Contributions to polynomial system solving: Recurrences and Gröbner bases - Sorbonne Université Access content directly
Habilitation À Diriger Des Recherches Year : 2023

Contributions to polynomial system solving: Recurrences and Gröbner bases

Jérémy Berthomieu

Abstract

This habilitation thesis deals with polynomial system solving through Gröbner bases computations. It focuses on the link between multivariate polynomials and linear recurrence relations satisfied by a multi-indexed sequence for computing Gröbner bases. Our contributions mainly lie on the theoretical and practical aspects on these Gröbner bases computations. First, we present \texttt{msolve}, a new open source \texttt{C} library, for solving polynomial systems using Gröbner bases. Second, we describe new algorithms and complexity estimates for computing Gröbner bases either for a total degree order or the lexicographic one. Then, we present linear algebras-based and polynomial-division-based algorithms for guessing linear recurrences with constant or polynomial coefficients, in generic and structured situations. Finally, we detail our research project for the forthcoming years on these aspects.
Fichier principal
Vignette du fichier
hdr_berthomieu (1).pdf (704.53 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

tel-04289532 , version 1 (16-11-2023)

Licence

Identifiers

  • HAL Id : tel-04289532 , version 1

Cite

Jérémy Berthomieu. Contributions to polynomial system solving: Recurrences and Gröbner bases. Symbolic Computation [cs.SC]. Sorbonne Université, 2023. ⟨tel-04289532⟩
77 View
44 Download

Share

Gmail Mastodon Facebook X LinkedIn More