The GAP 4 package ‘GBNP’

Summary

We provide algorithms, written in the GAP 4 programming language, for computing Grobner bases of non-commutative polynomials with coefficients from a field implemented in GAP, and some variations, such as a weighted and truncated version and a tracing facility.

The word algorithm is interpreted loosely: in general one cannot expect such an algorithm to terminate, as it would imply solvability of the word problem for finitely presented (semi)groups.

Distribution

• The GitHub package repository is at https://github.com/gap-packages/gbnp/
• and the latest release is available at https://gap-packages.github.io/gbnp/

Copyright

The ‘GBNP’ package is Copyright The GAP Group, 2001-2020.

‘GBNP’ 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

Installation

• unpack gbnp-<version_number>.tar.gz in the pkg subdirectory of the GAP root directory.

• From within GAP load the package with:

  gap> LoadPackage( “gbnp” );

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

Acknowledgments:

• The package is based on an earlier version by Rosane Ushirobira.

• The bulk of the package is written by Arjeh M. Cohen and Dié A.H. Gijsbers.

• The theory is mainly taken from literature by Teo Mora and Edward L. Green.

• From Version 0.8.3 on the package has three additional files by Chris Krook, based on work by Victor Ufnarovski. These files (fincheck.g, tree.g, graphs.g) contain routines for finding the Hilbert function and testing finite-dimensionality when given a GB.

• From Version 0.9 on the package is enriched with support for GAP fields and additional prefix rules for quotient modules as well as some speed improvements by Jan Willem Knopper. Knopper has also formatted the documentation in GAPDoc.

• From Version 1.0 on the package is extended with NMO (for Noncommutative Monomial Orderings) by Randall Cone. This enables the GBNP user to choose a wider selection of monomial orderings than the standard one built into GBNP itself. The files of this extension can be found in .../gbnp/doc/nmo, .../gbnp/doc/examples/nmo, and .../gbnp/lib/nmo.

Authors:

• Arjeh M. Cohen, A.M.Cohen@tue.nl

• Jan Willem Knopper, J.W.Knopper@tue.nl

• Address: RIACA, Dept. Math. and Comp. Sc., TU/e, POB 513, 5600 MB Eindhoven, The Netherlands.

Contact

If you have a question relating to ‘GBNP’ or encounter any problems, please report an issue on the GitHub issue tracker at: https://github.com/gap-packages/gbnp/issues/new