Solving Polynomial Systems with Gröbner Bases: An Introduction to F4 and FGLM
Published: Sep 3, 2025
Last Updated: Sep 3, 2025
Authors:Anna Maria Bigatti, Alessio Caminata, Tor Kristian Ellingsen, Evelina Lanteri, Andrea Sanguineti, Irene Villa
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.