[____] [____] [_____] [____] [__] [Index] [Root]
Index G
G-Sets (PERMUTATION GROUPS)
Lattices from Matrix Groups (LATTICES)
Modules (OVERVIEW)
Lattices from Matrix Groups (LATTICES)
Modules (OVERVIEW)
G-Sets (PERMUTATION GROUPS)
GrpFP_1_G23 (Example H19E53)
GabidulinCode(A, W, Z, t) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
GabidulinCode(A, W, Z, t) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
RngLoc_gal-desc (Example H55E7)
RngPad_gal-desc (Example H40E5)
FINITE FIELDS
Rings, Fields, and Algebras (OVERVIEW)
FiniteField(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
GaloisGroup(L) : FldAlg -> GrpPerm, [ FldPrElt, Any ]
GaloisGroup(f) : RngUPolElt -> GrpPerm, [ FldPrElt, Any ]
GaloisImage(x, i) : RngLocElt, RngIntElt -> RngLocElt
GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal
GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
Database of Galois Group Polynomials (OVERVIEW)
Galois Groups (ALGEBRAIC FUNCTION FIELDS)
Galois Groups (ORDERS AND ALGEBRAIC FIELDS)
Galois Module Structure (CLASS FIELD THEORY)
GALOIS RINGS
Galois Module Structure (CLASS FIELD THEORY)
GALOIS RINGS
GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
GaloisField(q) : RngIntElt -> FldFin
GF(q) : RngIntElt -> FldFin
FiniteField(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
GaloisGroup(L) : FldAlg -> GrpPerm, [ FldPrElt, Any ]
GaloisGroup(f) : RngUPolElt -> GrpPerm, [ FldPrElt, Any ]
FldFunG_GaloisGroups (Example H53E8)
RngOrd_GaloisGroups (Example H48E22)
GaloisImage(x, i) : RngLocElt, RngIntElt -> RngLocElt
GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
GR(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal
GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
Database of Galois Group Polynomials (OVERVIEW)
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
EulerGamma(R) : FldPr -> FldPrElt
Gamma(s) : FldPrElt -> FldPrElt
Gamma(s, t) : FldPrElt, FldPrElt -> FldPrElt
Gamma(f) : RngSerElt -> RngSerElt
GammaD(s) : FldPrElt -> FldPrElt
GammaUpper0(N) : RngIntElt -> GrpPSL2
GammaUpper1(N) : RngIntElt -> GrpPSL2
LogGamma(s) : FldPrElt -> FldPrElt
LogGamma(f) : RngSerElt -> RngSerElt
ProjectiveGammaLinearGroup(arguments)
ProjectiveGammaUnitaryGroup(arguments)
KBessel2(n, s) : FldPrElt, FldPrElt -> FldPrElt
Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)
KBessel2(n, s) : FldPrElt, FldPrElt -> FldPrElt
Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)
DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
Gamma0(N) : RngIntElt -> GrpPSL2
IsGamma0(G) : GrpPSL2 -> BoolElt
IsGamma0(M) : ModFrm -> BoolElt
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
Gamma1(N) : RngIntElt -> GrpPSL2
IsGamma1(G) : GrpPSL2 -> BoolElt
IsGamma1(M) : ModFrm -> BoolElt
GammaD(s) : FldPrElt -> FldPrElt
GammaUpper0(N) : RngIntElt -> GrpPSL2
GammaUpper1(N) : RngIntElt -> GrpPSL2
GapNumbers(D) : DivCrvElt -> SeqEnum
GapNumbers(D) : DivFunElt -> SeqEnum[RngIntElt]
GapNumbers(D, P) : DivFunElt, PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(F) : FldFunG -> SeqEnum[RngIntElt]
GapNumbers(F, P) : FldFunG, PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(p) : Pt -> SeqEnum
GapNumbers(D) : DivCrvElt -> SeqEnum
GapNumbers(D) : DivFunElt -> SeqEnum[RngIntElt]
GapNumbers(D, P) : DivFunElt, PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(F) : FldFunG -> SeqEnum[RngIntElt]
GapNumbers(F, P) : FldFunG, PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(p) : Pt -> SeqEnum
FldCyc_GaussianPeriods (Example H50E2)
GB_GBoverZ (Example H66E4)
Gcd(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GreatestCommonDivisor(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GreatestCommonDivisor(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GCD(Q) : [ RngMPolElt ] -> RngMPolElt
Gcd(m, n) : RngIntElt, RngIntElt -> RngIntElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GCD(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GCD(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GCD(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GCD(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GCD(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GCD(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
GCD(Q) : [RngIntResElt] -> RngIntResElt
HasGCD(R) : Rng -> BoolElt
Gcd(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GreatestCommonDivisor(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
Gcd(I, J) : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl
Gcd(m, n) : RngIntElt, RngIntElt -> RngIntElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
RngLoc_gcd (Example H55E13)
RngPad_gcd (Example H40E11)
Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
Comparison (OVERVIEW)
u ge v : AlgFPElt, AlgFPElt -> BoolElt
u ge v : GrpFPElt, GrpFPElt -> BoolElt
s ge t : MonStgElt, MonStgElt -> BoolElt
a ge b : RngElt, RngElt -> BoolElt
S ge T : SeqEnum, SeqEnum -> BoolElt
u ge v : SgpFPElt, SgpFPElt -> BoolElt
e ge f : SubGrpLatElt, SubGrpLatElt -> BoolElt
e ge f : SubGrpLatElt, SubGrpLatElt -> BoolElt
GegenbauerPolynomial(n, m) : RngIntElt, RngElt ->RngUPolElt
GegenbauerPolynomial(n, m) : RngIntElt, RngElt ->RngUPolElt
LocalGenera(G) : SymGen -> Lat
SpinorGenera(G) : SymGen -> [ SymGen ]
AGL(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GeneralOrthogonalGroup(arguments)
GeneralOrthogonalGroupMinus(arguments)
GeneralOrthogonalGroupPlus(arguments)
GeneralUnitaryGroup(arguments)
PGO(arguments)
PGOMinus(arguments)
PGOPlus(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralUnitaryGroup(arguments)
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Construction of a General Group (GROUPS)
Construction of a General Matrix Group (MATRIX GROUPS)
Construction of a General Permutation Group (PERMUTATION GROUPS)
Construction of General Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Construction of General Linear Codes (LINEAR CODES OVER FINITE RINGS)
Creation of a Matrix Group (MATRIX GROUPS)
FREE MODULES
General Constructions (MODULES OVER A MATRIX ALGEBRA)
General Factorization (RING OF INTEGERS)
General Function Field Places (ALGEBRAIC FUNCTION FIELDS)
General function fields (ALGEBRAIC FUNCTION FIELDS)
General Functions (ORDERS AND ALGEBRAIC FIELDS)
K[G]-MODULES AND GROUP REPRESENTATIONS
MODULES OVER A MATRIX ALGEBRA
Presentations (FINITELY PRESENTED SEMIGROUPS)
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Presentations (FINITELY PRESENTED SEMIGROUPS)
General Constructions (MODULES OVER A MATRIX ALGEBRA)
[Future release] GeneralisedRowReduction( rho ) : GrpLie, Map -> Map
[Future release] GeneralisedRowReduction( rho ) : GrpLie, Map -> Map
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
GL(arguments)
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GO(arguments)
GeneralOrthogonalGroup(arguments)
GOMinus(arguments)
GeneralOrthogonalGroupMinus(arguments)
GOPlus(arguments)
GeneralOrthogonalGroupPlus(arguments)
GU(arguments)
GeneralUnitaryGroup(arguments)
GenerateGraphs(n : parameters) : RngIntElt -> File
GenerateGraphs(n : parameters) : RngIntElt -> File
GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC]
GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC]
GrpPGp_GeneratepGroups (Example H25E2)
GeneratingWords(G, H) : GrpFP, GrpFP -> { GrpFPElt }
GrpPGp_Generating_p_groups (Example H25E1)
GeneratingWords(G, H) : GrpFP, GrpFP -> { GrpFPElt }
ClassGroupGenerationBound(F) : FldFun -> RngIntElt
ClassGroupGenerationBound(q, g) : RngIntElt, RngIntElt -> RngIntElt
Generating Graphs (GRAPHS)
Generator(F) : FldFin -> FldFinElt
F . 1 : FldFin, RngIntElt -> FldFinElt
R . 1 : RngGal -> RngGalElt
ActionGenerator(B, i) : AlgBas, RngIntElt -> SeqEnum
ActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
ActionGenerator(M, i) : ModGrp, RngIntElt -> AlgMatElt
ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
AddGenerator(G) : GrpFP -> GrpFP
AddGenerator(G, x) : GrpFp, . -> BoolElt, GrpFP, Map
AddGenerator(G, w) : GrpFP, GrpFPElt -> GrpFP
AddGenerator(S) : SgpFP -> SgpFP
AddGenerator(S, w) : SgpFP, SgpFPElt -> SgpFP
AddNormalizingGenerator(~H, x) : GrpPerm, GrpPermElt ->
AddSubgroupGenerator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, Tup, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P,C,n) : ModCpx, Tup, RngIntElt -> MapChn
DeleteGenerator(G, x) : GrpFP, GrpFPElt -> GrpFP
DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP
Generator(F, E) : FldFin, FldFin -> FldFinElt
GeneratorMatrix(C) : Code -> ModMatFldElt
GeneratorMatrix(C) : Code -> ModMatRngElt
GeneratorNumber(w) : GrpFPElt -> RngIntElt
GeneratorPolynomial(C) : Code -> RngUPolElt
GeneratorStructure(P) : Process(pQuot) ->
KeepGeneratorAction(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepGeneratorOrder(SQG, SQH) : SQProc, SQProc -> SeqEnum
LeadingGenerator(w) : GrpFPElt -> GrpFPElt
LeadingGenerator(x) : GrpGPCElt -> GrpGPCElt
LeadingGenerator(x) : GrpPCElt -> GrpPCElt
NaturalActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
ShrinkingGenerator(C1, S1, C2, S2, t) : RngUPolElt, SeqEnum, RngUPolElt,SeqEnum, RngIntElt -> SeqEnum
UnivariateEliminationIdealGenerator(I, i) : RngMPol, RngIntElt -> RngMPolElt
Base and Strong Generating Set (MATRIX GROUPS)
Base and Strong Generating Set (PERMUTATION GROUPS)
Construction of a Base and Strong Generating Set (PERMUTATION GROUPS)
Finding Special Elements (ORDERS AND ALGEBRAIC FIELDS)
Generator Assignment (OVERVIEW)
Generator Assignment (STATEMENTS AND EXPRESSIONS)
Special Elements (FINITE FIELDS)
The Generator Polynomial (LINEAR CODES OVER FINITE FIELDS)
Univariate Elimination Ideal Generators (IDEAL THEORY AND GRÖBNER BASES)
Generator Assignment (OVERVIEW)
Generator Assignment (STATEMENTS AND EXPRESSIONS)
The Generator Polynomial (LINEAR CODES OVER FINITE FIELDS)
Finding Special Elements (ORDERS AND ALGEBRAIC FIELDS)
Special Elements (FINITE FIELDS)
Reducing generating sets (FINITELY PRESENTED GROUPS)
BasisMatrix(C) : Code -> ModMatRngElt
GeneratorMatrix(C) : Code -> ModMatFldElt
GeneratorMatrix(C) : Code -> ModMatRngElt
CodeFld_GeneratorMatrix (Example H101E8)
State_GeneratorNaming (Example H1E5)
State_GeneratorNamingSequence (Example H1E4)
GeneratorNumber(w) : GrpFPElt -> RngIntElt
GeneratorPolynomial(C) : Code -> RngUPolElt
CodeFld_GeneratorPolynomial (Example H101E10)
ActionGenerators(M) : ModGrp -> [ AlgMatElt ]
AddLocalGenerators(X) : VSrfK3 -> VSrfK3
AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP
AlgebraicGenerators( G ) : GrpLie ->
ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt
CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup
CohomologyRightModuleGenerators(P, Q, CQ) : Tup, Tup, Tup -> Tup
CohomologyRingGenerators(P) : Tup -> Tup
DegreesOfCohomologyGenerators(C) : Tup -> SeqEnum
Dimension(C) : Code -> RngIntElt
Eliminate(~P: parameters) : Process(Tietze) ->
ExtGenerators(G, U) : GrpPC, GrpPC -> [<AlgMatElt, RngIntElt>]
ExtractGenerators(P) : Process(Lix) -> { GrpFPElt }
FindGenerators(G) : GrpFP -> []
Generators(B) : AlgBas -> SeqEnum
Generators(A) : AlgFP -> { AlgFPElt }
Generators(R) : AlgMat -> { AlgMatElt }
Generators(C) : Code -> { ModTupFldElt }
Generators(C) : Code -> { ModTupRngElt }
Generators(A) : FldAb -> [ ], [ ], [ ]
Generators(G) : Grp -> { GrpFinElt }
Generators(A) : GrpAb -> { GrpAbElt }
Generators(A) : GrpAbGen -> [ GrpAbGenElt ]
Generators(G) : GrpAtc -> [GrpAtcElt]
Generators(A) : GrpAuto -> SetEnum
Generators(G) : GrpFP -> { GrpFPElt }
Generators(G) : GrpGPC -> {@ GrpGPCElt @}
Generators(H, G) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}
Generators( G ) : GrpLie ->
Generators(G) : GrpMat -> { GrpMatElt }
Generators(G) : GrpPC -> SetEnum
Generators(G) : GrpPerm -> { GrpPermElt }
Generators(G) : GrpPSL2 -> SeqEnum
Generators(G) : GrpRWS -> [GrpRWSElt]
Generators(G) : GrpSLP -> { GrpSLPElt }
Generators(V) : ModTupFld -> { ModElt }
Generators(M) : ModTupRng -> { ModTupElt }
Generators(M) : ModTupRng -> { ModTupElt }
Generators(M) : MonRWS -> [ MonRWSElt]
Generators(I) : RngFunOrdIdl -> [ RngFunOrdElt ]
Generators(I) : RngOrdIdl -> [ RngOrdElt ]
Generators(H) : SetPtEll -> [ PtEll ]
Generators(H) : SetPtEll -> [ PtEll ]
Generators(S) : SgpFP -> { SgpFPElt }
Generators(FS) : SymFry -> SeqEnum
GeneratorsSequence(G) : GrpPerm -> [ GrpPermElt ]
HomGenerators(G, H) : GrpAb, GrpAb -> GrpAb, Map
HomGenerators(G, U) : GrpPC, GrpPC -> [<AlgMatElt, RngIntElt>]
IdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
IdempotentGenerators(B) : AlgBas -> SeqEnum
InnerGenerators(A) : GrpAuto -> SeqEnum
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
Ngens(A) : GrpAuto -> RngIntElt
Ngens(M) : ModDed -> RngIntElt
NonIdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
NonIdempotentGenerators(B) : AlgBas -> SeqEnum
NumberOfActionGenerators(L) : Lat -> RngIntElt
NumberOfActionGenerators(M) : ModGrp -> RngIntElt
NumberOfActionGenerators(M) : ModTupRng -> RngIntElt
NumberOfGenerators(B) : AlgBas -> RngIntElt
NumberOfGenerators(A) : AlgFP -> RngIntElt
NumberOfGenerators(R) : AlgMat -> { AlgMatElt }
NumberOfGenerators(C) : Code -> RngIntElt
NumberOfGenerators(G) : Grp -> RngIntElt
NumberOfGenerators(A) : GrpAb -> RngIntElt
NumberOfGenerators(A) : GrpAbGen -> RngIntElt
NumberOfGenerators(G) : GrpAtc -> RngIntElt
NumberOfGenerators(B) : GrpBrd -> RngIntElt
NumberOfGenerators(G) : GrpFP -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpMat -> RngIntElt
NumberOfGenerators(G) : GrpPC -> RngIntElt
NumberOfGenerators(G) : GrpPerm -> RngIntElt
NumberOfGenerators(G) : GrpRWS -> RngIntElt
NumberOfGenerators(G) : GrpSLP -> RngIntElt
NumberOfGenerators(M) : ModTupFld -> RngIntElt
NumberOfGenerators(M) : MonRWS -> RngIntElt
NumberOfGenerators(P) : Process(Tietze) -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(S) : SgpFP -> RngIntElt
NumberOfStrongGenerators(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt
PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
ReduceGenerators(G) : GrpFP -> GrpFP, Map
ReduceGenerators(~G) : GrpPerm ->
SchreierGenerators(G, H : parameters) : GrpFP, GrpFP -> { GrpFPElt }
SpinorGenerators(G) : SymGen -> [ RngIntElt ]
StrongGenerators(G) : GrpMat -> SetIndx(GrpMat)
StrongGenerators(G) : GrpPerm -> SetIndx(GrpPermElt)
StrongGenerators(G, i) : GrpPerm, RngIntElt -> SetIndx(GrpPermElt)
TwoGenerators(P) : PlcFunElt -> FldFunGElt, FldFunGElt
UnivariateEliminationIdealGenerators(I) : RngMPol -> [ RngMPolElt ]
UserGenerators(A) : GrpAbGen -> [ GrpAbGenElt ]
GrpLie_Generators (Example H35E3)
Grp_Generators (Example H16E11)
Addition of extra generators (GROUPS OF STRAIGHT-LINE PROGRAMS)
GeneratorsSequence(G) : GrpPerm -> [ GrpPermElt ]
GeneratorStructure(P) : Process(pQuot) ->
Generic(G) : SchGrpEll -> CrvEll
Curve(G) : SchGrpEll -> CrvEll
Generic(R) : AlgMat -> AlgMat
Generic(C) : Code -> Code
Generic(C) : Code -> Code
Generic(G) : Grp -> Grp
Generic(G) : GrpMat -> GrpMat
Generic(G) : GrpPerm -> GrpPerm
Generic(V) : ModFld -> ModFld
Generic(M) : ModMPol -> ModMPol
Generic(M) : ModRng -> ModRng
Generic(I) : RngMPol -> RngMPol
GenericAbelianGroup(U: parameters) : . -> GrpAbGen
GenericGroup(X) : [] -> GrpFp, Map
Generic Element Functions and Predicates (REAL AND COMPLEX FIELDS)
Generic Groups (CLASS FIELD THEORY)
Generic Ring Functions (INTRODUCTION [BASIC RINGS])
Parent and Category (ALGEBRAICALLY CLOSED FIELDS)
Parent and Category (FINITE FIELDS)
Parent and Category (GALOIS RINGS)
Parent and Category (RATIONAL FIELD)
Parent and Category (RING OF INTEGERS)
Parent and Category (RING OF INTEGERS)
Properties (LOCAL RINGS AND FIELDS)
Properties (p-ADIC RINGS AND FIELDS)
Related Structures (MULTIVARIATE POLYNOMIAL RINGS)
Related Structures (RATIONAL FIELD)
Related Structures (UNIVARIATE POLYNOMIAL RINGS)
Generic Groups (CLASS FIELD THEORY)
GENERIC ABELIAN GROUPS
GenericAbelianGroup(U: parameters) : . -> GrpAbGen
CrvEll_GenericCurve (Example H87E7)
GenericGroup(X) : [] -> GrpFp, Map
CrvEll_GenericPoint (Example H87E12)
Definition of Subgroups by Generators (FINITE SOLUBLE GROUPS)
ArithmeticGenus(C) : Crv -> RngIntElt
Genus(C) : Crv -> RngIntElt
Genus(C) : CrvHyp -> RngIntElt
Genus(X) : CrvMod -> RngIntElt
Genus(F) : FldFun -> RngIntElt
Genus(G) : GrpPSL2 -> RngIntElt
Genus(L) : Lat -> SymGen
Genus(X) : VSrfK3 -> RngIntElt
GenusContribution(g) : GrphRes -> RngIntElt
GenusField(A): FldAb -> FldAb
GenusRepresentatives(L) : Lat -> [ Lat ]
HyperellipticCurveOfGenus(g, h, f) : RngIntElt, RngUPolElt, RngUPolElt -> CrvHyp
IsGenus(G) : SymGen -> BoolElt
IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp
IsSpinorGenus(G) : SymGen -> BoolElt
SpinorGenus(L) : Lat -> SymGen
Lat_Genus (Example H64E20)
Genera and Spinor Genera (LATTICES)
Invariants of genera and spinor genera (LATTICES)
Genus constructions (LATTICES)
GenusContribution(g) : GrphRes -> RngIntElt
GenusField(A): FldAb -> FldAb
SpinorRepresentatives(L) : Lat -> [ Lat ]
Representatives(G) : SymGen -> [ Lat ]
GenusRepresentatives(L) : Lat -> [ Lat ]
Geodesic(u, v) : GrphVert, GrphVert -> [GrphVert]
GrpPSL2_geodesic-intersection (Example H31E7)
Points and geodesics (SUBGROUPS OF PSL_2(R))
GeodesicsIntersection(x,y) : [SpcHypElt],[SpcHypElt] -> SpcHypElt
GeodesicsIntersection(x,y) : [SpcHypElt],[SpcHypElt] -> SpcHypElt
Combinatorial and Geometrical Structures (OVERVIEW)
AlgebraicGeometricCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
Genus(C) : Crv -> RngIntElt
GeometricSupport(C) : Code -> DivCrvElt
IsAlgebraicGeometric(C) : Code -> BoolElt
Algebraic Geometric Codes (LINEAR CODES OVER FINITE FIELDS)
Combinatorial and Geometrical Structures (OVERVIEW)
Geometrical Restrictions (SCHEMES)
Geometrical Restrictions (SCHEMES)
GeometricGenus(C) : Crv -> RngIntElt
Genus(C) : Crv -> RngIntElt
GeometricSupport(C) : Code -> DivCrvElt
CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom
IncidenceGeometry(C) : CosetGeom -> IncGeom
IncidenceGeometry(G) : GrphUnd -> IncGeom
Construction of a Coset Geometry (INCIDENCE GEOMETRY)
Construction of an Incidence Geometry (INCIDENCE GEOMETRY)
geometry (OVERVIEW)
INCIDENCE GEOMETRY
GetViMode() : -> BoolElt
Set and Get (ENVIRONMENT AND OPTIONS)
GetAttributes(C) : Cat -> [ MonStgElt ]
GetChild(SQP, i) : SQProc, RngIntElt -> List
GetChildren(SQP) : SQProc -> List
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->
GetDefaultRealField() : Null -> FldPr
GetHelpExternalBrowser() : -> MonStgElt, MonStgElt
GetHelpExternalSystem() : -> MonStgElt
GetHelpUseExternal() : -> BoolElt, BoolElt
GetMaximumMemoryUsage() : -> RngIntElt
GetMemoryUsage() : -> RngIntElt
GetModules(SQP, p ) : SQProc, RngIntElt -> List
GetParent(SQP) : SQProc -> List
GetPreviousSize() : -> RngIntElt
GetPrimes(SQP) : SQProc -> SetEnum, BoolElt
GetQuotient(SQP) : SQProc -> GrpPC, Map
GetSeed() : -> RngIntElt, RngIntElt
GetVerbose(s) : MonStgElt -> RngIntElt
GetVersion() : -> RngIntElt, RngIntElt, RngIntElt
SetAssertions(b) : BoolElt ->
SetAutoColumns(b) : BoolElt ->
SetAutoCompact(b) : BoolElt ->
SetBeep(b) : BoolElt ->
SetColumns(n) : RngIntElt ->
SetEchoInput(b) : BoolElt ->
SetHistorySize(n) : RngIntElt ->
SetIgnorePrompt(b) : BoolElt ->
SetIgnoreSpaces(b) : BoolElt ->
SetIndent(n) : RngIntElt ->
SetLibraries(s) : MonStgElt ->
SetLibraryRoot(s) : MonStgElt ->
SetLineEditor(b) : BoolElt ->
SetMemoryLimit(n) : RngIntElt ->
SetPath(s) : MonStgElt ->
SetPrintLevel(l) : MonStgElt ->
SetPrompt(s) : MonStgElt ->
SetRows(n) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetTraceback(n) : BoolElt ->
SetViMode(b) : BoolElt ->
GetAssertions() : -> BoolElt
SetAssertions(b) : BoolElt ->
GetAttributes(C) : Cat -> [ MonStgElt ]
GetAutoColumns() : -> BoolElt
SetAutoColumns(b) : BoolElt ->
GetAutoCompact() : -> BoolElt
SetAutoCompact(b) : BoolElt ->
GetBeep() : -> BoolElt
SetBeep(b) : BoolElt ->
Getc(F) : File -> MonStgElt
GetChild(SQP, i) : SQProc, RngIntElt -> List
GetChildren(SQP) : SQProc -> List
GetColumns() : -> RngIntElt
SetColumns(n) : RngIntElt ->
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->
GetDefaultRealField() : Null -> FldPr
GetEchoInput() : ->
SetEchoInput(b) : BoolElt ->
GetHelpExternalBrowser() : -> MonStgElt, MonStgElt
GetHelpExternalSystem() : -> MonStgElt
GetHelpUseExternal() : -> BoolElt, BoolElt
GetHistorySize() : ->
SetHistorySize(n) : RngIntElt ->
GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->
GetIgnoreSpaces() : -> BoolElt
SetIgnoreSpaces(b) : BoolElt ->
GetIndent() : -> RngIntElt
SetIndent(n) : RngIntElt ->
GetLibraries() : -> MonStgElt
SetLibraries(s) : MonStgElt ->
GetLibraryRoot() : -> MonStgElt
SetLibraryRoot(s) : MonStgElt ->
GetLineEditor() : BoolElt ->
SetLineEditor(b) : BoolElt ->
GetMaximumMemoryUsage() : -> RngIntElt
GetMemoryLimit() : -> RngIntElt
SetMemoryLimit(n) : RngIntElt ->
GetMemoryUsage() : -> RngIntElt
GetModule(SQP, p, i) : SQProc, RngIntElt, RngIntElt -> ModGrp
GetModules(SQP, p ) : SQProc, RngIntElt -> List
GetModule(SQP, p, i) : SQProc, RngIntElt, RngIntElt -> ModGrp
GetModules(SQP, p ) : SQProc, RngIntElt -> List
GetParent(SQP) : SQProc -> List
GetPath() : -> MonStgElt
SetPath(s) : MonStgElt ->
Getpid() : ->
RngInt_GetPoly (Example H38E13)
GetPreviousSize() : -> RngIntElt
GetPrimes(SQP) : SQProc -> SetEnum, BoolElt
GetPrintLevel() : -> MonStgElt
SetPrintLevel(l) : MonStgElt ->
GetPrompt() : -> MonStgElt
SetPrompt(s) : MonStgElt ->
GetQuotient(SQP) : SQProc -> GrpPC, Map
GetRows() : -> RngIntElt
SetRows(n) : RngIntElt ->
Gets(F) : File -> MonStgElt
GetSeed() : -> RngIntElt, RngIntElt
SetSeed(s, c) : RngIntElt ->
IO_GetTime (Example H3E10)
GetTraceback() : -> BoolElt
SetTraceback(n) : BoolElt ->
Getuid() : ->
Getvecs(G) : GrpMat -> SeqEnum
GetVerbose(s) : MonStgElt -> RngIntElt
GetVersion() : -> RngIntElt, RngIntElt, RngIntElt
GetViMode() : -> BoolElt
SetViMode(b) : BoolElt ->
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
GaloisField(q) : RngIntElt -> FldFin
GF(q) : RngIntElt -> FldFin
FiniteField(q) : RngIntElt -> FldFin
GF(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
GF(p, n) : RngIntElt, RngIntElt -> FldFin
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
GilbertVarshamovAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
GilbertVarshamovBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GilbertVarshamovLinearBound(K, n, d) : FldFin,RngIntElt,RngIntElt -> RngIntElt
GilbertVarshamovAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
GilbertVarshamovBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GilbertVarshamovLinearBound(K, n, d) : FldFin,RngIntElt,RngIntElt -> RngIntElt
Girth(G) : GrphUnd -> RngIntElt
GirthCycle(G) : GrphUnd -> [GrphVert]
GirthCycle(G) : GrphUnd -> [GrphVert]
GL(arguments)
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
IsGL2Equivalent(f, g, n) : RngUPolElt, RngUPolElt, RngIntElt -> BoolElt, SeqEnum
IsGLattice(L) : Lat -> GrpMat
Graded Lexicographical: glex (IDEAL THEORY AND GRÖBNER BASES)
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
IsGlobal(F) : FldFun -> BoolElt
IsGlobalUnit(a) : FldFunElt -> BoolElt
IsGlobalUnit(a) : FldFunElt -> BoolElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
SetGlobalTCParameters(: parameters) : ->
UnsetGlobalTCParameters() : ->
RngMPol_Global (Example H43E2)
Global Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Global Geometry (PLANE ALGEBRAIC CURVES)
Global Geometry of Schemes (SCHEMES)
Local Conditions for Conics (RATIONAL CURVES AND CONICS)
Local--Global Correspondence (RATIONAL CURVES AND CONICS)
Norm Residue Symbol (RATIONAL CURVES AND CONICS)
Special forms of Curves (PLANE ALGEBRAIC CURVES)
Global Geometry (PLANE ALGEBRAIC CURVES)
FldFunG_global-function-fields (Example H53E21)
Special forms of Curves (PLANE ALGEBRAIC CURVES)
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
RootDtm_GLRootDatum (Example H33E4)
GrpMat_GLSylow (Example H21E4)
GModule(G, A) : Grp, AlgMat -> ModGrp
GModule(G, S) : Grp, AlgMat -> ModGrp
GModule(G, A, B) : Grp, Grp, Grp -> ModGrp, Map
GModule(G, A, B) : Grp, Grp, Grp -> ModGrp, Map
GModule(G, A, B) : Grp, Grp, Grp -> ModGrp, Map
GModule(G, P, d) : Grp, RngMPol, RngIntElt -> ModGrp, Map, @ RngMPolElt @
GModule(G, P, d) : Grp, RngMPol, RngIntElt -> ModGrp, Map, @ RngMPolElt @
GModule(G, I, J) : Grp, RngMPol, RngMPol -> ModGrp, Map, @ RngMPolElt @
GModule(G, I, J) : Grp, RngMPol, RngMPol -> ModGrp, Map, @ RngMPolElt @
GModule(G, I, J) : Grp, RngMPol, RngMPol -> ModGrp, Map, @ RngMPolElt @
GModule(G, I, J) : Grp, RngMPol, RngMPol -> ModGrp, Map, @ RngMPolElt @
GModule(G, Q) : Grp, RngMPolRes -> ModGrp, Map, @ RngMPolElt @
GModule(G, Q) : Grp, RngMPolRes -> ModGrp, Map, @ RngMPolElt @
GModule(G, Q) : Grp, RngMPolRes -> ModGrp, Map, @ RngMPolElt @
GModule(G, Q) : Grp, RngMPolRes -> ModGrp, Map, @ RngMPolElt @
GModule(G, Q) : Grp, [ GrpMatElt ] -> ModGrp
GModule(G, Q) : Grp, [ GrpMatElt ] -> ModGrp
GModule(G, S) : GrpFin, AlgMat -> ModGrpFin
GModule(G, A, B) : GrpFin, GrpFin, GrpFin -> ModGrpFin, Map
GModule(G, A, B, p) : GrpFP, GrpFP, GrpFP, RngIntElt -> ModGrp, Map
GModule(G, A, p) : GrpFP, GrpFP, RngIntElt -> ModGrp, Map
GModule(G, A, B, p) : GrpGPC, GrpGPC, GrpGPC, RngIntElt -> ModGrp, Map
GModule(G, A, p) : GrpGPC, GrpGPC, RngIntElt -> ModGrp, Map
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G, A) : GrpMat, AlgMat -> ModGrp
GModule(G, A, B) : GrpMat, GrpMat, GrpMat -> ModGrp, Map
GModule(G, Q) : GrpMat, [ AlgMatElt ] -> ModGrp
GModule(G, M) : GrpPC, AlgMat -> ModAlg
GModule(G, A) : GrpPC, GrpPC -> ModAlg, Map
GModule(G, A, B) : GrpPC, GrpPC, GrpPC -> ModAlg, Map
GModule(G, K) : GrpPerm, Rng -> ModGrp
GModuleAction(M) : ModGrp -> Map(Hom)
GModulePrimes(G, A) : GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A, B) : GrpFP, GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A) : GrpGPC, GrpGPC -> SetMulti
GModulePrimes(G, A, B) : GrpGPC, GrpGPC, GrpGPC -> SetMulti
GrpMat_GModule (Example H21E28)
GrpPerm_GModule (Example H20E31)
RngInvar_GModule (Example H80E2)
Construction of G-modules (INVARIANT RINGS OF FINITE GROUPS)
GModuleAction(M) : ModGrp -> Map(Hom)
GModulePrimes(G, A) : GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A, B) : GrpFP, GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A) : GrpGPC, GrpGPC -> SetMulti
GModulePrimes(G, A, B) : GrpGPC, GrpGPC, GrpGPC -> SetMulti
GrpFP_1_gmoduleprimes (Example H19E60)
GrpGPC_gmoduleprimes (Example H23E14)
ModGrp_GModules1 (Example H78E10)
GO(arguments)
GeneralOrthogonalGroup(arguments)
GolayCode(K, extend) : FldFin, BoolElt -> Code
GolayCode(K, extend) : FldFin, BoolElt -> Code
GOMinus(arguments)
GeneralOrthogonalGroupMinus(arguments)
GoodBasePoints(G: parameters) : GrpMat -> []
GoodBasePoints(G: parameters) : GrpMat -> []
GOPlus(arguments)
GeneralOrthogonalGroupPlus(arguments)
GoppaCode(L, G) : [ FldFinElt ], RngUPolElt -> Code
GoppaDesignedDistance(C) : Code -> RngIntElt
GoppaCode(L, G) : [ FldFinElt ], RngUPolElt -> Code
CodeFld_GoppaCode (Example H101E27)
GoppaDesignedDistance(C) : Code -> RngIntElt
The break statement (OVERVIEW)
The continue statement (OVERVIEW)
GPCGroup(G) : Grp -> GrpGPC, Hom(Grp)
GPCGroup(G) : GrpPC -> GrpGPC, Map
GPCGroup(G) : GrpPerm -> GrpGPC, Map
GR(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal
GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
Newton_grad-ex (Example H54E5)
GB_Graded (Example H66E20)
Creation of Graded Modules (MODULES OVER AFFINE ALGEBRAS)
Graded Polynomial Rings (IDEAL THEORY AND GRÖBNER BASES)
Graded Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
Graded Polynomial Rings (IDEAL THEORY AND GRÖBNER BASES)
Graded Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
GradientVector(F) : NwtnPgonFace -> Tup
GradientVector(F) : NwtnPgonFace -> Tup
Gradings(X) : Sch -> SeqEnum
NumberOfGradings(X) : Sch -> RngIntElt
OrthogonalizeGram(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Diagonalization(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
GramMatrix(S) : AlgQuatOrd -> AlgMat
GramMatrix(L) : Lat -> AlgMatElt
GramMatrix(M) : ModBrdt -> AlgMatElt
GramMatrix(X) : ModMatRngElt : -> AlgMatElt
GramMatrix(f) : QuadBinElt -> AlgMatElt
LatticeWithGram(F) : AlgMatElt -> Lat
LatticeWithGram(G, F) : GrpMat, AlgMatElt -> Lat
PairReduceGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
ReducedGramMatrix(S) : AlgQuatOrd -> AlgMat
SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
GramMatrix(S) : AlgQuatOrd -> AlgMat
GramMatrix(L) : Lat -> AlgMatElt
GramMatrix(M) : ModBrdt -> AlgMatElt
GramMatrix(X) : ModMatRngElt : -> AlgMatElt
GramMatrix(f) : QuadBinElt -> AlgMatElt
BipartiteGraph(m, n) : RngIntElt, RngIntElt -> GrphUnd
BlockGraph(D) : Inc -> Grph
BlockGraph(D) : Inc -> GrphUnd
CanonicalGraph(G) : Grph -> Grph
CayleyGraph(A) : Grp -> GrphDir
ClebschGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd
CompleteGraph(p) : RngIntElt -> GrphUnd
EmptyGraph(p: parameters) : RngIntElt -> GrphUnd
Graph(C) : CosetGeom -> GrphUnd
Graph(D, S, i) : DB, SeqEnum, RngIntElt -> GrphUnd
Graph(D) : IncGeom -> GrphUnd
Graph<p | edges: parameters> : RngIntElt, List -> GrphUnd
HadamardGraph(H: parameters) : Mtrx -> GrphUnd
IncidenceGraph(D) : Inc -> Grph
IncidenceGraph(D) : Inc -> GrphUnd
IncidenceGraph(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
IncidenceGraph(A) : ModHomElt -> GrphUnd
IncidenceGraph(P) : Plane -> Grph
IncidenceGraph(P) : Plane -> GrphUnd;
IsGraph(C) : CosetGeom -> GrphUnd
IsGraph(D) : IncGeom -> GrphUnd
KCubeGraph(k: parameters) : RngIntElt -> GrphUnd
LineGraph(G) : Grph -> Grph
LineGraph(P) : Plane -> Grph
LineGraph(P) : Plane -> GrphUnd
MakeResolutionGraph(g,s,t) : GrphDir,SeqEnum,SeqEnum -> GrphRes
MakeResolutionGraph(N) : NewtonPgon -> GrphRes
MultipartiteGraph(Q) : [RngIntElt] -> GrphUnd
NextGraph(F: parameters) : File -> BoolElt, GrphUnd
OddGraph(n) : RngIntElt -> GrphUnd
OpenGraphFile(s, f, p): MonStgElt, RngIntElt, RngIntElt -> File
OrbitalGraph(P, u, T) : GrpPerm, RngIntElt, { RngIntElt } -> GrphUnd
OrientatedGraph(G) : GrphUnd -> GrphDir
PaleyGraph(q) : RngIntElt -> GrphUnd
ParentGraph(s) : GrphVert -> Grph
ParentGraph(S) : GrphVertSet -> Grph
PathGraph(p: parameters) : RngIntElt -> GrphUnd
PointGraph(D) : Inc -> Grph
PointGraph(D) : Inc -> GrphUnd
PointGraph(P) : Plane -> GrphUnd;
PolygonGraph(p: parameters) : RngIntElt -> GrphUnd
RandomGraph(D) : DB -> GrphUnd
RandomGraph(D, S) : DB, SeqEnum -> GrphUnd
RandomGraph(p, r: parameters) : RngIntElt, FldReElt -> GrphUnd
ResolutionGraph(p) : Grm -> GrphRes
ResolutionGraph(v) : GrphResVert -> GrphRes
ResolutionGraph(P) : PnclJac -> GrphRes
ResolutionGraph(P,a,b) : PnclJac,RngElt,RngElt -> GrphRes
ResolutionGraph(C,p) : Sch,Pt -> GrphRes
ResolutionGraphVertex(g,i) : GrphRes,RngIntElt -> GrphResVert
SchreierGraph(A, B) : Grp, Grp -> GrphDir
SquareLatticeGraph(n) : RngIntElt -> GrphUnd
StandardGraph(G) : Grph -> Grph
TriangularGraph(n) : RngIntElt -> GrphUnd
UnderlyingGraph(D) : GrphDir -> GrphUnd
UnderlyingGraph(g) : GrphRes -> GrphDir
UnderlyingGraph(s) : GrphSpl -> GrphDir
VoronoiGraph(L) : Lat -> GrphUnd
A General Facility (GRAPHS)
Adjacency, Degree and Distance Functions for a Graph (GRAPHS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Combinatorial and Geometrical Structures (OVERVIEW)
Connectedness in a Graph (GRAPHS)
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
Construction of a General Graph (GRAPHS)
Construction of a Standard Graph (GRAPHS)
Construction of Graphs and Digraphs (GRAPHS)
Converting between Graphs and Digraphs (GRAPHS)
Generating Graphs (GRAPHS)
Graph Database and Graph Generation (GRAPHS)
GRAPHS
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
Paths and Circuits in a Graph (GRAPHS)
Planes, Graphs and Codes (FINITE PLANES)
Strongly Regular Graphs (GRAPHS)
The Graph of a Map (MAPPINGS)
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
Planes, Graphs and Codes (FINITE PLANES)
Graph Database and Graph Generation (GRAPHS)
Construction of Graphs and Digraphs (GRAPHS)
Generating Graphs (GRAPHS)
A General Facility (GRAPHS)
Strongly Regular Graphs (GRAPHS)
Graph_GraphGeneralAccess (Example H97E22)
Graph_GraphGeneration (Example H97E21)
GrpPSL2_Graphics (Example H31E10)
GrpPSL2_Graphics (Example H31E8)
Graphical output (SUBGROUPS OF PSL_2(R))
Graph_GraphIsomorphim (Example H97E17)
ChangGraphs() : -> [GrpUnd, GrpUnd, GrpUnd]
GenerateGraphs(n : parameters) : RngIntElt -> File
Graphs(D, S) : DB, SeqEnum -> SeqEnum
NumberOfGraphs(D) : DB -> RngIntElt
NumberOfGraphs(D, S) : DB, SeqEnum -> RngIntElt
StronglyRegularGraphsDatabase() : -> DB
Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Sparse Graphs (GRAPHS)
Design_graphs (Example H98E13)
GrayMap(C) : Code -> Map
GrayMapImage(C) : Code -> [ ModTupRngElt ]
HasLinearGrayMapImage(C) : Code -> BoolElt, Code
The Gray Map (LINEAR CODES OVER FINITE RINGS)
The Gray Map (LINEAR CODES OVER FINITE RINGS)
GrayMap(C) : Code -> Map
CodeRng_GrayMap (Example H102E9)
GrayMapImage(C) : Code -> [ ModTupRngElt ]
Comparison (OVERVIEW)
Xgcd(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt
XGCD(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt
ExtendedGreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt
ExtendedGreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt, RngUPolElt
ExtendedGreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt, RngValElt
ExtendedGreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt, [RngIntElt]
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
LCM(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
Greatest Common Divisors (QUADRATIC FIELDS)
LCM(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
Greatest Common Divisors (QUADRATIC FIELDS)
Gcd(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GreatestCommonDivisor(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
Graded Reverse Lexicographical: grevlex (IDEAL THEORY AND GRÖBNER BASES)
GriesmerBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GriesmerLengthBound(K, k, d) : FldFin,RngIntEt,RngIntElt -> RngIntElt
GriesmerMinimumWeightBound(K, n, k) : FldFin,RngIntElt,RngIntElt->RngIntElt
GriesmerBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GriesmerLengthBound(K, k, d) : FldFin,RngIntEt,RngIntElt -> RngIntElt
GriesmerMinimumWeightBound(K, n, k) : FldFin,RngIntElt,RngIntElt->RngIntElt
Groebner(M) : ModMPol ->
Groebner(I: parameters) : RngMPol ->
GroebnerBasis(I: parameters) : RngMPol -> RngMPolElt
GroebnerBasis(S, d : parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S, d: parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
GroebnerBasis(X) : Sch -> SeqEnum
GroebnerBasisUnreduced(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
HasGroebnerBasis(I) : RngMPol -> BoolElt
HilbertGroebnerBasis(S, H) : [ RngMPolElt ], FldFunRatUElt -> BoolElt, [ RngMPolElt ]
IsGroebner(S) : { RngMPolElt } -> BoolElt
MarkGroebner(I) : RngMPol ->
ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]
Gröbner Bases (IDEAL THEORY AND GRÖBNER BASES)
Hilbert-driven Gröbner Basis Construction (IDEAL THEORY AND GRÖBNER BASES)
IDEAL THEORY AND GRÖBNER BASES
GroebnerBasis(I: parameters) : RngMPol -> RngMPolElt
GroebnerBasis(S, d : parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S, d: parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
GroebnerBasis(X) : Sch -> SeqEnum
GroebnerBasisUnreduced(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
Graph_Grotzch (Example H97E12)
BaseField(F) : FldAlg -> Fld
CoefficientField(F) : FldAlg -> Fld
GroundField(F) : FldAlg -> Fld
GroundField(F) : FldFin -> FldFin
BaseField(F) : FldAlg -> Fld
CoefficientField(F) : FldAlg -> Fld
GroundField(F) : FldAlg -> Fld
GroundField(F) : FldFin -> FldFin
AbelianGroup(GrpAb, Q) : Cat, [ RngIntElt ] -> GrpAb
AbelianGroup(C, Q) : Cat, [ RngIntElt ] -> GrpFin
AbelianGroup(GrpFP, [n_1,...,n_r]): Cat, [ RngIntElt ] -> GrpFP
AbelianGroup(GrpPerm, Q) : Cat, [ RngIntElt ] -> GrpPerm
AbelianGroup(GrpGPC, Q) : Cat, [RngIntElt] -> GrpGPC
AbelianGroup(GrpPC, Q) : Cat, [RngIntElt] -> GrpPC
AbelianGroup(G) : Grp -> GrpAb, Hom
AbelianGroup(G) : GrpGPC -> GrpAb, Map
AbelianGroup(G) : GrpPC -> GrpAb, Map
AbelianGroup(J) : JacHyp -> GrpAb, Map
AbelianGroup< X | R > : List(Var), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
AbelianGroup(A: parameters) : GrpAbGen -> GrpAb, Map
AbelianGroup(H: parameters) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
AdditiveGroup(F) : FldFin -> GrpAb, Map
AdditiveGroup(Z) : RngInt -> GrpAb, Map
AdditiveGroup(R) : RngIntRes -> GrpAb, Map
AffineGammaLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineSigmaLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AlmostSimpleGroupDatabase() : -> DB
AlternatingGroup(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
AutomaticGroup(Q: parameters) : GrpFP -> GrpAtc
AutomorphismGroup(C) : CrvHyp -> GrpPerm, Map, Map
AutomorphismGroup(A) : FldAb -> GrpFP, [Map], Map
AutomorphismGroup(F) : FldAlg -> GrpPerm, PowMap, Map
AutomorphismGroup(G): Grp -> GrpAuto
AutomorphismGroup(G, Q, I): Grp, SeqEnum[GrpElt], SeqEnum[SeqEnum[GrpElt]] -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(D) : Inc -> GrpPerm, GSet, GSet, PowMap, Map
AutomorphismGroup(D) : IncGeom -> GrpPerm
AutomorphismGroup(L) : Lat -> GrpMat
AutomorphismGroup(L, F) : Lat, [ AlgMatElt ] -> GrpMat
AutomorphismGroup(M) : ModRng -> AlgMat
AutomorphismGroup(P) : P -> GrpMat,Map
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroup( G: parameters) : Grph -> GrpPerm, GSet, GSet, PowMap, Map, Grph
AutomorphismGroup(G: parameters) : GrpPerm -> GrpAuto
AutomorphismGroup(L) : RngLoc -> GrpPerm, Map
AutomorphismGroup(F) : [ AlgMatElt ] -> GrpMat
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map
BlockGroup(D) : Inc -> GrpPerm
BraidGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
BraidGroup( W ) : GrpCox -> GrpFP, Map
BraidGroup( F ) : GrpFP -> GrpFP, Map
BraidGroup(n) : RngIntElt -> GrpBrd
BravaisGroup(G) : GrpMat -> GrpMat
CentralCollineationGroup(P, l) : Plane, PlaneLn -> GrpPerm, PowMap, Map
CentralCollineationGroup(P, p) : Plane, PlanePt -> GrpPerm, PowMap, Map
CentralCollineationGroup(P, p, l) : Plane, PlanePt, PlaneLn -> GrpPerm, PowMap, Map
ChevalleyGroup(s, n, K: parameters) : MonStgElt, RngIntElt, FldFin -> GrpMat
ClassGroup(C) : Crv -> GrpAb, Map, Map
ClassGroup(K) : FldQuad -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map
ClassGroup(O: parameters) : RngOrd -> GrpAb, Map
ClassGroup(O) : RngFunOrd -> GrpAb, Map, Map
ClassGroup(Z) : RngInt -> GrpAb, Map
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(O) : RngFunOrd -> SeqEnum
ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt
ClassGroupExactSequence(F) : FldFun -> Map, Map, Map
ClassGroupExactSequence(O) : RngFunOrd -> Map, Map, Map
ClassGroupGenerationBound(F) : FldFun -> RngIntElt
ClassGroupGenerationBound(q, g) : RngIntElt, RngIntElt -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupStructure(Q: parameters) : QuadBin -> [ RngIntElt ]
CoisogenyGroup( G ) : GrpLie -> RootDtm
CoisogenyGroup( RD ) : RootDtm -> GrpAb
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
PointGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
CollineationGroupStabilizer(P, k) : Plane, RngIntElt -> GrpPerm, GSet, GSet, PowMap, Map
CommutatorSubgroup(G) : GrpPC -> GrpPC
ComponentGroupOrder(M, p) : ModSym, RngIntElt -> RngIntElt
ConditionalClassGroup(O) : RngOrd -> GrpAb, Map
ConditionedGroup(G) : GrpPC -> GrpPC
CongruenceGroup(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
CongruenceGroup(M : parameters) : ModSym -> GrpAb
CorrelationGroup(D) : IncGeom -> GrpPerm
CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm
CoxeterGroup( GrpFP, W ) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup(GrpFP, W) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( GrpFP, t ) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, t) : Cat, MonStgElt -> GrpFP
CoxeterGroup( F ) : GrpFP -> GrpCox, Map
CoxeterGroup( t ) : MonStgElt -> GrpCox
CoxeterGroup( RD ) : RootDtm -> GrpCox
CoxeterGroup( RD ) : RootDtm -> RngIntElt
CyclicGroup(C, n) : Cat, RngIntElt -> GrpFin
CyclicGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
CyclicGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
CyclicGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
CyclicGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
DecompositionGroup(p, A) : PlcNumElt, FldAb -> GrpAb
DecompositionGroup(p) : RngOrdIdl -> GrpPerm
DecompositionGroup(p, A) : RngOrdIdl, FldAb -> GrpAb
DerivedSubgroup(G) : GrpAb -> GrpAb
DerivedSubgroup(G) : GrpFin -> GrpFin
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
DihedralGroup(C, n) : Cat, RngIntElt -> GrpFin
DihedralGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
DihedralGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
DihedralGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
DihedralGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
DirichletGroup(N) : RngIntElt -> GrpDrch
DirichletGroup(N,R) : RngIntElt, Rng -> GrpDrch
DirichletGroup(N,R,z,r) : RngIntElt, Rng, RngElt, RngIntElt -> GrpDrch
DivisorGroup(C) : Crv -> DivCrv
DivisorGroup(D) : DivCrvElt -> DivCrv
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
EdgeGroup(G) : Grph -> GrpPerm, GSet
ElementaryAbelianGroup(GrpGPC, p, n) : Cat, RngIntElt, RngIntElt -> GrpGPC
ExistsGroupData(D, o1, o2): DB, RngIntElt, RngIntElt -> bool
ExtraSpecialGroup(G) : GrpMat -> GrpMat
ExtraSpecialGroup(C, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpFin
ExtraSpecialGroup(GrpFP, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpFP
ExtraSpecialGroup(GrpGPC, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpGPC
ExtraSpecialGroup(GrpPC, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpPC
ExtraSpecialGroup(GrpPerm, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpPerm
ExtractGroup(P) : Process(Lix) -> GrpFP
ExtractGroup(P) : Process(pQuot) -> GrpPC
FittingSubgroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpPC -> GrpPC
FixedGroup(K, L) : FldAlg, FldAlg -> GrpPerm
FreeAbelianGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
FreeAbelianGroup(n) : RngIntElt -> GrpAb
FreeGroup(n) : RngIntElt -> GrpFP
FreeNilpotentGroup(r, e) : RngIntElt, RngIntElt -> GrpGPC
FundamentalGroup( t ) : AlgMatElt -> GrpAb
FundamentalGroup( G ) : GrpLie -> RootDtm
FundamentalGroup( RD ) : RootDtm -> GrpAb
GaloisGroup(L) : FldAlg -> GrpPerm, [ FldPrElt, Any ]
GaloisGroup(f) : RngUPolElt -> GrpPerm, [ FldPrElt, Any ]
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GeneralOrthogonalGroup(arguments)
GeneralOrthogonalGroupMinus(arguments)
GeneralOrthogonalGroupPlus(arguments)
GeneralUnitaryGroup(arguments)
GenericAbelianGroup(U: parameters) : . -> GrpAbGen
GenericGroup(X) : [] -> GrpFp, Map
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
GlobalUnitGroup(F) : FldFun -> GrpAb, Map
Group(R) : AlgChtr -> Grp
Group(S) : AlgGrpSub -> Grp
Group(C) : CosetGeom -> GrpPerm
Group(D, i): DB, RngIntElt -> GrpFP, SeqEnum
Group(D, i): DB, RngIntElt -> GrpMat
Group(D, i): DB, RngIntElt -> GrpMat
Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
Group(V) : GrpFPCos -> GrpFP
Group(P) : GrpFPCosetEnumProc -> GrpFP
Group(Y) : GSet -> GrpPerm
Group(L) : Lat -> GrpMat
Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
AbelianGroup< X | R > : List(Identifiers), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
Group< X | R > : List(Var), List(GrpFPRel) -> GrpFP, Hom(Grp)
Group(M) : ModGrp -> Grp
Group(P) : Process(Tietze) -> GrpFP, Map
Group(R) : RngInvar -> Grp
Group(e) : SubGrpLatElt -> GrpFin
Group(FS) : SymFry -> GrpPSL2
GroupAlgebra(S) : AlgGrpSub -> AlgGrp
GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
GroupAlgebra(R, G) : Rng, Grp -> AlgGrp
GroupData(D, i): DB, RngIntElt -> Rec
GroupOfLieType( C, R ) : AlgMatElt, Rng -> AlgMatElt
GroupOfLieType( W, R ) : GrpCox, Rng -> AlgMatElt
GroupOfLieType( n, R ) : MonStgElt, Rng -> AlgMatElt
GroupOfLieType( RD, R ) : RootDtm, Rng -> AlgMatElt
GroupOfLieType( RD, k ) : RootDtm, Rng -> GrpLie
GroupOfLieType( W, R ) : RootDtm, Rng -> GrpLie
HadamardAutomorphismGroup(H) : AlgMatElt -> AlgMatElt
IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
IdentifyGroup(G): Grp -> Tup
IdentifyGroup(G): GrpFP -> Tup
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(m, p, n) : RngIntElt, RngIntElt, RngIntElt -> GrpMat, Fld
InertiaGroup(p) : RngOrdIdl -> GrpPerm
IntegralGroup(G) : GrpMat -> GrpMat, AlgMatElt
IntersectionGroup(M1, M2) : ModSym, ModSym -> GrpAb
IntersectionGroup(S) : SeqEnum -> GrpAb
IsInSmallGroupDatabase(o) : RngIntElt -> RngIntElt
IsLinearGroup(G) : GrpMat -> BoolElt
IsOrthogonalGroup(G) : GrpMat ->BoolElt
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSymplecticGroup(G) : GrpMat -> BoolElt
IsUnitaryGroup(G) : GrpMat -> BoolElt
IsogenyGroup( G ) : GrpLie -> RootDtm
IsogenyGroup( RD ) : RootDtm -> GrpAb
IsolGroup(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolGroupDatabase() : -> DB
IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat
IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> GrpMat
IsolGroupSatisfying(f) : Predicate -> GrpMat
LineGroup(P) : Plane -> GrpPerm, PowMap, Map
LocalCoxeterGroup( H ) : GrpCox -> GrpCox, Map
MatrixGroup(M) : ModGrp -> GrpMat
MatrixGroup< n, R | L > : RngIntElt, Rng, List -> GrpMat
MultiplicativeGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(Z) : RngInt -> GrpAb, Map
MultiplicativeGroup(R) : RngIntRes -> GrpAb, Map
NaturalGroup(L) : Lat -> GrpMat
NormGroup(A) : FldAb -> Map, RngOrdIdl, [RngIntElt]
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
PGO(arguments)
PGOMinus(arguments)
PGOPlus(arguments)
PSO(arguments)
PSOMinus(arguments)
PSOPlus(arguments)
PerfectGroupDatabase() : -> DB
PermutationGroup(C) : Code -> GrpPerm, PowMap, Map
PermutationGroup(A) : GrpAb -> GrpPerm, Hom(Grp)
PermutationGroup(D, i: parameters): DB, RngIntElt -> GrpFP
PermutationGroup< n | L > : RngIntElt, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
PicardGroup(O) : RngQuad -> GrpAb, Map
Places(K) : FldNum -> PlcNum
PointGroup(D) : Inc -> GrpPerm, GSet
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpGPC, Map
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map
PowerGroup(G) : GrpPC -> PowerGroup
ProjectiveGammaLinearGroup(arguments)
ProjectiveGammaUnitaryGroup(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralUnitaryGroup(arguments)
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
ProjectiveSpecialLinearGroup(arguments)
ProjectiveSpecialUnitaryGroup(arguments)
ProjectiveSuzukiGroup(arguments)
ProjectiveSymplecticGroup(arguments)
PureBraidGroup( W ) : GrpCox -> GrpFP, Map
PureBraidGroup( F ) : GrpFP -> GrpFP, Map
QuaternionicMatrixGroupDatabase() : -> DB
RamificationGroup(p) : RngOrdIdl -> GrpPerm
RamificationGroup(p, i) : RngOrdIdl, RngIntElt -> GrpPerm
RationalMatrixGroupDatabase() : -> DB
RayClassGroup(I) : RngOrdIdl -> GrpAb, Map
ReflectionGroup(M) : AlgMatElt -> GrpMat, Fld
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
SClassGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map, Map
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map
SUnitGroup(I) : RngOrdFracIdl -> GrpAb, Map
SUnitGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
SmallGroup(o: parameters) : RngIntElt -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupDatabase() : -> DB
SmallGroupDatabaseLimit() : -> RngIntElt
SmallGroupDecoding(c, o) : RngIntElt, RngIntElt -> GrpPC
SmallGroupEncoding(G) : GrpPC -> RngIntElt, RngIntElt
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupProcess(o: parameters) : RngIntElt -> Process
SmallGroupProcess(o, f: parameters) : RngIntElt, Program -> Process
SmallGroupProcess(S: parameters) : [RngIntElt] -> Process
SmallGroupProcess(S, f: parameters) : [RngIntElt], Program -> Process
SpecialLinearGroup(arguments)
SpecialOrthogonalGroup(arguments)
SpecialOrthogonalGroupMinus(arguments)
SpecialOrthogonalGroupPlus(arguments)
SpecialUnitaryGroup(arguments)
StandardActionGroup( W ) : GrpCox -> GrpPerm, Map
StandardGroup(G) : GrpPerm -> GrpPerm, Map
SuzukiGroup(arguments)
Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(n) : RngIntElt -> GrpPerm
Sym(X) : Set -> GrpPerm
SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin
SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
SymplecticGroup(arguments)
TorsionUnitGroup(O) : RngOrd -> GrpAb, Map
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupIdentification(G) : GrpPerm -> RngIntElt, RngIntElt
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
UnitGroup(S) : AlgQuatOrd -> GrpPerm, Map
UnitGroup(Q) : FldRat -> GrpAb, Map
UnitGroup(O) : RngFunOrd -> GrpAb, Map
UnitGroup(O) : RngOrd -> GrpAb, Map
UnitGroup(OQ) : RngOrdRes -> GrpAb, Map
WeylGroup( G ) : GrpLie -> GrpCox
WordGroup(G) : GrpMat -> GrpSLP, Map
WordGroup(G) : GrpPerm -> GrpBB, Map
pCoveringGroup(~P) : Process(pQuot) ->
pSelmerGroup(O, p, S) : RngOrd O, prime p, { RngOrdIdl } -> G, m
Invariants(G) : GrpMat -> [ RngIntElt ]
Abelian Group Functions (MATRIX GROUPS)
Abstract Group Predicates (GROUPS)
Abstract Group Predicates (MATRIX GROUPS)
Abstract Properties of a Group (PERMUTATION GROUPS)
Action of PSL_2(R) on the upper half plane (SUBGROUPS OF PSL_2(R))
Automatic Group Predicates (AUTOMATIC GROUPS)
Automorphism Group (FINITE SOLUBLE GROUPS)
Automorphism Group (LINEAR CODES OVER FINITE FIELDS)
Automorphism Group Algorithm (p-GROUPS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Automorphism Groups (LINEAR CODES OVER FINITE FIELDS)
Basic Group Properties (FINITE SOLUBLE GROUPS)
Class Group (BINARY QUADRATIC FORMS)
Construction from a Finite Permutation or Matrix Group (FINITELY PRESENTED GROUPS)
Construction of a General Matrix Group (MATRIX GROUPS)
Construction of an FP-Group (FINITELY PRESENTED GROUPS)
Construction of Graphs from Groups, Codes and Designs (GRAPHS)
Construction of Standard Groups (POLYCYCLIC GROUPS)
Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
Conversion from a Special Form of FP-Group (FINITELY PRESENTED GROUPS)
Counting p-groups (p-GROUPS)
Creation of a Matrix Group (MATRIX GROUPS)
Database of Galois Group Polynomials (OVERVIEW)
Databases of Structure Definitions (OVERVIEW)
Divisor Group (PLANE ALGEBRAIC CURVES)
Functions related to Divisor Class Groups of Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
General Group Properties (ABELIAN GROUPS)
General Group Properties (POLYCYCLIC GROUPS)
Generating p-groups (p-GROUPS)
Generators and Relations (PERMUTATION GROUPS)
Graphs Constructed from Groups (GRAPHS)
Group Actions (LINEAR CODES OVER FINITE FIELDS)
Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
Group Order (MATRIX GROUPS)
Group Order (PERMUTATION GROUPS)
Group Theoretic Functions (CLASS FIELD THEORY)
GROUPS
Groups (OVERVIEW)
Ideal Class Group (QUADRATIC FIELDS)
Ideal Class Groups (ORDERS AND ALGEBRAIC FIELDS)
Linear Equivalence and Class Group (PLANE ALGEBRAIC CURVES)
Mordell--Weil Group (ELLIPTIC CURVES)
p-group Functions (MATRIX GROUPS)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)
Permutations as Words (PERMUTATION GROUPS)
Power Groups (POLYCYCLIC GROUPS)
PowerGroup (FINITE SOLUBLE GROUPS)
Ray Class Groups (CLASS FIELD THEORY)
Rewrite Group Predicates (GROUPS DEFINED BY REWRITE SYSTEMS)
Small Group Identification (FINITELY PRESENTED GROUPS)
Soluble Matrix Groups (MATRIX GROUPS)
Standard Groups and Extensions (GROUPS)
Structure Operations (FINITE SOLUBLE GROUPS)
The 2-Selmer Group (HYPERELLIPTIC CURVES)
The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
The Collineation Group of a Plane (FINITE PLANES)
The FP-Group Constructor (FINITELY PRESENTED GROUPS)
The Quotient Group Constructor (FINITELY PRESENTED GROUPS)
Unit Groups (ORDERS AND ALGEBRAIC FIELDS)
Units and Unit Groups (QUATERNION ALGEBRAS)
Action of PSL_2(R) on the upper half plane (SUBGROUPS OF PSL_2(R))
Automorphism Groups (LINEAR CODES OVER FINITE FIELDS)
Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
Group Actions (LINEAR CODES OVER FINITE FIELDS)
General Group Properties (ABELIAN GROUPS)
General Group Properties (POLYCYCLIC GROUPS)
Construction of Graphs from Groups, Codes and Designs (GRAPHS)
Small Group Identification (FINITELY PRESENTED GROUPS)
Group Order (MATRIX GROUPS)
Group Order (PERMUTATION GROUPS)
GROUPS
Basic Group Properties (FINITE SOLUBLE GROUPS)
GrpPC_group-props (Example H24E4)
Group Theoretic Functions (CLASS FIELD THEORY)
RngInvar_GroupActions (Example H80E1)
GroupAlgebra(S) : AlgGrpSub -> AlgGrp
GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
GroupAlgebra(R, G) : Rng, Grp -> AlgGrp
GrpAbGen_GroupComputation (Example H17E3)
Grp_GroupConstructors (Example H16E3)
GroupData(D, i): DB, RngIntElt -> Rec
GroupOfLieType( C, R ) : AlgMatElt, Rng -> AlgMatElt
GroupOfLieType( W, R ) : GrpCox, Rng -> AlgMatElt
GroupOfLieType( n, R ) : MonStgElt, Rng -> AlgMatElt
GroupOfLieType( RD, R ) : RootDtm, Rng -> AlgMatElt
GroupOfLieType( RD, k ) : RootDtm, Rng -> GrpLie
GroupOfLieType( W, R ) : RootDtm, Rng -> GrpLie
NumberOfGroups(D) : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC]
IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum
IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> SeqEnum
IsolGroupsSatisfying(f) : Predicate -> SeqEnum
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, o) : DB, RngIntElt -> RngIntElt
NumberOfSmallGroups(o) : RngIntElt -> RngIntElt
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
SmallGroups(o, f: parameters) : RngIntElt, Program -> [* Grp *]
SmallGroups(S: parameters) : [RngIntElt] -> [* Grp *]
SmallGroups(S, f: parameters) : [RngIntElt], Program -> [* Grp *]
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
Accessing Information (BRAID GROUPS)
Arithmetic Operators and Functions for Elements (BRAID GROUPS)
Boolean Predicates for Elements (BRAID GROUPS)
Building Permutation Groups (PERMUTATION GROUPS)
Constructing Braid Groups and their Elements (BRAID GROUPS)
COXETER GROUPS
Generic Groups (CLASS FIELD THEORY)
Groups (OVERVIEW)
GROUPS OF LIE TYPE
Imprimitive Unitary Reflection Groups (REFLECTION GROUPS)
Introduction (BRAID GROUPS)
Introduction (POLYCYCLIC GROUPS)
Normal Form for Elements of a Braid Group (BRAID GROUPS)
p-GROUPS
Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)
Primitive Unitary Reflection Groups (REFLECTION GROUPS)
Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))
GROUPS OF LIE TYPE
GrowthFunction(G) : GrpAtc -> FldFunRatElt
GrowthFunction(G) : GrpAtc -> FldFunRatElt
GrpAtc_GrowthFunction (Example H28E8)
AUTOMORPHISM GROUPS OF GROUPS
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
Transfer from GrpPC (FINITE SOLUBLE GROUPS)
Transfer to GrpPC (FINITE SOLUBLE GROUPS)
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
AUTOMORPHISM GROUPS OF GROUPS
ALGEBRAS
ASSOCIATIVE ALGEBRAS
LIE ALGEBRAS
STRUCTURE CONSTANT ALGEBRAS
Groups (OVERVIEW)
Groups (OVERVIEW)
Groups (OVERVIEW)
Groups (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Groups (OVERVIEW)
GrpLie_GrpLieEltArith (Example H35E5)
GrpLie_GrpLieEltProduct (Example H35E4)
Groups (OVERVIEW)
Groups (OVERVIEW)
Groups (OVERVIEW)
SUBGROUPS OF PSL_2(R)
Basic Attributes (SUBGROUPS OF PSL_2(R))
Creation of Subgroups of PSL_2(R) (SUBGROUPS OF PSL_2(R))
Relations (SUBGROUPS OF PSL_2(R))
Basic Functions (SUBGROUPS OF PSL_2(R))
Elements of PSL_2(R) (SUBGROUPS OF PSL_2(R))
Membership and Equality testing (SUBGROUPS OF PSL_2(R))
Creation (SUBGROUPS OF PSL_2(R))
Groups (OVERVIEW)
GRSCode(A, V, k) : [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
CodeFld_GRSCode (Example H101E30)
GSet(G) : GrpPerm -> GSet
GSet(G) : GrpPerm -> GSet
GSet(G) : GrpPerm -> GSet
GSet(G, X, Y) : GrpPerm, GSet, SetEnum -> GSet
GSet(G, Y, f) : GrpPerm, Set, Map -> GSet
GSetFromIndexed(G, Y) : GrpPerm, SetIndx -> GSet
RootGSet( W ) : GrpCox -> GSet
GSetFromIndexed(G, Y) : GrpPerm, SetIndx -> GSet
GrpCox_GSets (Example H34E9)
GrpPerm_GSets (Example H20E18)
Comparison (OVERVIEW)
u gt v : AlgFPElt, AlgFPElt -> BoolElt
u gt v : GrpFPElt, GrpFPElt -> BoolElt
M1 gt M2 : ModBrdt, ModBrdt -> BoolElt
s gt t : MonStgElt, MonStgElt -> BoolElt
a gt b : RngElt, RngElt -> BoolElt
S gt T : SeqEnum, SeqEnum -> BoolElt
u gt v : SgpFPElt, SgpFPElt -> BoolElt
GU(arguments)
GeneralUnitaryGroup(arguments)
IsolGuardian(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
[____] [____] [_____] [____] [__] [Index] [Root]