# The GAP 4 Manual - Full Index F

_ 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

F, Function mark-up E 2.5
f_N R 18.4
Factor Groups R 37.18
Factor Groups of Polycyclic Groups - Modulo Pcgs R 43.9
Factor Groups of Polycyclic Groups in their Own Representation R 43.10
FactorCosetAction R 39.7.1
FactorCosetAction, for fp groups R 45.5.3
FactorCosetOperation R 45.5.3
FactorFreeSemigroupByRelations R 51.1.2
FactorGroup R 37.18.2
FactorGroupFpGroupByRels R 45.1.2
FactorGroupNC R 37.18.2
FactorGroupNormalSubgroupClasses R 69.21.4
FactorGroupTom R 68.9.11
Factorial R 17.1.1
Factorization R 37.5.1
factorization R 37.5
Factors R 54.5.8
Factors, of univariate polynomial R 64.10.1
FactorsInt R 14.3.6
FactorsOfDirectProduct R 69.18.2
FactorsSquarefree R 64.10.2
Fail R 20.1
fail R 20.1.1
Fail T 9.2
fail instead of false T 9.2.1
FaithfulModule R 60.10.20
FaithfulModule, for Lie algebras R 61.12.1
Families R 13.1
FamiliesOfGeneralMappingsAndRanges R 31.13.5
FamiliesOfRows R 69.20.5
family T 3.4
FamilyForOrdering R 29.2.4
FamilyObj R 13.1.1
FamilyPcgs R 44.1.1
FamilyRange R 31.13.3
FamilySource R 31.13.4
FAQ R 73.9
Fast access to last hash index N 2.7
features, under UNIX R 3.1
fi R 4.16
Fibonacci R 17.3.1
Fibonacci and Lucas Sequences R 17.3
Field R 56.1.3
field homomorphisms, Frobenius R 57.4
FieldExtension R 56.2.9
FieldOfMatrixGroup R 42.1.3
FieldOverItselfByGenerators R 56.2.2
fields R 56.0
Fields and Division Rings R 56.0
File Access R 9.6
File Operations R 9.7
File Streams R 10.5
File Structure E 3.2
File Types E 3.1
FileDescriptorOfStream R 10.2.2
Filename R 9.4 R 9.4.1
Files and Filenames R 9.0
Filtered R 21.20.18
Filters R 13.2
filters T 8.2
Filters Controlling the Arithmetic Behaviour of Lists R 21.12
Finding Implementations in the Library E 3.3
Finding Positions in Lists R 21.16
Finding Submodules R 67.6
FindSl2 R 61.9.7
Finish Installation and Cleanup R 73.7
Finite Field Elements R 57.1
Finite Fields R 57.0
Finite Perfect Groups R 48.8
Finitely Presented Algebras R 62.0
Finitely Presented Groups R 45.0
Finitely Presented Lie Algebras R 61.11
Finitely presented monoids R 51.4
Finitely Presented Semigroups and Monoids R 51.0
finiteness test, for a list or collection R 28.3
First R 21.20.20
FittingSubgroup R 37.12.5
Flat R 21.20.6
flush character R 26.1
FlushCaches P 3.17.9
FOA triples E 6.0
For R 4.19
For and While Loops T 3.6
for loop R 4.19.1
ForAll R 21.20.21
ForAny R 21.20.22
Forming Closures of Domains T 7.5
FpElmComparisonMethod R 45.2.3
FpGroupPresentation R 46.1.4
FpGrpMonSmgOfFpGrpMonSmgElement R 51.0
FpLieAlgebraByCartanMatrix R 61.11.1
Frame R 70.11
FrattiniSubgroup R 37.12.6
FrattiniSubgroup, for groups with pcgs R 43.16
Free Groups, Monoids and Semigroups R 35.2
Free Magma Rings R 63.1
Free Magmas R 34.4
Free Modules R 55.3
FreeAlgebra R 60.2.1
FreeAlgebraWithOne R 60.2.2
FreeAssociativeAlgebra R 60.2.3
FreeAssociativeAlgebraWithOne R 60.2.4
FreeGeneratorsOfFpGroup R 45.3.2
FreeGeneratorsOfFpSemigroup R 51.3.2
FreeGeneratorsOfWholeGroup R 45.3.2
FreeGroup R 35.2.1
FreeGroupOfFpGroup R 45.3.1
FreeLeftModule R 55.3.2
FreeLieAlgebra R 61.2.3
FreeMagma R 34.4.1
FreeMagmaRing R 63.1.1
FreeMagmaWithOne R 34.4.2
FreeMonoid, with example R 35.2.3
FreeMonoid R 50.0 R 50.0 R 50.0 R 50.0 R 50.0
FreeMonoidOfRewritingSystem R 51.5.7
FreeSemigroup R 35.2.4
FreeSemigroup, with examples R 49.0 R 49.0 R 49.0 R 49.0 R 49.0
FreeSemigroupOfFpSemigroup R 51.3.1
FreeSemigroupOfRewritingSystem R 51.5.6
Frobenius automorphism R 57.4
FrobeniusAutomorphism R 57.4 R 57.4.1
FrobeniusCharacterValue R 70.15.1
FullMatrixAlgebra R 60.4.4
FullMatrixAlgebraCentralizer R 60.8.15
FullMatrixLieAlgebra R 61.2.4
FullMatrixModule R 55.3.12
FullMatrixSpace R 59.8.5
FullRowModule R 55.3.10
FullRowSpace R 59.8.4
FullTransformationSemigroup R 49.1.5
Function R 4.22
function R 4.22.1
function call R 4.10.1
function call, with arguments R 4.10.1
function call, with options R 4.10.2
Function Calls R 4.10
Function that Modify Boolean Lists R 22.3
Function Types R 5.4
Function-Operation-Attribute Triples E 6.0
FunctionAction R 39.11.4
FunctionOperation R 75.1
Functions R 5.0
functions, definition by arrow notation R 4.22
functions, definition of R 4.22
functions, recursive R 4.22
functions, with a variable number of arguments R 4.10 R 4.22
Functions T 4.0
functions R 5.0 R 31.0
Functions for Coding Theory R 23.5
Functions for GAP Packages R 74.3
Functions that do nothing R 5.3
FunctionsFamily R 5.4.3
Further Improvements in Implementing Residue Class Rings P 5.5
Further Information about Domains T 7.8
Further Information about Functions T 4.5
Further Information about GAP T 1.5
Further Information about Groups and Homomorphisms T 5.6
Further Information about Lists T 3.10
Further Information about Vector Spaces and Algebras T 6.3
Further Information introducing the System T 2.9
FusionCharTableTom R 68.12.1
FusionConjugacyClasses R 71.2.1
FusionConjugacyClassesOp R 71.2.1
fusions R 71.2
FusionsAllowedByRestrictions R 71.5.4
FusionsTom R 68.7.6

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