# The GAP 4 Reference Manual - 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

Abelian Invariants for Subgroups 45.14
abelian number field 58.2
Abelian Number Fields 58.0
abelian number fields, CanonicalBasis 58.3
abelian number fields, Galois group 58.4
AbelianGroup 48.1.3
AbelianInvariants, for character tables 69.8
AbelianInvariants, for groups 37.15.1
AbelianInvariantsMultiplier 37.23.3
AbelianInvariantsNormalClosureFpGroup 45.14.4
AbelianInvariantsNormalClosureFpGroupRrs 45.14.5
AbelianInvariantsOfList 25.2.10
AbelianInvariantsSubgroupFpGroup 45.14.1
AbelianInvariantsSubgroupFpGroupMtc 45.14.2
AbelianInvariantsSubgroupFpGroupRrs 45.14.3
AbelianNumberField 58.1.2
AbelianSubfactorAction 39.7.3
About Group Actions 39.1
About the GAP Reference Manual 1.0
AbsInt 14.1.6
absolute value of an integer 14.1
AbsoluteIrreducibleModules 69.13.2
AbsoluteValue 18.1.6
AbsolutIrreducibleModules 69.13.2
abstract word 34.1
AbstractWordTietzeWord 46.4.2
Accessing a Module 67.4
Accessing Record Elements 27.1
Accessing Subgroups via Tables of Marks 68.11
accessing, list elements 21.3
accessing, record elements 27.1
AClosestVectorCombinationsMatFFEVecFFE 23.5.5
Acting OnRight and OnLeft 42.6
ActingAlgebra 60.10.13
ActingDomain 39.11.3
Action 39.6.2
Action of a group on itself 39.7
Action on Subfactors Defined by a Pcgs 43.14
action, by conjugation 39.2
action, on blocks 39.2
action, on sets 39.2
ActionHomomorphism 39.6.1
actions 39.2
Actions of Matrix Groups 42.2
ActorOfExternalSet 39.11.15
Add 21.4.4
add, an element to a set 21.19
AddCoeffs 23.3.2
AddGenerator 46.6.1
AddGenerators 36.1.13
AddGeneratorsExtendSchreierTree 41.10.10
addition 4.12.1
addition, list and non-list 21.13
addition, matrices 24.2.1
addition, matrix and scalar 24.2.2
addition, operation 30.12.1
addition, rational functions 64.2.1
addition, scalar and matrix 24.2.2
addition, scalar and matrix list 24.2.12
addition, scalar and vector 23.1.2
addition, vector and scalar 23.1.2
addition, vectors 23.1.1
Additive Arithmetic for Lists 21.13
Additive Magmas 53.0
AdditiveInverse 30.10.9
AdditiveInverseAttr 30.10.9
AdditiveInverseImmutable 30.10.9
AdditiveInverseMutable 30.10.9
AdditiveInverseOp 30.10.9
AdditiveInverseSameMutability 30.10.9
AdditiveInverseSM 30.10.9
AdditiveNeutralElement 53.3.5
AddRelator 46.6.3
AddRowVector 23.3.1
AddRule 36.1.9
AddRuleReduced 36.1.10
AddSet 21.19.4
AdjointAssociativeAlgebra 61.9.2
AdjointBasis 60.8.5
AdjointMatrix 61.9.1
AdjointModule 60.10.19
Advanced Features of GAP 3.2
Advanced List Manipulations 21.21
Advanced Methods for Dixon-Schneider Calculations 69.15
AffineAction 43.14.4
AffineActionLayer 43.14.5
AffineOperation 43.14.4
AffineOperationLayer 43.14.5
Agemo 37.13.2
Algebra 60.1.1
AlgebraByStructureConstants 60.3.5
AlgebraGeneralMappingByImages 60.9.1
AlgebraHomomorphismByImages 60.9.2
AlgebraHomomorphismByImagesNC 60.9.3
Algebraic extensions of fields 65.0
AlgebraicExtension 65.1.1
Algebras 60.0
AlgebraWithOne 60.1.2
AlgebraWithOneGeneralMappingByImages 60.9.4
AlgebraWithOneHomomorphismByImages 60.9.5
AlgebraWithOneHomomorphismByImagesNC 60.9.6
AllBlocks 39.10.4
AllIrreducibleSolvableGroups 48.11.3
AllLibraryGroups 48.5.1
AllPrimitiveGroups 48.5
AllSmallGroups 48.7.2
AllTransitiveGroups 48.5
Alpha 72.1.1
AlternatingGroup 48.1.7
An Example of Advanced Dixon-Schneider Calculations 69.17
and 20.3.2
and, for filters 13.2 20.3.3
ANFAutomorphism 58.4.1
antisymmetric relation 32.2
AntiSymmetricParts 70.11.3
Append 21.4.5
AppendTo 9.7.4
AppendTo, for streams 10.4.4
Apple 73.14 73.15
ApplicableMethod 7.2 7.2.1
ApplicableMethodTypes 7.2.1
Apply 21.20.9
ApplySimpleReflection 61.7.18
ApproximateSuborbitsStabilizerPermGroup 41.9.14
ARCH_IS_MAC 3.6.2
ARCH_IS_UNIX 3.6.1
ARCH_IS_WINDOWS 3.6.3
arg, special function argument 4.10 4.22
Arithmetic for External Representations of Polynomials 64.22
Arithmetic for Lists 21.11
Arithmetic Operations for Class Functions 70.4
Arithmetic Operations for Elements 30.12
Arithmetic Operations for General Mappings 31.5
Arithmetic Operators 4.12
Arrangements 17.2.3
arrow notation for functions 4.22.2
AsAlgebra 60.8.7
AsAlgebraWithOne 60.8.8
AsBinaryRelationOnPoints 32.3.3
AsBlockMatrix 24.15.1
AscendingChain 37.16.16
AsDivisionRing 56.1.9
AsDuplicateFreeList 21.20.5
AsField 56.1.9
AsFreeLeftModule 55.3.3
AsGroup 37.2.4
AsGroupGeneralMappingByImages 38.1.5
AsLeftIdeal 54.2.11
AsLeftModule 55.1.5
AsList 28.2.7
AsMagma 33.2.10
AsMonoid 50.0
AsPolynomial 64.4.5
AsRightIdeal 54.2.11
AsRing 54.1.7
AsSemigroup 49.0
Assert 7.5.3
AssertionLevel 7.5.2
Assertions 7.5
AsSet 28.2.9
AssignGeneratorVariables 35.2.5
assignment, to a list 21.4
assignment, to a record 27.2
assignment, variable 4.14.1
Assignments 4.14
AssignNiceMonomorphismAutomorphismGroup 38.8.1
AssociatedPartition 17.2.24
AssociatedReesMatrixSemigroupOfDClass 49.6.10
Associates 54.5.4
Associative Words 35.0
associativity 4.12
AssocWordByLetterRep 35.6.9
AsSortedList 28.2.8
AsSSortedList 28.2.9
AsStruct 30.4.1
AsSubalgebra 60.8.9
AsSubalgebraWithOne 60.8.10
AsSubgroup 37.3.4
AsSubgroupOfWholeGroupByQuotient 45.12.3
AsSubmagma 33.2.11
AsSubmonoid 50.0
AsSubsemigroup 49.0
AsSubspace 59.1.4
AsSubstruct 30.8.3
AsTransformation 52.0 52.0
AsTransformationNC 52.0
AsTwoSidedIdeal 54.2.11
AsVectorSpace 59.1.3
at exit functions 6.7
ATLAS Irrationalities 18.4
AtlasIrrationality 18.4.6
atomic irrationalities 18.4
Attributes 13.5
Attributes and Operations for Algebras 60.8
Attributes and Properties for (Near-)Additive Magmas 53.3
Attributes and Properties for Collections 28.3
Attributes and Properties for Magmas 33.4
Attributes and Properties for Matrix Groups 42.1
Attributes and Properties of Character Tables 69.8
Attributes and Properties of Elements 30.10
Attributes of and Operations on Equivalence Relations 32.6
Attributes of Tables of Marks 68.7
AttributeValueNotSet 13.6.3
AugmentationIdeal 63.1.7
Augmented Coset Tables and Rewriting 45.8
AugmentedCosetTableInWholeGroup 45.8.1
AugmentedCosetTableMtc 45.8.2
AugmentedCosetTableRrs 45.8.3
automatic loading of GAP packages 74.2
automorphism group, of number fields 58.4
AutomorphismDomain 38.7.2
AutomorphismGroup 38.7.3
AutomorphismGroup, for groups with pcgs 43.16
Automorphisms and Equivalence of Character Tables 69.20
AutomorphismsOfTable 69.8.8

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GAP 4 manual
March 2004