I'm doing computations in the integral group ring of a discrete group, in particular the discrete Heisenberg group. In this case elements are integral combinations of monomials $x^k y^m z^n$, where the generators $x$, $y$, and $z$ satisfy $xz=zx$, $yz=zy$, and $yx=xyz$. Is there mathematical software for doing calculations with such objects, for example to compute powers of an element?

I've not been able to do this inside standard mathematical software like Mathematica.