The GAP package BruhatDecomposition

Introduction

This package can be used to compute the Bruhat decomposition of elements in their natural representation in classical groups. Moreover, the elements can also be expressed as words in specific generators, namely the Leedham-Green and O'Brien generators, as MSLPs.

Installation

• unpack BruhatDecomposition-<version_number>.zip in the pkg subdirectory of the GAP root directory.

• From within GAP load the package with:

   gap> LoadPackage("BruhatDecomposition");
   true
  

• The file manual.pdf is in the doc subdirectory.

Tests

From the package directory:

gap tst/testall.g       # a few seconds, every family over small groups
gap tst/testallmain.g   # several minutes, many dimensions and field sizes

Both check that the straight-line program and the matrices returned by each decomposition reproduce the input. If the forms package is installed, the fast run additionally checks that the LGO standard generators really are elements of the classical group they belong to.

The parameters of the thorough run can be set beforehand, e.g.

gap -c 'BruhatTestDims := [6..9];; BruhatTestRandomElements := 10;;' tst/testallmain.g

Contact

If you have a question relating to BruhatDecomposition, encounter any problems, or have a suggestion for extending the package in any way, please

• email: daniel.rademacher@rwth-aachen.de
• or report an issue at: issue tracker

License

BruhatDecomposition is free software you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

For details, see https://www.gnu.org/licenses/gpl.html.