# The GAP 4 Manual - Full Index E

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

E R 18.1.1
e_N R 18.4
EANormalSeriesByPcgs R 43.11.4
Earns R 39.9.6
EB R 18.4.1
EC R 18.4.1
Echelonized Matrices R 24.9
ED R 18.4.1
Edit R 6.9.1
Editing Files R 6.9
Editor Support R 6.10
EE R 18.4.1
EF R 18.4.1
Efficiency of Homomorphisms R 38.3
EG R 18.4.1
EggBoxOfDClass R 49.5.6
EH R 18.4.1
EI R 18.4.2
Eigenspaces R 24.7.4
Eigenvalues R 24.7.3
EigenvaluesChar R 70.8.19
Eigenvectors R 24.7.5
Eigenvectors and eigenvalues R 24.7
EJ R 18.4.4
EK R 18.4.4
EL R 18.4.4
element test, for lists R 21.8.1
Elementary Divisors R 24.8
Elementary Operations for a Pcgs R 43.4
Elementary Operations for a Pcgs and an Element R 43.5
Elementary Operations for Integers R 14.1
Elementary Operations for Rationals R 16.1
Elementary Tietze Transformations R 46.8
ElementaryAbelianGroup R 48.1.4
ElementaryAbelianSeries R 37.17.9
ElementaryAbelianSeriesLargeSteps R 37.17.9
ElementaryDivisorsMat R 24.8.1
ElementaryDivisorsMatDestructive R 24.8.1
ElementOfFpGroup R 45.3.5
ElementOfFpSemigroup R 51.3.5
ElementOfMagmaRing R 63.2.5
ElementOrdersPowerMap R 71.1.3
ElementProperty R 41.11.2
Elements R 28.2.10
elements, definition R 12.2
elements, of a list or collection R 28.2
Elements T 9.4
elements T 2.6
Elements as equivalence classes R 12.2
Elements in Algebraic Extensions R 65.2
Elements of Finitely Presented Groups T 9.16
Elements of Free Magma Rings R 63.2
Elements of pc groups R 44.2
Elements with Prescribed Images R 39.5
ElementsFamily R 28.1.3
ElementsFamily P 3.6.3
ElementsStabChain R 41.9.9
elif R 4.16
EliminatedWord R 35.4.6
EliminationOrdering R 64.16.10
ElmWPObj E 7.3 E 7.3.1
else R 4.16
EM R 18.4.4
emacs R 6.10
email addresses T 1.5
Embedding R 31.1.10
Embedding, example for direct products R 47.1
Embedding, example for semidirect products R 47.2
Embedding, example for wreath products R 47.4
Embedding, for group products R 47.5.1
Embedding, for Lie algebras R 61.1
Embedding, for magma rings R 63.3
embeddings, find all R 38.9
Embeddings and Projections for Group Products R 47.5
EmptyBinaryRelation R 32.1.4
EmptyMatrix R 24.4.3
EmptySCTable R 60.3.1
EmptyStabChain R 41.10.7
EnableAttributeValueStoring R 13.6.6
End R 59.9.6
end R 4.22
Enforcing Property Tests P 4.3
Enlarging Internally Represented Lists R 21.9
Enumerator R 28.2.2
enumerator T 5.2
EnumeratorByBasis R 59.5.5
EnumeratorByFunctions R 28.2.4
Enumerators R 21.23
EnumeratorSorted R 28.2.3
environment R 4.22
EpimorphismFromFreeGroup R 37.5.1
EpimorphismNilpotentQuotient R 45.13.4
EpimorphismPGroup R 45.13.3
EpimorphismQuotientSystem R 45.13.2
epimorphisms, find all R 38.9
EpimorphismSchurCover R 37.24.1
equality, associative words R 35.3.1
equality, elements of finitely presented groups R 45.2.1
equality, nonassociative words R 34.2.1
equality, of records R 27.4.1
equality, operation R 30.11.1
equality, pcwords R 44.2.1
Equality and Comparison of Domains R 30.2
equality test R 4.11.1
equality test, for permutations R 40.1.1
equivalence class R 32.7
Equivalence Classes R 32.7
equivalence relation R 32.2 R 32.5
Equivalence Relations R 32.5
EquivalenceClasses, attribute R 32.7.3
EquivalenceClassOfElement R 32.7.4
EquivalenceClassOfElementNC R 32.7.4
EquivalenceClassRelation R 32.7.2
EquivalenceRelationByPairs R 32.5.3
EquivalenceRelationByPairsNC R 32.5.3
EquivalenceRelationByPartition R 32.5.1
EquivalenceRelationByPartitionNC R 32.5.1
EquivalenceRelationByProperty R 32.5.4
EquivalenceRelationByRelation R 32.5.2
EquivalenceRelationPartition R 32.6.1
ER R 18.4.2
Error R 6.5 R 6.5.1
ErrorCount R 6.6 R 6.6.1
ErrorNoTraceBack R 6.3
errors, syntax R 6.1
ES R 18.4.3
escaped characters R 26.1
escaping non-special characters R 26.1
ET R 18.4.3
EU R 18.4.3
Euclidean Rings R 54.6
EuclideanDegree R 54.6.2
EuclideanQuotient R 54.6.3
EuclideanRemainder R 54.6.4
Euler's totient function R 15.1
EulerianFunction R 37.16.3
EulerianFunctionByTom R 68.9.9
EV R 18.4.3
EvalStraightLineProgElm R 35.9.4
EvalString R 26.7.3
evaluation R 4.7
evaluation, strings R 26.7
EW R 18.4.3
EX R 18.4.3
ExactSizeConsiderFunction R 37.21.5
Example -- Constructing Enumerators P 3.12
Example -- Constructing Iterators P 3.13
Example: Groups with a decomposition as semidirect product P 4.11
Example: Groups with a word length P 4.10
Example: M-groups P 4.9
Examples, Lists, and Verbatim E 2.7
Examples of Extending the System P 4.0
Exec R 11.2 R 11.2.1
execution R 4.13
exit R 6.7
Expanded form of monomials R 64.20
Expert Windows installation R 73.17
Exponent R 37.16.2
Exponent, for character tables R 69.8
exponent, of the prime residue group R 15.1
exponentiation, operation R 30.12.1
ExponentOfPcElement R 43.5.2
Exponents of Special Products R 43.6
ExponentsConjugateLayer R 43.6.1
ExponentsOfCommutator R 43.6.4
ExponentsOfConjugate R 43.6.3
ExponentsOfPcElement R 43.5.3
ExponentsOfRelativePower R 43.6.2
ExponentSumWord R 35.4.2
ExponentSyllable R 35.5.2
Expressing Group Elements as Words in Generators R 37.5
Expressions R 4.7
ExtendedGroup N 5.1.2
ExtendedPcgs R 43.7.8
Extending the Range of Definition of an Existing Operation P 4.2
ExtendSchreierTransversal N 4.2.6
ExtendSchreierTransversalShortCube N 4.2.7
ExtendSchreierTransversalShortTree N 4.2.8
ExtendStabChain R 41.10.4
Extension R 44.8.5
ExtensionNC R 44.8.5
ExtensionRepresentatives R 44.8.9
Extensions R 44.8.4
Extensions of the p-adic Numbers R 66.2
ExteriorPowerOfAlgebraModule R 61.14.2
External Representation P 3.15
External Representation for Nonassociative Words R 34.5
External representation of polynomials R 64.20
external set T 5.2
External Sets R 39.11
ExternalOrbit R 39.11.9
ExternalOrbits R 39.11.11
ExternalOrbitsStabilizers R 39.11.12
ExternalSet R 39.11.2
ExternalSet E 6.3
ExternalSubset R 39.11.7
Extract R 70.10.5
ExtraspecialGroup R 48.1.6
ExtRepDenominatorRatFun R 64.20.3
ExtRepNumeratorRatFun R 64.20.2
ExtRepOfObj, external representation, for cyclotomics R 18.1.10
ExtRepOfObj P 3.15.1
ExtRepPolynomialRatFun R 64.20.6
EY R 18.4.3

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