<html><head><title>The GAP 4 Manual - Full Index F</title></head> <body bgcolor="ffffff"><h1>The GAP 4 Manual - Full Index F</h1> <p> <a href="theindex.htm">_</A> <a href="indxA.htm">A</A> <a href="indxB.htm">B</A> <a href="indxC.htm">C</A> <a href="indxD.htm">D</A> <a href="indxE.htm">E</A> <a href="indxF.htm">F</A> <a href="indxG.htm">G</A> <a href="indxH.htm">H</A> <a href="indxI.htm">I</A> <a href="indxJ.htm">J</A> <a href="indxK.htm">K</A> <a href="indxL.htm">L</A> <a href="indxM.htm">M</A> <a href="indxN.htm">N</A> <a href="indxO.htm">O</A> <a href="indxP.htm">P</A> <a href="indxQ.htm">Q</A> <a href="indxR.htm">R</A> <a href="indxS.htm">S</A> <a href="indxT.htm">T</A> <a href="indxU.htm">U</A> <a href="indxV.htm">V</A> <a href="indxW.htm">W</A> <a href="indxX.htm">X</A> <a href="indxY.htm">Y</A> <a href="indxZ.htm">Z</A> <dl> <dt>F, Function mark-up <a href="ext/CHAP002.htm#I44">E 2.5</a> <dt>f_N <a href="ref/CHAP018.htm#I15">R 18.4</a> <dt>Factor Groups <a href="ref/CHAP037.htm#SECT018">R 37.18</a> <dt>Factor Groups of Polycyclic Groups - Modulo Pcgs <a href="ref/CHAP043.htm#SECT009">R 43.9</a> <dt>Factor Groups of Polycyclic Groups in their Own Representation <a href="ref/CHAP043.htm#SECT010">R 43.10</a> <dt>FactorCosetAction <a href="ref/CHAP039.htm#SSEC007.1">R 39.7.1</a> <dt>FactorCosetAction, for fp groups <a href="ref/CHAP045.htm#SSEC005.3">R 45.5.3</a> <dt>FactorCosetOperation <a href="ref/CHAP045.htm#SSEC005.3">R 45.5.3</a> <dt>FactorFreeSemigroupByRelations <a href="ref/CHAP051.htm#SSEC001.2">R 51.1.2</a> <dt>FactorGroup <a href="ref/CHAP037.htm#SSEC018.2">R 37.18.2</a> <dt>FactorGroupFpGroupByRels <a href="ref/CHAP045.htm#SSEC001.2">R 45.1.2</a> <dt>FactorGroupNC <a href="ref/CHAP037.htm#SSEC018.2">R 37.18.2</a> <dt>FactorGroupNormalSubgroupClasses <a href="ref/CHAP069.htm#SSEC021.4">R 69.21.4</a> <dt>FactorGroupTom <a href="ref/CHAP068.htm#SSEC009.11">R 68.9.11</a> <dt>Factorial <a href="ref/CHAP017.htm#SSEC001.1">R 17.1.1</a> <dt>Factorization <a href="ref/CHAP037.htm#SSEC005.2">R 37.5.2</a> <dt>factorization <a href="ref/CHAP037.htm#I1">R 37.5</a> <dt>Factors <a href="ref/CHAP054.htm#SSEC005.8">R 54.5.8</a> <dt>Factors, of univariate polynomial <a href="ref/CHAP064.htm#SSEC010.1">R 64.10.1</a> <dt>FactorsInt <a href="ref/CHAP014.htm#SSEC003.6">R 14.3.6</a> <dt>FactorsOfDirectProduct <a href="ref/CHAP069.htm#SSEC018.2">R 69.18.2</a> <dt>FactorsSquarefree <a href="ref/CHAP064.htm#SSEC010.2">R 64.10.2</a> <dt>Fail <a href="ref/CHAP020.htm#SECT001">R 20.1</a> <dt>fail <a href="ref/CHAP020.htm#SSEC001.1">R 20.1.1</a> <dt>Fail <a href="tut/CHAP009.htm#SECT002">T 9.2</a> <dt>fail instead of false <a href="tut/CHAP009.htm#SSEC002.1">T 9.2.1</a> <dt>FaithfulModule <a href="ref/CHAP060.htm#SSEC010.20">R 60.10.20</a> <dt>FaithfulModule, for Lie algebras <a href="ref/CHAP061.htm#SSEC012.1">R 61.12.1</a> <dt>Families <a href="ref/CHAP013.htm#SECT001">R 13.1</a> <dt>FamiliesOfGeneralMappingsAndRanges <a href="ref/CHAP031.htm#SSEC013.5">R 31.13.5</a> <dt>FamiliesOfRows <a href="ref/CHAP069.htm#SSEC020.5">R 69.20.5</a> <dt>family <a href="tut/CHAP003.htm#I5">T 3.4</a> <dt>FamilyForOrdering <a href="ref/CHAP029.htm#SSEC002.4">R 29.2.4</a> <dt>FamilyObj <a href="ref/CHAP013.htm#SSEC001.1">R 13.1.1</a> <dt>FamilyPcgs <a href="ref/CHAP044.htm#SSEC001.1">R 44.1.1</a> <dt>FamilyRange <a href="ref/CHAP031.htm#SSEC013.3">R 31.13.3</a> <dt>FamilySource <a href="ref/CHAP031.htm#SSEC013.4">R 31.13.4</a> <dt>FAQ <a href="ref/CHAP073.htm#I3">R 73.9</a> <dt>Fast access to last hash index <a href="new/CHAP002.htm#SECT007">N 2.7</a> <dt>features, under UNIX <a href="ref/CHAP003.htm#I1">R 3.1</a> <dt>fi <a href="ref/CHAP004.htm#I31">R 4.16</a> <dt>Fibonacci <a href="ref/CHAP017.htm#SSEC003.1">R 17.3.1</a> <dt>Fibonacci and Lucas Sequences <a href="ref/CHAP017.htm#SECT003">R 17.3</a> <dt>Field <a href="ref/CHAP056.htm#SSEC001.3">R 56.1.3</a> <dt>field homomorphisms, Frobenius <a href="ref/CHAP057.htm#I3">R 57.4</a> <dt>FieldExtension <a href="ref/CHAP056.htm#SSEC002.9">R 56.2.9</a> <dt>FieldOfMatrixGroup <a href="ref/CHAP042.htm#SSEC001.3">R 42.1.3</a> <dt>FieldOverItselfByGenerators <a href="ref/CHAP056.htm#SSEC002.2">R 56.2.2</a> <dt>fields <a href="ref/CHAP056.htm#I0">R 56.0</a> <dt>Fields and Division Rings <a href="ref/CHAP056.htm">R 56.0</a> <dt>File Access <a href="ref/CHAP009.htm#SECT006">R 9.6</a> <dt>File Operations <a href="ref/CHAP009.htm#SECT007">R 9.7</a> <dt>File Streams <a href="ref/CHAP010.htm#SECT005">R 10.5</a> <dt>File Structure <a href="ext/CHAP003.htm#SECT002">E 3.2</a> <dt>File Types <a href="ext/CHAP003.htm#SECT001">E 3.1</a> <dt>FileDescriptorOfStream <a href="ref/CHAP010.htm#SSEC002.2">R 10.2.2</a> <dt>Filename <a href="ref/CHAP009.htm#SECT004">R 9.4</a> <a href="ref/CHAP009.htm#SSEC004.1">R 9.4.1</a> <dt>Files and Filenames <a href="ref/CHAP009.htm">R 9.0</a> <dt>Filtered <a href="ref/CHAP021.htm#SSEC020.18">R 21.20.18</a> <dt>Filters <a href="ref/CHAP013.htm#SECT002">R 13.2</a> <dt>filters <a href="tut/CHAP008.htm#I4">T 8.2</a> <dt>Filters Controlling the Arithmetic Behaviour of Lists <a href="ref/CHAP021.htm#SECT012">R 21.12</a> <dt>Finding Implementations in the Library <a href="ext/CHAP003.htm#SECT003">E 3.3</a> <dt>Finding Positions in Lists <a href="ref/CHAP021.htm#SECT016">R 21.16</a> <dt>Finding Submodules <a href="ref/CHAP067.htm#SECT006">R 67.6</a> <dt>FindSl2 <a href="ref/CHAP061.htm#SSEC009.7">R 61.9.7</a> <dt>Finish Installation and Cleanup <a href="ref/CHAP073.htm#SECT007">R 73.7</a> <dt>Finite Field Elements <a href="ref/CHAP057.htm#SECT001">R 57.1</a> <dt>Finite Fields <a href="ref/CHAP057.htm">R 57.0</a> <dt>Finite Perfect Groups <a href="ref/CHAP048.htm#SECT008">R 48.8</a> <dt>Finitely Presented Algebras <a href="ref/CHAP062.htm">R 62.0</a> <dt>Finitely Presented Groups <a href="ref/CHAP045.htm">R 45.0</a> <dt>Finitely Presented Lie Algebras <a href="ref/CHAP061.htm#SECT011">R 61.11</a> <dt>Finitely presented monoids <a href="ref/CHAP051.htm#SECT004">R 51.4</a> <dt>Finitely Presented Semigroups and Monoids <a href="ref/CHAP051.htm">R 51.0</a> <dt>finiteness test, for a list or collection <a href="ref/CHAP028.htm#I2">R 28.3</a> <dt>First <a href="ref/CHAP021.htm#SSEC020.20">R 21.20.20</a> <dt>FittingSubgroup <a href="ref/CHAP037.htm#SSEC012.5">R 37.12.5</a> <dt>Flat <a href="ref/CHAP021.htm#SSEC020.6">R 21.20.6</a> <dt>flush character <a href="ref/CHAP026.htm#I18">R 26.1</a> <dt>FlushCaches <a href="prg/CHAP003.htm#SSEC017.9">P 3.17.9</a> <dt>FOA triples <a href="ext/CHAP006.htm#I0">E 6.0</a> <dt>For <a href="ref/CHAP004.htm#SECT019">R 4.19</a> <dt>For and While Loops <a href="tut/CHAP003.htm#SECT006">T 3.6</a> <dt>for loop <a href="ref/CHAP004.htm#SSEC019.1">R 4.19.1</a> <dt>ForAll <a href="ref/CHAP021.htm#SSEC020.21">R 21.20.21</a> <dt>ForAny <a href="ref/CHAP021.htm#SSEC020.22">R 21.20.22</a> <dt>Forming Closures of Domains <a href="tut/CHAP007.htm#SECT005">T 7.5</a> <dt>FpElmComparisonMethod <a href="ref/CHAP045.htm#SSEC002.3">R 45.2.3</a> <dt>FpGroupPresentation <a href="ref/CHAP046.htm#SSEC001.4">R 46.1.4</a> <dt>FpGrpMonSmgOfFpGrpMonSmgElement <a href="ref/CHAP051.htm#">R 51.0</a> <dt>FpLieAlgebraByCartanMatrix <a href="ref/CHAP061.htm#SSEC011.1">R 61.11.1</a> <dt>Frame <a href="ref/CHAP070.htm#I38">R 70.11</a> <dt>FrattiniSubgroup <a href="ref/CHAP037.htm#SSEC012.6">R 37.12.6</a> <dt>FrattiniSubgroup, for groups with pcgs <a href="ref/CHAP043.htm#I6">R 43.16</a> <dt>Free Groups, Monoids and Semigroups <a href="ref/CHAP035.htm#SECT002">R 35.2</a> <dt>Free Magma Rings <a href="ref/CHAP063.htm#SECT001">R 63.1</a> <dt>Free Magmas <a href="ref/CHAP034.htm#SECT004">R 34.4</a> <dt>Free Modules <a href="ref/CHAP055.htm#SECT003">R 55.3</a> <dt>Free Products <a href="ref/CHAP047.htm#SECT005">R 47.5</a> <dt>FreeAlgebra <a href="ref/CHAP060.htm#SSEC002.1">R 60.2.1</a> <dt>FreeAlgebraWithOne <a href="ref/CHAP060.htm#SSEC002.2">R 60.2.2</a> <dt>FreeAssociativeAlgebra <a href="ref/CHAP060.htm#SSEC002.3">R 60.2.3</a> <dt>FreeAssociativeAlgebraWithOne <a href="ref/CHAP060.htm#SSEC002.4">R 60.2.4</a> <dt>FreeGeneratorsOfFpGroup <a href="ref/CHAP045.htm#SSEC003.2">R 45.3.2</a> <dt>FreeGeneratorsOfFpSemigroup <a href="ref/CHAP051.htm#SSEC003.2">R 51.3.2</a> <dt>FreeGeneratorsOfWholeGroup <a href="ref/CHAP045.htm#SSEC003.2">R 45.3.2</a> <dt>FreeGroup <a href="ref/CHAP035.htm#SSEC002.1">R 35.2.1</a> <dt>FreeGroupOfFpGroup <a href="ref/CHAP045.htm#SSEC003.1">R 45.3.1</a> <dt>FreeLeftModule <a href="ref/CHAP055.htm#SSEC003.2">R 55.3.2</a> <dt>FreeLieAlgebra <a href="ref/CHAP061.htm#SSEC002.3">R 61.2.3</a> <dt>FreeMagma <a href="ref/CHAP034.htm#SSEC004.1">R 34.4.1</a> <dt>FreeMagmaRing <a href="ref/CHAP063.htm#SSEC001.1">R 63.1.1</a> <dt>FreeMagmaWithOne <a href="ref/CHAP034.htm#SSEC004.2">R 34.4.2</a> <dt>FreeMonoid, with example <a href="ref/CHAP035.htm#SSEC002.3">R 35.2.3</a> <dt>FreeMonoid <a href="ref/CHAP050.htm#">R 50.0</a> <a href="ref/CHAP050.htm#">R 50.0</a> <a href="ref/CHAP050.htm#">R 50.0</a> <a href="ref/CHAP050.htm#">R 50.0</a> <a href="ref/CHAP050.htm#">R 50.0</a> <dt>FreeMonoidOfRewritingSystem <a href="ref/CHAP051.htm#SSEC005.7">R 51.5.7</a> <dt>FreeProduct <a href="ref/CHAP047.htm#SSEC005.1">R 47.5.1</a> <dt>FreeSemigroup <a href="ref/CHAP035.htm#SSEC002.4">R 35.2.4</a> <dt>FreeSemigroup, with examples <a href="ref/CHAP049.htm#">R 49.0</a> <a href="ref/CHAP049.htm#">R 49.0</a> <a href="ref/CHAP049.htm#">R 49.0</a> <a href="ref/CHAP049.htm#">R 49.0</a> <a href="ref/CHAP049.htm#">R 49.0</a> <dt>FreeSemigroupOfFpSemigroup <a href="ref/CHAP051.htm#SSEC003.1">R 51.3.1</a> <dt>FreeSemigroupOfRewritingSystem <a href="ref/CHAP051.htm#SSEC005.6">R 51.5.6</a> <dt>Frobenius automorphism <a href="ref/CHAP057.htm#I6">R 57.4</a> <dt>FrobeniusAutomorphism <a href="ref/CHAP057.htm#SECT004">R 57.4</a> <a href="ref/CHAP057.htm#SSEC004.1">R 57.4.1</a> <dt>FrobeniusCharacterValue <a href="ref/CHAP070.htm#SSEC015.1">R 70.15.1</a> <dt>FullMatrixAlgebra <a href="ref/CHAP060.htm#SSEC004.4">R 60.4.4</a> <dt>FullMatrixAlgebraCentralizer <a href="ref/CHAP060.htm#SSEC008.15">R 60.8.15</a> <dt>FullMatrixLieAlgebra <a href="ref/CHAP061.htm#SSEC002.4">R 61.2.4</a> <dt>FullMatrixModule <a href="ref/CHAP055.htm#SSEC003.12">R 55.3.12</a> <dt>FullMatrixSpace <a href="ref/CHAP059.htm#SSEC008.5">R 59.8.5</a> <dt>FullRowModule <a href="ref/CHAP055.htm#SSEC003.10">R 55.3.10</a> <dt>FullRowSpace <a href="ref/CHAP059.htm#SSEC008.4">R 59.8.4</a> <dt>FullTransformationSemigroup <a href="ref/CHAP049.htm#SSEC001.5">R 49.1.5</a> <dt>Function <a href="ref/CHAP004.htm#SECT022">R 4.22</a> <dt>function <a href="ref/CHAP004.htm#SSEC022.1">R 4.22.1</a> <dt>function call <a href="ref/CHAP004.htm#SSEC010.1">R 4.10.1</a> <dt>function call, with arguments <a href="ref/CHAP004.htm#SSEC010.1">R 4.10.1</a> <dt>function call, with options <a href="ref/CHAP004.htm#SSEC010.2">R 4.10.2</a> <dt>Function Calls <a href="ref/CHAP004.htm#SECT010">R 4.10</a> <dt>Function that Modify Boolean Lists <a href="ref/CHAP022.htm#SECT003">R 22.3</a> <dt>Function Types <a href="ref/CHAP005.htm#SECT004">R 5.4</a> <dt>Function-Operation-Attribute Triples <a href="ext/CHAP006.htm">E 6.0</a> <dt>FunctionAction <a href="ref/CHAP039.htm#SSEC011.4">R 39.11.4</a> <dt>FunctionOperation <a href="ref/CHAP075.htm#I7">R 75.1</a> <dt>Functions <a href="ref/CHAP005.htm">R 5.0</a> <dt>functions, definition by arrow notation <a href="ref/CHAP004.htm#I52">R 4.22</a> <dt>functions, definition of <a href="ref/CHAP004.htm#I43">R 4.22</a> <dt>functions, recursive <a href="ref/CHAP004.htm#I47">R 4.22</a> <dt>functions, with a variable number of arguments <a href="ref/CHAP004.htm#I9">R 4.10</a> <a href="ref/CHAP004.htm#I50">R 4.22</a> <dt>Functions <a href="tut/CHAP004.htm">T 4.0</a> <dt>functions <a href="ref/CHAP005.htm#I0">R 5.0</a> <a href="ref/CHAP031.htm#I0">R 31.0</a> <dt>Functions for Coding Theory <a href="ref/CHAP023.htm#SECT005">R 23.5</a> <dt>Functions for GAP Packages <a href="ref/CHAP074.htm#SECT003">R 74.3</a> <dt>Functions that do nothing <a href="ref/CHAP005.htm#SECT003">R 5.3</a> <dt>FunctionsFamily <a href="ref/CHAP005.htm#SSEC004.3">R 5.4.3</a> <dt>Further Improvements in Implementing Residue Class Rings <a href="prg/CHAP005.htm#SECT005">P 5.5</a> <dt>Further Information about Domains <a href="tut/CHAP007.htm#SECT008">T 7.8</a> <dt>Further Information about Functions <a href="tut/CHAP004.htm#SECT005">T 4.5</a> <dt>Further Information about GAP <a href="tut/CHAP001.htm#SECT005">T 1.5</a> <dt>Further Information about Groups and Homomorphisms <a href="tut/CHAP005.htm#SECT006">T 5.6</a> <dt>Further Information about Lists <a href="tut/CHAP003.htm#SECT010">T 3.10</a> <dt>Further Information about Vector Spaces and Algebras <a href="tut/CHAP006.htm#SECT003">T 6.3</a> <dt>Further Information introducing the System <a href="tut/CHAP002.htm#SECT009">T 2.9</a> <dt>FusionCharTableTom <a href="ref/CHAP068.htm#SSEC012.1">R 68.12.1</a> <dt>FusionConjugacyClasses <a href="ref/CHAP071.htm#SSEC002.1">R 71.2.1</a> <dt>FusionConjugacyClassesOp <a href="ref/CHAP071.htm#SSEC002.1">R 71.2.1</a> <dt>fusions <a href="ref/CHAP071.htm#I3">R 71.2</a> <dt>FusionsAllowedByRestrictions <a href="ref/CHAP071.htm#SSEC005.4">R 71.5.4</a> <dt>FusionsTom <a href="ref/CHAP068.htm#SSEC007.6">R 68.7.6</a> </dl><p> [<a href="../index.html">Top</a>] [<a href="chapters.htm">Up</a>] <p><P> <address>GAP 4 manual<br></address> </body></html>
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