76}
`SizesPerfectGroups', 523
`SizeStabChain', 424
`SL', 514
smaller, associative words, 334
\sub elements of finitely presented groups, 465
\sub nonassociative words, 328
\sub pcwords, 454
\sub rational functions, 672
`SmallerDegreePermutationRepresentation', 417
smaller or equal, 47
smaller test, 47
`SmallestGeneratorPerm', 413
`SmallestMovedPoint', 413
`SmallestRootInt', 128
`SmallGeneratingSet', 380
`SmallGroup', 521
Small Groups, \indexit{520}
`SmallGroupsInformation', 522
Smash MeatAxe Flags, \indexit{702}
smith normal form, 851
`SmithNormalFormIntegerMat', 243
`SmithNormalFormIntegerMatTransforms', 243
`SMTX.AbsoluteIrreducibilityTest', 701
`SMTX.AlgEl', 702
`SMTX.AlgElCharPol', 702
`SMTX.AlgElCharPolFac', 702
`SMTX.AlgElMat', 702
`SMTX.AlgElNullspaceDimension', 702
`SMTX.AlgElNullspaceVec', 702
`SMTX.CentMat', 702
`SMTX.CentMatMinPoly', 702
`SMTX.CompleteBasis', 701
`SMTX.Getter', 701
`SMTX.GoodElementGModule', 701
`SMTX.IrreducibilityTest', 701
`SMTX.MatrixSum', 701
`SMTX.MinimalSubGModule', 701
`SMTX.MinimalSubGModules', 701
`SMTX.RandomIrreducibleSubGModule', 701
`SMTX.Setter', 701
`SMTX.SortHomGModule', 701
`SMTX.Subbasis', 702
`SO', 515
`Socle', 365
`SocleTypePrimitiveGroup', 418
`SolutionIntMat', 241
`SolutionMat', 231
`SolutionMatDestructive', 231
`SolutionNullspaceIntMat', 241
Some Remarks about Character Theory in GAP, \indexit{725}
Some Special Algebras, \indexit{619}
`Sort', 196
`SortedCharacters', 761
`SortedCharacterTable', 762
Sorted Character Tables, \indexit{761}
`SortedList', 271
sorted list, 195
Sorted Lists and Sets, \indexit{197}
sorted lists as collections, 269
`SortedSparseActionHomomorphism', 404
`SortedTom', 707
`Sortex', 196
Sorting Lists, \indexit{196}
`SortingPerm', 197
Sorting Tables of Marks, \indexit{707}
`SortParallel', 196
`Source', 307
`SourceOfIsoclinicTable', 760
`SP', 515
`Sp', 515
space, 41
`SparseActionHomomorphism', 404
`SparseCartanMatrix', 648
Special Characters, \indexit{252}
special character sequences, 252
Special Filenames, \indexit{93}
Special Generating Sets, \indexit{380}
`SpecialLinearGroup', 514
Special Multiplication Algorithms for Matrices over GF(2), \indexit{239}
`SpecialOrthogonalGroup', 515
Special Pcgs, \indexit{448}
`SpecialPcgs', attribute, 448
Special Rules for Input Lines, \indexit{65}
`SpecialUnitaryGroup', 515
Specific and Parametrized Subgroups, \indexit{363}
Specific Methods for Subgroup Lattice Computations, \indexit{377}
`SplitCharacters', 756
`SplitExtension', 460
`SplitExtensions', 461
`SplitString', 255
`SplittingField', 674
`Sqrt', 297
square root, of an integer, 128
`SquareRoots', 325
`SSortedList', 271
`StabChain', 422
`StabChainBaseStrongGenerators', 423
`StabChainImmutable', 422
`StabChainMutable', 422
`StabChainOp', 422
`StabChainOptions', 423
`Stabilizer', 402
Stabilizer Chain Records, \indexit{423}
Stabilizer Chains, \indexit{419}
`StabilizerOfExternalSet', 410
`StabilizerPcgs', 451
Stabilizers, \indexit{402}
`StandardAssociate', 569
`StandardGeneratorsFunctions', 717
`StandardGeneratorsInfo', for groups, 716
\sub for tables of marks, 721
`StandardGeneratorsOfGroup', 718
Standard Generators of Groups, \indexit{716}
Standardization of coset tables, \indexit{470}
`StandardizeTable', 470
`StarCyc', 164
`State', 136
Statements, \indexit{49}
`StateRandom', 277
`Stirling1', 148
`Stirling2', 149
Stirling number of the first kind, 148
Stirling number of the second kind, 149
`StoredGroebnerBasis', 687
`StoreFusion', 808
Storing Normal Subgroup Information, \indexit{765}
`StraightLineProgElm', 343
`StraightLineProgGens', 344
`StraightLineProgram', 339
Straight Line Program Elements, \indexit{343}
`StraightLineProgramNC', 339
Straight Line Programs, \indexit{339}
`StraightLineProgramsTom', 719
`StreamsFamily', 98
`StretchImportantSLPElement', 344
strictly sorted list, 195
`String', 255
\sub for cyclotomics, 159
`StringDate', 260
`StringOfResultOfStraightLineProgram', 341
`StringPP', 255
strings, equality of, 254
\sub inequality of, 254
\sub lexicographic ordering of, 254
String Streams, \indexit{104}
`StringTime', 260
`StrongGeneratorsStabChain', 425
`StronglyConnectedComponents', 317
<Struct>, 288
`<Struct>ByGenerators', 289
`StructuralCopy', 113
\sub for lists, 181
structure constant, 747, 748
`StructureConstantsTable', 605
`StructureDescription', 355
Structure Descriptions, \indexit{355}
`<Struct>WithGenerators', 289
`SU', 515
`Subalgebra', 620
`SubAlgebraModule', 636
`SubalgebraNC', 620
Subalgebras, \indexit{620}
`SubalgebraWithOne', 620
`SubalgebraWithOneNC', 621
`SubdirectProduct', 508
Subdirect Products, \indexit{508}
`SubdirectProducts', 508
subdomains, 292
`Subfield', 580
`SubfieldNC', 580
`Subfields', 580
Subfields of Fields, \indexit{580}
`Subgroup', 352
`SubgroupByPcgs', 442
`SubgroupByProperty', 353
subgroup fusions, 806
subgroup generators tree, 500
Subgroup Lattice, \indexit{375}
`SubgroupNC', 352
`SubgroupOfWholeGroupByCosetTable', 471
`SubgroupOfWholeGroupByQuotientSubgroup', 476
Subgroup Presentations, \indexit{485}
`SubgroupProperty', 427
Subgroups, \indexit{352}
subgroups, polyhedral, 747
Subgroups characterized by prime powers, \indexit{366}
Subgroup Series, \indexit{370}
`SubgroupShell', 353
Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{442}
Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{441}
`SubgroupsSolvableGroup', 378
sublist, 175
\sub access, 175
\sub assignment, 177
\sub operation, 176
sublist assignment, operation, 178
`Submagma', 321
`SubmagmaNC', 321
`SubmagmaWithInverses', 321
`SubmagmaWithInversesNC', 321
`SubmagmaWithOne', 321
`SubmagmaWithOneNC', 321
`Submodule', 575
`SubmoduleNC', 575
Submodules, \indexit{575}
`Submonoid', 546
`SubmonoidNC', 546
`SubnearAdditiveGroup', 560
`SubnearAdditiveGroupNC', 560
`SubnearAdditiveMagma', 560
`SubnearAdditiveMagmaNC', 560
`SubnearAdditiveMagmaWithZero', 560
`SubnearAdditiveMagmaWithZeroNC', 560
`SubnormalSeries', 370
`Subring', 563
`SubringNC', 563
`SubringWithOne', 567
`SubringWithOneNC', 567
Subroutines for the Construction of Class Fusions, \indexit{821}
Subroutines for the Construction of Power Maps, \indexit{819}
`Subsemigroup', 539
`SubsemigroupNC', 539
subsets, 149
subset test, for collections, 275
`Subspace', 599
`SubspaceNC', 599
`Subspaces', 601
`SubstitutedWord', 336
`SubsTom', 709
`Sub<struct>', 292
`Sub<struct>NC', 292
`SubSyllables', 337
subtract, a set from another, 199
`SubtractBlist', 213
subtraction, 48
\sub matrices, 224
\sub matrix and scalar, 224
\sub rational functions, 671
\sub scalar and matrix, 224
\sub scalar and matrix list, 226
\sub scalar and vector, 216
\sub vector and scalar, 216
\sub vectors, 216
`SubtractSet', 199
`Subword', 335
`Successors', 316
Suitability for Compilation, \indexit{36}
`Sum', 205
Sum and Intersection of Pcgs, \indexit{447}
`SumFactorizationFunctionPcgs', 447
`SumIntersectionMat', 234
`SumX', 207
`SupersolvableResiduum', 365
`support', email address, 838
`SupportedCharacterTableInfo', 729
`SurjectiveActionHomomorphismAttr', 411
`SuzukiGroup', 513
`SylowComplement', 365
`SylowSubgroup', 365
Sylow Subgroups and Hall Subgroups, \indexit{365}
`SylowSystem', 366
Symbols, \indexit{40}
Symmetric and Alternating Groups, \indexit{417}
`SymmetricClosureBinaryRelation', 317
`SymmetricGroup', 513
symmetric group, powermap, 155
`SymmetricParentGroup', 418
`SymmetricParts', 790
`SymmetricPowerOfAlgebraModule', 661
symmetric relation, 316
`Symmetrizations', 790
symmetrizations, orthogonal, 790, 791
\sub symplectic, 791
Symmetrizations of Class Functions, \indexit{790}
`SymplecticComponents', 791
`SymplecticGroup', 515
syntax errors, 64
system getter, 121
system setter, 121
`Sz', 513
\letter T
$t_N$, 162
`TableAutomorphisms', 764
table automorphisms, 810, 822
table of chapters for help books, 23
`TableOfMarks', 704
`TableOfMarksByLattice', 705
`TableOfMarksComponents', 708
`TableOfMarksCyclic', 723
`TableOfMarksDihedral', 723
`TableOfMarksFamily', 708
`TableOfMarksFrobenius', 723
Table of Marks Objects in GAP, \indexit{704}
table of sections for help books, 23
tables, 725, 727
tabulator, 41
`Tau', 142
Technical Details about Tables of Marks, \indexit{708}
Technical Details about the Implementation of Magma Rings, \indexit{667}
Technical Matters Concerning General Mappings, \indexit{313}
`TemporaryGlobalVarName', 46
`Tensored', 781
`TensorProductGModule ', 697
`TensorProductOfAlgebraModules', 660
Tensor Products and Exterior and Symmetric Powers, \indexit{660}
test, for a primitive root, 140
\sub for a rational, 145
\sub for records, 262
\sub for set equality, 198
`TestConsistencyMaps', 815
`Tester', 122
tester, 122
Test Files, \indexit{84}
`TestHomogeneous', 825
`TestInducedFromNormalSubgroup', 827
Testing Finiteness of Finitely Presented Groups, \indexit{480}
Testing for the System Architecture, \indexit{35}
Testing Monomiality, \indexit{827}
`TestJacobi', 617
`TestMonomial', 827
`TestMonomialQuick', 828
`TestMonomialUseLattice', 828
Test of the installation, \indexit{834}
`TestPackageAvailability', 848
`TestPerm1', 797
`TestPerm2', 797
`TestPerm3', 797
`TestPerm4', 797
`TestPerm5', 797
`TestQuasiPrimitive', 826
`TestRelativelySM', 829
Tests for Actions, \indexit{407}
Tests for the Availability of Methods, \indexit{384}
`TestSubnormallyMonomial', 829
The .gaprc file, \indexit{33}
The Adjoint Representation, \indexit{652}
The Compiler, \indexit{35}
The Defining Attributes of Rational Functions, \indexit{689}
The Dixon-Schneider Algorithm, \indexit{754}
The Documentation, \indexit{836}
The External Representation for Associative Words, \indexit{339}
The family pcgs, \indexit{454}
The Interface between Character Tables and Groups, \indexit{731}
The Interface between Tables of Marks and Character Tables, \indexit{721}
The Library of Tables of Marks, \indexit{724}
`then', 51
The Natural Action, \indexit{416}
The Pager Command, \indexit{25}
The Permutation Image of an Action, \indexit{403}
The Representations of Rational Functions, \indexit{688}
The Smash MeatAxe, \indexit{701}
The Syntax in BNF, \indexit{59}
`ThreeGroup' library, 521
Tietze Options, \indexit{503}
Tietze Transformations, \indexit{490}
Tietze Transformations that introduce new Generators, \indexit{495}
`TietzeWordAbstractWord', 488
`time', 82
Timing, \indexit{81}
Todd-Coxeter Procedure, \indexit{554}
`Trace', 227
\sub for field elements, 582
\sub of a matrix, 227
`TracedCosetFpGroup', 468
`TraceImmediateMethods', 79
`TraceMat', 227
`TraceMethods', 79
`TracePolynomial', 581
Tracing generator images through Tietze transformations, \indexit{498}
Tracing Methods, \indexit{79}
`TransferDiagram', 815
`Transformation', 555
`TransformationData', 555
`TransformationFamily', 555
`TransformationNC', 555
`TransformationRelation', 557
`TransformationType', 555
`TransformingPermutations', 764
`TransformingPermutationsCharacterTables', 764
transitive, 407
`TransitiveClosureBinaryRelation', 317
`TransitiveGroup', 519
`TransitiveIdentification', 519
Transitive Permutation Groups, \indexit{519}
transitive relation, 316
`Transitivity', for characters, 780
\sub for class functions, 780
\sub for group actions, 407
`TranslatorSubalgebra', 639
transporter, 403
`TransposedMat', 228
`TransposedMatAttr', 228
`TransposedMatDestructive', 229
`TransposedMatImmutable', 228
`TransposedMatMutable', 228
`TransposedMatOp', 228
`TransposedMatrixGroup', 430
Transversals, \indexit{358}
Triangular Matrices, \indexit{235}
`TriangulizedIntegerMat', 242
`TriangulizedIntegerMatTransform', 242
`TriangulizedNullspaceMat', 230
`TriangulizedNullspaceMatDestructive', 230
`TriangulizeIntegerMat', 242
`TriangulizeMat', 230
`TrivialCharacter', 776
`TrivialGroup', 511
`TrivialIterator', 280
`TrivialSubalgebra', 621
`TrivialSubgroup', 363
`TrivialSubmagmaWithOne', 325
`TrivialSubmodule', 575
`TrivialSubmonoid', 546
`TrivialSubnearAdditiveMagmaWithZero', 560
`TrivialSubspace', 600
`TryCosetTableInWholeGroup', 471
`TryGcdCancelExtRepPolynomials', 691
`Tuples', 151
tuple stabilizer, 402
`TwoClosure', 427
`TwoCoboundaries', 459
`TwoCocycles', 459
`TwoCohomology', 459
`TwoGroup' library, 521
`TwoSidedIdeal', 564
`TwoSidedIdealByGenerators', 565
`TwoSidedIdealNC', 565
`TwoSquares', 144
type, boolean, 170
\sub cyclotomic, 157
\sub records, 262
\sub strings, 250
`TypeObj', 125
`TypeOfDefaultGeneralMapping', 314
Types, \indexit{125}
`TzEliminate', 493
`TzFindCyclicJoins', 494
`TzGo', 491
`TzGoGo', 492
`TzImagesOldGens', 499
`TzInitGeneratorImages', 498
`TzNewGenerator', 490
`TzOptions', 503
`TzPreImagesNewGens', 499
`TzPrint', 489
`TzPrintGeneratorImages', 499
`TzPrintGenerators', 488
`TzPrintLengths', 489
`TzPrintOptions', 504
`TzPrintPairs', 489
`TzPrintPresentation', 489
`TzPrintRelators', 488
`TzPrintStatus', 489
`TzSearch', 493
`TzSearchEqual', 494
`TzSort', 482
`TzSubstitute', 495
`TzSubstituteCyclicJoins', 498
\letter U
$u_N$, 162
`UglyVector', 613
`Unbind', 44
\sub for lists, 179
`UnbindGlobal', 45
`UnderlyingCharacteristic', 738
`UnderlyingCharacterTable', 770
`UnderlyingElement', fp group elements, 466
\sub fp semigroup elements, 552
`Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 545
`Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
`UnderlyingExternalSet', 411
`UnderlyingFamily', 641
`UnderlyingGeneralMapping', 307
`UnderlyingGroup', for character tables, 732
\sub for tables of marks, 710
`UnderlyingLeftModule', 603
`UnderlyingLieAlgebra', 647
`UnderlyingMagma', 664
`UnderlyingRelation', 307
`UnInstallCharReadHookFunc', 106
`Union', 276
union, of collections, 276
\sub of sets, 198
`Union2', 276
`UnionBlist', 212
`Unique', 200
`UniteBlist', 213
`UniteBlistList', 213
`UniteSet', 198
`Units', 568
Units and Factorizations, \indexit{568}
`UnivariatenessTestRationalFunction', 675
`UnivariatePolynomial', 674
`UnivariatePolynomialByCoefficients', 674
`UnivariatePolynomialRing', 683
Univariate Polynomial Rings, \indexit{683}
Univariate Polynomials, \indexit{674}
`Univariate\-Rational\-Function\-By\-Coefficients', 680
Univariate Rational Functions, \indexit{680}
`UniversalEnvelopingAlgebra', 653
Universal Enveloping Algebras, \indexit{653}
UNIX, features, 27
\sub options, 27
`UNIXSelect', 98
`Unknown', 168
`UnloadSmallGroupsData', 522
`UnorderedTuples', 150
Unpacking, \indexit{832}
`UnprofileFunctions', 83
`UnprofileMethods', 83
`until', 52
`UntraceMethods', 79
`UpdateMap', 813
`UpEnv', 71
`UpperCentralSeriesOfGroup', 372
`UpperSubdiagonal', 235
`UseBasis', 577
`UseFactorRelation', 298
Useful Categories for all Elements of a Family, \indexit{302}
Useful Categories of Elements, \indexit{300}
`UseIsomorphismRelation', 298
User Streams, \indexit{103}
`UseSubsetRelation', 298
utilities for editing GAP files, 75
\letter V
$v_N$, 162
`Valuation', 694
`Value', 677
`ValueCochain', 656
`ValueGlobal', 45
`ValueMolienSeries', 793
`ValueOption', 89
`ValuePol', 221
`ValuesOfClassFunction', 770
Variable Access in a Break Loop, \indexit{71}
Variables, \indexit{43}
Vectors as coefficients of polynomials, \indexit{220}
`VectorSpace', 599
`Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 450
Vector Space Homomorphisms, \indexit{610}
Vector Spaces Handled By Nice Bases, \indexit{612}
`vi', 75
`View', 66
View and Print, \indexit{66}
`ViewObj', 67
\sub for character tables, 748
\sub for class functions, 774
\sub for tables of marks, 706
`vim', 75
`VirtualCharacter', 775
virtual character, 777
virtual characters, 768
\letter W
$w_N$, 162
`WedgeGModule ', 697
`WeekDay', 260
`WeightLexOrdering', 284
`WeightOfGenerators', 285
`WeightsTom', 712
`WeightVecFFE', 220
`WeylGroup', 649
`WeylOrbitIterator', 650
`Where', 70
While, \indexit{52}
`while' loop, 52
Whitespaces, \indexit{41}
Why Class Functions?, \indexit{768}
`WordAlp', 255
words, in generators, 354
Working with large degree permutation groups, \indexit{428}
`WreathProduct', 508
wreath product embedding, 509
`WreathProductImprimitiveAction', 509
`WreathProductOrdering', 286
`WreathProductProductAction', 509
Wreath Products, \indexit{508}
`WriteAll', 101
`WriteByte', 101
`WriteLine', 101
\letter X
$x_N$, 162
\letter Y
$y_N$, 162
\letter Z
`Z', 584
`ZClassRepsQClass', 434
`Zero', 294
`ZeroAttr', 294
`ZeroCoefficient', 665
`ZeroCoefficientRatFun', 689
`ZeroImmutable', 294
`ZeroMapping', 306
`ZeroMutable', 294
`ZeroOp', 294
`ZeroSameMutability', 294
`ZeroSM', 294
`ZippedProduct', 691
`ZippedSum', 691
`ZmodnZ', 135
`ZmodnZObj', 135
`ZmodpZ', 135
`ZmodpZNC', 135
`ZumbroichBase', 595
`Zuppos', 377
