<html><head><title>The GAP 4 Reference Manual - Index A</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - Index A</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> <dt>Abelian Invariants for Subgroups <a href="CHAP045.htm#SECT014">45.14</a> <dt>abelian number field <a href="CHAP058.htm#I5">58.2</a> <dt>Abelian Number Fields <a href="CHAP058.htm">58.0</a> <dt>abelian number fields, CanonicalBasis <a href="CHAP058.htm#I7">58.3</a> <dt>abelian number fields, Galois group <a href="CHAP058.htm#I8">58.4</a> <dt>AbelianGroup <a href="CHAP048.htm#SSEC001.3">48.1.3</a> <dt>AbelianInvariants, for character tables <a href="CHAP069.htm#I11">69.8</a> <dt>AbelianInvariants, for groups <a href="CHAP037.htm#SSEC016.1">37.16.1</a> <dt>AbelianInvariantsMultiplier <a href="CHAP037.htm#SSEC024.3">37.24.3</a> <dt>AbelianInvariantsNormalClosureFpGroup <a href="CHAP045.htm#SSEC014.4">45.14.4</a> <dt>AbelianInvariantsNormalClosureFpGroupRrs <a href="CHAP045.htm#SSEC014.5">45.14.5</a> <dt>AbelianInvariantsOfList <a href="CHAP025.htm#SSEC002.10">25.2.10</a> <dt>AbelianInvariantsSubgroupFpGroup <a href="CHAP045.htm#SSEC014.1">45.14.1</a> <dt>AbelianInvariantsSubgroupFpGroupMtc <a href="CHAP045.htm#SSEC014.2">45.14.2</a> <dt>AbelianInvariantsSubgroupFpGroupRrs <a href="CHAP045.htm#SSEC014.3">45.14.3</a> <dt>AbelianNumberField <a href="CHAP058.htm#SSEC001.2">58.1.2</a> <dt>AbelianSubfactorAction <a href="CHAP039.htm#SSEC007.3">39.7.3</a> <dt>About Group Actions <a href="CHAP039.htm#SECT001">39.1</a> <dt>About the GAP Reference Manual <a href="CHAP001.htm">1.0</a> <dt>AbsInt <a href="CHAP014.htm#SSEC001.6">14.1.6</a> <dt>absolute value of an integer <a href="CHAP014.htm#I0">14.1</a> <dt>AbsoluteIrreducibleModules <a href="CHAP069.htm#SSEC013.2">69.13.2</a> <dt>AbsoluteValue <a href="CHAP018.htm#SSEC001.6">18.1.6</a> <dt>AbsolutIrreducibleModules <a href="CHAP069.htm#SSEC013.2">69.13.2</a> <dt>abstract word <a href="CHAP034.htm#I0">34.1</a> <dt>AbstractWordTietzeWord <a href="CHAP046.htm#SSEC004.2">46.4.2</a> <dt>Accessing a Module <a href="CHAP067.htm#SECT004">67.4</a> <dt>Accessing Record Elements <a href="CHAP027.htm#SECT001">27.1</a> <dt>Accessing Subgroups via Tables of Marks <a href="CHAP068.htm#SECT011">68.11</a> <dt>accessing, list elements <a href="CHAP021.htm#I0">21.3</a> <dt>accessing, record elements <a href="CHAP027.htm#I2">27.1</a> <dt>AClosestVectorCombinationsMatFFEVecFFE <a href="CHAP023.htm#SSEC005.5">23.5.5</a> <dt>AClosestVectorCombinationsMatFFEVecFFECoords <a href="CHAP023.htm#SSEC005.5">23.5.5</a> <dt>Acting OnRight and OnLeft <a href="CHAP042.htm#SECT006">42.6</a> <dt>ActingAlgebra <a href="CHAP060.htm#SSEC010.13">60.10.13</a> <dt>ActingDomain <a href="CHAP039.htm#SSEC011.3">39.11.3</a> <dt>Action <a href="CHAP039.htm#SSEC006.2">39.6.2</a> <dt>Action of a group on itself <a href="CHAP039.htm#SECT007">39.7</a> <dt>Action on Subfactors Defined by a Pcgs <a href="CHAP043.htm#SECT014">43.14</a> <dt>action, by conjugation <a href="CHAP039.htm#I7">39.2</a> <dt>action, on blocks <a href="CHAP039.htm#I9">39.2</a> <dt>action, on sets <a href="CHAP039.htm#I8">39.2</a> <dt>ActionHomomorphism <a href="CHAP039.htm#SSEC006.1">39.6.1</a> <dt>actions <a href="CHAP039.htm#I4">39.2</a> <dt>Actions of Matrix Groups <a href="CHAP042.htm#SECT002">42.2</a> <dt>ActorOfExternalSet <a href="CHAP039.htm#SSEC011.15">39.11.15</a> <dt>Add <a href="CHAP021.htm#SSEC004.4">21.4.4</a> <dt>add, an element to a set <a href="CHAP021.htm#I21">21.19</a> <dt>AddCoeffs <a href="CHAP023.htm#SSEC003.2">23.3.2</a> <dt>AddGenerator <a href="CHAP046.htm#SSEC006.1">46.6.1</a> <dt>AddGenerators <a href="CHAP036.htm#SSEC001.13">36.1.13</a> <dt>AddGeneratorsExtendSchreierTree <a href="CHAP041.htm#SSEC010.10">41.10.10</a> <dt>addition <a href="CHAP004.htm#SSEC012.1">4.12.1</a> <dt>addition, list and non-list <a href="CHAP021.htm#I8">21.13</a> <dt>addition, matrices <a href="CHAP024.htm#SSEC002.1">24.2.1</a> <dt>addition, matrix and scalar <a href="CHAP024.htm#SSEC002.2">24.2.2</a> <dt>addition, operation <a href="CHAP030.htm#SSEC012.1">30.12.1</a> <dt>addition, rational functions <a href="CHAP064.htm#SSEC002.1">64.2.1</a> <dt>addition, scalar and matrix <a href="CHAP024.htm#SSEC002.2">24.2.2</a> <dt>addition, scalar and matrix list <a href="CHAP024.htm#SSEC002.12">24.2.12</a> <dt>addition, scalar and vector <a href="CHAP023.htm#SSEC001.2">23.1.2</a> <dt>addition, vector and scalar <a href="CHAP023.htm#SSEC001.2">23.1.2</a> <dt>addition, vectors <a href="CHAP023.htm#SSEC001.1">23.1.1</a> <dt>Additive Arithmetic for Lists <a href="CHAP021.htm#SECT013">21.13</a> <dt>Additive Magmas <a href="CHAP053.htm">53.0</a> <dt>AdditiveInverse <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseAttr <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseImmutable <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseMutable <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseOp <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseSameMutability <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveInverseSM <a href="CHAP030.htm#SSEC010.9">30.10.9</a> <dt>AdditiveNeutralElement <a href="CHAP053.htm#SSEC003.5">53.3.5</a> <dt>AddRelator <a href="CHAP046.htm#SSEC006.3">46.6.3</a> <dt>AddRowVector <a href="CHAP023.htm#SSEC003.1">23.3.1</a> <dt>AddRule <a href="CHAP036.htm#SSEC001.9">36.1.9</a> <dt>AddRuleReduced <a href="CHAP036.htm#SSEC001.10">36.1.10</a> <dt>AddSet <a href="CHAP021.htm#SSEC019.4">21.19.4</a> <dt>AdjointAssociativeAlgebra <a href="CHAP061.htm#SSEC009.2">61.9.2</a> <dt>AdjointBasis <a href="CHAP060.htm#SSEC008.5">60.8.5</a> <dt>AdjointMatrix <a href="CHAP061.htm#SSEC009.1">61.9.1</a> <dt>AdjointModule <a href="CHAP060.htm#SSEC010.19">60.10.19</a> <dt>Advanced Features of GAP <a href="CHAP003.htm#SECT002">3.2</a> <dt>Advanced List Manipulations <a href="CHAP021.htm#SECT021">21.21</a> <dt>Advanced Methods for Dixon-Schneider Calculations <a href="CHAP069.htm#SECT015">69.15</a> <dt>AffineAction <a href="CHAP043.htm#SSEC014.4">43.14.4</a> <dt>AffineActionLayer <a href="CHAP043.htm#SSEC014.5">43.14.5</a> <dt>AffineOperation <a href="CHAP043.htm#SSEC014.4">43.14.4</a> <dt>AffineOperationLayer <a href="CHAP043.htm#SSEC014.5">43.14.5</a> <dt>Agemo <a href="CHAP037.htm#SSEC014.2">37.14.2</a> <dt>Algebra <a href="CHAP060.htm#SSEC001.1">60.1.1</a> <dt>AlgebraByStructureConstants <a href="CHAP060.htm#SSEC003.5">60.3.5</a> <dt>AlgebraGeneralMappingByImages <a href="CHAP060.htm#SSEC009.1">60.9.1</a> <dt>AlgebraHomomorphismByImages <a href="CHAP060.htm#SSEC009.2">60.9.2</a> <dt>AlgebraHomomorphismByImagesNC <a href="CHAP060.htm#SSEC009.3">60.9.3</a> <dt>Algebraic extensions of fields <a href="CHAP065.htm">65.0</a> <dt>AlgebraicExtension <a href="CHAP065.htm#SSEC001.1">65.1.1</a> <dt>Algebras <a href="CHAP060.htm">60.0</a> <dt>AlgebraWithOne <a href="CHAP060.htm#SSEC001.2">60.1.2</a> <dt>AlgebraWithOneGeneralMappingByImages <a href="CHAP060.htm#SSEC009.4">60.9.4</a> <dt>AlgebraWithOneHomomorphismByImages <a href="CHAP060.htm#SSEC009.5">60.9.5</a> <dt>AlgebraWithOneHomomorphismByImagesNC <a href="CHAP060.htm#SSEC009.6">60.9.6</a> <dt>AllBlocks <a href="CHAP039.htm#SSEC010.4">39.10.4</a> <dt>AllIrreducibleSolvableGroups <a href="CHAP048.htm#SSEC011.3">48.11.3</a> <dt>AllLibraryGroups <a href="CHAP048.htm#SSEC005.1">48.5.1</a> <dt>AllPrimitiveGroups <a href="CHAP048.htm#I2">48.5</a> <dt>AllSmallGroups <a href="CHAP048.htm#SSEC007.2">48.7.2</a> <dt>AllTransitiveGroups <a href="CHAP048.htm#I3">48.5</a> <dt>Alpha <a href="CHAP072.htm#SSEC001.1">72.1.1</a> <dt>AlternatingGroup <a href="CHAP048.htm#SSEC001.7">48.1.7</a> <dt>An Example of Advanced Dixon-Schneider Calculations <a href="CHAP069.htm#SECT017">69.17</a> <dt>and <a href="CHAP020.htm#SSEC003.2">20.3.2</a> <dt>and, for filters <a href="CHAP013.htm#I0">13.2</a> <a href="CHAP020.htm#SSEC003.3">20.3.3</a> <dt>ANFAutomorphism <a href="CHAP058.htm#SSEC004.1">58.4.1</a> <dt>antisymmetric relation <a href="CHAP032.htm#I6">32.2</a> <dt>AntiSymmetricParts <a href="CHAP070.htm#SSEC011.3">70.11.3</a> <dt>Append <a href="CHAP021.htm#SSEC004.7">21.4.7</a> <dt>AppendTo <a href="CHAP009.htm#SSEC007.4">9.7.4</a> <dt>AppendTo, for streams <a href="CHAP010.htm#SSEC004.4">10.4.4</a> <dt>Apple <a href="CHAP073.htm#I7">73.14</a> <a href="CHAP073.htm#I10">73.15</a> <dt>ApplicableMethod <a href="CHAP007.htm#SECT002">7.2</a> <a href="CHAP007.htm#SSEC002.1">7.2.1</a> <dt>ApplicableMethodTypes <a href="CHAP007.htm#SSEC002.1">7.2.1</a> <dt>Apply <a href="CHAP021.htm#SSEC020.9">21.20.9</a> <dt>ApplySimpleReflection <a href="CHAP061.htm#SSEC007.18">61.7.18</a> <dt>ApproximateSuborbitsStabilizerPermGroup <a href="CHAP041.htm#SSEC009.14">41.9.14</a> <dt>ARCH_IS_MAC <a href="CHAP003.htm#SSEC006.2">3.6.2</a> <dt>ARCH_IS_UNIX <a href="CHAP003.htm#SSEC006.1">3.6.1</a> <dt>ARCH_IS_WINDOWS <a href="CHAP003.htm#SSEC006.3">3.6.3</a> <dt>arg, special function argument <a href="CHAP004.htm#I10">4.10</a> <a href="CHAP004.htm#I51">4.22</a> <dt>Arithmetic for External Representations of Polynomials <a href="CHAP064.htm#SECT022">64.22</a> <dt>Arithmetic for Lists <a href="CHAP021.htm#SECT011">21.11</a> <dt>Arithmetic Operations for Class Functions <a href="CHAP070.htm#SECT004">70.4</a> <dt>Arithmetic Operations for Elements <a href="CHAP030.htm#SECT012">30.12</a> <dt>Arithmetic Operations for General Mappings <a href="CHAP031.htm#SECT005">31.5</a> <dt>Arithmetic Operators <a href="CHAP004.htm#SECT012">4.12</a> <dt>Arrangements <a href="CHAP017.htm#SSEC002.3">17.2.3</a> <dt>arrow notation for functions <a href="CHAP004.htm#SSEC022.2">4.22.2</a> <dt>AsAlgebra <a href="CHAP060.htm#SSEC008.7">60.8.7</a> <dt>AsAlgebraWithOne <a href="CHAP060.htm#SSEC008.8">60.8.8</a> <dt>AsBinaryRelationOnPoints <a href="CHAP032.htm#SSEC003.3">32.3.3</a> <dt>AsBlockMatrix <a href="CHAP024.htm#SSEC015.1">24.15.1</a> <dt>AscendingChain <a href="CHAP037.htm#SSEC017.16">37.17.16</a> <dt>AsDivisionRing <a href="CHAP056.htm#SSEC001.9">56.1.9</a> <dt>AsDuplicateFreeList <a href="CHAP021.htm#SSEC020.5">21.20.5</a> <dt>AsField <a href="CHAP056.htm#SSEC001.9">56.1.9</a> <dt>AsFreeLeftModule <a href="CHAP055.htm#SSEC003.3">55.3.3</a> <dt>AsGroup <a href="CHAP037.htm#SSEC002.4">37.2.4</a> <dt>AsGroupGeneralMappingByImages <a href="CHAP038.htm#SSEC001.5">38.1.5</a> <dt>AsLeftIdeal <a href="CHAP054.htm#SSEC002.11">54.2.11</a> <dt>AsLeftModule <a href="CHAP055.htm#SSEC001.5">55.1.5</a> <dt>AsList <a href="CHAP028.htm#SSEC002.7">28.2.7</a> <dt>AsMagma <a href="CHAP033.htm#SSEC002.10">33.2.10</a> <dt>AsMonoid <a href="CHAP050.htm#">50.0</a> <dt>AsPolynomial <a href="CHAP064.htm#SSEC004.5">64.4.5</a> <dt>AsRightIdeal <a href="CHAP054.htm#SSEC002.11">54.2.11</a> <dt>AsRing <a href="CHAP054.htm#SSEC001.7">54.1.7</a> <dt>AsSemigroup <a href="CHAP049.htm#">49.0</a> <dt>Assert <a href="CHAP007.htm#SSEC005.3">7.5.3</a> <dt>AssertionLevel <a href="CHAP007.htm#SSEC005.2">7.5.2</a> <dt>Assertions <a href="CHAP007.htm#SECT005">7.5</a> <dt>AsSet <a href="CHAP028.htm#SSEC002.9">28.2.9</a> <dt>AssignGeneratorVariables <a href="CHAP035.htm#SSEC002.5">35.2.5</a> <dt>assignment, to a list <a href="CHAP021.htm#I2">21.4</a> <dt>assignment, to a record <a href="CHAP027.htm#I3">27.2</a> <dt>assignment, variable <a href="CHAP004.htm#SSEC014.1">4.14.1</a> <dt>Assignments <a href="CHAP004.htm#SECT014">4.14</a> <dt>AssignNiceMonomorphismAutomorphismGroup <a href="CHAP038.htm#SSEC008.1">38.8.1</a> <dt>AssociatedPartition <a href="CHAP017.htm#SSEC002.24">17.2.24</a> <dt>AssociatedReesMatrixSemigroupOfDClass <a href="CHAP049.htm#SSEC006.10">49.6.10</a> <dt>Associates <a href="CHAP054.htm#SSEC005.4">54.5.4</a> <dt>Associative Words <a href="CHAP035.htm">35.0</a> <dt>associativity <a href="CHAP004.htm#I13">4.12</a> <dt>AssocWordByLetterRep <a href="CHAP035.htm#SSEC006.9">35.6.9</a> <dt>AsSortedList <a href="CHAP028.htm#SSEC002.8">28.2.8</a> <dt>AsSSortedList <a href="CHAP028.htm#SSEC002.9">28.2.9</a> <dt>AsStruct <a href="CHAP030.htm#SSEC004.1">30.4.1</a> <dt>AsSubalgebra <a href="CHAP060.htm#SSEC008.9">60.8.9</a> <dt>AsSubalgebraWithOne <a href="CHAP060.htm#SSEC008.10">60.8.10</a> <dt>AsSubgroup <a href="CHAP037.htm#SSEC003.4">37.3.4</a> <dt>AsSubgroupOfWholeGroupByQuotient <a href="CHAP045.htm#SSEC012.3">45.12.3</a> <dt>AsSubmagma <a href="CHAP033.htm#SSEC002.11">33.2.11</a> <dt>AsSubmonoid <a href="CHAP050.htm#">50.0</a> <dt>AsSubsemigroup <a href="CHAP049.htm#">49.0</a> <dt>AsSubspace <a href="CHAP059.htm#SSEC001.4">59.1.4</a> <dt>AsSubstruct <a href="CHAP030.htm#SSEC008.3">30.8.3</a> <dt>AsTransformation <a href="CHAP052.htm#">52.0</a> <a href="CHAP052.htm#">52.0</a> <dt>AsTransformationNC <a href="CHAP052.htm#">52.0</a> <dt>AsTwoSidedIdeal <a href="CHAP054.htm#SSEC002.11">54.2.11</a> <dt>AsVectorSpace <a href="CHAP059.htm#SSEC001.3">59.1.3</a> <dt>at exit functions <a href="CHAP006.htm#I15">6.8</a> <dt>ATLAS Irrationalities <a href="CHAP018.htm#SECT004">18.4</a> <dt>AtlasIrrationality <a href="CHAP018.htm#SSEC004.6">18.4.6</a> <dt>atomic irrationalities <a href="CHAP018.htm#I10">18.4</a> <dt>Attributes <a href="CHAP013.htm#SECT005">13.5</a> <dt>Attributes and Operations for Algebras <a href="CHAP060.htm#SECT008">60.8</a> <dt>Attributes and Properties for (Near-)Additive Magmas <a href="CHAP053.htm#SECT003">53.3</a> <dt>Attributes and Properties for Collections <a href="CHAP028.htm#SECT003">28.3</a> <dt>Attributes and Properties for Magmas <a href="CHAP033.htm#SECT004">33.4</a> <dt>Attributes and Properties for Matrix Groups <a href="CHAP042.htm#SECT001">42.1</a> <dt>Attributes and Properties of Character Tables <a href="CHAP069.htm#SECT008">69.8</a> <dt>Attributes and Properties of Elements <a href="CHAP030.htm#SECT010">30.10</a> <dt>Attributes of and Operations on Equivalence Relations <a href="CHAP032.htm#SECT006">32.6</a> <dt>Attributes of Tables of Marks <a href="CHAP068.htm#SECT007">68.7</a> <dt>AttributeValueNotSet <a href="CHAP013.htm#SSEC006.3">13.6.3</a> <dt>AugmentationIdeal <a href="CHAP063.htm#SSEC001.7">63.1.7</a> <dt>Augmented Coset Tables and Rewriting <a href="CHAP045.htm#SECT008">45.8</a> <dt>AugmentedCosetTableInWholeGroup <a href="CHAP045.htm#SSEC008.1">45.8.1</a> <dt>AugmentedCosetTableMtc <a href="CHAP045.htm#SSEC008.2">45.8.2</a> <dt>AugmentedCosetTableRrs <a href="CHAP045.htm#SSEC008.3">45.8.3</a> <dt>automatic loading of GAP packages <a href="CHAP074.htm#I1">74.2</a> <dt>automorphism group, of number fields <a href="CHAP058.htm#I10">58.4</a> <dt>AutomorphismDomain <a href="CHAP038.htm#SSEC007.2">38.7.2</a> <dt>AutomorphismGroup <a href="CHAP038.htm#SSEC007.3">38.7.3</a> <dt>AutomorphismGroup, for groups with pcgs <a href="CHAP043.htm#I13">43.16</a> <dt>Automorphisms and Equivalence of Character Tables <a href="CHAP069.htm#SECT020">69.20</a> <dt>AutomorphismsOfTable <a href="CHAP069.htm#SSEC008.8">69.8.8</a> </dl><p> [<a href="../index.htm">Top</a>] [<a href="chapters.htm">Up</a>]<p> <P> <font face="Gill Sans,Helvetica,Arial">GAP 4 manual<br>December 2008 </font></body></html>
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