Interoperating between Computer Algebra systems: computing homology of groups with Kenzo and GAP

In this paper we report on an experience communicating two computer algebra systems, namely GAP (and more con-cretely, its HAP package to compute in Homological Alge-bra) and Kenzo (to compute in Algebraic Topology). Both systems cooperate through an OpenMath link in computing homology of groups. In addition, once the output from HAP has been integrated in Kenzo, it can be used to compute more complicated algebraic invariants, as homology groups of some 2-types