# `simpcomp`

A &GAP; toolbox for simplicial complexes
Version <#Include SYSTEM "../version">
Felix Effenberger effenberger@mathematik.uni-stuttgart.de
Jonathan Spreer spreer@mathematik.uni-stuttgart.de

      	University of Stuttgart

    	Department of Mathematics

    	Institute of Geometry and Topology

    	D-70550 Stuttgart, Germany

January 2010

`simpcomp` is a &GAP; package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f-, g- and h-vectors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old (simplex links and stars, connected sums, cartesian products, handle additions, bistellar flips, etc.). Furthermore, it comes with an extensive library of known triangulations of manifolds and provides the user with the possibility to create own complex libraries.
`simpcomp` caches computed properties of a simplicial complex, thus avoiding unnecessary computations, internally handles the vertex labeling of the complexes and insures the consistency of a simplicial complex throughout all operations.
`simpcomp` relies on the &GAP; package `homology` for its homology computation, but also provides the user with an own (co-)homology algorithm in case the packacke `homology` is not available. For automorphism group computation the &GAP; package `GRAPE` is used, which in turn uses the program nauty by Brendan McKay . An internal automorphism group calculation algorithm in used as fallback if the `GRAPE` package is not available.

A few functions of `simpcomp` are based on code from other authors. The bistellar flips implementation is based upon work of Frank Lutz . Some functions were carried over from the `Homology` package by Dumas et al. -- these functions are marked in the documentation and the source code. The internal (co)homology algorithms were implemented by Armin Weiss.

Most of the complexes in the simplicial complex library are taken from the "Manifold Page" by Frank Lutz .

The first author acknowledges support by the Deutsche Forschungsgemeinschaft (DFG). This work was carried out as part of the DFG project "Ku 1203/5-2".
&copyright; 2009 by Felix Effenberger and Jonathan Spreer.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation, see http://www.fsf.org/licensing/licenses/fdl.html for a copy.

simpcomp
is free software. The code of `simpcomp` is released under the GPL version 2 or later (at your preference). For the text of the GPL see the file COPYING in the `simpcomp` directory or http://www.gnu.org/licenses/.