Index A

A-key

a-key

A5

abelian

Abelian Quotients (FINITELY PRESENTED GROUPS)

AbelianBasis

AbelianBasis(G) : GrpPC -> [ GrpPCElt ], [ RngIntElt ]

AbelianBasis(G) : GrpPerm -> [ GrpPermElt ], [ RngIntElt ]

AbelianGroup

AbelianGroup(C, Q) : Cat, [ RngIntElt ] -> GrpFin

AbelianGroup(GrpFP, [n_1,...,n_r]): Cat, [ RngIntElt ] -> GrpFP

AbelianGroup(GrpPerm, Q) : Cat, [ RngIntElt ] -> GrpPerm

AbelianGroup(GrpPC, Q) : Cat, [RngIntElt] -> GrpPC

AbelianGroup< X | R > : List(Var), List(GrpAbRel) -> GrpAb, Hom(GrpAb)

Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)

GrpAb_AbelianGroup (Example H18E3)

AbelianInvariants

AbelianInvariants(G) : GrpMat -> [ RngIntElt ]

AbelianInvariants(G) : GrpPC -> [RngIntElt]

AbelianInvariants(G) : GrpPerm -> [ RngIntElt ]

AbelianQuotient

AbelianQuotientInvariants

AbelianSubgroups

Abs

AbsoluteValue(q) : FldRatElt -> FldRatElt

AbsoluteValue(n) : RngIntElt -> RngIntElt

AbsoluteValue(f) : RngMPolElt -> RngMPolElt

AbsoluteValue(p) : RngUPolElt -> RngUPolElt

abs

abs-and-sign

AbsoluteCharacteristicPolynomial

AbsoluteDegree

AbsoluteField

AbsoluteLogarithmicHeight

AbsoluteMinimalPolynomial

AbsoluteNorm

AbsoluteNorm(a) : FldNumElt -> FldRatElt

AbsoluteOrder

AbsolutePrecision

AbsolutePrecision(f) : RngSerElt -> RngIntElt

AbsoluteRepresentation

AbsoluteRepresentation(M) : ModRng -> ModRng

AbsoluteRepresentationMatrix

AbsoluteTrace

AbsoluteTrace(a) : FldNumElt -> FldRatElt

AbsoluteValue

AbsoluteValue(q) : FldRatElt -> FldRatElt

AbsoluteValue(n) : RngIntElt -> RngIntElt

AbsoluteValue(f) : RngMPolElt -> RngMPolElt

AbsoluteValue(p) : RngUPolElt -> RngUPolElt

AbsoluteValues

Abstract

abstract

Abstract Group Predicates (MATRIX GROUPS)

Abstract Group Predicates (PERMUTATION GROUPS)

The Abstract Structure of a Group (GROUPS)

The Abstract Structure of a Group (MATRIX GROUPS)

The Abstract Structure of a Group (PERMUTATION GROUPS)

abstract-group

Abstract Group Predicates (MATRIX GROUPS)

Abstract Group Predicates (PERMUTATION GROUPS)

abstract-structure

The Abstract Structure of a Group (MATRIX GROUPS)

The Abstract Structure of a Group (PERMUTATION GROUPS)

Access

access

Access and Modification Functions (RECORDS)

Access Functions (ERROR-CORRECTING CODES)

Access Functions (LISTS)

Access Functions (SEQUENCES)

Access Functions for PC-Groups (SOLUBLE GROUPS)

Access Operations (ELLIPTIC CURVES)

Accessing and Modifying a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

Accessing and Modifying Sets (SETS)

Accessing Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)

Accessing Class Functions (CHARACTERS OF FINITE GROUPS)

Accessing Components of a Codeword (ERROR-CORRECTING CODES)

Accessing functions (COPRODUCTS)

Accessing Group Information (GROUPS)

Accessing Group Information (MATRIX GROUPS)

Accessing Group Information (PERMUTATION GROUPS)

Accessing Information (FINITELY PRESENTED GROUPS)

Accessing Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)

Accessing Module Information (GENERAL MODULES)

Accessing Sets and their Associated Structures (SETS)

Accessing the Base and Strong Generating Set (MATRIX GROUPS)

Accessing the Base and Strong Generating Set (PERMUTATION GROUPS)

Accessing the Databases (PERMUTATION GROUPS)

Accessing the Defining Generators and Relations (ABELIAN GROUPS)

Accessing the Defining Generators and Relations (BLACKBOX GROUPS)

Accessing the Defining Generators and Relations (FINITELY PRESENTED ALGEBRAS)

Accessing the Defining Generators and Relations (FINITELY PRESENTED GROUPS)

Accessing the Defining Generators and Relations (FINITELY PRESENTED SEMIGROUPS)

Accessing Vector Space Invariants (VECTOR SPACES)

Module Access (MODULES OVER AFFINE ALGEBRAS)

Module Element Access and Operations (MODULES OVER AFFINE ALGEBRAS)

Properties of Lattices (LATTICES)

Structures Associated with a Plane (FINITE PLANES)

Tuple Access Functions (TUPLES AND CARTESIAN PRODUCTS)

access-modification

Accessing and Modifying Sets (SETS)

ActingWord

Action

Action(A, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm

Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm

Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm

Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm

Action(Y) : GSet -> Map

Action(M) : ModTupRng -> AlgMat

action

Action of Automorphisms (INCIDENCE STRUCTURES AND DESIGNS)

Action on a Coset Space (GROUPS)

Action on a Coset Space (MATRIX GROUPS)

Action on a Coset Space (PERMUTATION GROUPS)

Action on a G-invariant Partition (PERMUTATION GROUPS)

Action on Orbits (PERMUTATION GROUPS)

General Action of Collineations (FINITE PLANES)

Group Actions on Codes (ERROR-CORRECTING CODES)

Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)

Matrix Action on Forms (QUADRATIC FIELDS)

Natural Actions for Primitive Groups (PERMUTATION GROUPS)

The Homomorphism Induced by G-action on Orbits (MATRIX GROUPS)

action-primitive

ActionGenerator

ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt

ActionImage

ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm

ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm

ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm

ActionKernel

ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm

ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm

ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm

Actions

GrpPerm_Actions (Example H20E13)

AddAttribute

AddColumn

AddColumn(~a, u, i, j) : ModMatElt, RngElt, RngIntElt, RngIntElt ->

AddColumn(~X, u, i, j) : ModMatRngElt, RngElt, RngIntElt, RngIntElt ->

AddEdge

AddEdges

AddGenerator

AddGenerator(S) : SgpFP -> SgpFP

addition

AdditiveGroup

AdditiveGroup(Z) : RngInt -> GrpAb, Map

AdditiveGroup(R) : RngIntRes -> GrpAb, Map

AddNormalizingGenerator

AddRedundantGenerators

AddRelation

AddRelation(S, r) : SgpFP, Rel -> SgpFP

address

AddRow

AddRow(~a, u, i, j) : ModMatElt, RngElt, RngIntElt, RngIntElt ->

AddRow(~X, u, i, j) : ModMatRngElt, RngElt, RngIntElt, RngIntElt ->

AddStrongGenerator

AddVertex

AddVertices

AdemMilgram

adic

adj

u adj v : GrphVert, GrphVert -> BoolElt

adjacency

adjacency-degree-distance

AdjacencyMatrix

Adjoint

AdjointMatrix

Advance

Advance(~p) : Process ->

affine

MODULES OVER AFFINE ALGEBRAS

The Connection between Projective and Affine Planes (FINITE PLANES)

AffineAction

AffineGammaLinearGroup

AffineGeneralLinearGroup

AffineImage

AffineKernel

AffinePlane

AffinePlane< v | X : parameters > : RngIntElt, List -> AffPl

AffinePlane(P, l) : ProjPl, PlaneLn -> AffPl, Map

AffineSigmaLinearGroup

AffineSpecialLinearGroup

AffPl

AGammaL

Agemo

Agemo(G, i) : GrpPC, RngIntElt -> GrpPC

aggregate

AGL

AGM

aInvariants

Alarm

alg

Homomorphisms (STRUCTURE CONSTANT ALGEBRAS)

Operations on Associative Algebras (ASSOCIATIVE ALGEBRAS)

Operations on Elements (ALGEBRAS)

Operations on Elements (ASSOCIATIVE ALGEBRAS)

Operations on Group Algebras (GROUP ALGEBRAS)

Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)

Operations on Structure Constant Algebras (STRUCTURE CONSTANT ALGEBRAS)

Operations on Subalgebras (ALGEBRAS)

Representations of Associative Algebras (ASSOCIATIVE ALGEBRAS)

The Module structure of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)

alg-hom

alg-mod

alg-oper

alg-ops

Operations on Associative Algebras (ASSOCIATIVE ALGEBRAS)

Operations on Elements (ALGEBRAS)

Operations on Elements (ASSOCIATIVE ALGEBRAS)

Operations on Subalgebras (ALGEBRAS)

Representations of Associative Algebras (ASSOCIATIVE ALGEBRAS)

alg_grp

AlgChtr

Algebra

Algebra(A) : AlgGrp -> AlgAss, Map

Algebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgGen

Algebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgGen

Algebra(R) : RngInvar -> RngMPol, [ RngMPolElt ]

algebra

Functions for Polynomial Algebra and Module Generators (MULTIVARIATE POLYNOMIAL RINGS)

Magmas (or Structures) (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

S-algebras (FINITELY PRESENTED ALGEBRAS)

The Algebra of an Invariant Ring and Algebraic Relations (INVARIANT RINGS OF FINITE GROUPS)

algebra-module

algebra-relations

algebras

Construction of a General Algebra (ALGEBRAS)

Construction of a Lie Structure Constant Algebra (LIE ALGEBRAS)

Construction of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)

Construction of an Associative Structure Constant Algebra (ASSOCIATIVE ALGEBRAS)

MODULES OVER AFFINE ALGEBRAS

Rings, Fields, and Algebras (OVERVIEW)

AlgFP

AlgMat

algorithm

Overview of Facilities (FINITELY PRESENTED GROUPS)

Sketch of the Algorithm (FINITELY PRESENTED ALGEBRAS)

Alldeg

Alldeg(G, n) : GrphUnd, RngIntElt -> { GrphVert }

AllInformationSets

AllIrreduciblePolynomials

AllPassants

AllRoots

AllSecants

AllSqrts

AllSquareRoots

AllTangents

AllTangents(P, U) : Plane, { PlanePt } -> { PlaneLn }

AlmostFermat

AlmostFermatIndexed

Alphabet

alphabet

Alt

AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP

AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

AlternantCode

Code_AlternantCode (Example H58E7)

AlternatingGroup

AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP

AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

AlternatingSum

AmbientSpace

Amicable

and

Expression (OVERVIEW)

x and y : BoolElt, BoolElt -> BoolElt

anf

angle

angle-bracket

AntisymmetricForms

Append

Append(~S, x) : SeqEnum, Elt ->

application

AQInvariants

arbitrary

arbitrary-fixed

arc

Arccos

Arccosec

Arccot

arcs

Arcsec

Arcsin

Arctan

Arctan2

Arg

Argcosech

Argcosh

Argcoth

Argsech

Argsinh

Argtanh

Argument

argument

Reference Arguments (MAGMA SEMANTICS)

Arithmetic

GrpPerm_Arithmetic (Example H20E3)

Grp_Arithmetic (Example H15E2)

KMod_Arithmetic (Example H41E5)

arithmetic

Arithmetic (CHARACTERS OF FINITE GROUPS)

Arithmetic (CYCLOTOMIC FIELDS)

Arithmetic (ELLIPTIC CURVES)

Arithmetic (MATRIX ALGEBRAS)

Arithmetic (MODULES OVER AFFINE ALGEBRAS)

Arithmetic (QUADRATIC FIELDS)

Arithmetic (QUADRATIC FIELDS)

Arithmetic (RATIONAL FUNCTION FIELDS)

Arithmetic (REAL AND COMPLEX FIELDS)

Arithmetic (RING OF INTEGERS)

Arithmetic (RING OF INTEGERS)

Arithmetic Functions (RING OF INTEGERS)

Arithmetic Operations (INTRODUCTION [RINGS AND FIELDS])

Arithmetic Operations (RING OF INTEGERS)

Arithmetic Operations (VALUATION RINGS)

Arithmetic Operations on Elements (SOLUBLE GROUPS)

Arithmetic Operations on Ideals (INTRODUCTION [RINGS AND FIELDS])

Arithmetic Operators (FINITE FIELDS)

Arithmetic Operators (MULTIVARIATE POLYNOMIAL RINGS)

Arithmetic Operators (POWER SERIES AND LAURENT SERIES)

Arithmetic Operators (RATIONAL FIELD)

Arithmetic Operators (RESIDUE CLASS RINGS)

Arithmetic Operators (UNIVARIATE POLYNOMIAL RINGS)

Arithmetic with Elements (GROUPS)

Arithmetic with Matrices (MATRIX GROUPS)

Arithmetic with Permutations (PERMUTATION GROUPS)

Arithmetic with Vectors (VECTOR SPACES)

Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)

Elementary Operators for Elements (FINITELY PRESENTED ALGEBRAS)

Generic Functions on Elements (LOCAL FIELDS)

Ideal Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)

Ideal Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

Ideal Arithmetic (RESIDUE CLASS RINGS)

Ideal Arithmetic (UNIVARIATE POLYNOMIAL RINGS)

Multiplication and Exponentiation (FINITELY PRESENTED SEMIGROUPS)

Sequences (OVERVIEW)

Sets (OVERVIEW)

The Arithmetic Progression Constructors (SEQUENCES)

The Arithmetic Progression Constructors (SETS)

arithmetic-function

arithmetic-other

arithmetic-progression

Sets (OVERVIEW)

The Arithmetic Progression Constructors (SEQUENCES)

The Arithmetic Progression Constructors (SETS)

ArithmeticGeometricMean

ASigmaL

ASL

assert

AssertAttribute

AssertAttribute(A, "Precision", n) : AlgPowSer, MonStgElt, RngIntElt ->

AssertAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->

AssertAttribute(FldPr, "OutputPrecision", l) : Cat, MonStgElt, BoolElt ->

AssertAttribute(FldPr, "Precision", n) : Cat, MonStgElt, BoolElt ->

AssertAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->

AssertAttribute(GrpMat, "FirstBasicOrbitBound", n) : Cat, MonStgElt, RngIntElt ->

AssertAttribute(RngInt, "CunninghamStorageLimit", l) : Cat, MonStgElt, RngIntElt ->

AssertAttribute(R, "Precision", n) : FldPow, MonStgElt, RngIntElt -> Null

AssertAttribute(G, "Order", n) : GrpMat, MonStgElt, RngIntElt ->

AssertAttribute(G, "Base", B) : GrpMat, MonStgElt, Tup ->

AssertAttribute(G, "Classes", Q) : GrpMat, MonStgElt, [ GrpMatElt ] ->

[Future release] AssertAttribute(G, "Classes", Q) : GrpPerm, MonStgElt, [ GrpPermElt ] ->

AssertAttribute(G, "Base", Q) : GrpPerm, MonStgElt, [ RngIntElt ] ->

AssertAttribute(M, "MatrixPrinting", l) : ModMPol, MonStgElt, BoolElt ->

AssertAttribute(A, "Precision", n) : RngPad, MonStgElt, RngIntElt ->

SetPowerPrinting(F, l) : FldFin, BoolElt ->

assign

assigned

assigned r`fieldname : Rec, Fieldname -> BoolElt

assigned S`fieldname : Str, Fieldname -> BoolElt

assigned x : Var -> BoolElt

assigninglabels

AssignLabel

AssignLabels

assignment

Assignment (OVERVIEW)

Assignment (STATEMENTS AND EXPRESSIONS)

Assignment Operator (LISTS)

Function Values Assigned to Identifiers (MAGMA SEMANTICS)

Generator Assignment (OVERVIEW)

Generator Assignment (STATEMENTS AND EXPRESSIONS)

Indexed Assignment (STATEMENTS AND EXPRESSIONS)

Multiple Assignment (OVERVIEW)

Simple Assignment (STATEMENTS AND EXPRESSIONS)

AssignNames

AssignNames(~K, s) : FldFun, [ MonStgElt ] ->

AssignNames(~F, s) : FldFun, [ MonStgElt ]) ->

AssignNames(~K, s) : FldNum, [ MonStgElt ] ->

AssignNames(~R, ["x"]) : FldPow, [ MonStgElt ] ->

AssignNames(~C, [s]) : FldPr, [ MonStgElt ]) ->

AssignNames(~F, [s]) : FldQuad, [ MonStgElt ]) ->

AssignNames(~P, s) : RngMPol, [ MonStgElt ]) ->

AssignNames(~P, s) : RngUPol, [ MonStgElt ]) ->

AssignNames(~S, [s_1, ... s_n] ) : Struct, [ MonStgElt ] ->

RngMPol_AssignNames (Example H29E2)

AssociativeAlgebra

AssociativeAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgAss

asymptotic

Attach

attach

attach-detach

AttachSpec

attribute

Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)

Attributes (INTRODUCTION [RINGS AND FIELDS])

Defining Values for Attributes (MATRIX GROUPS)

Defining Values for Attributes (PERMUTATION GROUPS)

Attributes

attributes

Attributes of Lattices (LATTICES)

Augmentation

AugmentationIdeal

AugmentationMap

AugmentCode

Aut

Aut(D) : Inc -> PowerStructure, Map

auto

Automorphism Group and Isometry Testing (LATTICES)

Design_auto (Example H56E10)

auto-isom

auto-print

IO_auto-print (Example H3E7)

AutoAction

AutoDepth

automatic

Magmas (or Structures) (OVERVIEW)

Automorphism

automorphism

Automorphism Group of a Graph or Digraph (GRAPHS)

Automorphisms and Isomorphisms (SOLUBLE GROUPS)

The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)

Design_automorphism (Example H56E11)

automorphism-group

The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)

automorphism-group-graph

automorphism-isomorphism

automorphism_group

AutomorphismAction

AutomorphismGroup

AutomorphismGroup(E) : CurveEll -> Rng

AutomorphismGroup(G) : Grph -> GrpPerm, GSet, GSet, PowMap, Map, Grph

AutomorphismGroup(G): GrpPC -> [Mtrx]

AutomorphismGroup(D) : Inc -> GrpPerm, GSet, GSet, PowMap, Map

AutomorphismGroup(L) : Lat -> GrpMat

CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map

Code_AutomorphismGroup (Example H58E20)

Graph_AutomorphismGroup (Example H55E14)

AutomorphismGroupStabilizer

AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map

AutomorphismSubgroup

AutomorphismSubgroup(D) : Inc -> GrpPerm, PowMap, Map

AutoStabilizers

average