MAGMA Computational Algebra System

Bases

The application of the functions in this section is restricted either to vector spaces or to torsion-free modules over a Euclidean Domain.

For a full description of the basis functions for a module defined over a field, the reader is referred to the chapter on vector spaces.

Basis(M) : ModTupRng -> [ModTupRngElt]

The current basis for the free R-module M, R an ED, returned as a sequence of module elements.

Rank(M) : ModTupRng -> RngIntElt

The rank of the free R-module M.

Coordinates(M, u) : ModTupRng, ModTupRngElt -> [RngElt]

Given a vector u belonging to the rank r free R-module M, R an Euclidean Domain, with basis u₁, ..., u_r, return a sequence [a₁, ..., a_r] giving the coordinates of u relative to the M-basis: u = a₁ * u₁ + ... + a_r * u_r.