What is RedHom?

RedHom is a software library for efficient computation of the homology of sets. The library implements algorithms based on geometric and algebraic reduction methods: acyclic subspace construction, elementary reductions and coreductions and discrete Morse theory. Reduction methods are applied to speed up the classical Smith diagonalization method, which is unsatisfactorily slow for large inputs due to is cubical complexity. RedHom may be used to compute Betti numbers, torsion coefficients, homology generators, persistence intervals and maps induced in homology.

The library is based on C++ templates. This allows us to have one efficient implementation of several reduction methods and use it for various complexes, in particular cubical complexes and simplicial complexes.

The library is oriented on users who just need ready-to-use stand-alone programs as well as programmers who need to use homology algorithms in their own programs.

RedHom originated from research in rigorous numerics of dynamical systems based on topological methods. In particular, RedHom constitutes a part of CAPD (Computer Assisted Proofs in Dynamics) project. We decided to make RedHom available also as a seperate library, because the area of its applicability turned out to go far beyond the original project.