<html><head><title>The GAP 4 Reference Manual - Index D</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - 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> <dt>d_N <a href="CHAP018.htm#I13">18.4</a> <dt>Darstellungsgruppe, see EpimorphismSchurCover <a href="CHAP037.htm#I12">37.24</a> <dt>data type, unknown <a href="CHAP019.htm#I0">19.0</a> <dt>DataType <a href="CHAP013.htm#SSEC009.2">13.9.2</a> <dt>DayDMY <a href="CHAP026.htm#SSEC008.4">26.8.4</a> <dt>DaysInMonth <a href="CHAP026.htm#SSEC008.2">26.8.2</a> <dt>DaysInYear <a href="CHAP026.htm#SSEC008.1">26.8.1</a> <dt>Debugging and Profiling Facilities <a href="CHAP007.htm">7.0</a> <dt>Debugging Recursion <a href="CHAP007.htm#SECT010">7.10</a> <dt>DEC <a href="CHAP025.htm#I2">25.4</a> <dt>DeclareAutoPackage <a href="CHAP075.htm#I9">75.2</a> <dt>DeclareHandlingByNiceBasis <a href="CHAP059.htm#SSEC011.1">59.11.1</a> <dt>DeclareInfoClass <a href="CHAP007.htm#SSEC004.2">7.4.2</a> <dt>DeclarePackage <a href="CHAP075.htm#I8">75.2</a> <dt>DeclarePackageAutoDocumentation <a href="CHAP075.htm#I11">75.2</a> <dt>DeclarePackageDocumentation <a href="CHAP075.htm#I10">75.2</a> <dt>DecodeTree <a href="CHAP046.htm#SECT011">46.11</a> <a href="CHAP046.htm#SSEC011.1">46.11.1</a> <dt>decompose, a group character <a href="CHAP070.htm#I24">70.8</a> <dt>DecomposedFixedPointVector <a href="CHAP068.htm#SSEC009.8">68.9.8</a> <dt>DecomposeTensorProduct <a href="CHAP061.htm#SSEC013.3">61.13.3</a> <dt>Decomposition <a href="CHAP025.htm#SSEC004.1">25.4.1</a> <dt>decomposition matrix <a href="CHAP025.htm#I1">25.4</a> <dt>DecompositionInt <a href="CHAP025.htm#SSEC004.5">25.4.5</a> <dt>DecompositionMatrix <a href="CHAP069.htm#SSEC009.4">69.9.4</a> <dt>Decompositions <a href="CHAP025.htm#SECT004">25.4</a> <dt>Decreased <a href="CHAP070.htm#SSEC010.7">70.10.7</a> <dt>DefaultField <a href="CHAP056.htm#SSEC001.4">56.1.4</a> <dt>DefaultField, for cyclotomics <a href="CHAP018.htm#I8">18.1</a> <dt>DefaultField, for finite field elements <a href="CHAP057.htm#I0">57.3</a> <dt>DefaultFieldByGenerators <a href="CHAP056.htm#SSEC001.5">56.1.5</a> <dt>DefaultFieldOfMatrix <a href="CHAP024.htm#SSEC003.2">24.3.2</a> <dt>DefaultFieldOfMatrixGroup <a href="CHAP042.htm#SSEC001.2">42.1.2</a> <dt>DefaultRing <a href="CHAP054.htm#SSEC001.3">54.1.3</a> <dt>DefaultRing, for finite field elements <a href="CHAP057.htm#I1">57.3</a> <dt>DefaultRingByGenerators <a href="CHAP054.htm#SSEC001.5">54.1.5</a> <dt>DefaultStabChainOptions <a href="CHAP041.htm#SSEC007.3">41.7.3</a> <dt>Defining a Pcgs Yourself <a href="CHAP043.htm#SECT003">43.3</a> <dt>DefiningPolynomial <a href="CHAP056.htm#SSEC002.7">56.2.7</a> <dt>DefiningQuotientHomomorphism <a href="CHAP045.htm#SSEC012.4">45.12.4</a> <dt>DegreeFFE <a href="CHAP057.htm#SSEC002.1">57.2.1</a> <dt>DegreeIndeterminate <a href="CHAP064.htm#SSEC006.1">64.6.1</a> <dt>DegreeOfBinaryRelation <a href="CHAP032.htm#SSEC002.10">32.2.10</a> <dt>DegreeOfCharacter <a href="CHAP070.htm#SSEC008.4">70.8.4</a> <dt>DegreeOfLaurentPolynomial <a href="CHAP064.htm#SSEC005.3">64.5.3</a> <dt>DegreeOfTransformation <a href="CHAP052.htm#">52.0</a> <dt>DegreeOfTransformationSemigroup <a href="CHAP049.htm#SSEC001.2">49.1.2</a> <dt>DegreeOverPrimeField <a href="CHAP056.htm#SSEC002.6">56.2.6</a> <dt>Delta <a href="CHAP072.htm#SSEC001.2">72.1.2</a> <dt>denominator, of a rational <a href="CHAP016.htm#I2">16.1</a> <dt>DenominatorCyc <a href="CHAP018.htm#SSEC001.9">18.1.9</a> <dt>DenominatorOfModuloPcgs <a href="CHAP043.htm#SSEC009.4">43.9.4</a> <dt>DenominatorOfRationalFunction <a href="CHAP064.htm#SSEC004.3">64.4.3</a> <dt>DenominatorRat <a href="CHAP016.htm#SSEC001.5">16.1.5</a> <dt>deprecated <a href="CHAP075.htm#I1">75.0</a> <dt>DepthOfPcElement <a href="CHAP043.htm#SSEC005.4">43.5.4</a> <dt>DepthOfUpperTriangularMatrix <a href="CHAP024.htm#SSEC011.3">24.11.3</a> <dt>Derangements <a href="CHAP017.htm#SSEC002.11">17.2.11</a> <dt>Derivations <a href="CHAP061.htm#SSEC002.5">61.2.5</a> <dt>Derivative <a href="CHAP064.htm#SSEC006.5">64.6.5</a> <dt>DerivedLength <a href="CHAP037.htm#SSEC017.8">37.17.8</a> <dt>DerivedSeriesOfGroup <a href="CHAP037.htm#SSEC017.7">37.17.7</a> <dt>DerivedSubgroup <a href="CHAP037.htm#SSEC012.3">37.12.3</a> <dt>DerivedSubgroupsTom <a href="CHAP068.htm#SSEC009.2">68.9.2</a> <dt>DerivedSubgroupsTomPossible <a href="CHAP068.htm#SSEC009.3">68.9.3</a> <dt>DerivedSubgroupsTomUnique <a href="CHAP068.htm#SSEC009.3">68.9.3</a> <dt>DerivedSubgroupTom <a href="CHAP068.htm#SSEC009.2">68.9.2</a> <dt>DescriptionOfRootOfUnity <a href="CHAP018.htm#SSEC001.11">18.1.11</a> <dt>Determinant <a href="CHAP024.htm#SSEC003.4">24.3.4</a> <dt>determinant character <a href="CHAP070.htm#I31">70.8</a> <dt>Determinant of an integer matrix <a href="CHAP025.htm#SECT003">25.3</a> <dt>determinant, integer matrix <a href="CHAP025.htm#I0">25.3</a> <dt>DeterminantIntMat <a href="CHAP025.htm#SSEC003.1">25.3.1</a> <dt>DeterminantMat <a href="CHAP024.htm#SSEC003.4">24.3.4</a> <dt>DeterminantMatDestructive <a href="CHAP024.htm#SSEC003.5">24.3.5</a> <dt>DeterminantMatDivFree <a href="CHAP024.htm#SSEC003.6">24.3.6</a> <dt>DeterminantOfCharacter <a href="CHAP070.htm#SSEC008.18">70.8.18</a> <dt>Developing rewriting systems <a href="CHAP036.htm#SECT005">36.5</a> <dt>DiagonalizeIntMat <a href="CHAP025.htm#SSEC002.8">25.2.8</a> <dt>DiagonalizeMat <a href="CHAP024.htm#SSEC008.2">24.8.2</a> <dt>DiagonalMat <a href="CHAP024.htm#SSEC004.4">24.4.4</a> <dt>DiagonalOfMat <a href="CHAP024.htm#SSEC011.1">24.11.1</a> <dt>Difference <a href="CHAP028.htm#SSEC004.4">28.4.4</a> <dt>DifferenceBlist <a href="CHAP022.htm#SSEC002.3">22.2.3</a> <dt>DihedralGroup <a href="CHAP048.htm#SSEC001.5">48.1.5</a> <dt>Dimension <a href="CHAP055.htm#SSEC003.4">55.3.4</a> <dt>DimensionOfHighestWeightModule <a href="CHAP061.htm#SSEC013.4">61.13.4</a> <dt>DimensionOfMatrixGroup <a href="CHAP042.htm#SSEC001.1">42.1.1</a> <dt>DimensionOfVectors <a href="CHAP059.htm#SSEC008.6">59.8.6</a> <dt>DimensionsLoewyFactors <a href="CHAP037.htm#SSEC017.15">37.17.15</a> <dt>DimensionsMat <a href="CHAP024.htm#SSEC003.1">24.3.1</a> <dt>Direct Products <a href="CHAP047.htm#SECT001">47.1</a> <dt>Direct Sum Decompositions <a href="CHAP061.htm#SECT006">61.6</a> <dt>Directories <a href="CHAP009.htm#SECT003">9.3</a> <dt>DirectoriesLibrary <a href="CHAP009.htm#SSEC003.4">9.3.4</a> <dt>DirectoriesPackageLibrary <a href="CHAP074.htm#SSEC003.4">74.3.4</a> <dt>DirectoriesPackagePrograms <a href="CHAP074.htm#SSEC003.5">74.3.5</a> <dt>DirectoriesSystemPrograms <a href="CHAP009.htm#SSEC003.5">9.3.5</a> <dt>Directory <a href="CHAP009.htm#SSEC003.1">9.3.1</a> <dt>DirectoryContents <a href="CHAP009.htm#SSEC003.6">9.3.6</a> <dt>DirectoryCurrent <a href="CHAP009.htm#SSEC003.3">9.3.3</a> <dt>DirectoryTemporary <a href="CHAP009.htm#SSEC003.2">9.3.2</a> <dt>DirectProduct <a href="CHAP047.htm#SSEC001.1">47.1.1</a> <dt>DirectProductOp <a href="CHAP047.htm#SSEC001.1">47.1.1</a> <dt>DirectSumDecomposition <a href="CHAP060.htm#SSEC008.18">60.8.18</a> <dt>DirectSumDecomposition, for Lie algebras <a href="CHAP061.htm#SSEC006.2">61.6.2</a> <dt>DirectSumOfAlgebraModules <a href="CHAP060.htm#SSEC010.23">60.10.23</a> <dt>DirectSumOfAlgebraModules, for Lie algebras <a href="CHAP061.htm#SSEC014.4">61.14.4</a> <dt>DirectSumOfAlgebras <a href="CHAP060.htm#SSEC008.14">60.8.14</a> <dt>disable automatic loading <a href="CHAP074.htm#I2">74.2</a> <dt>DisableAttributeValueStoring <a href="CHAP013.htm#SSEC006.5">13.6.5</a> <dt>Discriminant <a href="CHAP064.htm#SSEC006.6">64.6.6</a> <dt>Display <a href="CHAP006.htm#SSEC003.4">6.3.4</a> <dt>Display, for character tables <a href="CHAP069.htm#I33">69.11</a> <a href="CHAP070.htm#I18">70.5</a> <dt>Display, for tables of marks <a href="CHAP068.htm#I2">68.4</a> <dt>DisplayCacheStats <a href="CHAP007.htm#SSEC007.11">7.7.11</a> <dt>DisplayCompositionSeries <a href="CHAP037.htm#SSEC017.6">37.17.6</a> <dt>DisplayEggBoxOfDClass <a href="CHAP049.htm#SSEC005.7">49.5.7</a> <dt>DisplayImfInvariants <a href="CHAP048.htm#SSEC012.2">48.12.2</a> <dt>DisplayInformationPerfectGroups <a href="CHAP048.htm#SSEC008.7">48.8.7</a> <dt>DisplayOptions <a href="CHAP069.htm#SSEC011.1">69.11.1</a> <dt>DisplayOptionsStack <a href="CHAP008.htm#">8.0</a> <dt>DisplayProfile <a href="CHAP007.htm#SSEC007.8">7.7.8</a> <dt>DisplayRevision <a href="CHAP007.htm#SSEC008.1">7.8.1</a> <dt>DistancesDistributionMatFFEVecFFE <a href="CHAP023.htm#SSEC005.4">23.5.4</a> <dt>DistancesDistributionVecFFEsVecFFE <a href="CHAP023.htm#SSEC005.3">23.5.3</a> <dt>DistanceVecFFE <a href="CHAP023.htm#SSEC005.2">23.5.2</a> <dt>Distinguished Subalgebras <a href="CHAP061.htm#SECT003">61.3</a> <dt>division <a href="CHAP004.htm#SSEC012.1">4.12.1</a> <dt>division rings <a href="CHAP056.htm#I1">56.0</a> <dt>division, operation <a href="CHAP030.htm#SSEC012.1">30.12.1</a> <dt>DivisionRingByGenerators <a href="CHAP056.htm#SSEC001.8">56.1.8</a> <dt>divisors, of an integer <a href="CHAP014.htm#I9">14.3</a> <dt>DivisorsInt <a href="CHAP014.htm#SSEC003.10">14.3.10</a> <dt>Dixon-Schneider algorithm <a href="CHAP069.htm#I34">69.14</a> <dt>DixonInit <a href="CHAP069.htm#SSEC015.2">69.15.2</a> <dt>DixonRecord <a href="CHAP069.htm#SSEC015.1">69.15.1</a> <dt>DixonSplit <a href="CHAP069.htm#SSEC015.4">69.15.4</a> <dt>DixontinI <a href="CHAP069.htm#SSEC015.3">69.15.3</a> <dt>DMYDay <a href="CHAP026.htm#SSEC008.3">26.8.3</a> <dt>DMYhmsSeconds <a href="CHAP026.htm#SSEC008.11">26.8.11</a> <dt>DnLattice <a href="CHAP070.htm#SSEC010.8">70.10.8</a> <dt>DnLatticeIterative <a href="CHAP070.htm#SSEC010.9">70.10.9</a> <dt>do <a href="CHAP004.htm#I39">4.19</a> <dt>document formats (text, dvi, ps, pdf, HTML) <a href="CHAP002.htm#I0">2.3</a> <dt>Domain <a href="CHAP030.htm#SSEC009.3">30.9.3</a> <dt>Domain Categories <a href="CHAP030.htm#SECT006">30.6</a> <dt>DomainByGenerators <a href="CHAP030.htm#SSEC009.3">30.9.3</a> <dt>Domains <a href="CHAP012.htm#SECT004">12.4</a> <dt>Domains and their Elements <a href="CHAP030.htm">30.0</a> <dt>Domains Generated by Class Functions <a href="CHAP070.htm#SECT016">70.16</a> <dt>Domains of Subspaces of Vector Spaces <a href="CHAP059.htm#SECT003">59.3</a> <dt>DominantCharacter <a href="CHAP061.htm#SSEC013.2">61.13.2</a> <dt>DominantWeights <a href="CHAP061.htm#SSEC013.1">61.13.1</a> <dt>Double Cosets <a href="CHAP037.htm#SECT009">37.9</a> <dt>DoubleCoset <a href="CHAP037.htm#SSEC009.1">37.9.1</a> <dt>DoubleCosetRepsAndSizes <a href="CHAP037.htm#SSEC009.5">37.9.5</a> <dt>DoubleCosets, operation <a href="CHAP037.htm#SSEC009.3">37.9.3</a> <dt>DoubleCosetsNC, operation <a href="CHAP037.htm#SSEC009.3">37.9.3</a> <dt>doublequote character <a href="CHAP026.htm#I8">26.1</a> <dt>doublequotes <a href="CHAP026.htm#I1">26.0</a> <dt>DownEnv <a href="CHAP006.htm#SSEC005.1">6.5.1</a> <dt>Dummy Streams <a href="CHAP010.htm#SECT009">10.9</a> <dt>duplicate free <a href="CHAP021.htm#I15">21.17</a> <dt>DuplicateFreeList <a href="CHAP021.htm#SSEC020.4">21.20.4</a> <dt>Duplication of Lists <a href="CHAP021.htm#SECT007">21.7</a> <dt>Duplication of Objects <a href="CHAP012.htm#SECT007">12.7</a> <dt>DxIncludeIrreducibles <a href="CHAP069.htm#SSEC015.6">69.15.6</a> </dl><p> [<a 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