Accessing Module Information

M . i: ModTupRng, RngIntElt -> ModElt

Given an \(R\)-module \(M\) and a positive integer \(i\), return the \(i\)-th generator of \(M\). The integer \(i\) must lie in the range \([1, r]\), where \(r\) is the number of generators for \(M\).

CoefficientRing(M): ModTupRng -> Rng

BaseRing(M): ModTupRng -> Rng

CoefficientRing(M): ModRng -> Rng

BaseRing(M): ModRng -> Rng

CoefficientField(M): ModFld -> Fld

BaseField(M): ModFld -> Fld

Given an \(R\)-module \(M\) which is defined as a submodule of \(S^{(n)}\), return the ring \(S\).

Generators(M): ModTupRng -> { ModTupRngElt }

The generators for the \(R\)-module \(M\), returned as a set.

OverDimension(M): ModTupRng -> RngIntElt

Given an \(R\)-module \(M\) which is an embedded submodule of the module \(S^{(n)}\), return \(n\).

OverDimension(u): ModTupRngElt -> RngIntElt

Given an element \(u\) of an embedded submodule of the module \(S^{(n)}\), return \(n\).

Moduli(M): ModTupRng -> [ RngElt ]

The column moduli of the module \(M\) over a euclidean domain.

Parent(u): ModTupRngElt -> ModRng

Given an element \(u\) belonging to the \(R\)-module \(M\), return \(M\).

Generic(M): ModRng -> ModRng

Given an \(R\)-module \(M\) which is a submodule of the module \(R^{(n)}\), return the module \(R^{(n)}\) as an \(R\)-module.