# The GAP 4 Manual - Full Index A

_ 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

A, Attribute mark-up E 2.5
A First Attempt to Implement Elements of Residue Class Rings P 5.1
A First Session with GAP T 2.0
A Second Attempt to Implement Elements of Residue Class Rings P 5.3
Abelian Invariants for Subgroups R 45.14
abelian number field R 58.2
Abelian Number Fields R 58.0
abelian number fields, CanonicalBasis R 58.3
abelian number fields, Galois group R 58.4
AbelianGroup R 48.1.3
AbelianInvariants, for character tables R 69.8
AbelianInvariants, for groups R 37.16.1
AbelianInvariantsMultiplier R 37.24.3
AbelianInvariantsNormalClosureFpGroup R 45.14.4
AbelianInvariantsNormalClosureFpGroupRrs R 45.14.5
AbelianInvariantsOfList R 25.2.10
AbelianInvariantsSubgroupFpGroup R 45.14.1
AbelianInvariantsSubgroupFpGroupMtc R 45.14.2
AbelianInvariantsSubgroupFpGroupRrs R 45.14.3
AbelianNumberField R 58.1.2
AbelianSubfactorAction R 39.7.3
About Functions T 2.7
About Group Actions R 39.1
About Programming in GAP P 1.0
About the GAP Reference Manual R 1.0
About the New Features Manual N 1.0
About: Extending GAP E 1.0
AbsInt R 14.1.6
absolute value of an integer R 14.1
AbsoluteIrreducibleModules R 69.13.2
AbsoluteValue R 18.1.6
AbsolutIrreducibleModules R 69.13.2
abstract word R 34.1
AbstractWordTietzeWord R 46.4.2
accessing, list elements R 21.3
accessing, record elements R 27.1
Accessing a Module R 67.4
Accessing Record Elements R 27.1
Accessing Subgroups via Tables of Marks R 68.11
Accessing Weak Pointer Objects as Lists E 7.4
Acknowledgement T 10.0
Acknowledgements T 1.3
AClosestVectorCombinationsMatFFEVecFFE R 23.5.5
AClosestVectorCombinationsMatFFEVecFFECoords R 23.5.5
Acting OnRight and OnLeft R 42.6
ActingAlgebra R 60.10.13
ActingDomain R 39.11.3
Action R 39.6.2
action, by conjugation R 39.2
action, on blocks R 39.2
action, on sets R 39.2
Action of a group on itself R 39.7
Action on Subfactors Defined by a Pcgs R 43.14
ActionHomomorphism R 39.6.1
actions R 39.2
Actions of Groups T 5.2
Actions of Matrix Groups R 42.2
ActorOfExternalSet R 39.11.15
Add R 21.4.4
add, an element to a set R 21.19
AddCoeffs R 23.3.2
AddGenerator R 46.6.1
AddGenerators R 36.1.13
AddGeneratorsExtendSchreierTree R 41.10.10
AddHashEntry N 2.3.4
Adding a new Attribute P 4.5
Adding a new Operation P 4.4
Adding a new Representation P 4.6
Adding new Concepts P 4.8
addition R 4.12.1
addition, list and non-list R 21.13
addition, matrices R 24.2.1
addition, matrix and scalar R 24.2.2
addition, operation R 30.12.1
addition, rational functions R 64.2.1
addition, scalar and matrix R 24.2.2
addition, scalar and matrix list R 24.2.12
addition, scalar and vector R 23.1.2
addition, vector and scalar R 23.1.2
addition, vectors R 23.1.1
Addition of a Method P 4.1
Additive Arithmetic for Lists R 21.13
Additive Magmas R 53.0
AdditiveInverse R 30.10.9
AdditiveInverseAttr R 30.10.9
AdditiveInverseImmutable R 30.10.9
AdditiveInverseMutable R 30.10.9
AdditiveInverseOp R 30.10.9
AdditiveInverseSameMutability R 30.10.9
AdditiveInverseSM R 30.10.9
AdditiveNeutralElement R 53.3.5
AddRelator R 46.6.3
AddRowVector R 23.3.1
AddRule R 36.1.9
AddRuleReduced R 36.1.10
AddSet R 21.19.4
AdjointAssociativeAlgebra R 61.9.2
AdjointBasis R 60.8.5
AdjointMatrix R 61.9.1
AdjointModule R 60.10.19
Advanced Features of GAP R 3.2
Advanced List Manipulations R 21.21
Advanced Methods for Dixon-Schneider Calculations R 69.15
AffineAction R 43.14.4
AffineActionLayer R 43.14.5
AffineOperation R 43.14.4
AffineOperationLayer R 43.14.5
Agemo R 37.14.2
AgGroup T 9.4
Algebra R 60.1.1
AlgebraByStructureConstants R 60.3.5
AlgebraGeneralMappingByImages R 60.9.1
AlgebraHomomorphismByImages R 60.9.2
AlgebraHomomorphismByImagesNC R 60.9.3
Algebraic extensions of fields R 65.0
Algebraic Structure T 7.2
AlgebraicExtension R 65.1.1
Algebras R 60.0
Algebras T 6.2
AlgebraWithOne R 60.1.2
AlgebraWithOneGeneralMappingByImages R 60.9.4
AlgebraWithOneHomomorphismByImages R 60.9.5
AlgebraWithOneHomomorphismByImagesNC R 60.9.6
AllBlocks R 39.10.4
AllIrreducibleSolvableGroups R 48.11.3
AllLibraryGroups R 48.5.1
AllPrimitiveGroups R 48.5
AllSmallGroups R 48.7.2
AllTransitiveGroups R 48.5
Alpha R 72.1.1
AlternatingGroup R 48.1.7
An Example -- Designing Arithmetic Operations P 6.0
An Example -- Residue Class Rings P 5.0
An Example of a GAP Package E 4.3
An Example of Advanced Dixon-Schneider Calculations R 69.17
and R 20.3.2
and, for filters R 13.2 R 20.3.3
ANFAutomorphism R 58.4.1
antisymmetric relation R 32.2
AntiSymmetricParts R 70.11.3
Append R 21.4.5
AppendTo R 9.7.4
AppendTo, for streams R 10.4.4
Apple R 73.14 R 73.15
Applicable Methods and Method Selection P 2.3
ApplicableMethod T 8.4
ApplicableMethod R 7.2 R 7.2.1
ApplicableMethodTypes R 7.2.1
Apply R 21.20.9
ApplyFunc T 9.4
ApplySimpleReflection R 61.7.18
ApproximateSuborbitsStabilizerPermGroup R 41.9.14
ARCH_IS_MAC R 3.6.2
ARCH_IS_UNIX R 3.6.1
ARCH_IS_WINDOWS R 3.6.3
arg, special function argument R 4.10 R 4.22
Arithmetic for External Representations of Polynomials R 64.22
Arithmetic for Lists R 21.11
Arithmetic Issues in the Implementation of New Kinds of Lists P 3.14
Arithmetic Operations for Class Functions R 70.4
Arithmetic Operations for Elements R 30.12
Arithmetic Operations for General Mappings R 31.5
Arithmetic Operators R 4.12
ArithmeticElementCreator P 4.12.1
Arrangements R 17.2.3
arrow notation for functions R 4.22.2
AsAlgebra R 60.8.7
AsAlgebraWithOne R 60.8.8
AsBinaryRelationOnPoints R 32.3.3
AsBlockMatrix R 24.15.1
AscendingChain R 37.17.16
AsDivisionRing R 56.1.9
AsDuplicateFreeList R 21.20.5
AsField R 56.1.9
AsFreeLeftModule R 55.3.3
AsGroup R 37.2.4
AsGroupGeneralMappingByImages R 38.1.5
AsLeftIdeal R 54.2.11
AsLeftModule R 55.1.5
AsList R 28.2.7
AsMagma R 33.2.10
AsMonoid R 50.0
AsPolynomial R 64.4.5
AsRightIdeal R 54.2.11
AsRing R 54.1.7
AsSemigroup R 49.0
Assert R 7.5.3
AssertionLevel R 7.5.2
Assertions R 7.5
AsSet R 28.2.9
AssignGeneratorVariables R 35.2.5
assignment, to a list R 21.4
assignment, to a record R 27.2
assignment, variable R 4.14.1
assignment T 2.5
Assignments R 4.14
AssignNiceMonomorphismAutomorphismGroup R 38.8.1
AssociatedPartition R 17.2.24
AssociatedReesMatrixSemigroupOfDClass R 49.6.10
Associates R 54.5.4
Associative Words R 35.0
associativity R 4.12
AssocWordByLetterRep R 35.6.9
AsSomething T 7.6
AsSortedList R 28.2.8
AsSSortedList R 28.2.9
AsStruct R 30.4.1
AsSubalgebra R 60.8.9
AsSubalgebraWithOne R 60.8.10
AsSubgroup R 37.3.4
AsSubgroupOfWholeGroupByQuotient R 45.12.3
AsSubmagma R 33.2.11
AsSubmonoid R 50.0
AsSubsemigroup R 49.0
AsSubspace R 59.1.4
AsSubstruct R 30.8.3
AsTransformation R 52.0 R 52.0
AsTransformationNC R 52.0
AsTwoSidedIdeal R 54.2.11
AsVectorSpace R 59.1.3
at exit functions R 6.7
ATLAS Irrationalities R 18.4
AtlasIrrationality R 18.4.6
atomic irrationalities R 18.4
Attributes R 13.5
Attributes T 8.1
Attributes and Operations for Algebras R 60.8
Attributes and Properties for (Near-)Additive Magmas R 53.3
Attributes and Properties for Collections R 28.3
Attributes and Properties for Magmas R 33.4
Attributes and Properties for Matrix Groups R 42.1
Attributes and Properties of Character Tables R 69.8
Attributes and Properties of Elements R 30.10
Attributes of and Operations on Equivalence Relations R 32.6
Attributes of Tables of Marks R 68.7
Attributes vs. Record Components T 9.8
AttributeValueNotSet R 13.6.3
AugmentationIdeal R 63.1.7
Augmented Coset Tables and Rewriting R 45.8
AugmentedCosetTableInWholeGroup R 45.8.1
AugmentedCosetTableMtc R 45.8.2
AugmentedCosetTableRrs R 45.8.3
Authors T 10.0
Authorship and Maintenance T 1.2
automatic loading of GAP packages R 74.2
automorphism group, of number fields R 58.4
AutomorphismDomain R 38.7.2
AutomorphismGroup R 38.7.3
AutomorphismGroup, for groups with pcgs R 43.16
Automorphisms and Equivalence of Character Tables R 69.20
AutomorphismsOfTable R 69.8.8

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