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Index D


D

Quitting (OVERVIEW)

D-key

D

d-key

d range

Darstellungsgruppe

Darstellungsgruppe(G) : GrpFP -> GrpFP

data

Identifiers and variables (OVERVIEW)

database

Accessing the Databases (PERMUTATION GROUPS)

Databases of Structure Definitions (OVERVIEW)

Libraries of Functions in the Magma Language (OVERVIEW)

The Database of Groups of Order up to 1000 (GROUPS)

database-access

Accessing the Databases (PERMUTATION GROUPS)

databases

Databases of Structure Definitions (OVERVIEW)

Libraries of Functions in the Magma Language (OVERVIEW)

Permutation Group Databases (PERMUTATION GROUPS)

DawsonIntegral

DawsonIntegral(r) : FldReElt -> FldReElt

declaration

Local Declarations (MAGMA SEMANTICS)

declareattributes

declare attributes C: F1, ... Fn;

Decode

Decode(C, v) : Code, ModTupFldElt -> BoolElt, ModTupFldElt

Code_Decode (Example H58E18)

decoding

Decoding (ERROR-CORRECTING CODES)

Decompose

GrpMat_Decompose (Example H21E21)

DecomposeVector

DecomposeVector(U, v) : ModTupRng, ModTupRngElt -> ModTupRngElt, ModTupRngElt

Decomposition

Decomposition(O, p) : RngOrd, RngIntElt -> [Tup(RngOrdIdl, RngIntElt)]

Decomposition(T, y) : TabChtr, AlgChtrElt -> [ FldCycElt ]

decomposition

Accessing the decomposition information (MATRIX GROUPS)

Canonical Decomposition (ABELIAN GROUPS)

Composition and Decomposition (CHARACTERS OF FINITE GROUPS)

Decomposition (LIE ALGEBRAS)

Decomposition of Matrix Groups of Large Degree (MATRIX GROUPS)

Decompositions with Respect to a Normal Subgroup (MATRIX GROUPS)

Radical and Primary Decomposition of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

decon

Plane_decon (Example H57E8)

deconstruction

Deconstruction Functions (FINITE PLANES)

Deconstruction of a Vector (VECTOR SPACES)

Deconstruction of Module Elements (GENERAL MODULES)

DedekindEta

DedekindEta(q) : FldPowElt -> FldPowElt

DedekindEta(s) : FldPrElt -> FldPrElt

DedekindTest

DedekindTest(O) : RngFunOrd -> BoolElt

DedekindTest(p, m) : RngUPolElt, RngIntElt -> Boolelt

DeepHoles

DeepHoles(L) : Lat -> [ ModTupFldElt ]

default

Creation of Default Modules (MODULES OVER AFFINE ALGEBRAS)

The case expression (OVERVIEW)

DefiningAutomorphisms

GrpPC_DefiningAutomorphisms (Example H19E9)

DefiningIdeal

DefiningIdeal(E): CurveEllSubscheme -> RngUPolElt

DefiningPolynomial

DefiningPolynomial(E): CurveEllSubgroup -> RngUPolElt

DefiningPolynomial(F) : FldFin -> RngPolElt

DefiningPolynomial(K) : FldNum -> RngUPolElt

DefiningPolynomial(Q) : FldRat -> RngUPolElt

DefiningPolynomial(O) : RngFunOrd -> RngUPolElt

definite

Testing Matrices for Definiteness (LATTICES)

definition

Definition of Modules (MODULES OVER AFFINE ALGEBRAS)

General Modules (INTRODUCTION [MODULES AND LATTICES])

Introduction (FINITE PLANES)

Introduction (GRAPHS)

Introduction (INCIDENCE STRUCTURES AND DESIGNS)

Power-conjugate Presentations (SOLUBLE GROUPS)

Specification of Elements (SOLUBLE GROUPS)

Terminology (MAGMA SEMANTICS)

Terminology (PERMUTATION GROUPS)

The Concept of a G-Set (PERMUTATION GROUPS)

Degree

Degree(x) : AlgChtrElt -> RngIntElt

Degree(A) : AlgGen -> RngIntElt

Degree(R) : AlgMat -> RngIntElt

Degree(K) : FldCyc -> RngIntElt

Degree(F) : FldFin -> RngIntElt

Degree(K) : FldQuad -> RngIntElt

Degree(Q) : FldRat -> RngIntElt

Degree(u) : GrphVert -> RngIntElt

Degree(u) : GrphVert -> RngIntElt

Degree(G) : GrpMat -> RngIntElt

Degree(g) : GrpMatElt -> RngIntElt

Degree(G) : GrpPermElt -> RngIntElt

Degree(g) : GrpPermElt -> RngIntElt

Degree(g, Y) : GrpPermElt, GSet -> RngIntElt

Degree(L) : Lat -> RngIntElt

Degree(I) : Map -> RngIntElt

Degree(M) : ModMPol -> RngIntElt

Degree(V) : ModTupFld -> RngIntElt

Degree(O) : RngFunOrd -> RngIntElt

Degree(I) : RngFunOrdIdl -> RngIntElt

Degree(f, i) : RngMPolElt, RngIntElt -> RngIntElt

Degree(f) : RngMSerElt -> RngIntElt

Degree(O) : RngOrd -> RngIntElt

Degree(p) : RngUPolElt -> RngIntElt

degree

Adjacency, Degree and Distance (GRAPHS)

Coefficients and Degree (POWER SERIES AND LAURENT SERIES)

Degree (UNIVARIATE POLYNOMIAL RINGS)

Degrees (MULTIVARIATE POLYNOMIAL RINGS)

DegreeOfFieldExtension

DegreeOfFieldExtension (G) : GrpMat -> RngIntElt

DegreeOnePrimeIdeals

DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]

DegreeSequence

DegreeSequence(G) : Grph -> [ { GrphVert } ]

delete

Deleting an identifier (OVERVIEW)

delete S`fieldname;

delete r`fieldname : Rec, Fieldname -> Nil

delete x : Var; -> Nil

delete-clear

Deleting an identifier (OVERVIEW)

delete-key

<Backspace>

DeleteGenerator

DeleteGenerator(G, x) : GrpFP, GrpFPElt -> GrpFP

DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP

DeleteLabel

DeleteLabel(t) : GrphVert ->

DeleteLabels

DeleteLabels(S) : [GrphVert] ->

DeleteRelation

DeleteRelation(G, r) : GrpFP, GrpFPRel -> GrpFP

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

deletinglabels

Deleting Labels (GRAPHS)

deletion

Deleting an identifier (OVERVIEW)

Deletion of Values (STATEMENTS AND EXPRESSIONS)

Delta

Delta(n) : FldPowElt -> FldPowElt

Denominator

Denominator(f) : FldFunElt -> AlgPolElt

Denominator(a) : FldFunElt -> RngElt

Denominator(q) : FldRatElt -> RngIntElt

Denominator(I) : RngFunOrdIdl -> RngElt

Denominator(I) : RngOrdIdl -> RngIntElt

denominator

Numerator and Denominator (RATIONAL FIELD)

Numerator and Denominator (RATIONAL FUNCTION FIELDS)

Density

Density(L, K) : Lat, Fld -> FldReElt

dependency

Algebraic Dependencies (REAL AND COMPLEX FIELDS)

Depth

Depth(x) : GrpPCElt -> RngIntElt

Depth(u) : ModTupRngElt -> RngIntElt

Depth(v) : ModTupRngElt -> RngIntElt

Depth(R) : RngInvar -> RngIntElt

RngInvar_Depth (Example H30E11)

DepthFirstSearchTree

DepthFirstSearchTree(u) : GrphVert -> Grph

Derivative

Derivative(f, i) : RngMPolElt, RngIntElt -> RngMPolElt

Derivative(f) : RngSerElt -> RngSerElt

Derivative(p) : RngUPolElt -> RngUPolElt

derivative

Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)

Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)

Evaluation and Derivative (POWER SERIES AND LAURENT SERIES)

derivative-integral

Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)

Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)

DerivedGroup

DerivedSubgroup(G) : GrpAb -> GrpAb

DerivedSubgroup(G) : GrpFin -> GrpFin

DerivedSubgroup(G) : GrpMat -> GrpMat

DerivedSubgroup(G) : GrpPC -> GrpPC

DerivedSubgroup(G) : GrpPerm -> GrpPerm

DerivedLength

DerivedLength(G) : GrpAb -> RngIntElt

DerivedLength(G) : GrpFin -> RngIntElt

DerivedLength(G) : GrpMat -> RngIntElt

DerivedLength(G) : GrpPC -> RngIntElt

DerivedLength(G) : GrpPerm -> RngIntElt

DerivedSeries

DerivedSeries(L) : AlgLie -> [ AlgLie ]

DerivedSeries(G) : GrpAb -> [GrpAb]

DerivedSeries(G) : GrpFin -> [ GrpFin ]

DerivedSeries(G) : GrpMat -> [ GrpMat ]

DerivedSeries(G) : GrpPC -> [GrpPC]

DerivedSeries(G) : GrpPerm -> [ GrpPerm ]

DerivedSubgroup

DerivedSubgroup(G) : GrpAb -> GrpAb

DerivedSubgroup(G) : GrpFin -> GrpFin

DerivedSubgroup(G) : GrpMat -> GrpMat

DerivedSubgroup(G) : GrpPC -> GrpPC

DerivedSubgroup(G) : GrpPerm -> GrpPerm

DerSub

GrpFP_DerSub (Example H16E22)

Design

Design(I, t) : Inc, RngIntElt -> Dsgn

Design< t, v | X : parameters > : RngIntElt, RngIntElt, List -> Dsgn

Design(P) : Plane -> Dsgn, SetIncPt, SetIncBlk

design

Combinatorial and Geometrical Structures (OVERVIEW)

Construction of Graphs from Groups, Codes and Designs (GRAPHS)

Elementary Invariants of a Design (INCIDENCE STRUCTURES AND DESIGNS)

Graphs Constructed from Designs (GRAPHS)

INCIDENCE STRUCTURES AND DESIGNS

design-invar

Design_design-invar (Example H56E7)

design-invariant

Elementary Invariants of a Design (INCIDENCE STRUCTURES AND DESIGNS)

designs

Planes and Designs (FINITE PLANES)

Plane_designs (Example H57E17)

Detach

Detach(F); : file ->

detach

Attaching and Detaching Package Files (FUNCTIONS, PROCEDURES AND PACKAGES)

DetachSpec

DetachSpec(S) : file ->

detail

INTRODUCTION [MODULES AND LATTICES]

INTRODUCTION [RINGS AND FIELDS]

INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS]

MAPPINGS

SEQUENCES

SETS

Determinant

Determinant(a) : AlgMatElt -> RngElt

Determinant(g) : GrpMatElt -> RngElt

Determinant(L) : Lat -> RngElt

Determinant(a) : ModMatRngElt -> RngElt

DevelopDifferenceSet

Design_DevelopDifferenceSet (Example H56E6)

Development

Development(B) : { RngElt } -> Inc

development

Difference Sets and their Development (INCIDENCE STRUCTURES AND DESIGNS)

DFSTree

DepthFirstSearchTree(u) : GrphVert -> Grph

DiagonalJoin

DiagonalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt

DiagonalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt

DiagonalMatrix

DiagonalMatrix(R, Q) : AlgMat, [ RngElt ] -> AlgMatElt

diagram

Diagram of Contents of Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)

Diameter

Diameter(C) : Code -> RngIntElt

Diameter(G) : Grph -> RngIntElt

DiameterPath

DiameterPath(G) : Grph -> [GrphVert]

diff

R diff S : SetEnum, SetEnum -> SetEnum

DifferenceSet

DifferenceSet(p, t) : RngIntElt, MonStgElt -> { RngIntResElt }

Digraph

Digraph<p | edges> : RngIntElt, List -> GrphDir

digraph

Adjacency and Degree Functions for a Digraph (GRAPHS)

Combinatorial and Geometrical Structures (OVERVIEW)

Connectedness, Paths and Circuits in a Digraph (GRAPHS)

Construction of a General Digraph (GRAPHS)

Construction of a Standard Digraph (GRAPHS)

Construction of Graphs and Digraphs (GRAPHS)

Converting between Graphs and Digraphs (GRAPHS)

DihedralGroup

DihedralGroup(C, n) : Cat, RngIntElt -> GrpFin

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

DihedralGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC

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

Dilog

Dilog(s) : FldPrElt -> FldPrElt

Dimension

Dimension(A) : AlgGen -> RngIntElt

Dimension(R) : AlgMat -> RngIntElt

Dimension(C) : Code -> RngIntElt

Dimension(L) : Lat -> RngIntElt

Dimension(V) : ModTupFld -> RngIntElt

Dimension(V) : ModTupFld -> RngIntElt

Dimension(I) : RngMPol -> RngIntElt, [ RngIntElt ]

Dimension(Q) : RngMPolRes -> RngIntElt

Dimension(e) : SubModLatElt -> RngIntElt

dimension

Dimension of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Finite Dimensional Affine Algebras (MULTIVARIATE POLYNOMIAL RINGS)

DimensionOfCentreOfEndomorphismRing

DimensionOfCentreOfEndomorphismRing(G) : GrpMat -> RngIntElt

DimensionOfEndomorphismRing

DimensionOfEndomorphismRing(G) : GrpMat -> RngIntElt

DimensionOfExactConstantField

DimensionOfExactConstantField(K) : FldFun -> RngIntElt

directed

Combinatorial and Geometrical Structures (OVERVIEW)

DirectProduct

DirectProduct(G, H) : Grp, Grp -> Grp

DirectProduct(G, H) : GrpFP, GrpFP -> GrpFP

DirectProduct(G, H) : GrpMat, GrpMat -> GrpMat

DirectProduct(G, H) : GrpPC, GrpPC -> GrpPC, [Map], [Map]

DirectProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]

DirectProduct(R, S) : SgpFP, SgpFP -> SgpFP

GrpFP_DirectProduct (Example H16E12)

DirectSum

DirectSum(A, B) : AlgGen, AlgGen -> AlgGen

DirectSum(R, T) : AlgMat, AlgMat -> AlgMat

DirectSum(a, b) : AlgMatElt, AlgMatElt -> AlgMatElt

DirectSum(C, D) : Code, Code -> Code

DirectSum(A, B) : GrpAb, GrpAb -> GrpAb

DirectSum(L, M) : Lat, Lat -> Lat

DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map

DirectSumDecomposition

DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]

AlgLie_DirectSumDecomposition (Example H49E6)

DirichletElements

DirichletElements(K, a, m) : FldFun, RngIntElt, RngIntElt -> SeqEnum

disc

The Discriminant (QUADRATIC FIELDS)

Discriminant

Discriminant(E) : CurveEll -> RngElt

Discriminant(K) : FldCyc -> RngIntElt

Discriminant(K) : FldQuad -> RngIntElt

Discriminant(Q) : FldRat -> RngIntElt

Discriminant(f) : MagFormElt -> RngIntElt

Discriminant(O) : RngFunOrd -> RngElt

Discriminant(f, i) : RngMPolElt, RngIntElt -> RngMPolElt

Discriminant(O) : RngOrd -> RngIntElt

Discriminant(p) : RngUPolElt -> RngIntElt

FldNum_Discriminant (Example H36E12)

discriminant

Resultant and Discriminant (MULTIVARIATE POLYNOMIAL RINGS)

Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)

Display

Display(P) : Process(pQuot) ->

Distance

Distance(u, v) : GrphVert, GrphVert -> RngIntElt

Distance(u, v) : GrphVert, GrphVert -> RngIntElt

Distance(u, v) : ModTupFldElt, ModTupFldElt -> RngIntElt

Code_Distance (Example H58E12)

distance

Adjacency, Degree and Distance (GRAPHS)

DistanceMatrix

DistanceMatrix(G) : Grph -> AlgMatElt

DistancePartition

DistancePartition(u) : GrphVert -> [ { GrphVert } ]

DistancePartition(u) : GrphVert -> [ { GrphVert } ]

DistinctDegreeFactorization

DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]

distribution

The Weight Distribution (ERROR-CORRECTING CODES)

distributive

MULTIVARIATE POLYNOMIAL RINGS

distributive-multivariate-polynomial

MULTIVARIATE POLYNOMIAL RINGS

div

Rings, Fields, and Algebras (OVERVIEW)

v div d : LatElt, RngIntElt -> LatElt

f div s : ModMPolElt, RngMPolElt -> ModMPolElt

n div m : RngIntElt, RngIntElt -> RngIntElt

f div g : RngMPolElt, RngMPolElt -> RngMPolElt

w div v : RngOrdElt, RngOrdElt -> RngOrdElt

f div g : RngUPolElt, RngUPolElt -> RngUPolElt

v div w : RngValElt, RngValElt -> RngValElt

div:=

f div:= s : ModMPolElt, RngMPolElt ->

division

Operators (OVERVIEW)

Quotient and Reductum (MULTIVARIATE POLYNOMIAL RINGS)

Quotient and Remainder (UNIVARIATE POLYNOMIAL RINGS)

Rings, Fields, and Algebras (OVERVIEW)

DivisionPolynomial

DivisionPolynomial(K, n) : Fld, RngIntElt -> RngMPolElt

Elcu_DivisionPolynomial (Example H53E5)

divisor

Divisors (RING OF INTEGERS)

DivisorIdeal

DivisorIdeal(I) : RngMPolRes -> RngMPol

Divisors

Divisors(n) : RngIntElt -> [ RngIntElt ]

DivisorSigma

DivisorSigma(i, n) : RngIntElt, RngIntElt -> RngIntElt

do

The for statement (OVERVIEW)

The while statement (OVERVIEW)

documentation

Documentation (OVERVIEW)

Domain

Domain(f) : Map -> Struct

Domain(a) : ModMatElt -> ModTupFld

Domain(S) : ModMatRng -> ModTupRng

domain

(Co)Domain and (Co)Kernel (MAPPINGS)

Canonical Forms for Matrices over Euclidean Domains (MATRIX ALGEBRAS)

domain-kernel

(Co)Domain and (Co)Kernel (MAPPINGS)

DoubleCoset

DoubleCoset(G, H, g, K ) : GrpFP, GrpFP, GrpFPElt, GrpFP -> GrpFPDcosElt

DoubleCoset(G, H, g, K ) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> GrpPermDcosElt

DoubleCosets

DoubleCosets(G, H, K) : GrpFP, GrpFP, GrpFP -> { GrpFPDcosElt }

[Future release] DoubleCosets(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> { GrpPermDcosElt }

Dsgn

Combinatorial and Geometrical Structures (OVERVIEW)

Dual

Dual(C) : Code -> Code

Dual(D) : Inc -> Inc

Dual(L) : Lat -> Lat

Dual(M) : ModGrp -> ModGrp

Dual(P) : Plane -> Plane, PlanePtSet, PlaneLnSet

RMod_Dual (Example H42E10)

dual

Sum, Intersection and Dual (ERROR-CORRECTING CODES)

DualBasisLattice

DualBasisLattice(L) : Lat -> Lat

DualIsogeny

Elcu_DualIsogeny (Example H53E18)

DualQuotient

DualQuotient(L) : Lat -> GrpAb

DualWeightDistribution

DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]

dynamic

Dynamic Typing (MAGMA SEMANTICS)

dynamic-typing

Dynamic Typing (MAGMA SEMANTICS)


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