The following functions allow one to manipulate the bases of modules. Note that a Gröbner basis for a module will be automatically generated when necessary; the Groebner procedure just allows explicit immediate construction of the Gröbner basis.

Basis(M) : ModMPol -> RngMPolElt

Given a module M, return the current basis (whether it has been converted to a Gröbner basis or not) of M.

Given a module M together with an integer i, return the i-th element of the current basis of M. Note that this is not the same as M.i.

Given a module M, return the basis matrix of M, which is a k by r matrix over P, where k is the length of the basis of M and r is the degree of M.

(Procedure.) Explicitly force a Gröbner basis for M to be constructed.