Contributions to polynomial system solving: Recurrences and Gröbner bases
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
