Computational Homology
Persistent homology provides an algebraic topological tool for quantifying and characterizing geometric features of objects and functions. Perseus uses ideas from discrete Morse theory to provide an efficient preprocessor for the standard persistent homology algorithm.
morse reductions
There are several technical challenges to computing homology and induced maps on homology. On the algebraic level the key step is the Smith Normal form algorithm. The worst case analysis suggests a super cubical complexity with respect to the size of the complex. This is prohibitive for large or higher dimensional data sets. We use ideas from discrete Morse theory to replace the original complex by a much smaller complex on which the algebraic computations are performed. The code is capable of computing homology groups and induced maps on homology in very general settings.
the original chomp software