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Index G
G
G-Sets (PERMUTATION GROUPS)
Lattices from Matrix Groups (LATTICES)
Modules (OVERVIEW)
G-lattices
Lattices from Matrix Groups (LATTICES)
G-module
Modules (OVERVIEW)
G-set
G-Sets (PERMUTATION GROUPS)
G23
GrpFP_G23 (Example H16E25)
G8723
GrpFP_G8723 (Example H16E16)
GabidulinCode
GabidulinCode(A, W, Z, t) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
Galois
FINITE FIELDS
Rings, Fields, and Algebras (OVERVIEW)
galois
Database of Galois Group Polynomials (OVERVIEW)
Galois group (NUMBER FIELDS AND THEIR ORDERS)
GaloisConjugate
GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
GaloisField
FiniteField(q) : RngIntElt -> FldFin
GaloisGroup
GaloisGroup(K) : FldNum -> GrpPerm, [ FldPrElt ]
GaloisOrbit
GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
galpols
Database of Galois Group Polynomials (OVERVIEW)
Gamma
Gamma(s) : FldPrElt -> FldPrElt
gamma
Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)
gamma-bessel
Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)
GammaD
GammaD(s) : FldPrElt -> FldPrElt
GaussianPeriods
FldCyc_GaussianPeriods (Example H35E1)
GCD
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
Gcd
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
gcd
Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
gcd-lcm
Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
ge
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
general
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Construction of a General Group (GROUPS)
Construction of a General Permutation Group (PERMUTATION GROUPS)
Construction of General Linear Codes (ERROR-CORRECTING CODES)
Creation of the General Linear Group and its Elements (MATRIX GROUPS)
General Constructions (MATRIX GROUPS)
General Factorization (RING OF INTEGERS)
GENERAL MODULES
Presentations (FINITELY PRESENTED SEMIGROUPS)
general-magma
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Presentations (FINITELY PRESENTED SEMIGROUPS)
GeneralizedSrivastavaCode
GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
GeneralLinearGroup
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GeneralOrthogonalGroup
GeneralOrthogonalGroup(arguments)
GeneralOrthogonalGroupMinus
GeneralOrthogonalGroupMinus(arguments)
GeneralOrthogonalGroupPlus
GeneralOrthogonalGroupPlus(arguments)
GeneralUnitaryGroup
GeneralUnitaryGroup(arguments)
GeneratepGroups
GeneratepGroups (G : parameters) : GrpPC -> [pgaProc]
GrpPC_GeneratepGroups (Example H19E10)
GeneratingWords
GeneratingWords(G, H) : GrpFP, GrpFP -> { GrpFPElt }
Generator
F . 1 : FldFin, RngIntElt -> FldFinElt
Generator(F, E) : FldFin, FldFin -> FldFinElt
generator
Base and Strong Generator Functions (MATRIX GROUPS)
Base and Strong Generator Functions (PERMUTATION GROUPS)
Finding Special Elements (NUMBER FIELDS AND THEIR ORDERS)
Generator Assignment (OVERVIEW)
Generator Assignment (STATEMENTS AND EXPRESSIONS)
Special Elements (FINITE FIELDS)
Univariate Elimination Ideal Generators (MULTIVARIATE POLYNOMIAL RINGS)
generator-assignment
Generator Assignment (OVERVIEW)
Generator Assignment (STATEMENTS AND EXPRESSIONS)
generator-primitive
Finding Special Elements (NUMBER FIELDS AND THEIR ORDERS)
generator-primitive-normal
Special Elements (FINITE FIELDS)
GeneratorMatrix
GeneratorMatrix(C) : Code -> ModMatFldElt
GeneratorNaming
State_GeneratorNaming (Example H1E5)
GeneratorNamingSequence
State_GeneratorNamingSequence (Example H1E4)
GeneratorNumber
GeneratorNumber(w) : GrpFPElt -> RngIntElt
GeneratorPolynomial
GeneratorPolynomial(C) : Code -> RngUPolElt
Generators
Generators(A) : AlgFP -> { AlgFPElt }
Generators(R) : AlgMat -> { AlgMatElt }
Generators(C) : Code -> { ModTupFldElt }
Generators(E) : CurveEll -> [ CurveEllPt ]
Generators(G) : Grp -> { GrpFinElt }
Generators(A) : GrpAb -> { GrpAbElt }
Generators(G) : GrpBB -> { GrpBBElt }
Generators(G) : GrpFP -> { GrpFPElt }
Generators(G) : GrpMat -> { GrpMatElt }
Generators(G) : GrpPC -> { GrpPCElt }
Generators(G) : GrpPerm -> { GrpPermElt }
Generators(V) : ModTupFld -> { ModElt }
Generators(M) : ModTupRng -> { ModTupElt }
Generators(I) : RngFunOrdIdl -> [ RngFunOrdElt ]
Generators(I) : RngOrdIdl -> [ RngOrdElt ]
Generators(S) : SgpFP -> { SgpFPElt }
Grp_Generators (Example H15E10)
generators
Addition of extra generators (BLACKBOX GROUPS)
GeneratorStructure
GeneratorStructure(P) : Process(pQuot) ->
Generic
Generic(R) : AlgMat -> AlgMat
Generic(C) : Code -> Code
Generic(E): CurveEllSubgroup -> CurveEll
Generic(E): CurveEllSubscheme -> CurveEll
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
generic
Generic Element Constructions (LOCAL FIELDS)
Generic Element Functions and Predicates (REAL AND COMPLEX FIELDS)
Generic Ideal Functions (RESIDUE CLASS RINGS)
Generic Predicates (LOCAL FIELDS)
Generic Ring Functions (INTRODUCTION [RINGS AND FIELDS])
Parent and Category (FINITE FIELDS)
Parent and Category (RATIONAL FIELD)
Parent and Category (RESIDUE CLASS RINGS)
Parent and Category (RING OF INTEGERS)
Related Structures (MULTIVARIATE POLYNOMIAL RINGS)
Related Structures (RATIONAL FIELD)
Related Structures (UNIVARIATE POLYNOMIAL RINGS)
GenericPoint
Elcu_GenericPoint (Example H53E9)
Genus
Genus(K) : FldFun -> RngIntElt
Genus(L) : Lat -> [ Lat ]
genus
Genus (LATTICES)
Geodesic
Geodesic(u, v) : GrphVert, GrphVert -> [GrphVert]
GeomEC
Combinatorial and Geometrical Structures (OVERVIEW)
geometrical
Combinatorial and Geometrical Structures (OVERVIEW)
Get
Set and Get (ENVIRONMENT AND OPTIONS)
GetAssertions
SetAssertions(b) : BoolElt ->
GetAutoColumns
SetAutoColumns(b) : BoolElt ->
GetAutoCompact
SetAutoCompact(b) : BoolElt ->
GetBeep
SetBeep(b) : BoolElt ->
Getc
Getc(F) : File -> MonStgElt
GetColumns
SetColumns(n) : RngIntElt ->
GetCurrentDirectory
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->
GetDefaultRealField
GetDefaultRealField() : Null -> FldPr
GetEchoInput
SetEchoInput(b) : BoolElt ->
GetHistorySize
SetHistorySize(n) : RngIntElt ->
GetIgnorePrompt
SetIgnorePrompt(b) : BoolElt ->
GetIgnoreSpaces
SetIgnoreSpaces(b) : BoolElt ->
GetIndent
SetIndent(n) : RngIntElt ->
GetLibraries
SetLibraries(s) : MonStgElt ->
GetLibraryRoot
SetLibraryRoot(s) : MonStgElt ->
GetLineEditor
SetLineEditor(b) : BoolElt ->
GetMemoryLimit
SetMemoryLimit(n) : RngIntElt ->
GetPath
SetPath(s) : MonStgElt ->
Getpid
Getpid() : ->
GetPreviousSize
GetPreviousSize() : -> RngIntElt
GetPrintLevel
SetPrintLevel(l) : MonStgElt ->
GetPrompt
SetPrompt(s) : MonStgElt ->
GetRows
SetRows(n) : RngIntElt ->
Gets
Gets(F) : File -> MonStgElt
GetSeed
SetSeed(s) : RngIntElt ->
GetTime
IO_GetTime (Example H3E10)
GetVerbose
GetVerbose(s) : MonStgElt -> RngIntElt
GetViMode
SetViMode(b) : BoolElt ->
GF
FiniteField(q) : RngIntElt -> FldFin
GHom
GHom(M, N) : ModGrp, ModGrp -> ModMatGrp
GHomOverCentralizingField
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
GilbertVarshamovBound
GilbertVarshamovBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Girth
Girth(G) : GrphUnd -> RngIntElt
GirthCycle
GirthCycle(G) : GrphUnd -> [GrphVert]
GL
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
glex
Graded Lexicographical: glex (MULTIVARIATE POLYNOMIAL RINGS)
glnzgps
Database of Maximal Finite Subgroups of GL(n, Z) (OVERVIEW)
GLSylow
GrpMat_GLSylow (Example H21E6)
GModule
GModule(G, S) : Grp, AlgMat -> ModGrp
GModule(G, S) : Grp, AlgMat -> ModGrp
GModule(G, P, d) : Grp, RngMPol, RngIntElt -> ModGrp, Map, @ RngMPolElt @
GModule(G, S) : GrpFin, AlgMat -> ModGrpFin
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G) : GrpMat -> ModGrp
GModule(G, M) : GrpPC, AlgMat -> ModAlg
RngInvar_GModule (Example H30E2)
gmodule
Construction of G-modules (INVARIANT RINGS OF FINITE GROUPS)
GModules1
RMod_GModules1 (Example H42E12)
GModules2
RMod_GModules2 (Example H42E13)
GO
GeneralOrthogonalGroup(arguments)
GolayCode
GolayCode(K, extend) : FldFin, BoolElt -> Code
GOMinus
GeneralOrthogonalGroupMinus(arguments)
GoodBasePoints
GoodBasePoints(G: parameters) : GrpMat -> []
GOPlus
GeneralOrthogonalGroupPlus(arguments)
GoppaCode
GoppaCode(L, G) : [ FldFinElt ], RngUPolElt -> Code
Code_GoppaCode (Example H58E9)
goto
The break statement (OVERVIEW)
The continue statement (OVERVIEW)
gps100
Database of Groups of Order up to 100 (OVERVIEW)
Graded
RngMPol_Graded (Example H29E24)
graded
Creation of Graded Modules (MODULES OVER AFFINE ALGEBRAS)
Graded Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
graded-weight
Graded Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
GramMatrix
GramMatrix(L) : Lat -> AlgMatElt
Graph
Graph<p | edges> : RngIntElt, List -> GrphUnd
graph
Adjacency, Degree and Distance Functions for a Graph (GRAPHS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Combinatorial and Geometrical Structures (OVERVIEW)
Connectedness, Paths and Circuits 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)
GRAPHS
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
Planes, Graphs and Codes (FINITE PLANES)
The Graph of a Map (MAPPINGS)
graph-code
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
Planes, Graphs and Codes (FINITE PLANES)
graph-digraph
Construction of Graphs and Digraphs (GRAPHS)
graphs
Design_graphs (Example H56E12)
greater
Comparison (OVERVIEW)
GreatestCommonDivisor
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
grevlex
Graded Reverse Lexicographical: grevlex (MULTIVARIATE POLYNOMIAL RINGS)
GriesmerBound
GriesmerBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Groebner
Groebner(M) : ModMPol ->
Groebner(I: parameters) : RngMPol ->
groebner
Creation of Ideals and Computation of Gröbner Bases (MULTIVARIATE POLYNOMIAL RINGS)
Hilbert-driven Gröbner Basis Construction (MULTIVARIATE POLYNOMIAL RINGS)
GroebnerBasis
GroebnerBasis(I) : RngMPol -> RngMPolElt
GroebnerBasisUnreduced
GroebnerBasisUnreduced(S) : [ RngMPolElt ] -> [ RngMPolElt ]
GroebnerWalk
GroebnerWalk(I, J) : RngMPol, RngMPol -> RngMPol
RngMPol_GroebnerWalk (Example H29E12)
Grotzch
Graph_Grotzch (Example H55E11)
ground
Change Ground Ring (ELLIPTIC CURVES)
GroundField
GroundField(F) : FldFin -> FldFin
GroundField(K) : FldNum -> Fld
Group
Group(R) : AlgChtr -> Grp
Group(S) : AlgGrpSub -> Grp
Group(V) : GrpFPCos -> GrpFP
Group(Y) : GSet -> GrpPerm
Group(L) : Lat -> GrpMat
Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
Group< X | R > : List(Var), List(GrpFPRel) -> GrpFP, Hom(Grp)
Group(M) : ModGrp -> Grp
Group(R) : RngInvar -> Grp
Group(e) : SubGrpLatElt -> GrpFin
group
Abstract Group Predicates (GROUPS)
Abstract Group Predicates (MATRIX GROUPS)
Abstract Group Predicates (PERMUTATION GROUPS)
Automorphism Group Algorithm (SOLUBLE GROUPS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Construction of Graphs from Groups, Codes and Designs (GRAPHS)
Construction of Standard Groups (SOLUBLE GROUPS)
Creation of the General Linear Group and its Elements (MATRIX GROUPS)
Database of Galois Group Polynomials (OVERVIEW)
Databases of Structure Definitions (OVERVIEW)
General Constructions (MATRIX GROUPS)
General Group Properties (ABELIAN GROUPS)
General Group Properties (SOLUBLE GROUPS)
Generating p-groups (SOLUBLE GROUPS)
Graphs Constructed from Groups (GRAPHS)
Group Actions on Codes (ERROR-CORRECTING CODES)
Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
GROUPS
Groups (OVERVIEW)
Ideal Class Group (QUADRATIC FIELDS)
Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)
Matrix Group Predicates (MATRIX GROUPS)
p-group Functions (MATRIX GROUPS)
Permutation Group Predicates (PERMUTATION GROUPS)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)
Power Groups (SOLUBLE GROUPS)
PowerGroup (SOLUBLE GROUPS)
Soluble Matrix Groups (MATRIX GROUPS)
Standard Groups and Extensions (FINITELY PRESENTED GROUPS)
Standard Groups and Extensions (GROUPS)
Standard Groups and Extensions (PERMUTATION GROUPS)
Structure Operations (SOLUBLE GROUPS)
The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
The Collineation Group of a Plane (FINITE PLANES)
The Finitely Presented Group Associated with a Permutation Group (PERMUTATION GROUPS)
Unit Group (QUADRATIC FIELDS)
Unit Groups (NUMBER FIELDS AND THEIR ORDERS)
group-action
Group Actions on Codes (ERROR-CORRECTING CODES)
Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
group-Boolean
General Group Properties (ABELIAN GROUPS)
General Group Properties (SOLUBLE GROUPS)
group-code-design
Construction of Graphs from Groups, Codes and Designs (GRAPHS)
group-overview
GROUPS
GroupActions
RngInvar_GroupActions (Example H30E1)
GroupAlgebra
GroupAlgebra(S) : AlgGrpSub -> AlgGrp
GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
GroupAlgebra(R, G) : Rng, Grp -> AlgGrp
GroupConstructors
Grp_GroupConstructors (Example H15E3)
groups
Groups (OVERVIEW)
grp
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
grp-alg-ops
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
grp_alg
ALGEBRAS
ASSOCIATIVE ALGEBRAS
LIE ALGEBRAS
STRUCTURE CONSTANT ALGEBRAS
GrpAb
Groups (OVERVIEW)
GrpBB
Groups (OVERVIEW)
GrpFP
Groups (OVERVIEW)
GrphDir
Combinatorial and Geometrical Structures (OVERVIEW)
GrphUnd
Combinatorial and Geometrical Structures (OVERVIEW)
GrpMat
Groups (OVERVIEW)
GrpPC
Groups (OVERVIEW)
GrpPerm
Groups (OVERVIEW)
GRSCode
GRSCode(A, V, k) : [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
Code_GRSCode (Example H58E10)
GSet
GSet(G) : GrpPerm -> GSet
GSet(G, Y) : GrpPerm, SetIndx -> GSet
gt
Comparison (OVERVIEW)
u gt v : AlgFPElt, AlgFPElt -> BoolElt
u gt v : GrpFPElt, GrpFPElt -> 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
GeneralUnitaryGroup(arguments)
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