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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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