GAP — compute kernel of a matrix with coefficients in a finite ring

Question

I need to compute first cohomology group with coefficients in $(\mathbb{Z}/n\mathbb{Z})^m$ of specific finite groups. I reduced the computation of cocycles to the following problem: compute the kernel of a matrix $A$ with coefficients in $\mathbb{Z}/n\mathbb{Z}$.

1. How do I compute it in general? Is there some good algorithm?
2. Is there a GAP function / package for that?

Thanks for your answers!

Answer 1

You can use the function BasisNullspaceModN for that (it is undocumented, unfortunately, though we could change that in the next version of GAP). See also my answer here, which also describes a function NullspaceModN implemented using BasisNullspaceModN