Description
Date depot: 24 juillet 2023
Titre: Structured linear algebra for recurrences and Gröbner bases
Directeur de thèse:
Jérémy BERTHOMIEU (LIP6)
Domaine scientifique: Sciences pour l'ingénieur
Thématique CNRS : Calcul arithmétique et formel, codage et cryptologie
Resumé: The main topic of this Ph.D. subject is to exploit the link between polynomials and linear recurrence relations of a sequence in
order to accelerate either the computations of Gröbner bases for polynomial system solving or the guessing of all the recurrences satisfied by a multi-indexed sequence.
To do so, we aim to thoroughly analyze and take advantage of the structure of the linear systems that appear in these computations.
The main objective of this Ph.D. thesis is the design of fast
algorithms for guessing linear recurrence relations, whether with
constant or polynomial coefficients, in order to accelerate polynomial
system solving or the description of the nature of the sequences coming from
applications, such as combinatorics.
Doctorant.e: Tran Kevin