Contributions to polynomial system solving: Recurrences and Gröbner bases
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 msolve, a new open source 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.
Phd defence : 09/21/2023
Jury members :
Bernard Mourrain, Directeur de recherche, INRIA & Université Côte d’Azur [rapporteur]Cordian Riener, Professeur, Universitetet i Tromsø – Norges arktiske universitet [rapporteur]
Gilles Villard, Directeur de recherche, CNRS & École Normale Supérieure de Lyon [rapporteur]
Alin Bostan, Directeur de recherche, INRIA & Université Paris-Saclay (examinateur)
Manuel Kauers, Professeur, Johannes Kepler Universität Linz (examinateur)
Fatemeh Mohammadi, Professeure, Katholieke Universiteit Leuven (examinatrice)
Mohab Safey El Din, Professeur, Sorbonne Université (examinateur)
Associate Professor [HDR]