<html><head><title>The GAP 4 Manual - Full Index D</title></head> <body bgcolor="ffffff"><h1>The GAP 4 Manual - Full Index D</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>d_N <a href="ref/CHAP018.htm#I13">R 18.4</a> <dt>Darstellungsgruppe, see EpimorphismSchurCover <a href="ref/CHAP037.htm#I12">R 37.24</a> <dt>data type, unknown <a href="ref/CHAP019.htm#I0">R 19.0</a> <dt>DataType <a href="ref/CHAP013.htm#SSEC009.2">R 13.9.2</a> <dt>DayDMY <a href="ref/CHAP026.htm#SSEC008.4">R 26.8.4</a> <dt>DaysInMonth <a href="ref/CHAP026.htm#SSEC008.2">R 26.8.2</a> <dt>DaysInYear <a href="ref/CHAP026.htm#SSEC008.1">R 26.8.1</a> <dt>Debugging <a href="tut/CHAP009.htm#SECT019">T 9.19</a> <dt>Debugging and Profiling Facilities <a href="ref/CHAP007.htm">R 7.0</a> <dt>Debugging Recursion <a href="ref/CHAP007.htm#SECT010">R 7.10</a> <dt>DEC <a href="ref/CHAP025.htm#I2">R 25.4</a> <dt>Declaration and Implementation Part <a href="ext/CHAP004.htm#SECT007">E 4.7</a> <dt>Declaration and Implementation Part <a href="prg/CHAP003.htm#SECT018">P 3.18</a> <dt>DeclareAttribute <a href="prg/CHAP003.htm#SSEC017.2">P 3.17.2</a> <dt>DeclareAttribute, example <a href="prg/CHAP004.htm#I1">P 4.5</a> <a href="prg/CHAP004.htm#I7">P 4.11</a> <dt>DeclareAutoPackage <a href="ref/CHAP075.htm#I9">R 75.2</a> <dt>DeclareAutoreadableVariables <a href="ext/CHAP004.htm#SECT013">E 4.13</a> <a href="ext/CHAP004.htm#SSEC013.1">E 4.13.1</a> <dt>DeclareCategory <a href="prg/CHAP003.htm#SSEC017.2">P 3.17.2</a> <dt>DeclareFilter <a href="prg/CHAP003.htm#SSEC017.2">P 3.17.2</a> <dt>DeclareGlobalFunction <a href="prg/CHAP003.htm#SSEC017.3">P 3.17.3</a> <dt>DeclareGlobalVariable <a href="prg/CHAP003.htm#SSEC017.5">P 3.17.5</a> <dt>DeclareHandlingByNiceBasis <a href="ref/CHAP059.htm#SSEC011.1">R 59.11.1</a> <dt>DeclareInfoClass <a href="ref/CHAP007.htm#SSEC004.2">R 7.4.2</a> <dt>DeclareOperation <a href="prg/CHAP003.htm#SSEC017.3">P 3.17.3</a> <dt>DeclarePackage <a href="ref/CHAP075.htm#I8">R 75.2</a> <dt>DeclarePackageAutoDocumentation <a href="ref/CHAP075.htm#I11">R 75.2</a> <dt>DeclarePackageDocumentation <a href="ref/CHAP075.htm#I10">R 75.2</a> <dt>DeclareProperty <a href="prg/CHAP003.htm#SSEC017.2">P 3.17.2</a> <dt>DeclareRepresentation <a href="prg/CHAP003.htm#SSEC017.2">P 3.17.2</a> <dt>DeclareRepresentation, belongs to implementation part <a href="prg/CHAP003.htm#I0">P 3.18</a> <dt>DeclareRepresentation, example <a href="prg/CHAP004.htm#I4">P 4.6</a> <dt>DeclareSynonym <a href="prg/CHAP003.htm#SSEC017.7">P 3.17.7</a> <dt>DeclareSynonymAttr <a href="prg/CHAP003.htm#SSEC017.8">P 3.17.8</a> <dt>DecodeTree <a href="ref/CHAP046.htm#SECT011">R 46.11</a> <a href="ref/CHAP046.htm#SSEC011.1">R 46.11.1</a> <dt>decompose, a group character <a href="ref/CHAP070.htm#I24">R 70.8</a> <dt>DecomposedFixedPointVector <a href="ref/CHAP068.htm#SSEC009.8">R 68.9.8</a> <dt>DecomposeTensorProduct <a href="ref/CHAP061.htm#SSEC013.3">R 61.13.3</a> <dt>Decomposition <a href="ref/CHAP025.htm#SSEC004.1">R 25.4.1</a> <dt>decomposition matrix <a href="ref/CHAP025.htm#I1">R 25.4</a> <dt>DecompositionInt <a href="ref/CHAP025.htm#SSEC004.5">R 25.4.5</a> <dt>DecompositionMatrix <a href="ref/CHAP069.htm#SSEC009.4">R 69.9.4</a> <dt>Decompositions <a href="ref/CHAP025.htm#SECT004">R 25.4</a> <dt>Decreased <a href="ref/CHAP070.htm#SSEC010.7">R 70.10.7</a> <dt>DefaultField <a href="ref/CHAP056.htm#SSEC001.4">R 56.1.4</a> <dt>DefaultField, for cyclotomics <a href="ref/CHAP018.htm#I8">R 18.1</a> <dt>DefaultField, for finite field elements <a href="ref/CHAP057.htm#I0">R 57.3</a> <dt>DefaultFieldByGenerators <a href="ref/CHAP056.htm#SSEC001.5">R 56.1.5</a> <dt>DefaultFieldOfMatrix <a href="ref/CHAP024.htm#SSEC003.2">R 24.3.2</a> <dt>DefaultFieldOfMatrixGroup <a href="ref/CHAP042.htm#SSEC001.2">R 42.1.2</a> <dt>DefaultRing <a href="ref/CHAP054.htm#SSEC001.3">R 54.1.3</a> <dt>DefaultRing, for finite field elements <a href="ref/CHAP057.htm#I1">R 57.3</a> <dt>DefaultRingByGenerators <a href="ref/CHAP054.htm#SSEC001.5">R 54.1.5</a> <dt>DefaultStabChainOptions <a href="ref/CHAP041.htm#SSEC007.3">R 41.7.3</a> <dt>Defining a Pcgs Yourself <a href="ref/CHAP043.htm#SECT003">R 43.3</a> <dt>DefiningPolynomial <a href="ref/CHAP056.htm#SSEC002.7">R 56.2.7</a> <dt>DefiningQuotientHomomorphism <a href="ref/CHAP045.htm#SSEC012.4">R 45.12.4</a> <dt>DegreeFFE <a href="ref/CHAP057.htm#SSEC002.1">R 57.2.1</a> <dt>DegreeIndeterminate <a href="ref/CHAP064.htm#SSEC006.1">R 64.6.1</a> <dt>DegreeOfBinaryRelation <a href="ref/CHAP032.htm#SSEC002.10">R 32.2.10</a> <dt>DegreeOfCharacter <a href="ref/CHAP070.htm#SSEC008.4">R 70.8.4</a> <dt>DegreeOfLaurentPolynomial <a href="ref/CHAP064.htm#SSEC005.3">R 64.5.3</a> <dt>DegreeOfTransformation <a href="ref/CHAP052.htm#">R 52.0</a> <dt>DegreeOfTransformationSemigroup <a href="ref/CHAP049.htm#SSEC001.2">R 49.1.2</a> <dt>DegreeOverPrimeField <a href="ref/CHAP056.htm#SSEC002.6">R 56.2.6</a> <dt>Delta <a href="ref/CHAP072.htm#SSEC001.2">R 72.1.2</a> <dt>denominator, of a rational <a href="ref/CHAP016.htm#I2">R 16.1</a> <dt>Denominator <a href="tut/CHAP009.htm#I4">T 9.4</a> <dt>DenominatorCyc <a href="ref/CHAP018.htm#SSEC001.9">R 18.1.9</a> <dt>DenominatorOfModuloPcgs <a href="ref/CHAP043.htm#SSEC009.4">R 43.9.4</a> <dt>DenominatorOfRationalFunction <a href="ref/CHAP064.htm#SSEC004.3">R 64.4.3</a> <dt>DenominatorRat <a href="ref/CHAP016.htm#SSEC001.5">R 16.1.5</a> <dt>Dense hash tables <a href="new/CHAP002.htm#SECT005">N 2.5</a> <dt>DenseHashTable <a href="new/CHAP002.htm#SSEC005.1">N 2.5.1</a> <dt>DenseIntKey <a href="new/CHAP002.htm#SSEC004.2">N 2.4.2</a> <dt>deprecated <a href="ref/CHAP075.htm#I1">R 75.0</a> <dt>DepthOfPcElement <a href="ref/CHAP043.htm#SSEC005.4">R 43.5.4</a> <dt>DepthOfUpperTriangularMatrix <a href="ref/CHAP024.htm#SSEC011.3">R 24.11.3</a> <dt>DepthVector <a href="tut/CHAP009.htm#I5">T 9.4</a> <dt>Derangements <a href="ref/CHAP017.htm#SSEC002.11">R 17.2.11</a> <dt>Derivations <a href="ref/CHAP061.htm#SSEC002.5">R 61.2.5</a> <dt>Derivative <a href="ref/CHAP064.htm#SSEC006.5">R 64.6.5</a> <dt>DerivedLength <a href="ref/CHAP037.htm#SSEC017.8">R 37.17.8</a> <dt>DerivedSeriesOfGroup <a href="ref/CHAP037.htm#SSEC017.7">R 37.17.7</a> <dt>DerivedSubgroup <a href="ref/CHAP037.htm#SSEC012.3">R 37.12.3</a> <dt>DerivedSubgroupsTom <a href="ref/CHAP068.htm#SSEC009.2">R 68.9.2</a> <dt>DerivedSubgroupsTomPossible <a href="ref/CHAP068.htm#SSEC009.3">R 68.9.3</a> <dt>DerivedSubgroupsTomUnique <a href="ref/CHAP068.htm#SSEC009.3">R 68.9.3</a> <dt>DerivedSubgroupTom <a href="ref/CHAP068.htm#SSEC009.2">R 68.9.2</a> <dt>DescriptionOfRootOfUnity <a href="ref/CHAP018.htm#SSEC001.11">R 18.1.11</a> <dt>Designing new Multiplicative Objects <a href="prg/CHAP006.htm#SECT002">P 6.2</a> <dt>Determinant <a href="ref/CHAP024.htm#SSEC003.4">R 24.3.4</a> <dt>determinant, integer matrix <a href="ref/CHAP025.htm#I0">R 25.3</a> <dt>determinant character <a href="ref/CHAP070.htm#I31">R 70.8</a> <dt>Determinant of an integer matrix <a href="ref/CHAP025.htm#SECT003">R 25.3</a> <dt>DeterminantIntMat <a href="ref/CHAP025.htm#SSEC003.1">R 25.3.1</a> <dt>DeterminantMat <a href="ref/CHAP024.htm#SSEC003.4">R 24.3.4</a> <dt>DeterminantMatDestructive <a href="ref/CHAP024.htm#SSEC003.5">R 24.3.5</a> <dt>DeterminantMatDivFree <a href="ref/CHAP024.htm#SSEC003.6">R 24.3.6</a> <dt>DeterminantOfCharacter <a href="ref/CHAP070.htm#SSEC008.18">R 70.8.18</a> <dt>Developing rewriting systems <a href="ref/CHAP036.htm#SECT005">R 36.5</a> <dt>DiagonalizeIntMat <a href="ref/CHAP025.htm#SSEC002.8">R 25.2.8</a> <dt>DiagonalizeMat <a href="ref/CHAP024.htm#SSEC008.2">R 24.8.2</a> <dt>DiagonalMat <a href="ref/CHAP024.htm#SSEC004.4">R 24.4.4</a> <dt>DiagonalOfMat <a href="ref/CHAP024.htm#SSEC011.1">R 24.11.1</a> <dt>Dictionaries <a href="new/CHAP002.htm#SECT001">N 2.1</a> <dt>Dictionaries and General Hash Tables <a href="new/CHAP002.htm">N 2.0</a> <dt>DictionaryByPosition <a href="new/CHAP002.htm#SSEC001.6">N 2.1.6</a> <dt>Difference <a href="ref/CHAP028.htm#SSEC004.4">R 28.4.4</a> <dt>DifferenceBlist <a href="ref/CHAP022.htm#SSEC002.3">R 22.2.3</a> <dt>Different Notions of Generation <a href="tut/CHAP009.htm#SECT009">T 9.9</a> <dt>DihedralGroup <a href="ref/CHAP048.htm#SSEC001.5">R 48.1.5</a> <dt>Dimension <a href="ref/CHAP055.htm#SSEC003.4">R 55.3.4</a> <dt>DimensionOfHighestWeightModule <a href="ref/CHAP061.htm#SSEC013.4">R 61.13.4</a> <dt>DimensionOfMatrixGroup <a href="ref/CHAP042.htm#SSEC001.1">R 42.1.1</a> <dt>DimensionOfVectors <a href="ref/CHAP059.htm#SSEC008.6">R 59.8.6</a> <dt>DimensionsLoewyFactors <a href="ref/CHAP037.htm#SSEC017.15">R 37.17.15</a> <dt>DimensionsMat <a href="ref/CHAP024.htm#SSEC003.1">R 24.3.1</a> <dt>Direct product chain subgroups <a href="new/CHAP005.htm#SECT003">N 5.3</a> <dt>Direct Products <a href="ref/CHAP047.htm#SECT001">R 47.1</a> <dt>Direct Sum Decompositions <a href="ref/CHAP061.htm#SECT006">R 61.6</a> <dt>Directories <a href="ref/CHAP009.htm#SECT003">R 9.3</a> <dt>DirectoriesLibrary <a href="ref/CHAP009.htm#SSEC003.4">R 9.3.4</a> <dt>DirectoriesPackageLibrary <a href="ref/CHAP074.htm#SSEC003.4">R 74.3.4</a> <dt>DirectoriesPackagePrograms <a href="ref/CHAP074.htm#SSEC003.5">R 74.3.5</a> <dt>DirectoriesSystemPrograms <a href="ref/CHAP009.htm#SSEC003.5">R 9.3.5</a> <dt>Directory <a href="ref/CHAP009.htm#SSEC003.1">R 9.3.1</a> <dt>DirectoryContents <a href="ref/CHAP009.htm#SSEC003.6">R 9.3.6</a> <dt>DirectoryCurrent <a href="ref/CHAP009.htm#SSEC003.3">R 9.3.3</a> <dt>DirectoryTemporary <a href="ref/CHAP009.htm#SSEC003.2">R 9.3.2</a> <dt>DirectProduct <a href="ref/CHAP047.htm#SSEC001.1">R 47.1.1</a> <dt>DirectProductOp <a href="ref/CHAP047.htm#SSEC001.1">R 47.1.1</a> <dt>DirectSumDecomposition <a href="ref/CHAP060.htm#SSEC008.18">R 60.8.18</a> <dt>DirectSumDecomposition, for Lie algebras <a href="ref/CHAP061.htm#SSEC006.2">R 61.6.2</a> <dt>DirectSumOfAlgebraModules <a href="ref/CHAP060.htm#SSEC010.23">R 60.10.23</a> <dt>DirectSumOfAlgebraModules, for Lie algebras <a href="ref/CHAP061.htm#SSEC014.4">R 61.14.4</a> <dt>DirectSumOfAlgebras <a href="ref/CHAP060.htm#SSEC008.14">R 60.8.14</a> <dt>disable automatic loading <a href="ref/CHAP074.htm#I2">R 74.2</a> <dt>DisableAttributeValueStoring <a href="ref/CHAP013.htm#SSEC006.5">R 13.6.5</a> <dt>Discriminant <a href="ref/CHAP064.htm#SSEC006.6">R 64.6.6</a> <dt>Display <a href="ref/CHAP006.htm#SSEC003.4">R 6.3.4</a> <dt>Display, for character tables <a href="ref/CHAP069.htm#I33">R 69.11</a> <a href="ref/CHAP070.htm#I18">R 70.5</a> <dt>Display, for tables of marks <a href="ref/CHAP068.htm#I2">R 68.4</a> <dt>DisplayCacheStats <a href="ref/CHAP007.htm#SSEC007.11">R 7.7.11</a> <dt>DisplayCompositionSeries <a href="ref/CHAP037.htm#SSEC017.6">R 37.17.6</a> <dt>DisplayEggBoxOfDClass <a href="ref/CHAP049.htm#SSEC005.7">R 49.5.7</a> <dt>DisplayImfInvariants <a href="ref/CHAP048.htm#SSEC012.2">R 48.12.2</a> <dt>DisplayInformationPerfectGroups <a href="ref/CHAP048.htm#SSEC008.7">R 48.8.7</a> <dt>DisplayOptions <a href="ref/CHAP069.htm#SSEC011.1">R 69.11.1</a> <dt>DisplayOptionsStack <a href="ref/CHAP008.htm#">R 8.0</a> <dt>DisplayProfile <a href="ref/CHAP007.htm#SSEC007.8">R 7.7.8</a> <dt>DisplayRevision <a href="ref/CHAP007.htm#SSEC008.1">R 7.8.1</a> <dt>DistancesDistributionMatFFEVecFFE <a href="ref/CHAP023.htm#SSEC005.4">R 23.5.4</a> <dt>DistancesDistributionVecFFEsVecFFE <a href="ref/CHAP023.htm#SSEC005.3">R 23.5.3</a> <dt>DistanceVecFFE <a href="ref/CHAP023.htm#SSEC005.2">R 23.5.2</a> <dt>Distinguished Subalgebras <a href="ref/CHAP061.htm#SECT003">R 61.3</a> <dt>division <a href="ref/CHAP004.htm#SSEC012.1">R 4.12.1</a> <dt>division, operation <a href="ref/CHAP030.htm#SSEC012.1">R 30.12.1</a> <dt>division rings <a href="ref/CHAP056.htm#I1">R 56.0</a> <dt>DivisionRingByGenerators <a href="ref/CHAP056.htm#SSEC001.8">R 56.1.8</a> <dt>divisors, of an integer <a href="ref/CHAP014.htm#I9">R 14.3</a> <dt>DivisorsInt <a href="ref/CHAP014.htm#SSEC003.10">R 14.3.10</a> <dt>Dixon-Schneider algorithm <a href="ref/CHAP069.htm#I34">R 69.14</a> <dt>DixonInit <a href="ref/CHAP069.htm#SSEC015.2">R 69.15.2</a> <dt>DixonRecord <a href="ref/CHAP069.htm#SSEC015.1">R 69.15.1</a> <dt>DixonSplit <a href="ref/CHAP069.htm#SSEC015.4">R 69.15.4</a> <dt>DixontinI <a href="ref/CHAP069.htm#SSEC015.3">R 69.15.3</a> <dt>DMYDay <a href="ref/CHAP026.htm#SSEC008.3">R 26.8.3</a> <dt>DMYhmsSeconds <a href="ref/CHAP026.htm#SSEC008.11">R 26.8.11</a> <dt>DnLattice <a href="ref/CHAP070.htm#SSEC010.8">R 70.10.8</a> <dt>DnLatticeIterative <a href="ref/CHAP070.htm#SSEC010.9">R 70.10.9</a> <dt>do <a href="ref/CHAP004.htm#I39">R 4.19</a> <dt>document formats, for help books <a href="ext/CHAP005.htm#I0">E 5.3</a> <dt>document formats (text, dvi, ps, pdf, HTML) <a href="ref/CHAP002.htm#I0">R 2.3</a> <dt>Domain <a href="ref/CHAP030.htm#SSEC009.3">R 30.9.3</a> <dt>Domain Categories <a href="ref/CHAP030.htm#SECT006">R 30.6</a> <dt>Domain Constructors <a href="tut/CHAP007.htm#SECT004">T 7.4</a> <dt>DomainByGenerators <a href="ref/CHAP030.htm#SSEC009.3">R 30.9.3</a> <dt>Domains <a href="ref/CHAP012.htm#SECT004">R 12.4</a> <dt>Domains <a href="tut/CHAP007.htm">T 7.0</a> <dt>Domains and their Elements <a href="ref/CHAP030.htm">R 30.0</a> <dt>Domains as Sets <a href="tut/CHAP007.htm#SECT001">T 7.1</a> <dt>Domains Generated by Class Functions <a href="ref/CHAP070.htm#SECT016">R 70.16</a> <dt>Domains of Subspaces of Vector Spaces <a href="ref/CHAP059.htm#SECT003">R 59.3</a> <dt>DominantCharacter <a href="ref/CHAP061.htm#SSEC013.2">R 61.13.2</a> <dt>DominantWeights <a href="ref/CHAP061.htm#SSEC013.1">R 61.13.1</a> <dt>Double Cosets <a href="ref/CHAP037.htm#SECT009">R 37.9</a> <dt>DoubleCoset <a href="ref/CHAP037.htm#SSEC009.1">R 37.9.1</a> <dt>DoubleCosetRepsAndSizes <a href="ref/CHAP037.htm#SSEC009.5">R 37.9.5</a> <dt>DoubleCosets, operation <a href="ref/CHAP037.htm#SSEC009.3">R 37.9.3</a> <dt>DoubleCosetsNC, operation <a href="ref/CHAP037.htm#SSEC009.3">R 37.9.3</a> <dt>DoubleHashArraySize <a href="new/CHAP002.htm#SSEC006.3">N 2.6.3</a> <dt>doublequote character <a href="ref/CHAP026.htm#I8">R 26.1</a> <dt>doublequotes <a href="ref/CHAP026.htm#I1">R 26.0</a> <dt>DownEnv <a href="ref/CHAP006.htm#SSEC005.1">R 6.5.1</a> <dt>DownEnv <a href="tut/CHAP009.htm#I21">T 9.19</a> <dt>Dummy Streams <a href="ref/CHAP010.htm#SECT009">R 10.9</a> <dt>duplicate free <a href="ref/CHAP021.htm#I15">R 21.17</a> <dt>DuplicateFreeList <a href="ref/CHAP021.htm#SSEC020.4">R 21.20.4</a> <dt>Duplication of Lists <a href="ref/CHAP021.htm#SECT007">R 21.7</a> <dt>Duplication of Objects <a href="ref/CHAP012.htm#SECT007">R 12.7</a> <dt>DxIncludeIrreducibles <a href="ref/CHAP069.htm#SSEC015.6">R 69.15.6</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>