## Background

I am currently working on the homology of some modulispace and there exists a much simpler chaincomplex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say, that some faces are degenrated, thus are zero. Unfortunatly its to hard to compute the homology groups by hand.

Given a free chaincomplex of finite type over the coefficientring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime. I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external programm that:

- computes the homology groups
- describes the image of one or multiple cycles as linear combination of homology classes
- is efficient ( e.g. it is caplable of using multiple CPUs )

(descending order of importance)