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Index G
G
G-Sets (PERMUTATION GROUPS)
Modules (OVERVIEW)
G-module
Modules (OVERVIEW)
G-set
G-Sets (PERMUTATION GROUPS)
G23
GrpFP_G23 (Example H12E25)
G8723
GrpFP_G8723 (Example H12E16)
Galois
FINITE FIELDS
Rings, Fields, and Algebras (OVERVIEW)
galois
Galois group (NUMBER FIELDS AND THEIR ORDERS)
GaloisConjugate
GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
GaloisField
FiniteField(q) : RngIntElt -> FldFin
GaloisGroup
GaloisGroup(K) : FldNum -> GrpPerm
GaloisOrbit
GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
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 H27E1)
GCD
GreatestCommonDivisor(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
Gcd
GreatestCommonDivisor(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
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)
GcdReduce
GcdReduce(~P: parameters) : Process(Tietze) ->
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 MODULES
Presentations (FINITELY PRESENTED SEMIGROUPS)
The General Mapping Constructor (MAPPINGS)
general-magma
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Presentations (FINITELY PRESENTED SEMIGROUPS)
GeneralLinearGroup
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GeneralLinearGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
GeneralUnitaryGroup
GeneralUnitaryGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
GeneratepGroups
GeneratepGroups (G : parameters) : GrpPC -> [pgaProc]
GrpPC_GeneratepGroups (Example H13E9)
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)
Special Elements (FINITE FIELDS)
generator-assignment
Generator Assignment (OVERVIEW)
generator-primitive
Finding Special Elements (NUMBER FIELDS AND THEIR ORDERS)
generator-primitive-normal
Special Elements (FINITE FIELDS)
GeneratorMatrix
GeneratorMatrix(C) : Code -> ModMatFldElt
GeneratorNaming
Lang_GeneratorNaming (Example H1E6)
GeneratorNumber
GeneratorNumber(w) : GrpFPElt -> RngIntElt
Generators
Generators(A) : AlgFP -> { AlgFPElt }
Generators(R) : AlgMat -> { AlgMatElt }
Generators(C) : Code -> { ModTupFldElt }
Generators(G) : Grp -> { GrpFinElt }
Generators(A) : GrpAb -> { GrpAbElt }
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) : RngOrdIdl -> [ RngOrdElt ]
Generators(S) : SgpFP -> { SgpFPElt }
Grp_Generators (Example H9E10)
GeneratorStructure
GeneratorStructure(P) : Process(pQuot) ->
Generic
Generic(R) : AlgMat -> AlgMat
Generic(C) : Code -> Code
Generic(G) : Grp -> Grp
Generic(G) : GrpMat -> GrpMat
Generic(G) : GrpPerm -> GrpPerm
Generic(V) : ModFld -> ModFld
Generic(M) : ModRng -> ModRng
Generic(I) : RngDPol -> RngDPol
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)
Geodesic
Geodesic(u, v) : Vert, Vert -> [Vert]
geometrical
Combinatorial and Geometrical Structures (OVERVIEW)
Get
Set and Get (SYSTEM FEATURES)
GetAssertions
SetAssertions(b) : BoolElt ->
GetAutoColumns
SetAutoColumns(b) : BoolElt ->
GetBeep
SetBeep(b) : BoolElt ->
GetColumns
SetColumns(n) : RngIntElt ->
GetCurrentDirectory
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->
GetDefaultRealField
GetDefaultRealField() : Null -> FldPr
GetHistorySize
SetHistorySize(n) : RngIntElt ->
GetIgnorePrompt
SetIgnorePrompt(b) : BoolElt ->
GetIndent
SetIndent(n) : RngIntElt ->
GetLibraries
SetLibraries(s) : MonStgElt ->
GetLibraryRoot
SetLibraryRoot(s) : MonStgElt ->
GetLineEditor
SetLineEditor(b) : BoolElt ->
GetMemoryExtensionSize
SetMemoryExtensionSize(n) : RngIntElt ->
GetMemoryLimit
SetMemoryLimit(n) : RngIntElt ->
GetPath
SetPath(s) : MonStgElt ->
GetPrintLevel
SetPrintLevel(l) : MonStgElt ->
GetPrompt
SetPrompt(s) : MonStgElt ->
GetRows
SetRows(n) : RngIntElt ->
GetSeed
SetSeed(s) : RngIntElt ->
GetVerbose
SetVerbose(s, i) : 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
Girth
Girth(G) : GrphUnd -> RngIntElt
GirthCycle
GirthCycle(G) : GrphUnd -> [Vert]
GL
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GeneralLinearGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
glnzgps
Database of Maximal Finite Subgroups of GL(n, Z) (OVERVIEW)
GLSylow
GrpMat_GLSylow (Example H15E6)
GModule
GModule(G, S) : Grp, AlgMat -> ModGrp
GModule(G, S) : Grp, AlgMat -> ModGrp
GModule(G, S) : GrpFin, AlgMat -> ModGrpFin
GModule(G) : GrpMat -> Mod
GModule(G) : GrpMat -> Mod
GModule(G, M) : GrpPC, AlgMat -> ModAlg
GModules1
RMod_GModules1 (Example H34E11)
GModules2
RMod_GModules2 (Example H34E12)
GModuleTup
GModuleTup(MGT) : SetCartElt -> ModRng
GolayCode
GolayCode(K, extend) : FldFin, BoolElt -> Code
GoppaCode
GoppaCode(L, G) : [ FldFinElt ], RngUPolElt -> Code
Code_GoppaCode (Example H40E9)
goto
The break statement (OVERVIEW)
The continue statement (OVERVIEW)
gps100
Database of Groups of Order up to 100 (OVERVIEW)
Graph
Graph<p | edges> : RngIntElt, List -> GrphUnd
graph
Adjacency, Degree and Distance Functions for a Graph (GRAPHS)
Combinatorial and Geometrical Structures (OVERVIEW)
Connectedness, Paths and Circuits in a Graph (GRAPHS)
Constructing Complements, Line Graphs; Contraction and 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
The Automorphism Group of a Graph or Digraph (GRAPHS)
The Graph of a Map (MAPPINGS)
graph-digraph
Construction of Graphs and Digraphs (GRAPHS)
greater
Comparison (OVERVIEW)
GreatestCommonDivisor
GreatestCommonDivisor(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt
GreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
Groebner
Groebner(I: parameters) : RngDPol ->
RngDPol_Groebner (Example H23E8)
groebner
Ideals and Gr"obner Bases (MULTIVARIATE POLYNOMIAL RINGS)
GroebnerBasis
GroebnerBasis(I) : RngDPol -> RngDPolElt
GroebnerWalk
GroebnerWalk(I, J) : RngDPol, RngDPol -> RngDPol
RngDPol_GroebnerWalk (Example H23E9)
Grotzch
Graph_Grotzch (Example H39E2)
ground
Change Ground Ring (ELLIPTIC CURVES)
GroundField
GroundField(F) : FldFin -> FldFin
GroundField(K) : FldNum -> FldNum
Group
Group(R) : AlgChtr -> Grp
Group(V) : GrpFPCos -> GrpFP
Group(Y) : GSet -> GrpPerm
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(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 Design or Set System (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)
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 (MULTIVARIATE POLYNOMIAL RINGS)
Group Actions on Codes (ERROR-CORRECTING CODES)
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 (MATRIX GROUPS)
Standard Groups and Extensions (PERMUTATION GROUPS)
Structure Operations (SOLUBLE GROUPS)
The Automorphism Group of a Graph or Digraph (GRAPHS)
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 (MULTIVARIATE POLYNOMIAL RINGS)
Group Actions on Codes (ERROR-CORRECTING CODES)
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
RngDPol_GroupActions (Example H23E18)
RngDPol_GroupActions (Example H23E19)
GroupConstructors
Grp_GroupConstructors (Example H9E3)
groups
Groups (OVERVIEW)
GroupTup
GroupTup(MGT) : SetCartElt -> GrpMat
GrpAb
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 H40E10)
GSet
GSet(G) : GrpPerm -> GSet
GSet(G, S) : GrpPerm, Set -> 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(n, q) : RngIntElt, RngIntElt -> GrpMat
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