I am new to programming in general but in my project, I am required to work with a finite set $S = {A_1,...,A_n}$ of $m \times n$ matrices over a finite ring $R$, and the submodule $M$ 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 $S$, minimal generating set of $M$, span of S, length of $M$ and a composition series if it exists, and free rank of largest free submodule of $M$ (or possibly the set of all submodules/free submodules of $M$, which is finite since $R$ and $S$ 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 $R$, could someone point out a source that refers to (some of) the above commands? I apologize in advance if the question violates forum rules.
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