Editing Homology (mathematics) (section)

== Software ==

Various software packages have been developed for the purposes of computing homology groups of finite cell complexes. [http://linalg.org Linbox] is a [[C++]] library for performing fast matrix operations, including [[Smith normal form]]; it interfaces with both [http://www.gap-system.org Gap] and [http://www.maplesoft.com Maple]. [http://chomp.rutgers.edu Chomp], [http://redhom.ii.uj.edu.pl CAPD::Redhom] {{Webarchive|url=https://web.archive.org/web/20130715025307/http://www.redhom.ii.uj.edu.pl/ |date=2013-07-15 }} and [http://www.sas.upenn.edu/~vnanda/perseus Perseus] are also written in C++. All three implement pre-processing algorithms based on [[simple-homotopy equivalence]] and [[discrete Morse theory]] to perform homology-preserving reductions of the input cell complexes before resorting to matrix algebra. [http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/ Kenzo] is written in Lisp, and in addition to homology it may also be used to generate [[Presentation of a group|presentations]] of [[homotopy]] groups of finite simplicial complexes. [[Gmsh]] includes a homology solver for finite element meshes, which can generate [[Cohomology]] bases directly usable by finite element software.<ref name=Pellikka2013 />