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Acknowledgements
Introduction
Reduced Modules
Creation of Free Modules
Creation of Module Elements
Module Element Access and Operations
Access
Arithmetic
Predicates
Creation of Submodules and Quotient Modules
Module Access
Predicates
Module Operations
Free Resolutions
Homomorphisms between Modules and Matrix Modules
Embedded Modules
Introduction
Definition of Modules
Creation of Generic Free Modules
Creation of Default Modules
Creation of Graded Modules
Print Options
Creation of Module Elements
Module Element Access and Operations
Access
Arithmetic
Predicates
Other Operations
Creation of Submodules and Quotient Modules
Module Access
Predicates
Module Bases
Module Operations
Homogeneous Modules
Syzygy Modules
Free Resolutions
Bibliography
DETAILS
Introduction
Reduced Modules
Creation of Free Modules
RModule(R, n) : Rng, RngIntElt -> RngMPol
Example PMod_Create (H95E1)
Creation of Module Elements
M ! Q : ModMPol, [ RngElt ] -> ModMPolElt
M ! v : ModMPol, ModTupRngElt -> ModMPolElt
M ! 0 : ModMPol, RngIntElt -> ModMPolElt
M . i : ModMPol, RngIntElt -> ModMPolElt
Module Element Access and Operations
Access
Eltseq(v) : ModMPolElt -> [ RngMPolElt ]
Arithmetic
f + g : ModMPolElt, ModMPolElt -> ModMPolElt
Predicates
IsZero(f) : ModMPolElt -> BoolElt
f eq g : ModMPolElt, ModMPolElt -> BoolElt
f in M : ModMPolElt, ModMPol -> BoolElt
Creation of Submodules and Quotient Modules
sub<M | L> : ModMPol, List -> ModMPol
quo<M | L> : ModMPol, List -> ModMPol
Submodule(I) : RngMPol -> ModMPol
QuotientModule(I) : RngMPol -> ModMPol
Module Access
CoefficientRing(M) : ModMPol -> ModMPol
Degree(M) : ModMPol -> RngIntElt
Morphism(M, N) : ModMPol, ModMPol -> ModMatRngElt
RelationMatrix(M) : ModMPol -> ModMatRngElt
Predicates
IsZero(M) : ModMPol -> ModMPol
M subset N : ModMPol, ModMPol -> BoolElt
M eq N : ModMPol, ModMPol -> BoolElt
Module Operations
M + N : ModMPol, ModMPol -> ModMPol
M meet N : ModMPol, ModMPol -> ModMPol
M / N : ModMPol, ModMPol -> ModMPol
Example PMod_SubQuo (H95E2)
Free Resolutions
FreeResolution(M) : ModMPol -> ModCpx, ModMatRngElt
MinimalFreeResolution(M) : ModMPol -> ModCpx, ModMatRngElt
Example PMod_FreeResolution (H95E3)
Homomorphisms between Modules and Matrix Modules
RMatrixSpace(M, N) : ModMPol, ModMPol -> ModMatRng
Hom(M, N) : ModMPol, ModMPol -> ModMPol, Map
Example PMod_FreeResolution (H95E4)
Embedded Modules
Introduction
Definition of Modules
Creation of Generic Free Modules
Creation of Default Modules
Module(P, r) : Rng, RngIntElt -> RngMPol
Module(P, r, S) : Rng, RngIntElt, MonStgElt -> RngMPol
RModule(P, r) : Rng, RngIntElt -> RngMPol
Creation of Graded Modules
Module(P, W) : Rng, [ RngIntElt ] -> RngMPol
Module(P, W, S) : Rng, [ RngIntElt ], MonStgElt -> RngMPol
Example PMod_Create (H95E5)
Print Options
AssertAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(M, "MatrixPrinting", l) : ModMPol, MonStgElt, BoolElt ->
HasAttribute(M, "MatrixPrinting") : ModMPol, MonStgElt -> BoolElt, BoolElt
Creation of Module Elements
M ! Q : ModMPol, [ RngElt ] -> ModMPolElt
M ! v : ModMPol, ModTupRngElt -> ModMPolElt
M ! 0 : ModMPol, RngIntElt -> ModMPolElt
M . i : ModMPol, RngIntElt -> ModMPolElt
Module Element Access and Operations
Access
Eltseq(f) : ModMPolElt -> [ RngMPolElt ]
Arithmetic
f + g : ModMPolElt, ModMPolElt -> ModMPolElt
f - g : ModMPolElt, ModMPolElt -> ModMPolElt
- f : ModMPolElt -> ModMPolElt
s * f : RngMPolElt, ModMPolElt -> ModMPolElt
f * s : ModMPolElt, RngMPolElt -> ModMPolElt
f div s : ModMPolElt, RngMPolElt -> ModMPolElt
f div:= s : ModMPolElt, RngMPolElt ->
SPolynomial(f, g) : ModMPolElt, ModMPolElt -> ModMPolElt
Predicates
IsZero(f) : ModMPolElt -> BoolElt
f eq g : ModMPolElt, ModMPolElt -> BoolElt
f in M : ModMPolElt, ModMPol -> BoolElt
Other Operations
Normalize(f) : ModMPolElt -> ModMPolElt
NormalForm(f, M) : ModMPolElt, ModMPol -> ModMPolElt
Coordinates(f, M) : ModMPolElt, ModMPol -> [ RngMPolElt ]
Example PMod_Element (H95E6)
Creation of Submodules and Quotient Modules
sub<M | L> : ModMPol, List -> ModMPol
quo<M | L> : ModMPol, List -> ModMPol
Module Access
Generic(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModMPol -> ModMPol
Degree(M) : ModMPol -> RngIntElt
QuotientRelations(M) : ModMPol -> [ ModMPol ]
Predicates
IsZero(M) : ModMPol -> ModMPol
M subset N : ModMPol, ModMPol -> BoolElt
M eq N : ModMPol, ModMPol -> BoolElt
IsHomogeneous(M) : ModMPol -> BoolElt
Module Bases
Basis(M) : ModMPol -> RngMPolElt
BasisElement(M, i) : ModMPol, RngIntElt -> RngMPolElt
BasisMatrix(M) : ModMPol -> ModMatRngElt
Groebner(M) : ModMPol ->
Module Operations
M + N : ModMPol, ModMPol -> ModMPol
M meet N : ModMPol, ModMPol -> ModMPol
M / N : ModMPol, ModMPol -> ModMPol
Example PMod_SubQuo (H95E7)
Homogeneous Modules
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalBasis(S) : [ ModMPolElt ] -> [ ModMPolElt ]
HilbertSeries(M) : ModMPol -> FldFunElt
Example PMod_Hilbert (H95E8)
Syzygy Modules
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
Example PMod_Hilbert (H95E9)
Free Resolutions
FreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
HomologicalDimension(M) : ModMPol -> RngInt
Bibliography
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