Solving Polynomial Systems with Gr\"obner Bases: An Introduction to F4 and FGLM
Symbolic Computation
2025-09-04 v1 Commutative Algebra
Abstract
These notes originate from a reading course held by the authors in the spring of 2024 at the Universit\`a di Genova. They provide a hands-on introduction to the F4 and FGLM algorithms. In addition to the notes, we present two implementations of the algorithms: FGLM in CoCoALib and F4 in Sage. These implementations closely follow the structure of the algorithms as described here and are intended to help readers experiment with them in practice, thereby gaining a deeper understanding.
Cite
@article{arxiv.2509.03346,
title = {Solving Polynomial Systems with Gr\"obner Bases: An Introduction to F4 and FGLM},
author = {Anna Maria Bigatti and Alessio Caminata and Tor Kristian Ellingsen and Evelina Lanteri and Andrea Sanguineti and Irene Villa},
journal= {arXiv preprint arXiv:2509.03346},
year = {2025}
}
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