[____] [____] [_____] [____] [__] [Index] [Root]
Index D
Quitting (OVERVIEW)
GammaD(s) : FldPrElt -> FldPrElt
PolylogD(m, s) : FldPrElt -> FldPrElt
D
d range
Darstellungsgruppe(G) : GrpFP -> GrpFP
Data(D, o, n) : DB, RngIntElt, RngIntElt -> List
EisensteinData(f) : ModFrmElt -> Tup
ExistsGroupData(D, o1, o2): DB, RngIntElt, RngIntElt -> bool
GroupData(D, i): DB, RngIntElt -> Rec
IsomorphismData(I) : Map -> [ RngElt ]
LatticeData(D, i): DB, RngIntElt -> Rec
TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List
FundamentalCoweights( W ) : GrpCox -> SeqEnum
Accessing the Root Datum (COXETER GROUPS)
Classification of Root Data (ROOT DATA FOR LIE THEORY)
Identifiers and variables (OVERVIEW)
Numerical Data Associated to a Graph (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Numerical Functions of Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Operations (COXETER GROUPS)
Operators on Root Data (ROOT DATA FOR LIE THEORY)
Permutation Group Databases (DATABASES OF GROUPS)
Properties (COXETER GROUPS)
ROOT DATA FOR LIE THEORY
Roots, Coroots and Weights (COXETER GROUPS)
AlmostSimpleGroupDatabase() : -> DB
CremonaDatabase(: parameters) : -> DB
ExistsModularCurveDatabase(t) : MonStgElt -> BoolElt
IsInSmallGroupDatabase(o) : RngIntElt -> RngIntElt
IsolGroupDatabase() : -> DB
K3Database() : -> SeqEnum
LatticeDatabase() : -> DB
ModularCurveDatabase(t) : MonStgElt -> DB
PerfectGroupDatabase() : -> DB
QuaternionicMatrixGroupDatabase() : -> DB
RationalMatrixGroupDatabase() : -> DB
SmallGroupDatabase() : -> DB
SmallGroupDatabaseLimit() : -> RngIntElt
StronglyRegularGraphsDatabase() : -> DB
TransitiveGroupDatabaseLimit() : -> RngIntElt
Accessing the Databases (DATABASES OF GROUPS)
Accessing the K3 Database (THE K3 DATABASE)
Databases of Structure Definitions (OVERVIEW)
Elliptic Curve Database (ELLIPTIC CURVES)
Libraries of Functions in the Magma Language (OVERVIEW)
The Database of Irreducible Soluble Matrix Groups (DATABASES OF GROUPS)
The Database of Small Groups (DATABASES OF GROUPS)
THE K3 DATABASE
Accessing the Databases (DATABASES OF GROUPS)
DATABASES OF GROUPS
Databases of Groups (GROUPS)
Databases of Structure Definitions (OVERVIEW)
Graph Database and Graph Generation (GRAPHS)
Libraries of Functions in the Magma Language (OVERVIEW)
Permutation Group Databases (PERMUTATION GROUPS)
DATABASES OF GROUPS
RootDatum(L) : AlgLie -> RootDtm
RootDatum( C ) : AlgMatElt -> RootDtm
RootDatum( A, B ) : AlgMatElt, AlgMatElt -> RootDtm
RootDatum( F ) : GrpCox -> RootDtm
RootDatum( W ) : GrpCox -> RootDtm
RootDatum( G ) : GrpLie -> RootDtm
RootDatum( t ) : MonStgElt -> RootDtm
Constants Associated with Crystallographic Root Data (ROOT DATA FOR LIE THEORY)
Creating New Root Data from Old (ROOT DATA FOR LIE THEORY)
Creating Root Data (ROOT DATA FOR LIE THEORY)
Properties of Root Data (ROOT DATA FOR LIE THEORY)
DawsonIntegral(r) : FldReElt -> FldReElt
DawsonIntegral(r) : FldReElt -> FldReElt
InverseJeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
JeuDeTaquin(~t) : Tbl ->
JeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
PseudoRandom_decimate (Example H103E4)
Decimation(S, f, d) : SeqEnum, RngIntElt, RngIntElt -> SeqEnum
Decimation(S, f, d, t) : SeqEnum, RngIntElt, RngIntElt, RngIntElt -> SeqEnum
Local Declarations (MAGMA SEMANTICS)
declare attributes C: F_1, ..., F_n;
declare verbose F, m;
Decode(C, v: parameters) : Code, ModTupFldElt -> BoolElt, ModTupFldElt
Decode(C, Q: parameters) : Code, [ ModTupFldElt ] -> [ BoolElt ], [ ModTupFldElt ]
CodeFld_Decode (Example H101E42)
SmallGroupDecoding(c, o) : RngIntElt, RngIntElt -> GrpPC
Decoding (LINEAR CODES OVER FINITE FIELDS)
IsDecomposable(M) : ModRng -> BoolElt, ModRng, ModRng
ModAlg_Decomposable (Example H77E8)
DecomposeTensorProduct(D, w, x) : RootDtm, [ ], [ ] -> [ ModTupRngElt ], [ RngIntElt ]
DecomposeVector(U, v) : ModTupRng, ModTupRngElt -> ModTupRngElt, ModTupRngElt
GrpMat_Decompose (Example H21E35)
Scheme_decompose-automorphism (Example H83E24)
AlgLie_DecomposeTensor (Example H76E15)
DecomposeTensorProduct(D, w, x) : RootDtm, [ ], [ ] -> [ ModTupRngElt ], [ RngIntElt ]
DecomposeVector(U, v) : ModTupRng, ModTupRngElt -> ModTupRngElt, ModTupRngElt
AffineDecomposition(f) : MapSch -> MapSch,MapSch
AffineDecomposition(P) : Prj -> [MapSch],Pt
Decomposition(D) : DivCrvElt -> SeqEnum
Decomposition(F, P) : FldFun, PlcFunElt -> [ PlcFunElt ]
Decomposition(K, p) : FldNum, RngIntElt -> SeqEnum
Decomposition(M,B) : ModBrdt, RngIntElt -> [ModBrdt]
Decomposition(M, n) : ModSS -> [ModSS]
Decomposition(M, bound : parameters) : ModSym, RngIntElt -> SeqEnum
Decomposition(O) : RngFunOrd -> [ RngFunOrdIdl ]
Decomposition(O, p) : RngFunOrd, RngElt -> [ RngFunOrdIdl ]
Decomposition(R, p) : RngInt, RngIntElt -> SeqEnum
Decomposition(O, p) : RngOrd, RngIntElt -> [<RngOrdIdl, RngIntElt>]
Decomposition(a): RngOrdElt -> SeqEnum[<RngOrdIdl, RngIntElt>]
Decomposition(T, y) : TabChtr, AlgChtrElt -> [ FldCycElt ], AlgChtrElt
DecompositionField(p, A) : PlcNumElt, FldAb -> FldAb
DecompositionField(p) : RngOrdIdl -> FldNum, Map
DecompositionField(p, A) : RngOrdIdl, FldAb -> FldAb
DecompositionGroup(p, A) : PlcNumElt, FldAb -> GrpAb
DecompositionGroup(p) : RngOrdIdl -> GrpPerm
DecompositionGroup(p, A) : RngOrdIdl, FldAb -> GrpAb
DecompositionType(A, p) : FldAb, PlcNumElt -> [Tpl]
DecompositionType(A, p) : FldAb, RngIntElt -> [Tpl]
DecompositionType(A, p) : FldAb, RngOrdIdl -> [Tpl]
DecompositionType(F, P) : FldFun, PlcFunElt -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O) : RngFunOrd -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O, p) : RngFunOrd, RngElt -> [ <RngIntElt, RngIntElt> ]
DecompositionTypeFrequency(A, a, b) : FldAb, RngIntElt, RngIntElt -> Mset
DecompositionTypeFrequency(A, l) : FldAb, [ ] -> Mset
DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]
DirectSumDecomposition( RD ) : RootDtm -> []
NewformDecomposition(M : parameters) : ModSym -> SeqEnum
OrthogonalDecomposition(L) : Lat -> [Lat]
PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
PrimaryDecomposition(I) : RngMPol -> [ RngMPol ], [ RngMPol ]
PrimaryDecomposition(I) : RngMPolRes -> [ RngMPolRes ], [ RngMPolRes ]
ProbableRadicalDecomposition(I) : RngMPol -> [ RngMPol ]
RadicalDecomposition(I) : RngMPol -> [ RngMPol ]
RadicalDecomposition(I) : RngMPolRes -> [ RngMPolRes ]
SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt
SignDecomposition(D) : DivCrvElt -> DivElt,DivElt
SortDecomposition(D) : [ModBrdt] -> SeqEnum
SortDecomposition(D) : [ModSym] -> SeqEnum
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
TriangularDecomposition(I) : RngMPol -> [ RngMPol ]
ModSym_Decomposition (Example H90E11)
Accessing the Decomposition Information (MATRIX GROUPS)
Canonical Decomposition (ABELIAN GROUPS)
Composition and Decomposition (CHARACTERS OF FINITE GROUPS)
Decomposition (LIE ALGEBRAS)
Decomposition (MODULAR SYMBOLS)
Decompositions with Respect to a Normal Subgroup (MATRIX GROUPS)
Primary Decomposition (IDEAL THEORY AND GRÖBNER BASES)
Radical and Decomposition of Ideals (IDEAL THEORY AND GRÖBNER BASES)
Triangular Decomposition (IDEAL THEORY AND GRÖBNER BASES)
DecompositionField(p, A) : PlcNumElt, FldAb -> FldAb
DecompositionField(p) : RngOrdIdl -> FldNum, Map
DecompositionField(p, A) : RngOrdIdl, FldAb -> FldAb
DecompositionGroup(p, A) : PlcNumElt, FldAb -> GrpAb
DecompositionGroup(p) : RngOrdIdl -> GrpPerm
DecompositionGroup(p, A) : RngOrdIdl, FldAb -> GrpAb
DecompositionType(A, p) : FldAb, PlcNumElt -> [Tpl]
DecompositionType(A, p) : FldAb, RngIntElt -> [Tpl]
DecompositionType(A, p) : FldAb, RngOrdIdl -> [Tpl]
DecompositionType(F, P) : FldFun, PlcFunElt -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O) : RngFunOrd -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O, p) : RngFunOrd, RngElt -> [ <RngIntElt, RngIntElt> ]
DecompositionTypeFrequency(A, a, b) : FldAb, RngIntElt, RngIntElt -> Mset
DecompositionTypeFrequency(A, l) : FldAb, [ ] -> Mset
Plane_decon (Example H99E8)
Deconstruction Functions (FINITE PLANES)
Deconstruction of a Vector (VECTOR SPACES)
Deconstruction of Elements (FREE MODULES)
Deconstruction of Module Elements (MODULES OVER A MATRIX ALGEBRA)
DedekindEta(s) : FldPrElt -> FldPrElt
DedekindEta(z) : RngSerElt -> RngSerElt
DedekindTest(p, m) : RngUPolElt, RngIntElt -> Boolelt
Eltseq(a) : ModDedElt -> SeqEnum
MODULES OVER DEDEKIND DOMAINS
The Jacobi theta and Dedekind eta-functions (REAL AND COMPLEX FIELDS)
Eltseq(a) : ModDedElt -> SeqEnum
MODULES OVER DEDEKIND DOMAINS
DedekindEta(s) : FldPrElt -> FldPrElt
DedekindEta(z) : RngSerElt -> RngSerElt
DedekindTest(p, m) : RngUPolElt, RngIntElt -> Boolelt
DeepHoles(L) : Lat -> [ ModTupFldElt ]
DeepHoles(L) : Lat -> [ ModTupFldElt ]
Definition of Subgroups by Generators (FINITE SOLUBLE GROUPS)
Definition of Subgroups by Generators (FINITE SOLUBLE GROUPS)
GetDefaultRealField() : Null -> FldPr
SetDefaultRealField(R) : FldRe ->
Creation of Default Modules (MODULES OVER AFFINE ALGEBRAS)
The case expression (OVERVIEW)
IsDeficient(C, p) : CrvHyp, RngIntElt -> BoolElt
HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt
IsDefined(S, i) : SeqEnum, RngIntElt -> BoolElt
AlternateDefiningPolynomials(f) : MapSch -> SeqEnum
ConstantField(F) : FldFun -> Rng
DefiningIdeal(C) : Crv -> RngMPol
DefiningIdeal(C) : Sch -> RngMPol
DefiningIdeal(X) : Sch -> RngMPol
DefiningPoints(N) : NwtnPgon -> SeqEnum
DefiningPolynomial(C) : Crv -> RngMPolElt
DefiningPolynomial(E) : CrvEll -> RngMPolElt
DefiningPolynomial(F) : FldAlg -> RngUPolElt
DefiningPolynomial(F) : FldFin -> RngPolElt
DefiningPolynomial(F, E) : FldFin -> RngPolElt
DefiningPolynomial(F) : FldFun -> RngUPolElt
DefiningPolynomial(Q) : FldRat -> RngUPolElt
DefiningPolynomial(L) : RngLoc -> RngUPolElt
DefiningPolynomial(C) : Sch -> RngMPolElt
DefiningPolynomial(C) : Sch -> RngMPolElt
DefiningPolynomial(X) : Sch -> RngMPolElt
DefiningPolynomial(K) : SrfKum -> RngMPolElt
DefiningPolynomials(f) : MapSch -> SeqEnum
DefiningPolynomials(X) : Sch -> SeqEnum
DefiningSubschemePolynomial(G) : SchGrpEll -> RngUPolElt
FactoredDefiningPolynomials(f) : MapSch -> SeqEnum
FactoredInverseDefiningPolynomials(f) : MapSch -> SeqEnum
InverseDefiningPolynomials(f) : MapSch -> SeqEnum
DefiningConstantField(F) : FldFun -> Rng
ConstantField(F) : FldFun -> Rng
DefiningIdeal(C) : Crv -> RngMPol
DefiningIdeal(C) : Sch -> RngMPol
DefiningIdeal(X) : Sch -> RngMPol
DefiningPoints(N) : NwtnPgon -> SeqEnum
DefiningPolynomial(C) : Crv -> RngMPolElt
DefiningPolynomial(E) : CrvEll -> RngMPolElt
DefiningPolynomial(F) : FldAlg -> RngUPolElt
DefiningPolynomial(F) : FldFin -> RngPolElt
DefiningPolynomial(F, E) : FldFin -> RngPolElt
DefiningPolynomial(F) : FldFun -> RngUPolElt
DefiningPolynomial(Q) : FldRat -> RngUPolElt
DefiningPolynomial(L) : RngLoc -> RngUPolElt
DefiningPolynomial(C) : Sch -> RngMPolElt
DefiningPolynomial(C) : Sch -> RngMPolElt
DefiningPolynomial(X) : Sch -> RngMPolElt
DefiningPolynomial(K) : SrfKum -> RngMPolElt
DefiningPolynomials(f) : MapSch -> SeqEnum
DefiningPolynomials(X) : Sch -> SeqEnum
DefiningSubschemePolynomial(G) : SchGrpEll -> RngUPolElt
IsDefinite(A) : AlgQuat -> BoolElt
IsNegativeDefinite(F) : ModMatRngElt -> BoolElt
IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
PositiveDefiniteForm(G) : GrpMat -> AlgMatElt
Testing Matrices for Definiteness (LATTICES)
Creation of Finite Soluble Groups (FINITE SOLUBLE GROUPS)
Definition of Elements (FINITE SOLUBLE GROUPS)
Definition of Modules (MODULES OVER AFFINE ALGEBRAS)
General Modules (INTRODUCTION [LINEAR ALGEBRA AND MODULE THEORY])
Introduction (FINITE PLANES)
Introduction (GRAPHS)
Introduction (INCIDENCE STRUCTURES AND DESIGNS)
Specification of Elements (POLYCYCLIC GROUPS)
Terminology (MAGMA SEMANTICS)
Terminology (PERMUTATION GROUPS)
Definitions (LOCAL RINGS AND FIELDS)
Definitions (p-ADIC RINGS AND FIELDS)
Definition of a Root Datum (ROOT DATA FOR LIE THEORY)
DegeneracyMap(M1, M2, d) : ModSym, ModSym, RngIntElt -> Map
DegeneracyMatrix(M1, M2, d) : ModSym, ModSym, RngIntElt -> AlgMatElt
DegeneracyMap(M1, M2, d) : ModSym, ModSym, RngIntElt -> Map
DegeneracyMatrix(M1, M2, d) : ModSym, ModSym, RngIntElt -> AlgMatElt
[Future release] IsDegenerate(N) : NwtnPgon -> BoolElt
[Future release] IsDegenerate(F) : NwtnPgon,Tup -> BoolElt
AbsoluteDegree(A) : FldAb -> RngIntElt
AbsoluteDegree(F) : FldFun -> RngIntElt
AbsoluteDegree(O) : RngOrd -> RngIntElt
BlockDegree(D) : Dsgn -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt
Degree(A, v) : AC, RngIntElt -> RngIntElt
Degree(x) : AlgChtrElt -> RngIntElt
Degree(A) : AlgGen -> RngIntElt
Degree(a) : AlgGenElt -> RngIntElt
Degree(R) : AlgMat -> RngIntElt
Degree(Z) : Clstr -> RngIntElt
Degree(C) : CrvHyp -> RngIntElt
Degree(D) : DivCrvElt -> RngIntElt
Degree(D) : DivFunElt -> RngIntElt
Degree(A) : FldAb -> RngIntElt
Degree(A) : FldAC -> RngIntElt
Degree(F) : FldFin -> RngIntElt
Degree(F, E) : FldFin, FldFin -> RngIntElt
Degree(F) : FldFun -> RngIntElt
Degree(a) : FldFunElt -> RngIntElt
Degree(f) : FldFunRatElt -> RngIntElt
Degree(Q) : FldRat -> RngIntElt
Degree(s) : GrphSpl -> RngIntElt
Degree(u) : GrphVert -> RngIntElt
Degree(u) : GrphVert -> RngIntElt
Degree(G) : GrpMat -> RngIntElt
Degree(g) : GrpMatElt -> RngIntElt
Degree(G, Y) : GrpPerm, GSet -> RngIntElt
Degree(G) : GrpPermElt -> RngIntElt
Degree(g) : GrpPermElt -> RngIntElt
Degree(g, Y) : GrpPermElt, GSet -> RngIntElt
Degree(L) : Lat -> RngIntElt
Degree(L) : LinSys -> RngIntElt
Degree(I) : Map -> RngIntElt
Degree(M) : ModBrdt -> RngIntElt
Degree(M) : ModDed -> RngIntElt
Degree(f) : ModFrmElt -> RngIntElt
Degree(f) : ModMatCpxElt -> RngIntElt
Degree(M) : ModMPol -> RngIntElt
Degree(P) : ModSSElt -> RngElt
Degree(V) : ModTupFld -> RngIntElt
Degree(u) : ModTupFldElt -> RngIntElt
Degree(P) : PlcFunElt -> RngIntElt
Degree(I) : RngFunOrdIdl -> RngIntElt
ResidueClassDegree(I) : RngFunOrdIdl -> RngIntElt
Degree(R) : RngGal -> RngIntElt
Degree(I) : RngInt -> RngIntElt
Degree(g,B) : RngIntElt,SeqEnum -> FldRatElt
Degree(L) : RngLoc -> RngIntElt
Degree(f, i) : RngMPolElt, RngIntElt -> RngIntElt
Degree(f) : RngMSerElt -> RngIntElt
Degree(O) : RngOrd -> RngIntElt
Degree(I) : RngOrdIdl -> RngIntElt
Degree(p) : RngUPolElt -> RngIntElt
Degree(C) : Sch -> RngIntElt
Degree(X) : Sch -> RngIntElt
Degree(e) : SubFldLatElt -> RngIntElt
Degree(X) : VSrfK3 -> FldRatElt
DegreeOfFieldExtension(G) : GrpMat -> RngIntElt
DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
DegreeReduction(G) : GrpPerm -> GrpPerm, Hom
DegreeSequence(G) : Grph -> [ { GrphVert } ]
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]
DivisorOfDegreeOne(F) : FldFun -> DivFunElt
EqualDegreeFactorization(f, d, g) : RngUPolElt, RngIntElt, RngUPolElt -> [ RngUPolElt ]
FunctionDegree(f) : MapSch -> RngIntElt
HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapIsoSch
InDegree(u) : GrphVert -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
InertiaDegree(L) : RngLoc -> RngIntElt
InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
InvariantsOfDegree(R, d, k) : RngInvar, RngIntElt, RngIntElt -> [ RngMPolElt ]
IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat
IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> GrpMat
IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum
IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> SeqEnum
IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt
IsolProcessOfDegree(d) : . -> Process
IsolProcessOfDegreeField(d, p) : ., . -> Process
LeadingTotalDegree(f) : RngMPolElt -> RngIntElt
LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
ModularDegree(M) : ModSym -> RngIntElt
MonomialsOfDegree(P) : RngMPolElt -> {@ RngMPolElt @}
MonomialsOfWeightedDegree(P) : RngMPolElt -> {@ RngMPolElt @}
NumberOfPlacesOfDegreeOne(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F, m) : FldFun, RngIntElt -> RngIntElt
OutDegree(u) : GrphVert -> RngIntElt
PointDegree(D, p) : Inc, IncPt -> RngIntElt
PrintTermsOfDegree(s, l, n) : RngPowLazElt, RngIntElt, RngIntElt ->
RamificationDegree(L) : RngLoc -> RngIntElt
RamificationIndex(P) : PlcFunElt -> RngIntElt
RamificationIndex(I) : RngFunOrdIdl -> RngIntElt
RamificationIndex(I) : RngOrdIdl -> RngIntElt
SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
ShiftToDegreeZero(C) : ModCpx -> ModCpx
TotalDegree(f) : FldFunRatElt -> RngIntElt
TotalDegree(L) : RngLoc -> RngIntElt
TotalDegree(f) : RngMPolElt -> RngIntElt
WeightedDegree(f) : FldFunRatElt -> RngIntElt
WeightedDegree(f) : RngMPolElt -> RngIntElt
OutNeighbors(u) : GrphVert -> { GrphVert }
Adjacency, Degree and Distance (GRAPHS)
Coefficients and Degree (POWER, LAURENT AND PUISEUX SERIES)
Degree (UNIVARIATE POLYNOMIAL RINGS)
Degree-d Gröbner Bases (IDEAL THEORY AND GRÖBNER BASES)
Degrees (MULTIVARIATE POLYNOMIAL RINGS)
Matrix Groups of Large Degree (MATRIX GROUPS)
Numerator, Denominator and Degree (RATIONAL FUNCTION FIELDS)
GB_Degree-d (Example H66E21)
DegreeOfExactConstantField(F) : FldFun -> RngIntElt
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
DegreeOfFieldExtension(G) : GrpMat -> RngIntElt
DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
DegreeReduction(G) : GrpPerm -> GrpPerm, Hom
BasicDegrees( W ) : GrpCox -> RngIntElt
BlockDegrees(D) : Inc -> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
Degrees(C) : ModCpx -> RngIntElt
DegreesOfCohomologyGenerators(C) : Tup -> SeqEnum
EqualizeDegrees(C, D) : ModCpx, ModCpx -> ModCpx, ModCpx
EqualizeDegrees(C, D, n) : ModCpx, ModCpx, RngIntElt -> ModCpx, ModCpx
PointDegrees(D) : Inc -> [ RngIntElt ]
DegreeSequence(G) : Grph -> [ { GrphVert } ]
DegreesOfCohomologyGenerators(C) : Tup -> SeqEnum
AbsolutelyIrreducibleRepresentationProcessDelete( P) : SolRepProc ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP, p) : SQProc, RngIntElt ->
DeleteGenerator(G, x) : GrpFP, GrpFPElt -> GrpFP
DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP
DeleteLabel(G, i) : Grph, RngIntElt ->
DeleteLabel(G, i, j) : Grph, RngIntElt, RngIntElt ->
DeleteLabel(t) : GrphVert ->
DeleteLabels(G, S) : Grph, SeqEnum ->
DeleteLabels(G, S) : Grph, [RngIntElt] ->
DeleteLabels(T) : GrphVertSet ->
DeleteLabels(S) : [GrphVert] ->
DeleteRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
DeleteRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
DeleteRelation(G, i) : GrpFP, RngIntElt -> GrpFP
DeleteRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(S, i) : SgpFP, RngIntElt -> SgpFP
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
Deleting an identifier (OVERVIEW)
delete S`fieldname;
delete D : DB; -> Nil
delete r`fieldname : Rec, Fieldname -> Nil
delete x : Var; -> Nil
Deleting an identifier (OVERVIEW)
<Delete>
<Backspace>
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteGenerator(G, x) : GrpFP, GrpFPElt -> GrpFP
DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP
DeleteLabel(G, i) : Grph, RngIntElt ->
DeleteLabel(G, i, j) : Grph, RngIntElt, RngIntElt ->
DeleteLabel(t) : GrphVert ->
DeleteLabels(G, S) : Grph, SeqEnum ->
DeleteLabels(G, S) : Grph, [RngIntElt] ->
DeleteLabels(T) : GrphVertSet ->
DeleteLabels(S) : [GrphVert] ->
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteNonsplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
DeleteRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
DeleteRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
DeleteRelation(G, i) : GrpFP, RngIntElt -> GrpFP
DeleteRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(S, i) : SgpFP, RngIntElt -> SgpFP
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteNonsplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
Deleting Labels (GRAPHS)
Deleting an identifier (OVERVIEW)
Deletion of Values (STATEMENTS AND EXPRESSIONS)
Delta(t, p) : FldPrElt, RngIntElt -> FldPrElt
Delta(z) : RngSerElt -> RngSerElt
Delta(L, p) : SeqEnum, RngIntElt -> RngPrElt
Denominator(D) : DivFunElt -> DivFunElt
Denominator(a) : FldAlgElt -> RngIntElt
Denominator(a, O) : FldFunElt, RngFunOrd -> RngElt
Denominator(f) : FldFunRatElt -> RngElt
Denominator(q) : FldRatElt -> RngIntElt
Denominator(I) : RngFunOrdIdl -> RngElt
Denominator(x) : RngLocElt -> RngIntElt
Denominator(I) : RngOrdFracIdl -> RngIntElt
ExponentDenominator(f) : RngMSerElt -> RngElt
Numerator and Denominator (RATIONAL FIELD)
Numerator, Denominator and Degree (RATIONAL FUNCTION FIELDS)
HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
CenterDensity(L) : Lat -> FldReElt
CentreDensity(L) : Lat -> FldReElt
Density(L) : Lat -> FldReElt
Density(A) : Mtrx -> FldRe
Density(A) : MtrxSprs -> FldRe
Algebraic Dependencies (REAL AND COMPLEX FIELDS)
Depth(x) : GrpGPCElt -> RngIntElt
Depth(x) : GrpPCElt -> RngIntElt
Depth(u) : ModTupRngElt -> RngIntElt
Depth(v) : ModTupRngElt -> RngIntElt
Depth(R) : RngInvar -> RngIntElt
DepthFirstSearchTree(u) : GrphVert -> Grph
RngInvar_Depth (Example H80E11)
DFSTree(u) : GrphVert -> Grph
DepthFirstSearchTree(u) : GrphVert -> Grph
BaerDerivation(q2) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet
OvalDerivation(q: parameters) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet
Derivative(f, v) : FldFunRatMElt, RngIntElt -> FldFunRatMElt
Derivative(f, v, k) : FldFunRatMElt, RngIntElt, RngIntElt -> FldFunRatMElt
Derivative(f) : FldFunRatUElt -> FldFunRatUElt
Derivative(f, k) : FldFunRatUElt, RngIntElt -> FldFunRatUElt
Derivative(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Derivative(f, k, i) : RngMPolElt, RngIntElt -> RngMPolElt
Derivative(s) : RngPowLazElt -> RngPowLazElt
Derivative(f) : RngSerElt -> RngSerElt
Derivative(f, n) : RngSerElt, RngIntElt -> RngSerElt
Derivative(p) : RngUPolElt -> RngUPolElt
Derivative(p, n) : RngUPolElt, RngIntElt -> RngUPolElt
LogDerivative(s) : FldPrElt -> FldPrElt
Derivative (RATIONAL FUNCTION FIELDS)
Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)
Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)
Evaluation and Derivative (POWER, LAURENT AND PUISEUX SERIES)
Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)
Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)
DerivedSubgroup(G) : GrpPC -> GrpPC
DerivedGroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G) : GrpPC -> GrpPC
DerivedGroup(G) : GrpPC -> GrpPC
DerivedLength(G) : GrpAb -> RngIntElt
DerivedLength(G) : GrpFin -> RngIntElt
DerivedLength(G) : GrpGPC -> RngIntElt
DerivedLength(G) : GrpMat -> RngIntElt
DerivedLength(G) : GrpPC -> RngIntElt
DerivedLength(G) : GrpPerm -> RngIntElt
DerivedSeries(L) : AlgLie -> [ AlgLie ]
DerivedSeries(G) : GrpAb -> [GrpAb]
DerivedSeries(G) : GrpFin -> [ GrpFin ]
DerivedSeries(G) : GrpGPC -> [GrpGPC]
DerivedSeries(G) : GrpMat -> [ GrpMat ]
DerivedSeries(G) : GrpPC -> [GrpPC]
DerivedSeries(G) : GrpPerm -> [ GrpPerm ]
DerivedSubgroup(G) : GrpAb -> GrpAb
DerivedSubgroup(G) : GrpFin -> GrpFin
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
DerivedSubgroup(G) : GrpPC -> GrpPC
DerivedGroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G) : GrpPC -> GrpPC
DerivedSubgroup(G) : GrpAb -> GrpAb
DerivedSubgroup(G) : GrpFin -> GrpFin
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
DerivedLength(G) : GrpAb -> RngIntElt
DerivedLength(G) : GrpFin -> RngIntElt
DerivedLength(G) : GrpGPC -> RngIntElt
DerivedLength(G) : GrpMat -> RngIntElt
DerivedLength(G) : GrpPC -> RngIntElt
DerivedLength(G) : GrpPerm -> RngIntElt
DerivedSeries(L) : AlgLie -> [ AlgLie ]
DerivedSeries(G) : GrpAb -> [GrpAb]
DerivedSeries(G) : GrpFin -> [ GrpFin ]
DerivedSeries(G) : GrpGPC -> [GrpGPC]
DerivedSeries(G) : GrpMat -> [ GrpMat ]
DerivedSeries(G) : GrpPC -> [GrpPC]
DerivedSeries(G) : GrpPerm -> [ GrpPerm ]
DerivedSubgroup(G) : GrpPC -> GrpPC
DerivedGroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G) : GrpPC -> GrpPC
DerivedSubgroup(G) : GrpAb -> GrpAb
DerivedSubgroup(G) : GrpFin -> GrpFin
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
GrpFP_1_DerSub (Example H19E48)
IsDesarguesian(P) : Plane -> BoolElt
SIntegralDesbovesPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
CrvEll_Desboves (Example H87E24)
Descendants(G : parameters) : GrpPC -> [GrpPC]
LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
RightDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
GrpCox_DescentSets (Example H34E6)
PrimitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
Design(I, t) : Inc, RngIntElt -> Dsgn
Design< t, v | X : parameters > : RngIntElt, RngIntElt, List -> Dsgn
Design(P) : Plane -> Dsgn, SetIncPt, SetIncBlk
HadamardColumnDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
HadamardRowDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
IsDesign(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
WittDesign(n) : RngIntElt -> Dsgn
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_design-invar (Example H98E7)
Elementary Invariants of a Design (INCIDENCE STRUCTURES AND DESIGNS)
GoppaDesignedDistance(C) : Code -> RngIntElt
Planes and Designs (FINITE PLANES)
Plane_designs (Example H99E17)
Detach(F); : file ->
DetachSpec(S) : file ->
Attaching and Detaching Package Files (FUNCTIONS, PROCEDURES AND PACKAGES)
DetachSpec(S) : file ->
INTRODUCTION [BASIC RINGS]
INTRODUCTION [LINEAR ALGEBRA AND MODULE THEORY]
INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS]
MAPPINGS
SEQUENCES
SETS
Determinant(a) : AlgMatElt -> RngElt
Determinant(g) : GrphRes -> RngElt
Determinant(g) : GrpMatElt -> RngElt
Determinant(L) : Lat -> RngElt
Determinant(M) : ModDed -> RngOrdIdl
Determinant(A: parameters) : Mtrx -> RngElt
Determinant(G) : SymGen -> Lat
Determinant(G) : SymGenLoc -> RngIntElt
EdgeDeterminant(u,v) : GrphSplVert,GrphSplVert -> RngIntElt
Design_DevelopDifferenceSet (Example H98E6)
Development(B) : { RngElt } -> Inc
Development(T) : { { Elt } } -> Inc
Difference Sets and their Development (INCIDENCE STRUCTURES AND DESIGNS)
DFSTree(u) : GrphVert -> Grph
DepthFirstSearchTree(u) : GrphVert -> Grph
DiagonalForm(f) : RngMPolElt -> RngMPolElt, ModMatRngElt
DiagonalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt
DiagonalJoin(X, Y) : Mtrx, Mtrx -> Mtrx
DiagonalJoin(Q) : [ ModMatRngElt ] -> ModMatRngElt
DiagonalJoin(Q) : [ Mtrx ] -> Mtrx
DiagonalMatrix(R, Q) : AlgMat, [ RngElt ] -> AlgMatElt
DiagonalMatrix(R, n, Q) : Rng, RngIntElt, [ RngElt ] -> Mtrx
DiagonalMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
DiagonalMatrix(Q) : [ RngElt ] -> Mtrx
DiagonalSum(t1, t2) : Tbl,Tbl -> Tbl
IsDiagonal(a) : AlgMatElt -> BoolElt
IsDiagonal(A) : Mtrx -> BoolElt
DiagonalForm(f) : RngMPolElt -> RngMPolElt, ModMatRngElt
OrthogonalizeGram(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Diagonalization(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Diagonalizing a Polynomial of Degree 2 (MULTIVARIATE POLYNOMIAL RINGS)
DiagonalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt
DiagonalJoin(X, Y) : Mtrx, Mtrx -> Mtrx
DiagonalJoin(Q) : [ ModMatRngElt ] -> ModMatRngElt
DiagonalJoin(Q) : [ Mtrx ] -> Mtrx
DiagonalMatrix(R, Q) : AlgMat, [ RngElt ] -> AlgMatElt
DiagonalMatrix(R, n, Q) : Rng, RngIntElt, [ RngElt ] -> Mtrx
DiagonalMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
DiagonalMatrix(Q) : [ RngElt ] -> Mtrx
DiagonalSum(t1, t2) : Tbl,Tbl -> Tbl
Diagram(C) : CosetGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
Diagram(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
DynkinDiagram( W ) : GrpCox ->
DynkinDiagram( G ) : GrpLie -> .
DynkinDiagram( t ) : List -> .
DynkinDiagram( RD ) : RootDtm ->
MakeSpliceDiagram(g,e,a) : GrphDir,SeqEnum,SeqEnum -> GrphSpl
MakeSpliceDiagram(e,l,a) : SeqEnum,SeqEnum,SeqEnum -> GrphSpl
RegularSpliceDiagram(P) : PnclJac -> GrphSpl
SpliceDiagram(g) : GrphRes -> GrphSpl
SpliceDiagram(g,v) : GrphRes,GrphResVert -> GrphSpl
SpliceDiagram(v) : GrphSplVert -> GrphSpl
SpliceDiagram(C,p) : Sch,Pt -> GrphSpl
SpliceDiagramVertex(s,i) : GrphSpl,RngIntElt -> GrphSplVert
Diagram of an Incidence Geometry (INCIDENCE GEOMETRY)
Diagram of Contents of Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
IncidenceGeometry_diagram (Example H100E10)
IncidenceGeometry_diagram (Example H100E11)
IncidenceGeometry_diagram (Example H100E12)
IncidenceGeometry_diagram (Example H100E9)
Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Diameter(C) : Code -> RngIntElt
Diameter(G) : Grph -> RngIntElt
DiameterPath(G) : Grph -> [GrphVert]
DiameterPath(G) : Grph -> [GrphVert]
DickmanRho(u) : FldPrElt -> FldReElt;
DickmanRho(u) : FldPrElt -> FldReElt;
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
FldFin_Dickson (Example H45E6)
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
Differential Space (PLANE ALGEBRAIC CURVES)
Differentials (PLANE ALGEBRAIC CURVES)
Operations on Differentials (PLANE ALGEBRAIC CURVES)
R diff S : SetEnum, SetEnum -> SetEnum
DifferenceSet(p, t) : RngIntElt, MonStgElt -> { RngIntResElt }
IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt
SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }
DifferenceSet(p, t) : RngIntElt, MonStgElt -> { RngIntResElt }
Different(O) : RngOrd -> RngOrdIdl
DifferentDivisor(F) : FldFun -> DivFunElt
DifferentDivisor(F) : FldFun -> DivFunElt
Differential(a) : FldFunElt -> DiffFunElt
Differential(a) : FldFunGElt -> DiffFunElt
DifferentialBasis(D) : DivCrvElt -> SeqEnum
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
DifferentialSpace(C) : Crv -> DiffFun
DifferentialSpace(D) : DivCrvElt -> ModTup,Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(F) : FldFun -> DiffFun
DifferentialSpace(F) : FldFunG -> DiffFun
DifferentialBasis(D) : DivCrvElt -> SeqEnum
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
BasisOfHolomorphicDifferentials(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map
Differentials (ALGEBRAIC FUNCTION FIELDS)
DifferentialSpace(C) : Crv -> DiffFun
DifferentialSpace(D) : DivCrvElt -> ModTup,Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(F) : FldFun -> DiffFun
DifferentialSpace(F) : FldFunG -> DiffFun
Differentiation(x, a) : FldFunGElt, FldFunGElt -> FldFunGElt
Differentiation(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> FldFunGElt
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
PrimePowerRepresentation(x, k, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
CompleteDigraph(p) : RngIntElt -> GrphDir
Digraph<p | edges: parameters> : RngIntElt, List -> GrphDir
EmptyDigraph(p: parameters) : RngIntElt -> GrphDir
IncidenceDigraph(A) : ModHomElt -> GrphDir
RandomDigraph(p, r: parameters) : RngIntElt, FldReElt -> GrphDir
UnderlyingDigraph(G) : GrphUnd -> GrphDir
OutNeighbors(u) : GrphVert -> { GrphVert }
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(C, n) : Cat, RngIntElt -> GrpFin
DihedralGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
DihedralGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
DihedralGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
DihedralGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
DihedralGroup(C, n) : Cat, RngIntElt -> GrpFin
DihedralGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
DihedralGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
DihedralGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
DihedralGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Dilog(s) : FldPrElt -> FldPrElt
BestDimensionLinearCode(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BDLC(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BrandtModuleDimension(D,N) : RngIntElt, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, i) : GrpFin, ModRng, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, i) : GrpPerm, ModRng, RngIntElt -> RngIntElt
Dimension(B) : AlgBas -> RngIntElt
Dimension(A) : AlgGen -> RngIntElt
Dimension(R) : AlgMat -> RngIntElt
Dimension(C) : Code -> RngIntElt
Dimension(C) : Code -> RngIntElt
Dimension(D) : DivFunElt -> RngIntElt
Dimension( W ) : GrpCox -> RngIntElt
Dimension(J) : JacHyp -> RngIntElt
Dimension(L) : Lat -> RngIntElt
Dimension(L) : LinSys -> RngIntElt
Dimension(M) : ModAlg -> RngIntElt
Dimension(M) : ModBrdt -> RngIntElt
Dimension(M) : ModDed -> RngIntElt
Dimension(M) : ModFrm -> RngIntElt
Dimension(M) : ModSS -> RngIntElt
Dimension(V) : ModTupFld -> RngIntElt
Dimension(V) : ModTupFld -> RngIntElt
Dimension(I) : RngMPol -> RngIntElt, [ RngIntElt ]
Dimension(Q) : RngMPolRes -> RngIntElt
Dimension( RD ) : RootDtm -> RngIntElt
Dimension(X) : Sch -> RngIntElt
Dimension(e) : SubModLatElt -> RngIntElt
Dimension(G) : SymGenLoc -> RngIntElt
DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionOfCentreOfEndomorphismRing(G) : GrpMat -> RngIntElt
DimensionOfEndomorphismRing(G) : GrpMat -> RngIntElt
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
DimensionOfHighestWeightModule(D, w) : RootDtm, [ ] -> RngIntElt
DimensionOfHomology(C, n) : ModCpx, RngIntElt -> RngIntElt
HomologicalDimension(M) : ModMPol -> RngInt
HomologicalDimension(M) : ModMPol -> RngInt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D): DB -> RngIntElt
OverDimension(V) : ModTupFld -> RngIntElt
OverDimension(u) : ModTupFldElt -> RngIntElt
OverDimension(M) : ModTupRng -> RngIntElt
OverDimension(u) : ModTupRngElt -> RngIntElt
Dimension Formulas (MODULAR SYMBOLS)
Dimension of Ideals (IDEAL THEORY AND GRÖBNER BASES)
Finite Dimensional Affine Algebras (AFFINE ALGEBRAS)
Dimension Formulas (MODULAR SYMBOLS)
IsZeroDimensional(I) : RngMPol -> BoolElt
DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
ModSym_DimensionFormulas (Example H90E28)
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionOfCentreOfEndomorphismRing(G) : GrpMat -> RngIntElt
DimensionOfEndomorphismRing(G) : GrpMat -> RngIntElt
DegreeOfExactConstantField(F) : FldFun -> RngIntElt
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
DimensionOfHighestWeightModule(D, w) : RootDtm, [ ] -> RngIntElt
DimensionOfHomology(C, n) : ModCpx, RngIntElt -> RngIntElt
DimensionsOfHomology(C) : ModCpx -> SeqEnum
DimensionsOfInjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfProjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfTerms(C) : ModCpx -> SeqEnum
SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum
SimpleHomologyDimensions(M) : ModAlg -> SeqEnum
DimensionsOfHomology(C) : ModCpx -> SeqEnum
DimensionsOfInjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfProjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfTerms(C) : ModCpx -> SeqEnum
MAGMA_HELP_DIR
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(G, H) : Grp, Grp -> Grp
DirectProduct(G, H) : GrpFP, GrpFP -> GrpFP
DirectProduct(G, H) : GrpGPC, GrpGPC -> GrpGPC, [Map], [Map]
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(A,B) : Prj,Prj -> PrjProd,SeqEnum
DirectProduct(A,B) : Sch,Sch -> Sch,SeqEnum
DirectProduct(R, S) : SgpFP, SgpFP -> SgpFP
DirectProduct(Q) : [ Grp ] -> Grp
DirectProduct(Q) : [ GrpFP ] -> GrpFP
DirectProduct(Q) : [ GrpMat ] -> GrpMat
DirectProduct(Q) : [ GrpPerm ] -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
DirectProduct(Q) : [GrpPC] -> GrpPC, [ Map ], [ Map ]
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(C, D) : Code, Code -> Code
DirectSum(A, B) : GrpAb, GrpAb -> GrpAb
DirectSum(L, M) : Lat, Lat -> Lat
DirectSum(C, D) : ModCpx, ModCpx -> ModCpx
DirectSum(M, N) : ModGrp, ModGrp -> ModGrp, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum( RD1, RD2 ) : RootDtm, RootDtm -> RootDtm
DirectSum(Q) : [ ModGrp ] -> [ ModGrp ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [Code] -> Code
DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]
DirectSumDecomposition( RD ) : RootDtm -> []
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
[Future release] KeepDirect(SQG, SQH) : SQProc, SQProc -> SeqEnum
Direct Sum (K[G]-MODULES AND GROUP REPRESENTATIONS)
Direct Sum (MODULES OVER A MATRIX ALGEBRA)
Functions returning roots (LOCAL RINGS AND FIELDS)
Functions returning roots (p-ADIC RINGS AND FIELDS)
Direct Sum (K[G]-MODULES AND GROUP REPRESENTATIONS)
Direct Sum (MODULES OVER A MATRIX ALGEBRA)
Combinatorial and Geometrical Structures (OVERVIEW)
Directed Trees (GRAPHS)
Directed Trees (GRAPHS)
ChangeDirectory(s) : MonStgElt ->
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(G, H) : Grp, Grp -> Grp
DirectProduct(G, H) : GrpFP, GrpFP -> GrpFP
DirectProduct(G, H) : GrpGPC, GrpGPC -> GrpGPC, [Map], [Map]
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(A,B) : Prj,Prj -> PrjProd,SeqEnum
DirectProduct(A,B) : Sch,Sch -> Sch,SeqEnum
DirectProduct(R, S) : SgpFP, SgpFP -> SgpFP
DirectProduct(Q) : [ Grp ] -> Grp
DirectProduct(Q) : [ GrpFP ] -> GrpFP
DirectProduct(Q) : [ GrpMat ] -> GrpMat
DirectProduct(Q) : [ GrpPerm ] -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
DirectProduct(Q) : [GrpPC] -> GrpPC, [ Map ], [ Map ]
GrpFP_1_DirectProduct (Example H19E16)
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(C, D) : Code, Code -> Code
DirectSum(A, B) : GrpAb, GrpAb -> GrpAb
DirectSum(L, M) : Lat, Lat -> Lat
DirectSum(C, D) : ModCpx, ModCpx -> ModCpx
DirectSum(M, N) : ModGrp, ModGrp -> ModGrp, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum( RD1, RD2 ) : RootDtm, RootDtm -> RootDtm
DirectSum(Q) : [ ModGrp ] -> [ ModGrp ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [Code] -> Code
DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]
DirectSumDecomposition( RD ) : RootDtm -> []
AlgLie_DirectSumDecomposition (Example H76E8)
RootDtm_DirectSumDual (Example H33E15)
DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
DirichletGroup(N) : RngIntElt -> GrpDrch
DirichletGroup(N,R) : RngIntElt, Rng -> GrpDrch
DirichletGroup(N,R,z,r) : RngIntElt, Rng, RngElt, RngIntElt -> GrpDrch
ModSym_Dirichlet (Example H90E7)
Dirichlet Characters (MODULAR SYMBOLS)
DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
DirichletGroup(N) : RngIntElt -> GrpDrch
DirichletGroup(N,R) : RngIntElt, Rng -> GrpDrch
DirichletGroup(N,R,z,r) : RngIntElt, Rng, RngElt, RngIntElt -> GrpDrch
Disconnect(v,w) : GrphResVert -> GrphRes
Discrete Logarithms (ELLIPTIC CURVES)
SMat_DiscreteLog (Example H60E3)
AbsoluteDiscriminant(K) : FldAlg -> FldRatElt
AbsoluteDiscriminant(O) : RngOrd -> RngIntElt
Discriminant(A) : AlgQuat -> FldRatElt
Discriminant(S) : AlgQuatOrd -> RngIntElt
Discriminant(C) : CrvCon -> FldElt
Discriminant(E) : CrvEll -> RngElt
Discriminant(C) : CrvHyp -> RngElt
Discriminant(A) : FldAb -> RngOrdIdl, [RngIntElt]
Discriminant(K) : FldQuad -> RngIntElt
Discriminant(Q) : FldRat -> RngIntElt
Discriminant(M) : ModBrdt -> RngIntElt
Discriminant(Q) : QuadBin -> RngIntElt
Discriminant(f) : QuadBinElt -> RngIntElt
Discriminant(O) : RngFunOrd -> .
Discriminant(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Discriminant(O) : RngOrd -> RngIntElt
Discriminant(I) : RngQuadFracIdl -> RngIntElt
Discriminant(f) : RngUPolElt -> RngIntElt
DiscriminantOfHeckeAlgebra(M : Bound) : ModSym -> RngIntElt
FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
IsDiscriminant(D) : RngIntElt -> BoolElt
IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt
ReducedDiscriminant(O) : RngOrd -> RngIntElt
RngOrd_Discriminant (Example H48E16)
Elementary invariants (RATIONAL CURVES AND CONICS)
Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)
Resultants and Discriminants (MULTIVARIATE POLYNOMIAL RINGS)
DiscriminantOfHeckeAlgebra(M : Bound) : ModSym -> RngIntElt
Geometry and Basic Conventions (THE K3 DATABASE)
IsDisjoint(R, S) : SetEnum, SetEnum -> BoolElt
DisownChildren(M) : ModSym ->
DisownChildren(M) : ModSym ->
Display(P) : Process(pQuot) ->
DisplayBurnsideMatrix(G) : GrpPC ->
DisplayFareySymbolDomain(FS,file) : SymFry, MonStgElt -> SeqEnum
DisplayPolygons(P,file) : SeqEnum, MonStgElt ->
SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->
DisplayBurnsideMatrix(G) : GrpPC ->
DisplayFareySymbolDomain(FS,file) : SymFry, MonStgElt -> SeqEnum
DisplayPolygons(P,file) : SeqEnum, MonStgElt ->
CosetDistanceDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
Distance(u, v) : GrphVert, GrphVert -> RngIntElt
Distance(u, v) : GrphVert, GrphVert -> RngIntElt
Distance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
Distance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
DistanceMatrix(G) : Grph -> AlgMatElt
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
GoppaDesignedDistance(C) : Code -> RngIntElt
IsDistanceRegular(G) : GrphUnd -> BoolElt
IsDistanceTransitive(G) : GrphUnd -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
LeeDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
MinimumWeight(C) : Code -> RngIntElt
MinimumWeight(C: parameters) : Code -> RngIntElt
VerifyMinimumDistanceLowerBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
VerifyMinimumDistanceUpperBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
CodeFld_Distance (Example H101E11)
CodeRng_Distance (Example H102E6)
OutNeighbors(u) : GrphVert -> { GrphVert }
Adjacency, Degree and Distance (GRAPHS)
Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)
Distance and Weight (LINEAR CODES OVER FINITE FIELDS)
Vector Space and Related Operations (LINEAR CODES OVER FINITE FIELDS)
DistanceMatrix(G) : Grph -> AlgMatElt
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]
DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]
CosetDistanceDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
WeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
WeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
WeightDistribution(C, u) : Code, ModTupFldElt -> [ <RngIntElt, RngIntElt> ]
The Weight Distribution (LINEAR CODES OVER FINITE FIELDS)
The Weight Distribution (LINEAR CODES OVER FINITE RINGS)
MULTIVARIATE POLYNOMIAL RINGS
MULTIVARIATE POLYNOMIAL RINGS
LeftDiv(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftDiv(u, ~v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
Arithmetic with places and divisors (ORDERS AND ALGEBRAIC FIELDS)
Creation of elements (ORDERS AND ALGEBRAIC FIELDS)
Creation of structures (ORDERS AND ALGEBRAIC FIELDS)
Other functions for Divisors and Places (ORDERS AND ALGEBRAIC FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
D + E : DivCrvElt,DivCrvElt -> DivCrvElt
v div d : LatElt, RngIntElt -> LatElt
f div s : ModMPolElt, RngMPolElt -> ModMPolElt
n div m : RngIntElt, RngIntElt -> RngIntElt
x div y : RngLocElt, RngLocElt -> RngLocElt
f div g : RngMPolElt, RngMPolElt -> RngMPolElt
w div v : RngOrdElt, RngOrdElt -> RngOrdElt
f div g : RngUPolElt, RngUPolElt -> RngUPolElt
v div w : RngValElt, RngValElt -> RngValElt
Arithmetic with places and divisors (ORDERS AND ALGEBRAIC FIELDS)
Creation of elements (ORDERS AND ALGEBRAIC FIELDS)
DivisorGroup(K) : FldNum -> DivNum
Creation of structures (ORDERS AND ALGEBRAIC FIELDS)
Other functions for Divisors and Places (ORDERS AND ALGEBRAIC FIELDS)
f div:= s : ModMPolElt, RngMPolElt ->
FldFunG_div_diff (Example H53E22)
IsDivisibleBy(a, b) : FldFunElt, FldFunElt -> BoolElt, FldFunElt
IsDivisibleBy(n, d) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
IsDivisibleBy(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt
DivisionFunction(E, n) : Fld, RngIntElt -> RngFunOrdElt
DivisionPolynomial(E, n) : CrvEll, RngIntElt -> RngUPolElt, RngUPolElt, RngUPolElt
IsDivisionRing(R) : Rng -> BoolElt
TrialDivision(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
TrialDivision(n, B) : RngQuadElt, RngIntElt -> SeqEnum, SeqEnum, Tup
RngLoc_Division (Example H55E8)
RngPad_Division (Example H40E6)
Operators (OVERVIEW)
Quotient and Reductum (MULTIVARIATE POLYNOMIAL RINGS)
Quotient and Remainder (UNIVARIATE POLYNOMIAL RINGS)
Rings, Fields, and Algebras (OVERVIEW)
DivisionFunction(E, n) : Fld, RngIntElt -> RngFunOrdElt
DivisionPolynomial(E, n) : CrvEll, RngIntElt -> RngUPolElt, RngUPolElt, RngUPolElt
CrvEll_DivisionPolynomial (Example H87E15)
CurveDivisor(D) : DivFunElt -> DivCrvElt
Div ! D : DivCrv, DivFunElt -> DivCrvElt
Div ! p : DivCrv, PlcCrvElt -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
Div ! a : DivFun, RngElt -> DivFunElt
Div ! I : DivFun, RngFunOrdIdl -> DivFunElt
CanonicalDivisor(F) : FldFun -> DivFunElt
ComplementaryDivisor(D,p) : DivCrvElt,Pt -> DivCrvElt
ComplementaryDivisor(D) : DivFunElt -> DivFunElt
DifferentDivisor(F) : FldFun -> DivFunElt
Divisor(C) : Code -> DivCrvElt
Divisor(d) : DiffFunElt -> DivFunElt
Divisor(Div,L) : DivCrv, Crv -> DivCrvElt
Divisor(Div,S) : DivCrv, SeqEnum -> DivCrvElt
Divisor(Div,a) : DivCrv,DiffFunElt -> DivCrvElt
Divisor(Div,p,q) : DivCrv,Pt,Pt -> DivCrvElt
Divisor(a) : FldFunGElt -> DivFunElt
Divisor(P) : PlcFunElt -> DivFunElt
Divisor(pl) : PlcNumElt -> DivNumElt
Divisor(I) : RngFunOrdIdl -> DivFunElt
Divisor(I, J) : RngFunOrdIdl, RngFunOrdIdl -> DivFunElt
Divisor(I, J) : RngFunOrdIdl, RngFunOrdIdl -> DivFunElt
Divisor(I) : RngOrdFracIdl -> DivNumElt
Divisor(Q) : SeqEnum -> DivCrvElt
DivisorGroup(C) : Crv -> DivCrv
DivisorGroup(D) : DivCrvElt -> DivCrv
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
DivisorIdeal(I) : RngMPolRes -> RngMPol
DivisorMap(D) : DivCrvElt -> MapSch
DivisorOfDegreeOne(F) : FldFun -> DivFunElt
DivisorSigma(i, n) : RngIntElt, RngIntElt -> RngIntElt
ExtendedGreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt
ExtendedGreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt, RngUPolElt
ExtendedGreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt, RngValElt
ExtendedGreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt, [RngIntElt]
FunctionFieldDivisor(D) : DivCrvElt -> DivFunElt
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
IsZeroDivisor(a) : AlgGenElt -> BoolElt
IsZeroDivisor(x) : RngElt -> BoolElt
Places(K) : FldNum -> PlcNum
PrincipalDivisor(Div,f) : DivCrv, FldFunElt -> DivCrvElt
PrincipalDivisorMap(F) : FldFun -> Map
RamificationDivisor(D) : DivCrvElt -> DivCrvElt
RamificationDivisor(D) : DivFunElt -> DivFunElt
RamificationDivisor(F) : FldFunG -> DivFunElt
SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map
Abstract Function Fields (PLANE ALGEBRAIC CURVES)
Arithmetic of Divisors (PLANE ALGEBRAIC CURVES)
Creation of Divisors (PLANE ALGEBRAIC CURVES)
Divisor Group (PLANE ALGEBRAIC CURVES)
Divisors (RING OF INTEGERS)
Functions related to Divisor Class Groups of Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Greatest Common Divisors (QUADRATIC FIELDS)
Arithmetic of Divisors (PLANE ALGEBRAIC CURVES)
Functions related to Divisor Class Groups of Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Crv_divisor-class-group-example (Example H84E19)
Creation of Divisors (PLANE ALGEBRAIC CURVES)
Crv_divisor-equations (Example H84E15)
Divisor Group (PLANE ALGEBRAIC CURVES)
Abstract Function Fields (PLANE ALGEBRAIC CURVES)
Crv_divisor1 (Example H84E16)
Crv_divisor2 (Example H84E17)
DivisorGroup(C) : Crv -> DivCrv
DivisorGroup(D) : DivCrvElt -> DivCrv
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
DivisorGroup(F) : FldFun -> DivFun
Places(K) : FldNum -> PlcNum
DivisorIdeal(I) : RngMPolRes -> RngMPol
DivisorMap(D) : DivCrvElt -> MapSch
DivisorOfDegreeOne(F) : FldFun -> DivFunElt
Divisors (ALGEBRAIC FUNCTION FIELDS)
Divisors(n) : RngIntElt -> [ RngIntElt ]
Divisors(a) : RngOrdElt -> SeqEnum[RngOrdElt]
Divisors(I) : RngOrdIdl -> [<RngOrdIdl, RngIntElt>]
ElementaryDivisors(a) : AlgMatElt -> [RngElt]
ElementaryDivisors(M, N) : ModDed, ModDed -> SeqEnum
ElementaryDivisors(A) : Mtrx -> [RngElt]
ElementaryDivisors(A) : MtrxSprs -> [RngElt]
NumberOfDivisors(n) : RngIntElt -> RngIntElt
NumberOfSmoothDivisors(n, m, P) : RngIntElt, RngIntElt, SeqEnum[RngElt] -> RngElt
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
SumOfDivisors(n) : RngIntElt -> RngIntElt
Coefficient Arithmetic (PLANE ALGEBRAIC CURVES)
Divisors (PLANE ALGEBRAIC CURVES)
Elementary Divisors (Smith Form) (SPARSE MATRICES)
Places and Divisors of Number Fields (ORDERS AND ALGEBRAIC FIELDS)
FldFunG_divisors (Example H53E18)
Coefficient Arithmetic (PLANE ALGEBRAIC CURVES)
DivisorSigma(i, n) : RngIntElt, RngIntElt -> RngIntElt
The for statement (OVERVIEW)
The while statement (OVERVIEW)
Documentation (OVERVIEW)
PolylogDold(m, s) : FldPrElt -> FldPrElt
PolylogP(m, s) : FldPrElt -> FldPrElt
PolylogD(m, s) : FldPrElt -> FldPrElt
DisplayFareySymbolDomain(FS,file) : SymFry, MonStgElt -> SeqEnum
Domain(f) : Map -> Grp
Domain(f) : Map -> Grp
Domain(f) : Map -> Grp
Domain(f) : Map -> Grp
Domain(f) : Map -> Struct
Domain(f) : MapIsoSch -> CrvHyp
Domain(f) : MapSch -> Sch
Domain(a) : ModMatElt -> ModTupFld
Domain(f) : ModMatFldElt -> ModAlg
Domain(S) : ModMatRng -> ModTupRng
Domain(a) : ModMatRngElt -> ModTupRng
Domain(P) : PowMap -> Str
FundamentalDomain(G) : GrpPSL2 -> SeqEnum
FundamentalDomain(FS) : SymFry -> SeqEnum
IsDomain(R) : Rng -> BoolElt
IsEuclideanDomain(F) : FldAlg -> BoolElt
IsEuclideanDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt
(Co)Domain and (Co)Kernel (MAPPINGS)
Canonical Forms for Matrices over Euclidean Domains (MATRIX ALGEBRAS)
(Co)Domain and (Co)Kernel (MAPPINGS)
DominantCharacter(D, w) : RootDtm, [ ] -> [ ModTupRngElt ], [ RngIntElt ]
DominantWeight( W, v ) : GrpCox, . -> ModTupFldElt, []
IsDominant(f) : AmbMap -> BoolElt
DominantCharacter(D, w) : RootDtm, [ ] -> [ ModTupRngElt ], [ RngIntElt ]
AlgLie_DominantCharacter (Example H76E14)
DominantWeight( W, v ) : GrpCox, . -> ModTupFldElt, []
GrpCox_DominantWeights (Example H34E19)
MinimumDominatingSet(G) : GrphUnd -> SetEnum
Double(P) : SrfKumPt -> SrfKumPt
DoubleCoset(G, H, g, K ) : GrpFP, GrpFP, GrpFPElt, GrpFP -> GrpFPDcosElt
DoubleCoset(G, H, g, K ) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> GrpPermDcosElt
DoubleCosets(G, H, K) : GrpFP, GrpFP, GrpFP -> { GrpFPDcosElt }
InverseRSKCorrespondenceDoubleWord(t1, t2) : Tbl, Tbl -> MonOrdElt, MonOrdElt
IsDoublePoint(p) : Crv,Pt -> BoolElt
Double Coset Spaces: Construction (FINITELY PRESENTED GROUPS)
Double Coset Spaces: Construction (FINITELY PRESENTED GROUPS)
DoubleCoset(G, H, g, K ) : GrpFP, GrpFP, GrpFPElt, GrpFP -> GrpFPDcosElt
DoubleCoset(G, H, g, K ) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> GrpPermDcosElt
DoubleCosets(G, H, K) : GrpFP, GrpFP, GrpFP -> { GrpFPDcosElt }
GrpFP_1_DoubleCosets (Example H19E50)
BorderedDoublyCirculantQRCode(p,a,b) : RngIntElt, RngElt, RngElt -> Code
DoublyCirculantQRCode(p) : RngIntElt -> Code
IsDoublyEven(C) : Code -> BoolElt
DoublyCirculantQRCode(p) : RngIntElt -> Code
Combinatorial and Geometrical Structures (OVERVIEW)
DualCoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterForm( RD ) : RootDtm -> AlgMatElt
Dual(C) : Code -> Code
Dual(C) : Code -> Code
Dual(C) : Code -> Code
Dual(G) : GrpAp -> GrpAb, Map
Dual(D) : Inc -> Inc
Dual(L) : Lat -> Lat
Dual(M) : ModAlg -> ModAlg
Dual(C) : ModCpx -> ModCpx
Dual(M) : ModDed -> ModDed
Dual(M) : ModGrp -> ModGrp
Dual(P) : Plane -> Plane, PlanePtSet, PlaneLnSet
Dual( RD ) : RootDtm -> RootDtm
DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
DualBasisLattice(L) : Lat -> Lat
DualHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
DualQuotient(L) : Lat -> GrpAb
DualStarInvolution(M) : ModSym -> AlgMatElt
DualVectorSpace(M) : ModSym -> ModTupFld
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(D) : Inc -> BoolElt
IsSelfDual(P) : PlaneProj -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
MatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
WordToMatrix( W, w ) : GrpCox, [] -> AlgMatElt
ModGrp_Dual (Example H78E9)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE FIELDS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE RINGS)
The Dual Space (LINEAR CODES OVER FINITE FIELDS)
The Dual Space (LINEAR CODES OVER FINITE FIELDS)
DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
DualBasisLattice(L) : Lat -> Lat
DualCoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterForm( RD ) : RootDtm -> AlgMatElt
DualHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
CrvEll_DualIsogeny (Example H87E37)
DualMatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
DualMatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
MatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
DualQuotient(L) : Lat -> GrpAb
CodeFld_DualRS (Example H101E16)
DualStarInvolution(M) : ModSym -> AlgMatElt
DualVectorSpace(M) : ModSym -> ModTupFld
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
DualWeightDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
DuvalPuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum
Operations associated with Duval's algorithm (NEWTON POLYGONS)
Operations not associated with Duval's Algorithm (NEWTON POLYGONS)
Newton_duval-ex (Example H54E9)
DuvalPuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum
SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
Swinnerton-Dyer Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Dynamic Typing (MAGMA SEMANTICS)
Dynamic Typing (MAGMA SEMANTICS)
DynkinDiagram( W ) : GrpCox ->
DynkinDiagram( G ) : GrpLie -> .
DynkinDiagram( t ) : List -> .
DynkinDiagram( RD ) : RootDtm ->
DynkinDiagram( W ) : GrpCox ->
DynkinDiagram( G ) : GrpLie -> .
DynkinDiagram( t ) : List -> .
DynkinDiagram( RD ) : RootDtm ->
[____] [____] [_____] [____] [__] [Index] [Root]