# Compute facts about modules

I am new to programming in general but in my project, I am required to work with a finite set ๐={๐ด_1,...,๐ด_๐} of ๐ร๐ matrices over a finite ring ๐ , and the submodule ๐ they generate. To be more specific, I would like to compute facts such as: Maximal lin. indep. set of columns for each matrix, maximal lin. indep. subset of ๐ , minimal generating set of ๐ , span of S, length of ๐ and a composition series if it exists, and free rank of largest free submodule of ๐ (or possibly the set of all submodules/free submodules of ๐ , which is finite since ๐ and ๐ are finite). However, while browsing through the documentation in the Sage website, I found very little in terms of commands that compute the above facts for suitable ๐ , could someone point out a package or set of commands that compute (some of) the above stuff? I apologize in advance if the question violates forum rules.

Homework ?

It is not homework, I recently started a project where I will have to compute invariants like this all the time

Can you please specify what sorts of finite rings you will be working over?

I sincerely apologize for the late reply, but I'll be working with the ring Z/nZ, for possibly composite n, a Galois ring GR(p,n,r), or a suitable extension of the latter two.