<html><head><title>The GAP 4 Reference Manual - Index E</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - Index E</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>E <a href="CHAP018.htm#SSEC001.1">18.1.1</a> <dt>e_N <a href="CHAP018.htm#I14">18.4</a> <dt>EANormalSeriesByPcgs <a href="CHAP043.htm#SSEC011.4">43.11.4</a> <dt>Earns <a href="CHAP039.htm#SSEC009.6">39.9.6</a> <dt>EB <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>EC <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>Echelonized Matrices <a href="CHAP024.htm#SECT009">24.9</a> <dt>ED <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>Edit <a href="CHAP006.htm#SSEC010.1">6.10.1</a> <dt>Editing Files <a href="CHAP006.htm#SECT010">6.10</a> <dt>Editor Support <a href="CHAP006.htm#SECT011">6.11</a> <dt>EE <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>EF <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>Efficiency of Homomorphisms <a href="CHAP038.htm#SECT003">38.3</a> <dt>EG <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>EggBoxOfDClass <a href="CHAP049.htm#SSEC005.6">49.5.6</a> <dt>EH <a href="CHAP018.htm#SSEC004.1">18.4.1</a> <dt>EI <a href="CHAP018.htm#SSEC004.2">18.4.2</a> <dt>Eigenspaces <a href="CHAP024.htm#SSEC007.4">24.7.4</a> <dt>Eigenvalues <a href="CHAP024.htm#SSEC007.3">24.7.3</a> <dt>EigenvaluesChar <a href="CHAP070.htm#SSEC008.19">70.8.19</a> <dt>Eigenvectors <a href="CHAP024.htm#SSEC007.5">24.7.5</a> <dt>Eigenvectors and eigenvalues <a href="CHAP024.htm#SECT007">24.7</a> <dt>EJ <a href="CHAP018.htm#SSEC004.4">18.4.4</a> <dt>EK <a href="CHAP018.htm#SSEC004.4">18.4.4</a> <dt>EL <a href="CHAP018.htm#SSEC004.4">18.4.4</a> <dt>element test, for lists <a href="CHAP021.htm#SSEC008.1">21.8.1</a> <dt>Elementary Divisors <a href="CHAP024.htm#SECT008">24.8</a> <dt>Elementary Operations for a Pcgs <a href="CHAP043.htm#SECT004">43.4</a> <dt>Elementary Operations for a Pcgs and an Element <a href="CHAP043.htm#SECT005">43.5</a> <dt>Elementary Operations for Integers <a href="CHAP014.htm#SECT001">14.1</a> <dt>Elementary Operations for Rationals <a href="CHAP016.htm#SECT001">16.1</a> <dt>Elementary Tietze Transformations <a href="CHAP046.htm#SECT008">46.8</a> <dt>ElementaryAbelianGroup <a href="CHAP048.htm#SSEC001.4">48.1.4</a> <dt>ElementaryAbelianSeries <a href="CHAP037.htm#SSEC017.9">37.17.9</a> <dt>ElementaryAbelianSeriesLargeSteps <a href="CHAP037.htm#SSEC017.9">37.17.9</a> <dt>ElementaryDivisorsMat <a href="CHAP024.htm#SSEC008.1">24.8.1</a> <dt>ElementaryDivisorsMatDestructive <a href="CHAP024.htm#SSEC008.1">24.8.1</a> <dt>ElementOfFpGroup <a href="CHAP045.htm#SSEC003.5">45.3.5</a> <dt>ElementOfFpSemigroup <a href="CHAP051.htm#SSEC003.5">51.3.5</a> <dt>ElementOfMagmaRing <a href="CHAP063.htm#SSEC002.5">63.2.5</a> <dt>ElementOrdersPowerMap <a href="CHAP071.htm#SSEC001.3">71.1.3</a> <dt>ElementProperty <a href="CHAP041.htm#SSEC011.2">41.11.2</a> <dt>Elements <a href="CHAP028.htm#SSEC002.10">28.2.10</a> <dt>Elements as equivalence classes <a href="CHAP012.htm#SECT002">12.2</a> <dt>Elements in Algebraic Extensions <a href="CHAP065.htm#SECT002">65.2</a> <dt>Elements of Free Magma Rings <a href="CHAP063.htm#SECT002">63.2</a> <dt>Elements of pc groups <a href="CHAP044.htm#SECT002">44.2</a> <dt>Elements with Prescribed Images <a href="CHAP039.htm#SECT005">39.5</a> <dt>elements, definition <a href="CHAP012.htm#I0">12.2</a> <dt>elements, of a list or collection <a href="CHAP028.htm#I1">28.2</a> <dt>ElementsFamily <a href="CHAP028.htm#SSEC001.3">28.1.3</a> <dt>ElementsStabChain <a href="CHAP041.htm#SSEC009.9">41.9.9</a> <dt>elif <a href="CHAP004.htm#I34">4.16</a> <dt>EliminatedWord <a href="CHAP035.htm#SSEC004.6">35.4.6</a> <dt>EliminationOrdering <a href="CHAP064.htm#SSEC016.10">64.16.10</a> <dt>else <a href="CHAP004.htm#I33">4.16</a> <dt>EM <a href="CHAP018.htm#SSEC004.4">18.4.4</a> <dt>emacs <a href="CHAP006.htm#I20">6.11</a> <dt>Embedding <a href="CHAP031.htm#SSEC001.10">31.1.10</a> <dt>Embedding, example for direct products <a href="CHAP047.htm#I0">47.1</a> <dt>Embedding, example for semidirect products <a href="CHAP047.htm#I2">47.2</a> <dt>Embedding, example for wreath products <a href="CHAP047.htm#I5">47.4</a> <dt>Embedding, for group products <a href="CHAP047.htm#SSEC006.1">47.6.1</a> <dt>Embedding, for Lie algebras <a href="CHAP061.htm#I0">61.1</a> <dt>Embedding, for magma rings <a href="CHAP063.htm#I2">63.3</a> <dt>Embeddings and Projections for Group Products <a href="CHAP047.htm#SECT006">47.6</a> <dt>embeddings, find all <a href="CHAP038.htm#I6">38.9</a> <dt>EmptyBinaryRelation <a href="CHAP032.htm#SSEC001.4">32.1.4</a> <dt>EmptyMatrix <a href="CHAP024.htm#SSEC004.3">24.4.3</a> <dt>EmptyPlist <a href="CHAP021.htm#SSEC009.1">21.9.1</a> <dt>EmptySCTable <a href="CHAP060.htm#SSEC003.1">60.3.1</a> <dt>EmptyStabChain <a href="CHAP041.htm#SSEC010.7">41.10.7</a> <dt>EmptyString <a href="CHAP026.htm#SSEC002.4">26.2.4</a> <dt>EnableAttributeValueStoring <a href="CHAP013.htm#SSEC006.6">13.6.6</a> <dt>End <a href="CHAP059.htm#SSEC009.6">59.9.6</a> <dt>end <a href="CHAP004.htm#I44">4.22</a> <dt>Enlarging Internally Represented Lists <a href="CHAP021.htm#SECT009">21.9</a> <dt>Enumerator <a href="CHAP028.htm#SSEC002.2">28.2.2</a> <dt>EnumeratorByBasis <a href="CHAP059.htm#SSEC005.5">59.5.5</a> <dt>EnumeratorByFunctions <a href="CHAP028.htm#SSEC002.4">28.2.4</a> <dt>Enumerators <a href="CHAP021.htm#SECT023">21.23</a> <dt>EnumeratorSorted <a href="CHAP028.htm#SSEC002.3">28.2.3</a> <dt>environment <a href="CHAP004.htm#I48">4.22</a> <dt>Epicentre <a href="CHAP037.htm#SSEC024.4">37.24.4</a> <dt>EpimorphismFromFreeGroup <a href="CHAP037.htm#SSEC005.1">37.5.1</a> <dt>EpimorphismNilpotentQuotient <a href="CHAP045.htm#SSEC013.4">45.13.4</a> <dt>EpimorphismNonabelianExteriorSquare <a href="CHAP037.htm#SSEC024.6">37.24.6</a> <dt>EpimorphismPGroup <a href="CHAP045.htm#SSEC013.3">45.13.3</a> <dt>EpimorphismQuotientSystem <a href="CHAP045.htm#SSEC013.2">45.13.2</a> <dt>epimorphisms, find all <a href="CHAP038.htm#I4">38.9</a> <dt>EpimorphismSchurCover <a href="CHAP037.htm#SSEC024.1">37.24.1</a> <dt>Equality and Comparison of Domains <a href="CHAP030.htm#SECT002">30.2</a> <dt>equality test <a href="CHAP004.htm#SSEC011.1">4.11.1</a> <dt>equality test, for permutations <a href="CHAP040.htm#SSEC001.1">40.1.1</a> <dt>equality, associative words <a href="CHAP035.htm#SSEC003.1">35.3.1</a> <dt>equality, elements of finitely presented groups <a href="CHAP045.htm#SSEC002.1">45.2.1</a> <dt>equality, nonassociative words <a href="CHAP034.htm#SSEC002.1">34.2.1</a> <dt>equality, of records <a href="CHAP027.htm#SSEC004.1">27.4.1</a> <dt>equality, operation <a href="CHAP030.htm#SSEC011.1">30.11.1</a> <dt>equality, pcwords <a href="CHAP044.htm#SSEC002.1">44.2.1</a> <dt>equivalence class <a href="CHAP032.htm#I11">32.7</a> <dt>Equivalence Classes <a href="CHAP032.htm#SECT007">32.7</a> <dt>equivalence relation <a href="CHAP032.htm#I9">32.2</a> <a href="CHAP032.htm#I10">32.5</a> <dt>Equivalence Relations <a href="CHAP032.htm#SECT005">32.5</a> <dt>EquivalenceClasses, attribute <a href="CHAP032.htm#SSEC007.3">32.7.3</a> <dt>EquivalenceClassOfElement <a href="CHAP032.htm#SSEC007.4">32.7.4</a> <dt>EquivalenceClassOfElementNC <a href="CHAP032.htm#SSEC007.4">32.7.4</a> <dt>EquivalenceClassRelation <a href="CHAP032.htm#SSEC007.2">32.7.2</a> <dt>EquivalenceRelationByPairs <a href="CHAP032.htm#SSEC005.3">32.5.3</a> <dt>EquivalenceRelationByPairsNC <a href="CHAP032.htm#SSEC005.3">32.5.3</a> <dt>EquivalenceRelationByPartition <a href="CHAP032.htm#SSEC005.1">32.5.1</a> <dt>EquivalenceRelationByPartitionNC <a href="CHAP032.htm#SSEC005.1">32.5.1</a> <dt>EquivalenceRelationByProperty <a href="CHAP032.htm#SSEC005.4">32.5.4</a> <dt>EquivalenceRelationByRelation <a href="CHAP032.htm#SSEC005.2">32.5.2</a> <dt>EquivalenceRelationPartition <a href="CHAP032.htm#SSEC006.1">32.6.1</a> <dt>ER <a href="CHAP018.htm#SSEC004.2">18.4.2</a> <dt>Error <a href="CHAP006.htm#SECT006">6.6</a> <a href="CHAP006.htm#SSEC006.1">6.6.1</a> <dt>ErrorCount <a href="CHAP006.htm#SECT007">6.7</a> <a href="CHAP006.htm#SSEC007.1">6.7.1</a> <dt>ErrorNoTraceBack <a href="CHAP006.htm#I10">6.4</a> <dt>errors, syntax <a href="CHAP006.htm#I5">6.1</a> <dt>ES <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>escaped characters <a href="CHAP026.htm#I3">26.1</a> <dt>escaping non-special characters <a href="CHAP026.htm#I21">26.1</a> <dt>ET <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>EU <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>Euclidean Rings <a href="CHAP054.htm#SECT006">54.6</a> <dt>EuclideanDegree <a href="CHAP054.htm#SSEC006.2">54.6.2</a> <dt>EuclideanQuotient <a href="CHAP054.htm#SSEC006.3">54.6.3</a> <dt>EuclideanRemainder <a href="CHAP054.htm#SSEC006.4">54.6.4</a> <dt>Euler's totient function <a href="CHAP015.htm#I4">15.1</a> <dt>EulerianFunction <a href="CHAP037.htm#SSEC016.3">37.16.3</a> <dt>EulerianFunctionByTom <a href="CHAP068.htm#SSEC009.9">68.9.9</a> <dt>EV <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>EvalStraightLineProgElm <a href="CHAP035.htm#SSEC009.4">35.9.4</a> <dt>EvalString <a href="CHAP026.htm#SSEC007.3">26.7.3</a> <dt>evaluation <a href="CHAP004.htm#I5">4.7</a> <dt>evaluation, strings <a href="CHAP026.htm#I23">26.7</a> <dt>EW <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>EX <a href="CHAP018.htm#SSEC004.3">18.4.3</a> <dt>ExactSizeConsiderFunction <a href="CHAP037.htm#SSEC021.5">37.21.5</a> <dt>Exec <a href="CHAP011.htm#SECT002">11.2</a> <a href="CHAP011.htm#SSEC002.1">11.2.1</a> <dt>execution <a href="CHAP004.htm#I30">4.13</a> <dt>exit <a href="CHAP006.htm#I14">6.8</a> <dt>Expanded form of monomials <a href="CHAP064.htm#I1">64.20</a> <dt>Expert Windows installation <a href="CHAP073.htm#SECT017">73.17</a> <dt>Exponent <a href="CHAP037.htm#SSEC016.2">37.16.2</a> <dt>Exponent, for character tables <a href="CHAP069.htm#I13">69.8</a> <dt>exponent, of the prime residue group <a href="CHAP015.htm#I7">15.1</a> <dt>exponentiation, operation <a href="CHAP030.htm#SSEC012.1">30.12.1</a> <dt>ExponentOfPcElement <a href="CHAP043.htm#SSEC005.2">43.5.2</a> <dt>Exponents of Special Products <a href="CHAP043.htm#SECT006">43.6</a> <dt>ExponentsConjugateLayer <a href="CHAP043.htm#SSEC006.1">43.6.1</a> <dt>ExponentsOfCommutator <a href="CHAP043.htm#SSEC006.4">43.6.4</a> <dt>ExponentsOfConjugate <a href="CHAP043.htm#SSEC006.3">43.6.3</a> <dt>ExponentsOfPcElement <a href="CHAP043.htm#SSEC005.3">43.5.3</a> <dt>ExponentsOfRelativePower <a href="CHAP043.htm#SSEC006.2">43.6.2</a> <dt>ExponentSumWord <a href="CHAP035.htm#SSEC004.2">35.4.2</a> <dt>ExponentSyllable <a href="CHAP035.htm#SSEC005.2">35.5.2</a> <dt>Expressing Group Elements as Words in Generators <a href="CHAP037.htm#SECT005">37.5</a> <dt>Expressions <a href="CHAP004.htm#SECT007">4.7</a> <dt>ExtendedPcgs <a href="CHAP043.htm#SSEC007.8">43.7.8</a> <dt>ExtendStabChain <a href="CHAP041.htm#SSEC010.4">41.10.4</a> <dt>Extension <a href="CHAP044.htm#SSEC008.5">44.8.5</a> <dt>ExtensionNC <a href="CHAP044.htm#SSEC008.5">44.8.5</a> <dt>ExtensionRepresentatives <a href="CHAP044.htm#SSEC008.9">44.8.9</a> <dt>Extensions <a href="CHAP044.htm#SSEC008.4">44.8.4</a> <dt>Extensions of the p-adic Numbers <a href="CHAP066.htm#SECT002">66.2</a> <dt>ExteriorCentre <a href="CHAP037.htm#SSEC024.4">37.24.4</a> <dt>ExteriorPowerOfAlgebraModule <a href="CHAP061.htm#SSEC014.2">61.14.2</a> <dt>External Representation for Nonassociative Words <a href="CHAP034.htm#SECT005">34.5</a> <dt>External representation of polynomials <a href="CHAP064.htm#I2">64.20</a> <dt>External Sets <a href="CHAP039.htm#SECT011">39.11</a> <dt>ExternalOrbit <a href="CHAP039.htm#SSEC011.9">39.11.9</a> <dt>ExternalOrbits <a href="CHAP039.htm#SSEC011.11">39.11.11</a> <dt>ExternalOrbitsStabilizers <a href="CHAP039.htm#SSEC011.12">39.11.12</a> <dt>ExternalSet <a href="CHAP039.htm#SSEC011.2">39.11.2</a> <dt>ExternalSubset <a href="CHAP039.htm#SSEC011.7">39.11.7</a> <dt>Extract <a href="CHAP070.htm#SSEC010.5">70.10.5</a> <dt>ExtraspecialGroup <a href="CHAP048.htm#SSEC001.6">48.1.6</a> <dt>ExtRepDenominatorRatFun <a href="CHAP064.htm#SSEC020.3">64.20.3</a> <dt>ExtRepNumeratorRatFun <a href="CHAP064.htm#SSEC020.2">64.20.2</a> <dt>ExtRepOfObj, external representation, for cyclotomics <a href="CHAP018.htm#SSEC001.10">18.1.10</a> <dt>ExtRepPolynomialRatFun <a href="CHAP064.htm#SSEC020.6">64.20.6</a> <dt>EY <a href="CHAP018.htm#SSEC004.3">18.4.3</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>
