The GAP Manual -- Index

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

69.0
$D_n$ lattices 50.40
$e_N$ 13.12
$f_N$ 13.12
$g_N$ 13.12
$h_N$ 13.12
$i_N$ 13.12
$j_N$ 13.12
$k_N$ 13.12
$l_N$ 13.12
$m_N$ 13.12
$n_k$ 13.12
$r_N$ 13.12
$s_N$ 13.12
$t_N$ 13.12
$u_N$ 13.12
$v_N$ 13.12
$w_N$ 13.12
$x_N$ 13.12
$y_N$ 13.12
'/' for character tables 48.9
.gaprc 55.4 55.8 55.16
2-groups 37.8
3-groups 37.9
4.2BSD 55.2
4.3BSD 55.2
AbelianComponent 69.5
AbelianGroup 37.1
AbelianGroup for ag groups 25.9
AbelianInvariants for character tables 48.8
AbelianInvariants for finitely presented groups 23.3
AbelianInvariantsNormalClosureFpGroup 23.3
AbelianInvariantsNormalClosureFpGroupRrs 23.3
AbelianInvariantsSubgroupFpGroup 23.3
AbelianInvariantsSubgroupFpGroupMtc 23.3
AbelianInvariantsSubgroupFpGroupRrs 23.3
absolute value of an integer 10.7
abstract word 22.0
AbstractWordTietzeWord 23.8
accessing list elements 27.4
accessing record elements 45.1
Actor for cat1-groups 73.126
Actor for xmods 73.122
ActorSquare for cat1s 73.114
ActorSquare for xmods 73.114
add an element to a list 27.7
add an element to a set 28.4
add elements to a list 27.8
add the elements of a list 27.37
AddBase for vector space 9.7
AddGenerator 23.9
AddOriginalEqnsRWS 66.2
AddRelator 23.9
Ag Groups 25.0
AG system 24.1
Ag Words 24.0
Agemo for character tables 48.8
AgGroup for Permutation Groups 21.21
AgGroupQClass 37.13
Algebra for MeatAxe Matrices 68.7
AllIrreducibleSolvableGroups 37.10
AllPrimitiveGroups 37.5
AllSmallGroups 37.14
AllSolvableGroups 37.7
AllThreeGroups 37.9
AllTransitiveGroups 37.6
AllTwoGroups 37.8
AlternatingGroup 37.1
and 44.2
append elements to a list 27.8
append one string to another 30.2
append to a file 3.16
Apple 55.9
AsGroup for ag groups 25.9
assignment to a list 27.6
assignment to a record 45.2
assignment variable 2.12
Associates for gaussians 14.7
associativity 2.10
Atari ST 55.13
atomic irrationalities 13.12
augmented coset table 23.11 23.11
Automata 66.6
automatic groups program 66.6
automorphism group of a character table 48.42
automorphism group of a field 6.7
automorphism group of a matrix 48.41
automorphism group of an extension field 16.8
automorphism group of number fields 15.8
AutomorphismPermGroup for groups 73.141
AutomorphismPermGroup for xmods 73.117
Automorphisms for character tables 48.8
automorphisms of p groups 57.6 57.8
backslash 30.0
Base for MeatAxe Modules 68.19
Base of vector space 9.6
base of vector space 32.0
blank 2.3
Blocks for Permutation Groups 21.22
BNF 2.20
body 2.18
bound 2.7
Bounds Elias 65.115
Bounds Griesmer 65.116
Bounds Hamming 65.112
Bounds Johnson 65.113
Bounds Plotkin 65.114
Bounds Singleton 65.111
Bounds Sphere packing bound 65.112
Bounds UpperBound 65.117
Brauer tables format 48.3
BrauerTableOps 48.7
BSD 55.2
CallPCQA 69.3
CallVE 72.2
candidates for permutation characters 50.26 50.27
Canonical basis 71.3
Carmichaels lambda function 11.3
Cartan matrices 75.1
Cartan matrices type of 75.2
Cartesian product 48.17
CAS tables,CAS format,CAS 48.54
Centralizer for ag groups 25.9
Centralizer for matrix groups 36.2
Centralizer for Permutation Groups 21.21
centralizer in $GL(d,\Z)$ 60.24
Centre for class functions 53.4
Centre for character tables 48.8
Centre for xmods 73.124
character table display 48.37
character tables 48.11
character tables access to 48.12
character tables calculate 48.12
character tables CAS 52.4
character tables computation 48.13
character tables conventions 48.10
character tables format 48.2
character tables generic 49.2
character tables libraries of 52.1
character tables of groups 48.12
character tables sort 48.38 48.39 48.40
character permutation 7.66
CharacterDegrees for character tables 48.8
characteristic polynom of a field element 6.9
characteristic of a finite field element 18.5
CharacteristicPolynomial for MeatAxe matrices 68.7
Characters of Finite Polycyclic Groups 48.26
characters induce from cyclic subgroups 50.23
characters induced 50.22
characters inflated 50.21
characters irreducible differences of 50.19
characters permutation 50.26 50.27
characters reduced 50.10 50.11
characters restricted 50.20
characters scalar product of 50.1 50.2
characters sort 48.38
characters symmetrisations of 50.13 50.14 50.15 50.16
Characters table of inductions 86.1
characters tensor products of 50.12
CharTableOps 48.7
CharTableQClass 37.13
chinese remainder 10.9
ChooseRandomElements 67.52
class functions 51.1
class multiplication coefficient 48.30 48.31 48.32
class names 48.29
classes collapse 50.24
classes of cyclic subgroup 48.34
classes real 48.33
classes roots of 48.35
clone an object 45.11 45.12
coefficient binomial 46.2
Coefficients in vector space 9.10
colorings inequivalent!for space groups 60.40
CombinatoricSplit 48.13
Comm for group elements 7.3
Comm for words 22.4
comments 2.3
CommutatorFactorGroup for finitely presented groups 23.3
Commutators 67.52
CommutatorSubgroup for ag groups 25.9
comparison of double cosets 7.95
comparison of right cosets 7.87
comparisons of booleans 44.1
comparisons of finite field elements 18.2
comparisons of integers 10.1
comparisons of lists 27.12
comparisons of polynomials 19.5
comparisons of rationals 12.4
comparisons of strings 30.4
Composite for derivations 73.99
Composite for morphisms of cat1-groups 73.71
Composite for morphisms of crossed modules 73.45
Composite for sections 73.100
CompositionFactors for MeatAxe Modules 68.20
CompositionMapping for Frobenius automorphisms 18.11
CompositionMapping for GroupHomomorphismByImages 7.112
CompositionMapping for GroupHomomorphismByImages for permutation groups 21.23
CompositionSeries for Permutation Groups 21.21
concatenation of lists 27.19
concatenation of strings 30.2
ConjugacyClasses for ag groups 25.9
ConjugacyClasses for matrix groups 36.2
Conjugate Subgroup of Permutation Group 21.21
conjugate of a group 7.116
conjugate of a group element 7.3
conjugate of a word 22.4
Conjugates for finite fields 18.13
Conjugates for gaussians 14.6
conjugates of a field element, Galois 6.12
ConjugateSubgroup for ag groups 25.9
convert a finite field element to an integer 18.8
convert to a list 27.2
convert to a set 28.2
convert to a string 30.1
convert to an integer 10.6
copy an object 45.11 45.12
Coset 7.85
coset double 7.93 7.94
Coset for Permutation Groups 21.21
coset left 7.90 7.91
coset right 7.85 7.86
cosets double 7.92
Cosets for Permutation Groups 21.21
cosets left 7.89
cosets right 7.84
counting and enumerating irreducible words 66.8
Coxeter Groups name of 75.3
cross product of lists 27.23
crystallographic groups 37.13
CrystGroup conjugated 60.10
CrystGroups other functions 60.29
CyclicGroup 37.1
CyclicGroup for ag groups 25.9
DadeGroup 37.13
DadeGroupNumbersZClass 37.13
data type unknown 17.0
DEC 50.3
decomposition matrix 50.3
decomposition of polynomials 16.18
DecompositionInt 50.4
DecompositionMatrix TeX 71.5
default field for cyclotomics 15.5
default functions 4.2
default ring for cyclotomic integers 15.6
DefaultField for algebraic extensions 16.10
defect 16.15
Degree for class functions 53.4
degree of a finite field element 18.6
denominator of a rational 12.3
Derivations all 73.90
Derivations regular 73.89
DerivedSeries for ag groups 25.9
DerivedSubgroup for character tables 48.8
Determinant for characters 53.4
difference of algebra elements 38.26
difference of gaussians 14.2
difference of list and algebra element 38.26
difference of records 45.5
DihedralGroup 37.1
Dimension for MeatAxe Modules 68.19
Dimension of vector space 9.8
dimension of vector space 32.0
Dimensions for MeatAxe matrices 68.7
direct product 48.17
DirectProduct for ag groups 25.9
DirectProduct for groups 7.99
DirectProduct for Permutation Groups 21.21
DirectProduct for xmods 73.28
DirectProductPermGroupCentralizer 21.21
DirectProductPermGroupCentre 21.21
DirectProductPermGroupSylowSubgroup 21.21
discrete logarithm of a finite field element 18.9
dispatcher functions 4.2
Display for MeatAxe matrices 68.7
Display for MeatAxe Permutations 68.12
Display for character tables 48.8
DisplayCrystalFamily 37.13
DisplayCrystalSystem 37.13
DisplayImfInvariants 37.12
DisplayInformationPerfectGroups 37.11
DisplayMat 67.52
DisplayQClass 37.13
DisplaySpaceGroupGenerators 37.13
DisplaySpaceGroupType 37.13
DisplayZClass 37.13
divisors of an integer 10.21
Dixon Schneider 48.12
DixonInit 48.13
DixonSplit 48.13
DixontinI 48.13
DnLatticeIterative 50.40
do 2.17
domain record for right cosets 7.88
DoubleCosetGroupOps 7.95
doublequotes 30.0
Dynkin Diagrams 75.4
E 13.1
EAbacus 71.44
EB 13.12
EC 13.12
ED 13.12
EE 13.12
EF 13.12
EG 13.12
EH 13.12
EI 13.12
EJ 13.12
EK 13.12
EL 13.12
ElementaryAbelianGroup 37.1
ElementaryAbelianGroup for ag groups 25.9
ElementaryAbelianSeries for ag groups 25.9
ElementaryAbelianSeries for character tables 48.8
ElementaryAbelianSeries for Permutation Groups 21.21
ElementOfOrder 67.52
Elements for ag groups 25.5
Elements for cat1-groups 73.55
Elements for Conjugacy Classes 7.71
Elements for conjugacy classes of subgroups 7.77
Elements for double cosets 7.95
Elements for finite fields 18.12
Elements for finitely presented groups 23.2
Elements for groups 7.113
Elements for Permutation Groups 21.20
Elements for right cosets 7.87
Elements for vector spaces 9.4
Elements for xmods 73.18
elements of a domain 4.6
ElementWithCharPol 67.52
elif 2.14
else 2.14
EM 13.12
Embedding into direct products 7.98
Embedding into semidirect products 7.100
embeddings of lattices 50.36
end 2.18
EnumerateRWS 66.8
environment 2.18
equality for field homomorphisms 6.16
equality of ag words 24.2
equality of algebra elements 38.26
equality of gaussians 14.1
equality of group elements 7.2
equality of group homomorphisms 7.108
equality of records 45.4
ER 13.12
errors syntax 3.1
ES 13.12
ET 13.12
EU 13.12
EuclideanDegree for gaussians 14.7
EuclideanDegree for polynomials 19.18 19.19
EuclideanQuotient for gaussians 14.7
EuclideanQuotient for polynomials 19.18
EuclideanRemainder for gaussians 14.7
EuclideanRemainder for polynomials 19.18
Eulers totient function 11.2
EV 13.12
EvaluateRelation 67.36
evaluation 2.6
EW 13.12
EX 13.12
execution 2.11
Exponent for character tables 48.8
exponent of the prime residue group 11.3
ExponentsPermSolvablePermGroup 21.21
ExtendPCQA 69.4
EY 13.12
factor group table of 48.15
Factor for xmods 73.40
FactorGroup for ag groups 25.58
factorization of an integer 10.20
Factors for gaussians 14.7
Factors for polynomials 19.18 19.19
features under MS-DOS 55.8
features under TOS 55.16
features under UNIX 55.4
fi 2.14
Field Extensions 16.0
field homomorphisms Frobenius 18.11
field homomorphisms of algebraic extensions 16.9
field finite 18.0
Field for algebraic extensions 16.10
field for cyclotomics 15.5
field galois 18.0
file append to a 3.16
file load a 3.12
file load a library 3.13
file log input to a 3.18
file log to a 3.17
file print to a 3.15
file read a 3.12
file read a library 3.13
find an element in a list 27.15
find an element in a sorted list 27.16 27.17
Fingerprint for MeatAxe Matrix Algebras 68.16
finiteness test for domains 4.9
FittingSubgroup for character tables 48.8
Fock space 71.3
for 2.17
for loop 2.17
FpAlgebraOps.OperationQuotientModule 72.2
FpGroup for ag groups 25.9
FpGroup for CrystGroups 60.12
FpGroup for point groups 60.11
FpGroup for space groups 37.13
FpGroupPresentation 23.8
FpGroupQClass 37.13
FpGroupToRWS 66.1
Frame 50.17
FrattiniSubgroup for character tables 48.8
Frobenius Schur indicator 50.7
ftp 55.1
function 2.18
fusion map get 48.45
fusion of classes 48.22
fusion store 48.46
FusionConjugacyClasses for character tables 48.8
Galois 16.16
Galois conjugates of a field element 6.12
galois field 18.0
Galois group of a field 6.7
Galois group of an extension field 16.8
GaloisGroup for finite fields 18.13
GAP for MS-DOS 55.5
gap.rc 55.8 55.16
Gcd for polynomials 19.18 19.19
GeneralLinearGroup 37.1
GeneralUnitaryGroup 37.1
generator of the prime residue group 11.5 11.6
generic character tables 48.11 52.0
GenericParameters 67.23
GF 18.10
GoodNodeSequences 71.34
Group for MeatAxe Matrices 68.7
group homomorphisms by images 7.112
group homomorphisms conjugation 7.110
group homomorphisms inner 7.111
group homomorphisms natural 7.109
group homomorphisms operation 8.19
Group for ag groups 25.9
GroupHomomorphismsByImages for permutation groups 21.23
H.Ordering Specht 71.5
Hecke algebras crystal decomposition matrix 71.6
Hecke algebras decomposition matrix 71.5
Hecke Specht 71.1
help abbreviating 3.10
help browsing 3.8
help format 3.7
help index 3.11
help redisplaying 3.9
help scrolling 3.6
HirschLength 69.6
homomorphisms by images, group 7.112
homomorphisms conjugation, group 7.110
homomorphisms Frobenius, field 18.11
homomorphisms inner, group 7.111
homomorphisms natural, group 7.109
homomorphisms of algebras 38.24
homomorphisms of fields 6.13
homomorphisms of groups 7.105
homomorphisms operation, group 8.19
HP-UX 55.2
ideal decomposition 16.18
IdGroup 37.14
IdWord 22.0
if 2.14
if statement 2.14
Image for a derivation 73.80
Image for blocks homomorphisms 21.23
Image for field homomorphisms 6.16
Image for Frobenius automorphisms 18.11
Image for group homomorphisms 7.108
Image for GroupHomomorphismByImages 7.112
Image for GroupHomomorphismByImages for permutation groups 21.23
Image for OperationHomomorphism 8.19
Image for transitive constituent homomorphisms 21.23
Image for xmod morphisms 73.42
Images for a derivation 73.81
Images for field homomorphisms 6.16
Images for group homomorphisms 7.108
ImagesRepresentative for GroupHomomorphismByImages 7.112
ImfInvariants 37.12
ImfMatGroup 37.12
ImfNumberQClasses 37.12
ImfNumberQZClasses 37.12
ImfNumberZClasses 37.12
in for ag groups 25.5
in for algebraic Elements 16.5
in for Conjugacy Classes 7.71
in for conjugacy classes of subgroups 7.77
in for domains 4.8
in for finite fields 18.12
in for finitely presented groups 23.2
in for gaussians 14.5
in for matrix groups 36.1
in for records 45.6
IncludeIrreducibles 48.13
InclusionMorphism for cat1-groups 73.74
InclusionMorphism for groups 73.132
InclusionMorphism for xmods 73.37
Index for finitely presented groups 23.3
Induced for character tables 48.8
InfoLattice1 7.74
initialize classlengths 48.27
InnerActor for xmods 73.125
InnerAutomorphism for xmods 73.10 73.43
InnerAutomorphismGroup for groups 73.137
InnerDerivations list 73.83
InnerMorphism for xmods 73.123
installation 55.0
installation under MS-DOS 55.7
installation under TOS 55.15
installation under UNIX 55.3
installation under Windows 55.7
integer part of a quotient 10.3
IntegralizedMat 50.4
Intersection for MeatAxe Modules 68.18
Intersection for ag groups 25.5
Intersection for double cosets 7.95
Intersection for finite fields 18.12
Intersection for finitely presented groups 23.2
Intersection for groups 7.113
Intersection for matrix groups 36.1
Intersection for Permutation Groups 21.20
Intersection for right cosets 7.87
intersection of domains 4.12
intersection of sets 28.7 28.9
Intersection of vector spaces 9.4
InverseMapping for GroupHomomorphismByImages 7.112
InverseMatMod 50.4
irreducible maximal finite integral matrix groups 37.12
IrreducibleSolvableGroup 37.10
IsAbelian for character tables 48.8
IsAbsolutelyIrreducible for MeatAxe Modules 68.20
IsAssociated for gaussians 14.7
IsAutomorphism for crossed modules 73.33
IsAvailableNormalForm 66.2
IsAvailableReductionRWS 66.2
IsConfluentRWS 66.2
IsCoset 7.86
IsCyclic for ag groups 25.9
IsCyclic for character tables 48.8
IsDiagonal 67.52
IsEndomorphism for crossed modules 73.33
IsEpimorphism for crossed modules 73.33
IsEquivalent for MeatAxe Modules 68.20
IsExtensionField 67.23
IsFinite for ag groups 25.9
IsFinite for double cosets 7.95
IsFinite for right cosets 7.87
IsFinite for vector spaces 9.4
IsFpAlgebraElement 39.9
IsGeneric 67.23
IsGenericNearlySimple 67.23
IsHomomorphism for fields 6.14
IsHomomorphism for groups 7.106
IsInjective for field homomorphisms 6.16
IsInjective for group homomorphisms 7.108
IsIrreducible for MeatAxe Modules 68.20
IsIrreducible for gaussians 14.7
IsIsomorphism for crossed modules 73.33
IsMapping for GroupHomomorphismByImages 7.112
IsMapping for GroupHomomorphismByImages for permutation groups 21.23
IsMonomial for characters 54.11
IsMonomial for group orders 54.11
IsMonomial for groups 54.11
IsMonomorphism for crossed modules 73.33
IsNilpotent for ag group 25.9
IsNilpotent for character tables 48.8
IsNormal for ag groups 25.9
IsNormal for xmods 73.38
isoclinic table 48.20
IsPerfect for ag group 25.9
IsPrime for gaussians 14.7
IsQuasiPrimitive 54.6
IsReducedWordRWS 66.7
IsRModule for xmods 73.26
IsRWS 66.2
IsScalar 67.52
IsSemiRegular for Permutation Groups 21.22
IsSimple for character tables 48.8
IsSolvable for character tables 48.8
IsSolvable for Permutation Groups 21.21
IsSubgroup for ag groups 25.9
IsSubnormallyMonomial 54.9
IsSubset for ag groups 25.5
IsSubset for groups 7.113
IsSubset for sets 28.9
IsSupersolvable for character tables 48.8
IsSurjective for field homomorphisms 6.16
IsSurjective for group homomorphisms 7.108
IsTrivial for groups 7.64
IsUnit for gaussians 14.7
IsUnit for matrix rings 35.2
IsWyckoffPosition 60.17
iterate a function over a list 27.40
KB 66.5
kbmag 66.0
Kernel for class functions 53.4
Kernel for blocks homomorphisms 21.23
Kernel for fields 6.15
Kernel for groups 7.107
Kernel for OperationHomomorphism 8.19
Kernel for xmod morphisms 73.41
Knuth-Bendix 66.5
Kronecker product 48.17
KroneckerFactors 67.12
KroneckerProduct for MeatAxe matrices 68.7
KroneckerProduct for MeatAxe Modules 68.20
larger prime 10.18
LargestPrimeOrderElement 67.52
LargestPrimePowerOrderElement 67.52
last 3.1
lattice base reduction 50.33 50.34 50.35
Lattice for MeatAxe Modules 68.20
LeftNormedComm for group elements 7.3
LeftQuotient for group elements 7.3
LeftQuotient for words 22.4
length of a list 27.5
length of a string 30.6
length of a word 22.6
libraries of character tables 52.1
library of character tables 52.3 52.4 52.5
library tables 48.11 52.0
library tables generic 49.0
LinearCombination in vector space 9.9
LinearIndependentColumns 50.4
List for InverseDerivations 73.104
list of primes 10.15
ListERegulars 71.59
Lists sublist 86.10
LLL algorithm for characters 50.35
LLL algorithm for Gram matrices 50.34
LLL algorithm for vectors 50.33
load a file 3.12
load a library file 3.13
local 2.18
log input to a file 3.18
log to a file 3.17
logarithm of an integer 10.10
logarithm of a finite field element, discrete 18.9
logical 44.0
logical operations 44.2
loop for 2.17
loop read eval print 3.1
loop repeat 2.16
loop while 2.15
LowerCentralSeries for ag groups 25.9
LowerCentralSeries for character tables 48.8
Macintosh 55.9
MacOS 55.9
map 27.2
map parametrized 51.1
MatGroupZClass 37.13
MathieuGroup 37.1
Matrices block decomposition of 86.6
Matrices direct sum of 86.5
matrix 34.0
matrix automorphisms 51.26 51.28
Matrix Representations of Finite Polycyclic Groups 48.25
MaximalNormalSubgroups for character tables 48.8
MaximalSubgroupsRepresentatives for CrystGroups 60.13
maximum of a list 27.38
maximum of integers 27.38
membership test for ag groups 25.5
membership test for algebraic extensions 16.5
membership test for domains 4.8
membership test for finite fields 18.12
membership test for gaussians 14.5
membership test for records 45.6
membershiptest for groups 7.116
mersenne primes 10.22
minimal polynom of a field element 6.8
minimum of a list 27.39
minimum of integers 27.39
MOC interface to 48.48 48.49 48.50 48.51 48.52 48.53
mod for character tables 48.9
Modified Todd-Coxeter 23.11
modular roots 11.10
Module for MeatAxe Matrix Algebras 68.16
ModuleAction 69.7
Moebius inversion function 10.24
Monomial Representations of Finite Polycyclic Groups 48.25
Morphism for cat1-groups 73.61
Morphism for xmods 73.29
MS-DOS features 55.8
MS-DOS installation 55.7
MS-DOS options 55.8
MSDOS 55.5
multiplicative order of an integer 11.4
multiply the elements of a list 27.36
multisets 28.0
Murnaghan components 50.17 50.18
Name for cat1-groups 73.51
Name for cat1-morphisms 73.63
Name for xmod morphisms 73.32
Name for xmods 73.7
NaturalModule for MeatAxe Matrix Algebras 68.16
newline 2.3
NilpotentQuotient 56.10
NK 13.12
NoMessageScalarProduct for character tables 48.8
Norm for class functions 53.4
Norm for algebraic extensions 16.10
Norm for finite fields 18.13
Norm for gaussians 14.6
norm of a field element 6.10
normal subgroup table of 48.16
NormalClosure for character tables 48.8
NormalIntersection for ag groups 25.9
NormalizedAutomorphisms 70.4
NormalizedOuterAutomorphisms 70.4
Normalizer for ag groups 25.9
Normalizer for finitely presented groups 23.3
Normalizer for matrix groups 36.2
Normalizer for Permutation Groups 21.21
normalizer in $GL(d,\Z)$ 60.23
normalizer in affine group 60.27
normalizer in translation group 60.26
NormalizerZClass 37.13
NormalSubgroups for character tables 48.8
not 44.2
NotifyCharTable 52.7
NrCombinations 46.6
NrCrystalFamilies 37.13
NrCrystalSystems 37.13
NrDadeGroups 37.13
NrDerangements 46.11
NrOrderedPartitions 46.14
NrPartitions 46.13
NrPartitionsSet 46.12
NrPermutationsList 46.10
NrQClassesCrystalSystem 37.13
NrRestrictedPartitions 46.15
NrSpaceGroupTypesZClass 37.13
NrTuples 46.9
NrUnorderedTuples 46.8
NrZClassesQClass 37.13
number fields Galois group 15.8
number Bell 46.3
number binomial 46.2
number of divisors of an integer 10.23
number of elements in a list 27.24
number Stirling, of the first kind 46.4
number Stirling, of the second kind 46.5
NumberPerfectGroups 37.11
NumberPerfectLibraryGroups 37.11
NumberSmallGroups 37.14
numerator of a rational 12.2
od 2.17
Omega for characters 53.4
OneIrreducibleSolvableGroup 37.10
OnePrimitiveGroup 37.5
OneSolvableGroup 37.7
OneThreeGroup 37.9
OneTwoGroup 37.8
OnLeft 8.1
OnLeftAntiOperation 8.1
OnLeftCosets 8.1
OnLeftInverse 8.1
OnLines 8.1
OnPairs 8.1
OnPoints 8.1
OnRight 8.1
OnRightCosets 8.1
OnSets 8.1
OnTuples 8.1
Operation for MeatAxe Matrix Groups 68.14
OperationHomomorphism for Modules 41.17
OperationHomomorphism for blocks 21.23
OperationHomomorphism for transitive constituents 21.23
OperationModule 41.17
Operations for algebraic elements 16.4
operations record 4.2
operations for booleans 44.2
operations for groups 7.116
operations for integers 10.2
operations for lists 27.13
operations for polynomials 19.6
operations for rationals 12.5
operations for vectors 32.1
operators for cyclotomics 13.10
options 55.0
options under MS-DOS 55.8
options under TOS 55.16
options under UNIX 55.4
or 44.2
Orbit for ag groups 25.9
OrbitMat 67.45
Order for MeatAxe matrices 68.7
Order for MeatAxe Permutations 68.12
Order for finitely presented groups 23.3
Order for xmod morphisms 73.44
order of a finite field element 18.7
order of a group element 7.5
order of the prime residue group 11.2
ordering of ag words 24.2
ordering of algebra elements 38.26
ordering of gaussians 14.1
ordering of group elements 7.2
ordering of group homomorphisms 7.108
ordering of records 45.4
OrthogonalEmbeddingsSpecialDimension 50.36
OuterAutomorphisms 70.4
output suppressing 3.1
p-regular table 48.19
PadicCoefficients 50.4
Pair for automorphism groups 73.139
Pair for FpGroups 73.142
Pair for semidirect groups 73.144
paramap 51.1
Parity check 65.87
part of a string 30.3
partitions 46.0
partitions improper, of an integer 46.14
partitions of a set 46.12
partitions of an integer 46.13
partitions ordered, of an integer 46.14
partitions restricted, of an integer 46.15
perfect groups 37.11
PerfectGroup 37.11
PermGroup for Imf matrix groups 37.12
PermGroup for matrix groups 36.2
PermGroup for perfect groups 37.11
PermGroupImfGroup 37.12
permutation character 51.19
permutation characters 50.31
permutation characters candidates for 50.26 50.27
permutation characters faithful candidates for 50.32
PermutationCharacter 21.21
permutations fixpointfree 46.11
permutations list 46.10
PointGroup for color CrystGroups 60.39
PointGroup of a CrystGroup 60.6
PolyhedralGroup 37.1
power of algebra elements 38.26
power of gaussians 14.2
power of group elements 7.3
power of records 45.5
power of words 22.4
powerset 46.6
precedence 2.10
PreImage for blocks homomorphisms 21.23
PreImage for field homomorphisms 6.16
PreImage for group homomorphisms 7.108
PreImage for OperationHomomorphism 8.19
PreImages for field homomorphisms 6.16
PreImages for group homomorphisms 7.108
PreImages for transitive constituent homomorphisms 21.23
PresentationFpGroup 23.8
PresentationNormalClosure 23.11
PresentationNormalClosureRrs 23.11
PresentationSubgroup 23.11
PresentationSubgroupMtc 23.11
PresentationSubgroupRrs 23.11
PresentationViaCosetTable 23.10
previous result 3.1
primary subgroup generators 23.11 23.11 23.14
prime residue group 11.0 11.1
prime residue group exponent 11.3
prime residue group generator 11.5 11.6
prime residue group order 11.2
primes mersenne 10.22
primitive element 16.3
primitive root modulo an integer 11.6
PrimitiveGroup 37.5
Print for cat1-group morphism 73.64
Print for cat1-groups 73.50
Print for character tables 48.8
Print for double cosets 7.95
Print for lists 73.146
Print for right cosets 7.87
Print for xmod morphisms 73.31
Print for xmods 73.5 73.16
print to a file 3.15
PrintClassSubgroupLattice 7.74 7.74
PrintLevelFlag 67.37
PrintToLib 52.7
product for double cosets 7.95
product for right cosets 7.87
product of a group and a group element 7.116
product of algebra elements 38.26
product of gaussians 14.2
product of group elements 7.3
product of list and algebra element 38.26
product of list and group element 7.3 22.4
product of records 45.5
product of words 22.4
Projection for subdirect products 7.102
Projection onto component of direct products 7.98
Projection onto component of semidirect products 7.100
ProjectiveOrderMat 67.47
prompt 3.1
prompt partial 3.1
quadratic number fields 13.14
quadratic residue 11.7 11.8 11.9
quotient of gaussians 14.2
quotient of group elements 7.3
quotient of groups 7.116
quotient of list and group element 7.3
quotient of list and word 22.4
quotient of records 45.5
quotient of words 22.4
QuotientGModule 67.24
QuotientRemainder for gaussians 14.7
QuotientRemainder for polynomials 19.18
random element of a domain 4.16
Random Methods for Permutation Groups 21.24
Random for ag groups 25.9
Random for algebraic Extensions 16.5
Random for Conjugacy Classes 7.71
Random for double cosets 7.95
Random for finite fields 18.12
Random for gaussians 14.5
Random for matrix groups 36.1
Random for Permutation Groups 21.20
Random for right cosets 7.87
RandomIrreducibleSubGModule 67.24
RandomOrders for MeatAxe Matrix Algebras 68.16
RandomOrders for MeatAxe Matrix Groups 68.14
RandomSeed 27.41
Rank for MeatAxe matrices 68.7
read eval print loop 3.1
read a file 3.12
read a library file 3.13
record fields for algebraic extension fields 16.11
record fields for extension elements 16.12
record operations 4.2
recursion 2.18
recursive functions 2.18
Reduced Reidemeister-Schreier 23.11
ReduceWordRWS 66.7
regular classes 48.19
remainder of a quotient 10.4
remove an element from a set 28.5
RemoveRelator 23.9
ReorderGeneratorsRWS 66.3
repeat 2.16
repeat loop 2.16
representation as a sum of two squares 14.8
representative of a domain 4.15
RepresentativeOperation for matrix groups 36.2
RepresentativeOperation for Permutation Groups 21.22
ResetRWS 66.2
residue quadratic 11.7 11.8 11.9
Restricted for character tables 48.8
return 2.19
reverse the elements of a list 27.21
rewriting systems control parameters 66.4
rewriting systems creating 66.1
rewriting systems elementary functions 66.2
rewriting systems examples 66.9
rewriting systems setting the ordering 66.3
RightCoset for ag groups 25.9
RightCosetGroupOps 7.87
RightNormedComm for group elements 7.3
ring for cyclotomic integers 15.6
root of 1 modulo an integer 11.10
root of an integer 10.11
root of an integer modulo another 11.9
root of an integer, smallest 10.12
roots of unity 13.1
Save for presentation records 23.8
ScalarProduct for character tables 48.8
scalars 32.0
Schreier-Sims Random 21.24
scope 2.7
secondary subgroup generators 23.11 23.11 23.14
Sections all 73.95
Sections regular 73.94
Select for cat1-groups 73.60
Select for xmods 73.14
selections 46.0
SemidirectProduct for groups 7.101
sequence bernoulli 46.22
sequence fibonacci 46.20
sequence lucas 46.21
set difference of domains 4.14
SetOrderingRWS 66.3
SetPrintLevel 7.74
SetPrintLevelFlag 67.37
short vectors spanning a lattice 50.33 50.35
sign of an integer 10.8
SimplifyPresentation 23.13
Size for MeatAxe Modules 68.18
Size for ag groups 25.5
Size for cat1-groups 73.54
Size for character tables 48.8
Size for Conjugacy Classes 7.71
Size for conjugacy classes of subgroups 7.77
Size for double cosets 7.95
Size for finitely presented groups 23.2
Size for matrix groups 36.1
Size for Permutation Groups 21.20
Size for right cosets 7.87
Size for xmods 73.17
size of a domain 4.10
Size of vector spaces 9.4
SizeEnumerateRWS 66.8
SizeNumbersPerfectGroups 37.11
SizeRWS 66.8
SizesConjugacyClasses for character tables 48.8
smaller prime 10.19
SmallGroup 37.14
SmallGroups 37.14
SolvableGroup 37.7
sort a list 27.30
SortEnumerateRWS 66.8
space 2.3
SpaceGroup 37.13
SpechtDirectory 71.5 71.19
special character sequences 30.0
SpecialLinearGroup 37.1
SpecialUnitaryGroup 37.1
split classes 48.21
SplitCharacters 48.13
SplittingField for MeatAxe Modules 68.20
Sq 56.4
square root of an integer 10.11
StabChainOptions 21.24
Stabilizer for ag groups 25.9
Stabilizer for matrix groups 36.2
Stabilizer for Permutation Groups 21.22
StandardAssociate for gaussians 14.7
StandardAssociate for polynomials 19.18 19.19
Stirling number of the first kind 46.4
Stirling number of the second kind 46.5
structure constant 48.30 48.31 48.32
SubGModule 67.24
subgroup and permutation character 50.28
subgroup fusions 48.45 48.46 51.19
subgroup generators tree 23.14
Subgroup for color groups 60.38
subgroups polyhedral 48.36
subset test for domains 4.11
subsets 46.6
substring of a string 30.3
subtract a set from another 28.8
sum of algebra elements 38.26
sum of divisors of an integer 10.22
sum of gaussians 14.2
sum of list and algebra element 38.26
sum of records 45.5
SumIntersectionSpaces for MeatAxe matrices 68.7
SunOS 55.2
SupersolvableResiduum for character tables 48.8
SylowSubgroup for ag groups 25.9
SylowSubgroup for matrix groups 36.2
SylowSubgroup for Permutation Groups 21.21
SymmetricGroup 37.1
symmetrizations orthogonal 50.17
symmetrizations symplectic 50.18
SymplecticGroup 37.1
syntax errors 3.1
System V 55.2
SysV 55.2
table automorphisms 51.22 51.25 51.27
table of factor group 48.15
table of normal subgroup 48.16
Table for derivations 73.92
Table for RangeEndomorphismDerivations 73.108
Table for SourceEndomorphismDerivations 73.106
Table for WhiteheadGroup 73.101
Table for WhiteheadMonoid 73.102
TableOfMarks 47.4
tables 48.0 48.11 52.0
tables add to a library 52.7
tables format 48.2 48.3
tables generic 49.0 49.3
tables libraries of 52.1
tables library 52.3 52.4 52.5
tables sort 48.38 48.39 48.40
tabulator 2.3
tensor product 48.17
test for sections record 73.96
test for a boolean 44.3
test for a derivation 73.79
test for a finite field element 18.4
test for a list 27.1
test for a power of a prime 10.17
test for a prime 10.16
test for a primitive root 11.5
test for a rational 12.1
test for a set 28.1
test for a string 30.5
test for a vector 32.2
test for algebra element 38.26
test for algebraic element 16.13
test for algebraic extension 16.2
test for an integer 10.5
test for asherical xmod 73.20
test for automorphism group 73.138
test for automorphism pair 73.140
test for automorphism xmod 73.23
test for cat1-group morphism 73.62
test for cat1-groups 73.49
test for central extension xmod 73.22
test for common transversal 73.150
test for conjugation xmod 73.19
test for derivations record 73.93
test for Fp-pair 73.143
test for gaussian integer 14.4
test for gaussian rational 14.3
test for group element 7.4
test for list elements 45.9
test for membership 27.14
test for normal extension 16.6
test for record elements 45.9
test for records 45.8
test for regular cat1-groups 73.87
test for regular xmods 73.87
test for RModules 73.12
test for sections 73.86
test for semidirect pair 73.145
test for set equality 28.3
test for simply connected xmod 73.21
test for sub-xmod 73.36
test for subsets 28.9
test for trivial action xmod 73.24
test for xmod morphism 73.30
test for xmods 73.4
test for zero boundary xmod 73.25
TeX DecompositionMatrix 71.5
then 2.14
ThreeGroup 37.9
Tietze options 23.13
TietzeWordAbstractWord 23.8
TOS 55.13
TOS features 55.16
TOS installation 55.15
TOS options 55.16
total length of a presentation 23.13
Trace for MeatAxe matrices 68.7
Trace for algebraic extensions 16.10
Trace for gaussians 14.6
trace of a field element 6.11
TransitiveGroup 37.6
TransitiveIdentification 37.6
TranslationsCrystGroup add translations 60.8
TranslationsCrystGroup check translations 60.9
Transposed for MeatAxe matrices 68.7
TransposedSpaceGroup 37.13
tree decoding 23.14
TwoGroup 37.8
type algebraic elements 16.4
type boolean 44.0
type gaussian integers 14.0
type gaussian rationals 14.0
type integer 10.0
type list 27.0
type matrices 34.0
type rationals 12.0
type records 45.0
type strings 30.0
type words 22.0
TzEliminate 23.13
TzFindCyclicJoins 23.13
TzGo 23.13
TzGoGo 23.13
TzInitGeneratorImages 23.13
TzPrint 23.8
TzPrintGeneratorImages 23.13
TzPrintGenerators 23.8
TzPrintLengths 23.13
TzPrintOptions 23.13
TzPrintPairs 23.13
TzPrintPresentation 23.8
TzPrintRelators 23.8
TzPrintStatus 23.8
TzSearch 23.13
TzSearchEqual 23.13
TzSubstitute 23.13 23.13
TzSubstituteCyclicJoins 23.13
ULTRIX 55.2
union of domains 4.13
union of sets 28.6 28.9
Units for gaussians 14.7
UNIX features 55.4
UNIX installation 55.3
UNIX options 55.4
UnloadSmallGroups 37.14
until 2.16
UpperCentralSeries for character tables 48.8
ValueMolienSeries 50.9
VEInput 72.2
VEOutput 72.2
WedgeGModule 67.42
while 2.15
while loop 2.15
Whitehead for xmods 73.116
Windows 55.5
Windows installation 55.7
word reduction 66.7
words 22.0
wreath product character table 48.18
WreathProduct for ag groups 25.9
WyckoffBasis 60.17
WyckoffPosClass 60.17
WyckoffSpaceGroup 60.17
WyckoffStabilizer 60.17
WyckoffTranslation 60.17
X 19.2
xxx Coefficient 86.11
Z 18.1
ZClassRepsDadeGroup 37.13
ZeroMorphism for groups 73.133

GAP 3.4.4
April 1997