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Documentation on the GBNP package

Version 1.0.2

27 April 2011

Arjeh M. Cohen
Email: A.M.Cohen@tue.nl

Jan Willem Knopper
Email: J.W.Knopper@tue.nl

Address:
TU/e,
POB 513, 5600 MB Eindhoven, the Netherlands

Abstract

We provide algorithms, written in the GAP 4 programming language, for computing Gröbner bases of non-commutative polynomials, and some variations, such as a weighted and truncated version and a tracing facility. In addition, there are algorithms for analyzing the quotient of a non-commutative polynomial algebra by a 2-sided ideal generated by a set of polynomials whose Gröbner basis has been determined and for computing quotient modules of free modules over quotient algebras.

The notion of algorithm is interpreted loosely: in general one cannot expect a non-commutative Gröbner basis algorithm to terminate, as it would imply solvability of the word problem for finitely presented (semi)groups.

This documentation gives a short description of the mathematical content, explains the functions of the package, and provides more than twenty worked out examples.

Acknowledgements

 

Contents

1 Introduction
2 Description
3 Functions
4 Info Level
A Examples
References
Index

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