Projects / matrixss

matrixss is a package for the GAP system (gap-system.org) implementing the Schreier-Sims algorithm for matrix groups, using different approaches. This can be used as an alternative to the built-in GAP implementation.

Tags | Scientific/Engineering Mathematics |
---|---|

Licenses | GPL |

Operating Systems | OS Independent |

Implementation | Other |

- 11 Sep 2004 12:46

**Release Notes:** A somewhat-complete manual now exists, and the code has had some
cosmetic updates and more documentation. The package is now considered
to be in beta stage, and the Debian packages has been changed.

- 19 Aug 2004 16:14

**Release Notes:** The so-called Verify routine by Sims has been implemented from
the description in Seress's book. This seems to be a better
strong-generating test than the STCS algorithm, and one can now choose
between them with an Option when using the probabilistic algorithm. The
Verify algorithm is still neither cleaned up nor optimized in any way,
so it is not fast, but it appears to be both sound and complete. The
probabilistic algorithm now again uses the GAP function PseudoRandom to
generate random group elements, since this appears to be faster.

- 10 Aug 2004 13:02

**Release Notes:** An algorithm highly inspired by the nearly linear
time algorithm, described in Seress book as well
as in the 1991 paper by Babai et al, has been
implemented. However, some parts of the nearly
linear time algorithm has not yet been
implemented; in particular, the "short Schreier
trees". The implementation is still very slow,
though, so the fastest version is still the
standard deterministic algorithm. Other changes
include the use of random subproducts in the
probabilistic algorithm and changes in the
representation of Schreier trees.

- 31 Jul 2004 00:01

**Release Notes:** A rudimentary manual has been created, and it is both included in the package distribution and available from the package homepage. The code is now more GAP-connected in the sense that the algorithms are methods of an operation StabChainMatrixGroup, and the package installs a method for the Size attribute for finite matrix groups that uses that attribute to compute the order of a group.

- 14 Jul 2004 05:49

**Release Notes:** The Schreier-Todd-Coxeter-Sims algorithm has been
optimized and the handling of relations has been fixed.
Homomorphisms are now only used when needed, and
otherwise normal lists are used to map generator matrices
to each corresponding free group.