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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, ..., ur, return a sequence [a1, ..., ar] giving the coordinates of u relative to the M-basis: u = a1 * u1 + ... + ar * ur.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013