Suppose I have a group acting on some Hadamard manifold, and I want to understand as much as possible about the (co)homology of the quotient. In my case I can find a fundamental domain for the action and the side-pairing transformations. Is there some canned piece of software which will compute the homology groups (I know how to do this in principle, but rather not actually do all the work) and the cohomology ring structure (in my ignorance, I don't know how to do this even in principle, so references would certainly be appreciated)?

**EDIT*

To elaborate slightly: think of the projective model of $\mathbb{H}^n,$ and a group (discrete, but not known a priori to act without fixed points), and construct the Dirichlet domain, which is a convex polytope, for which we have the side-pairing transformations. Now, clearly by triangulating the fundamental domain enough we get a simplicial decomposition of the quotient, but since all this is happening in high dimensions (five or higher), this is already a pain to program....