| Simplicial Homology - A proposed share package for GAP (2000) | |||||||||||||||
Abstract | |||||||||||||||
| eorems. It is our expectation that working with the package will allow many application of that kind. The functionality of GAP 4 fits perfectly in this picture. The algebraic and combinatorial objects, their constructors and invariants already implemented facilitate the development of the routines of the package whose average running time and memory consumption is not critical. In general, we hope the interaction between the algorithmic and geometric/combinatorial side will continue and grow once the package has been released. Algorithms: Simplicial complex constructions can easily lead to cases where some of the boundary maps of simplicial homology are very large, very sparse matrices. Each of the four algorithms for invariant factors implemented in the package each has strengths and weaknesses. We are involved in continuing research on better methods for this. We would appreciate learning about examples that are hard or impossible to compute by our f | |||||||||||||||
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