Creation of Generic Free Modules
Creation of Default Modules
Module(P, r) : Rng, RngIntElt -> RngMPol
Module(P, r, S) : Rng, RngIntElt, MonStgElt -> RngMPol
Creation of Graded Modules
Module(P, W) : Rng, [ RngIntElt ] -> RngMPol
Module(P, W, S) : Rng, [ RngIntElt ], MonStgElt -> RngMPol
Example PMod_Create (H49E1)
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 ]
f[i] : ModMPolElt, RngIntElt -> 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 (H49E2)
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 (H49E3)
Homogeneous Modules
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalBasis(S) : [ ModMPolElt ] -> [ ModMPolElt ]
HilbertSeries(M) : ModMPol -> FldFunElt
Example PMod_Hilbert (H49E4)
Syzygy Modules
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
Example PMod_Hilbert (H49E5)
Free Resolutions
FreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
HomologicalDimension(M) : ModMPol -> RngInt