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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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