# The GAP 4 Manual - Full Index C

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

C, Category mark-up E 2.5
c_N R 18.4
Calculating with Group Automorphisms R 38.8
Calendar Arithmetic R 26.8
CallFuncList R 5.2.1
Calling a function with a list argument that is interpreted as several arguments R 5.2
Calling of and Communication with External Binaries E 4.11
Cancellation Tests for Rational Functions R 64.23
CanComputeIndex R 37.25.4
CanComputeIsSubset R 37.25.5
CanComputeSize R 37.25.2
CanComputeSizeAnySubgroup R 37.25.3
candidates, for permutation characters R 70.13 R 70.14
CanEasilyCompareElements R 30.11.2
CanEasilyCompareElementsFamily R 30.11.2
CanEasilyComputePcgs R 43.2.3
CanEasilySortElements R 30.11.2
CanEasilySortElementsFamily R 30.11.2
CanEasilyTestMembership R 37.25.1
canonical basis, for matrix spaces R 59.8
canonical basis, for row spaces R 59.8
CanonicalBasis R 59.4.3
CanonicalElt N 3.2.4
CanonicalGenerators R 61.7.14
CanonicalPcElement R 43.5.9
CanonicalPcgs R 43.8.2
CanonicalPcgsByGeneratorsWithImages R 43.9.7
CanonicalRepresentativeDeterminatorOfExternalSet R 39.11.14
CanonicalRepresentativeOfExternalSet R 39.11.13
CanonicalRightCosetElement R 37.7.3
Carmichael's lambda function R 15.1
carriage return character R 26.1
CartanMatrix R 61.7.12
CartanSubalgebra R 61.3.7
Cartesian R 21.20.15
Categories R 13.3
Categories and Properties of Algebras R 60.7
Categories for Streams and the StreamsFamily R 10.1
Categories of Associative Words R 35.1
Categories of Matrices R 24.1
Categories of Words and Nonassociative Words R 34.1
CategoriesOfObject R 13.3.1
CategoryCollections R 28.1.4
CategoryCollections P 3.1.2
CategoryFamily P 3.1.3
Catering for Plain Text and HTML Formats E 2.11
Center R 33.4.5
center R 33.4
central character R 70.8
CentralCharacter R 70.8.17
CentralIdempotentsOfAlgebra R 60.8.17
centraliser R 33.4
Centralizer R 33.4.4
Centralizer, for groups with pcgs R 43.16
CentralizerInGLnZ R 42.5.8
CentralizerModulo R 37.18.7
CentralizerSizeLimitConsiderFunction R 43.17.2
CentralNormalSeriesByPcgs R 43.11.8
Centre R 33.4.5
Centre, for groups with pcgs R 43.16
centre, of a character R 70.8
CentreOfCharacter R 70.8.11
CF R 58.1
ChainHomomorphicImage N 5.0
Chains of subgroups N 5.0
ChainStatistics N 5.0
ChainSubgroup N 5.0
ChainSubgroupByDirectProduct N 5.3.1
ChainSubgroupByHomomorphism N 5.2.1
ChainSubgroupByProjectionFunction N 5.2.2
ChainSubgroupByPSubgroupOfAbelian N 5.3.2
ChainSubgroupBySiftFunction N 5.4.2
ChainSubgroupByStabiliser N 5.1.4
ChainSubgroupByTrivialSubgroup N 5.4.1
ChainSubgroupQuotient N 5.2.4
Changed Command Line Options T 9.1
Changed Functionality T 9.3
Changed Variable Names T 9.4
ChangedBaseGroup N 5.1.7
Changes from Earlier Versions T 1.4
ChangeStabChain R 41.10.3
Changing Presentations R 46.6
Changing the Help Viewer R 2.3
Changing the Representation R 30.5
Changing the Structure R 30.4
Changing the Structure T 7.6
Chapters and Sections E 2.2
CHAR_INT R 26.6.2
CHAR_SINT R 26.6.4
Character R 70.6.3
Character Conversion R 26.6
Character Degrees and Derived Length R 72.1
Character Table Categories R 69.4
Character Tables R 69.0
character tables R 69.3
character tables, access to R 69.3
character tables, calculate R 69.3
character tables, infix operators R 69.7
character tables, of groups R 69.3
character value, of group element using powering operator R 70.4
CharacterDegrees R 69.8.1
Characteristic R 30.10.1
characteristic, for class functions R 70.4
characteristic polynomial, for field elements R 56.3
CharacteristicPolynomial R 24.12.1
CharacterNames R 69.8.10
characters R 70.0
characters, permutation R 70.13 R 70.14
characters, symmetrizations of R 70.11
CharacterTable R 69.3.1
CharacterTableDirectProduct R 69.18.1
CharacterTableFactorGroup R 69.18.3
CharacterTableIsoclinic R 69.18.4
CharacterTableWithSortedCharacters R 69.19.1
CharacterTableWithSortedClasses R 69.19.3
CharacterTableWreathSymmetric R 69.18.5
CharsFamily R 26.2.4
CharTable T 9.4
CheckFixedPoints R 71.3.10
CheckForHandlingByNiceBasis R 59.11.3
CheckPermChar R 71.5.2
ChevalleyBasis R 61.7.2
ChiefNormalSeriesByPcgs R 43.11.16
ChiefSeries R 37.17.1
ChiefSeriesThrough R 37.17.2
ChiefSeriesUnderAction R 37.17.3
Chinese remainder R 14.2
ChineseRem R 14.2.9
Chomp R 26.5.11
CIUnivPols R 64.1.5
class function R 70.0
class function objects R 70.0
Class Functions R 70.0
class functions R 71.3
class functions, as ring elements R 70.4
Class Fusions between Character Tables R 71.2
class multiplication coefficient R 69.10
ClassElementLattice R 37.20.2
classes, real R 69.8
ClassesSolvableGroup R 43.17.1
ClassFunction R 70.6.1
ClassFunctionSameType R 70.6.4
Classical Groups R 48.2
ClassMultiplicationCoefficient, for character tables R 69.10.6
ClassNames R 69.8.10
ClassNamesTom R 68.7.5
ClassOrbit R 69.8.15
ClassPermutation R 69.19.5
ClassPositionsOfAgemo R 69.8.18
ClassPositionsOfCentre, for character tables R 69.8.19
ClassPositionsOfCentre, for characters R 70.8.12
ClassPositionsOfDerivedSubgroup R 69.8.21
ClassPositionsOfDirectProductDecompositions R 69.8.20
ClassPositionsOfElementaryAbelianSeries R 69.8.22
ClassPositionsOfFittingSubgroup R 69.8.23
ClassPositionsOfKernel R 70.8.10
ClassPositionsOfLowerCentralSeries R 69.8.24
ClassPositionsOfMaximalNormalSubgroups R 69.8.17
ClassPositionsOfNormalClosure R 69.8.27
ClassPositionsOfNormalSubgroup R 69.21.2
ClassPositionsOfNormalSubgroups R 69.8.17
ClassPositionsOfSupersolvableResiduum R 69.8.26
ClassPositionsOfUpperCentralSeries R 69.8.25
ClassRoots R 69.8.16
ClassStructureCharTable R 69.10.7
ClassTypesTom R 68.7.4
CleanedTailPcElement R 43.5.11
ClearCacheStats R 7.7.12
ClearProfile R 7.7.10
clone, an object R 12.7
CloseMutableBasis R 59.7.6
CloseStream R 10.2.1
Closure Operations and Other Constructors R 32.4
ClosureGroup R 37.4.1
ClosureGroupAddElm R 37.4.2
ClosureGroupCompare R 37.4.2
ClosureGroupDefault R 37.4.3
ClosureGroupIntest R 37.4.2
ClosureLeftModule R 55.2.3
ClosureNearAdditiveGroup R 53.4.1
ClosureRing R 54.1.9
Closures of (Sub)groups R 37.4
ClosureSomething T 7.5
ClosureStruct R 30.3.6
ClosureSubgroup R 37.4.4
ClosureSubgroupNC R 37.4.4
Coboundaries R 61.12.8
Cochain R 61.12.3
CochainSpace R 61.12.4
Cocycles R 61.12.7
cocycles R 37.23
CodePcGroup R 44.9.2
CodePcgs R 44.9.1
Coding a Pc Presentation R 44.9
coefficient, binomial R 17.1
Coefficient List Arithmetic R 23.3
Coefficients R 59.5.3
coefficients, for cyclotomics R 18.1
CoefficientsAndMagmaElements R 63.2.3
CoefficientsFamily R 64.18.3
CoefficientsMultiadic R 14.2.8
CoefficientsOfLaurentPolynomial R 64.12.2
CoefficientsOfUnivariatePolynomial R 64.4.9
CoefficientsOfUnivariateRationalFunction R 64.4.7
CoefficientsQadic R 14.2.7
CoefficientsRing R 64.14.3
CoeffsCyc R 18.1.8
CoeffsMod R 23.3.4
cohomology R 37.23
COHORTS_PRIMITIVE_GROUPS R 48.9.4
cokernel T 5.4
CoKernelOfAdditiveGeneralMapping R 31.9.6
CoKernelOfMultiplicativeGeneralMapping R 31.8.6
CollapsedMat R 71.3.16
Collected R 21.20.3
Collection Families R 28.1
Collections R 28.0
CollectionsFamily R 28.1.1
CollectionsFamily P 3.6.2
Coloring the Prompt and Input R 3.12
ColorPrompt R 3.12.1
ColumnIndexOfReesMatrixSemigroupElement R 49.6.8
ColumnIndexOfReesZeroMatrixSemigroupElement R 49.6.8
Combinations R 17.2.1
Combinations, Arrangements and Tuples R 17.2
Combinatorial Numbers R 17.1
CombinatorialCollector R 44.4.2
Combinatorics R 17.0
Comm R 30.12.3
Comm, for words R 35.4
Command Line Options R 3.1
command mark-up E 2.5
comments R 4.4
comments T 2.1
CommutativeDiagram R 71.3.9
CommutatorFactorGroup R 37.18.3
CommutatorLength R 37.12.4
CommutatorLength, for character tables R 69.8
CommutatorSubgroup R 37.12.2
Compacted R 21.20.2
CompanionMat R 24.12.5
CompareVersionNumbers R 74.3.6
comparison, fp semigroup elements R 51.2.1
comparison, operation R 30.11.1
comparison, rational functions R 64.3.1
Comparison of Associative Words R 35.3
Comparison of Class Functions R 70.3
Comparison of Elements of Finitely Presented Groups R 45.2
Comparison of Elements of Finitely Presented Semigroups R 51.2
Comparison of Permutations R 40.1
Comparison of Rational Functions R 64.3
Comparison of Words R 34.2
Comparison Operations for Elements R 30.11
Comparisons R 4.11
comparisons, of booleans R 20.2.1
comparisons, of lists R 21.10
Comparisons of Booleans R 20.2
Comparisons of Cyclotomics R 18.3
Comparisons of Lists R 21.10
Comparisons of Records R 27.4
Comparisons of Strings R 26.4
Compatibility Mode T 9.20
Compatibility of Residue Class Rings with Prime Fields P 5.4
CompatibleConjugacyClasses R 69.6.5
CompatiblePairs R 44.8.8
Compilation R 73.4
Compiling Library Code R 3.9
Complementclasses R 37.11.6
ComplementclassesEA R 37.23.4
ComplementIntMat R 25.1.6
ComplementSystem R 37.13.5
CompleteSchreierTransversal N 4.2.9
Completion Files R 3.5
ComplexConjugate R 18.5.2
ComplexConjugate, for class functions R 70.4
ComplexificationQuat R 60.4.2
Component Objects P 3.9
Components of a Dixon Record R 69.16
Components versus Attributes P 4.7
CompositionMapping R 31.1.4
CompositionMapping, for Frobenius automorphisms R 57.4
CompositionMapping2 R 31.1.5
CompositionMaps R 71.3.1
CompositionOfStraightLinePrograms R 35.8.7
CompositionSeries R 37.17.5
CompositionSeries, for groups with pcgs R 43.16
ComputedBrauerTables R 69.3.2
ComputedClassFusions R 71.2.2
ComputedIndicators R 69.10.4
ComputedIsPSolvableCharacterTables R 69.10.2
ComputedPowerMaps R 71.1.1
ComputedPrimeBlockss R 69.9.1
Computing a Pcgs R 43.2
Computing a Permutation Representation R 41.2
Computing Pc Groups R 44.5
Computing Possible Permutation Characters R 70.14
Computing the Irreducible Characters of a Group R 69.12
Concatenation R 21.20.1
concatenation, of lists R 21.20
Conductor R 18.1.5
ConfluentRws R 36.1.6
Congruences, for character tables R 71.4.2
Congruences for semigroups R 49.3
Conjugacy Classes R 37.10
Conjugacy Classes in Classical Groups R 48.3
Conjugacy Classes in Solvable Groups R 43.17
ConjugacyClass R 37.10.1
ConjugacyClasses, attribute R 37.10.2
ConjugacyClasses, for character tables R 69.6.2
ConjugacyClasses, for groups with pcgs R 43.16
ConjugacyClasses, for linear groups R 48.3
ConjugacyClassesByOrbits R 37.10.4
ConjugacyClassesByRandomSearch R 37.10.3
ConjugacyClassesMaximalSubgroups R 37.19.4
ConjugacyClassesPerfectSubgroups R 37.20.6
ConjugacyClassesSubgroups R 37.19.3
ConjugacyClassSubgroups R 37.19.1
conjugate, matrix R 24.2.10
conjugate, of a word R 35.4
ConjugateDominantWeight R 61.7.20
ConjugateDominantWeightWithWord R 61.7.20
ConjugateGroup R 37.2.5
Conjugates R 56.3.6
ConjugateSubgroup R 37.3.8
ConjugateSubgroups R 37.3.9
conjugation R 39.2
ConjugatorAutomorphism R 38.6.2
ConjugatorAutomorphismNC R 38.6.2
ConjugatorIsomorphism R 38.6.1
ConjugatorOfConjugatorIsomorphism R 38.6.5
ConnectGroupAndCharacterTable R 69.6.4
ConsiderKernels R 71.4.3
ConsiderSmallerPowerMaps R 71.4.4
ConsiderStructureConstants R 71.2.9
ConsiderTableAutomorphisms R 71.5.3
constants T 2.4
Constants and Operators T 2.4
ConstantTimeAccessList R 21.17.6
constituent, of a group character R 70.8
ConstituentsCompositionMapping R 31.1.7
ConstituentsOfCharacter R 70.8.8
Constructing Algebras as Free Algebras R 60.2
Constructing Algebras by Generators R 60.1
Constructing Algebras by Structure Constants R 60.3
Constructing Character Tables from Others R 69.18
Constructing Domains R 30.3
Constructing Lie algebras R 61.2
Constructing Pc Groups R 44.4
Constructing Subdomains R 30.8
Constructing Tables of Marks R 68.3
Constructing Vector Spaces R 59.1
Construction of Abelian Number Fields R 58.1
Construction of Stabilizer Chains R 41.7
Constructors for Basic Groups R 48.4
ContainedCharacters R 71.3.17
ContainedDecomposables R 71.3.17
ContainedMaps R 71.3.6
ContainedPossibleCharacters R 71.3.15 R 71.3
ContainedPossibleVirtualCharacters R 71.3.15 R 71.3
ContainedSpecialVectors R 71.3.15 R 71.3
ContainedTom R 68.9.5
ContainingTom R 68.9.6
continuation E 2.10
Continue R 4.21
continue statement R 4.21.1
Continued Fractions R 15.5
ContinuedFractionApproximationOfRoot R 15.5.2
ContinuedFractionExpansionOfRoot R 15.5.1
Conventions for Character Tables R 69.5
convert, to a string R 26.2
Converting Groups to Finitely Presented Groups R 45.10
ConvertToCharacterTable R 69.3.4
ConvertToCharacterTableNC R 69.3.4
ConvertToMatrixRep R 24.13.2
ConvertToMatrixRepNC R 24.13.2
ConvertToRangeRep R 21.22.2
ConvertToStringRep R 26.2.2
ConvertToTableOfMarks R 68.6.5
ConvertToVectorRep R 23.2.1
ConvertToVectorRepNC R 23.2.1
Conway Polynomials R 57.5
ConwayPolynomial R 57.5.1
coprime R 4.12
Copy R 12.7
copy, an object R 12.7
Copy T 9.7
Copying Weak Pointer Objects E 7.5
CopyOptionsDefaults R 41.10.2
Copyright R 76.0
Copyright N 6.0
Copyright Notice R 76.0
Copyright Notice N 6.0
Copyrights R 73.18
CopyStabChain R 41.10.1
Core R 37.11.2
CorrespondingGeneratorsByModuloPcgs R 43.9.6
coset R 37.7
Coset Tables and Coset Enumeration R 45.5
Coset tables for subgroups in the whole group R 45.7
CosetLeadersMatFFE R 23.5.6
Cosets R 37.7
CosetTable R 45.5.1
CosetTableBySubgroup R 45.5.4
CosetTableDefaultLimit R 45.5.7
CosetTableDefaultMaxLimit R 45.5.6
CosetTableFromGensAndRels R 45.5.5
CosetTableInWholeGroup R 45.7.1
CosetTableOfFpSemigroup R 51.6.1
CosetTableStandard R 45.6.1
CRC R 3.10
CRC Numbers R 3.10
CrcFile R 9.7.11
CrcFile, example R 3.10
CreateCompletionFiles R 3.5.1
CreateCompletionFilesPackage E 4.12.1
CreateCompletionFilesPkg R 75.2
Creating Attributes and Properties P 3.3
Creating Categories P 3.1
Creating Character Tables R 69.3
Creating Class Functions from Values Lists R 70.6
Creating Class Functions using Groups R 70.7
Creating Families P 3.6
Creating Finite Fields R 57.3
Creating Finitely Presented Groups R 45.1
Creating Finitely Presented Semigroups R 51.1
Creating Group Homomorphisms R 38.1
Creating Groups R 37.2
Creating hom cosets and quotient groups N 3.1
Creating Mappings R 31.1
Creating New Objects P 3.0
Creating Objects P 3.8
Creating Operations P 3.5
Creating Other Filters P 3.4
Creating Own Arithmetic Objects P 4.12
Creating Permutations R 40.4
Creating Presentations R 46.1
Creating Representations P 3.2
Creating Types P 3.7
Creation of Algebraic Extensions R 65.1
Creation of Rational Functions R 64.21
Credit R 1.2
CrystGroupDefaultAction R 42.6.1
Cycle R 39.8.3
CycleLength R 39.8.4
CycleLengths R 39.8.6
Cycles R 39.8.5
CycleStructureClass R 70.8.14
CycleStructurePerm R 40.3.2
CyclicExtensionsTom R 68.9.7
CyclicGroup R 48.1.2
cyclotomic field elements R 18.0
cyclotomic fields, CanonicalBasis R 58.3
Cyclotomic Numbers R 18.0
Cyclotomic Polynomials R 64.9
CyclotomicField R 58.1.1
CyclotomicPolynomial R 64.9.1
Cyclotomics R 18.1.2
cyclotomics, DefaultField R 58.2

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