Elementary Functions

Various simple properties of a module can be retrieved using the following functions.

BaseRing(M) : ModOrd -> Rng

CoefficientRing(M) : ModOrd -> Rng

The order M is a module over.

Degree(M) : ModOrd -> RngIntElt

The dimension of the vector space M embeds into.

Ngens(M) : ModOrd -> RngIntElt

NumberOfGenerators(M) : ModOrd -> RngIntElt

The minimum number of vectors and ideals which generate M.

M . i : ModOrd, RngIntElt -> ModTupRngElt

The vector of the ith vector and ideal pair generating M.

Determinant(M) : ModOrd -> RngOrdIdl

The determinant of M.

Dimension(M) : ModOrd -> RngIntElt

The dimension of the vector space spanned by M over its base order. This is the same as the number of generators of M.