Compute facts about modules

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This doesn't work for me over a ring like Z/8, which I think is what the poster has in mind.

It's hard to understand what they really want without an example.

See https://math.stackexchange.com/questi... — same question before it appeared here.

Dear Max Alekseyev, I apologize for the late reply. For example, given a matrix with rows {a,b,c},{d,e,f},{g,h,i},{j,k,l} (he ring Z/nZ, for possibly composite n, a Galois ring GR(p,n,r), or a suitable extension of the latter two), I would like to compute the minimal generating set of vectors for its row or column space, the maximal independent set of rows etc. Or, given a set of matrices, possibly compute linear dependence between them etc. I had the same idea as you, to flatten the matrix before doing computations, but I do not know how to implement it in the case of the rings in question.

Flattening matrix M into a vector can be done via vector(M.list()). There still may an issue that linear algebra is poorly implemented over rings in Sage. For rings like $Z/nZ$, we may consider a workaround working with the integer lattice spanned by the original basis together with the columns of $n$ times the identity matrix.