f4ncgb: High Performance Gr\"obner Basis Computations in Free Algebras
Mathematical Software
2026-01-05 v2 Symbolic Computation
Abstract
We present f4ncgb, a new open-source C++ library for Gr\"obner basis computations in free algebras, which transfers recent advancements in commutative Gr\"obner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state-of-the-art for noncommutative Gr\"obner basis computations. We also discuss implementation details and design choices.
Keywords
Cite
@article{arxiv.2505.19304,
title = {f4ncgb: High Performance Gr\"obner Basis Computations in Free Algebras},
author = {Maximilian Heisinger and Clemens Hofstadler},
journal= {arXiv preprint arXiv:2505.19304},
year = {2026}
}
Comments
21 pages, 2 figures, 3 tables