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IBNP

Involutive Bases for Noncommutative Polynomials

0.17

11 September 2025

Gareth A. Evans
Email: gareth@mathemateg.com
Address:
Ysgol y Creuddyn
Ffordd Derwen, Bae Penrhyn
Llandudno, LL30 3LB
U.K.

Christopher D. Wensley
Email: cdwensley.maths@btinternet.com
Homepage: https://github.com/cdwensley

Abstract

The IBNP package provides methods for computing an involutive (Gröbner) basis B for an ideal J over a polynomial ring R in both the commutative and noncommutative cases.

Secondly, methods are provided to involutively reduce a given polynomial to its normal form in R/J.

Bug reports, comments, suggestions for additional features, and offers to implement some of these, will all be very welcome.

Please submit any issues at https://github.com/gap-packages/ibnp/issues/ or send an email to the second author at cdwensley.maths@btinternet.com.

Copyright

© 2024-2025, Gareth Evans and Chris Wensley.

The IBNP package 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.

Acknowledgements

This documentation was prepared with the GAPDoc [LN17] and AutoDoc [GH23] packages.

The procedure used to produce new releases uses the package GitHubPagesForGAP [Hor19] and the package ReleaseTools.

Contents

1 Introduction
2 Using the packages GBNP and NMO
3 Commutative Involutive Bases
4 Functions for Noncommutative Monomials
5 Functions for Noncommutative Polynomials
6 Noncommutative Involutive Bases
References
Index

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