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The study of topological invariants of finite topological spaces is relevant because they can be used as models of a wide class of topological spaces, including regular CW-complexes. In this work, we present a new module for the Kenzo system that allows the computation of homology groups with generators of finite topological spaces in different situations. Our algorithms combine new constructive versions of well-known results about topological spaces with combinatorial methods used on finite spaces. In the particular case of h-regular spaces, effective and reasonably efficient methods are implemented and the technique of discrete vector fields is applied in order to improve the previous algorithms.

In this work we present an interface between SageMath and Kenzo, together with an optional Kenzo package. Our work makes it possible to communicate both computer algebra programs and enhances the SageMath system with new capabilities in algebraic topology, dealing in particular with simplicial objects of infinite nature.