Computing points in connected components defined by a real inequation: algorithms, complexity and implementations, Part I.
Preprint
Research
Publications
Computer algebra and polynomial system solving.
2026
Multiword matrix multiplication over large finite fields in floating-point arithmetic.
Preprint
Computing submatrices of the Hermite normal form of a structured polynomial matrix.
Proceedings of the 51st International Symposium on Symbolic and Algebraic Computation, ISSAC 2026, 29–38, Oldenburg, Germany
2025
Quasi-Linear Guessing of Minimal Lexicographic Gröbner Bases of Ideals of C-Relations of Random Bi-Indexed Sequences.
Proceedings of the 50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025, 258–266, Guanajuato, Mexico
Extracting Linear Relations from Gröbner Bases for Formal Verification of And-Inverter Graphs.
Proceedings of the 31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2025, 355–374, Hamilton, ON, Canada
2024
Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting.
Proceedings of the 49th International Symposium on Symbolic and Algebraic Computation, ISSAC 2024, 307–315, Raleigh, NC, USA
2023
New efficient algorithms for computing Gröbner bases of saturation ideals (F₄SAT) and colon ideals (Sparse-FG LM-colon).
Preprint
Modular matrix multiplication on GPU for polynomial system solving.
ACM Communications in Computer Algebra 57 (2), 35–38
Contributions to polynomial system solving: Recurrences and Gröbner bases.
Habilitation thesis, Sorbonne Université
2022
Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems.
Journal of Algebra 602, 154–180
Guessing Gröbner Bases of Structured Ideals of Relations of Sequences.
Journal of Symbolic Computation 111, 1–26
Polynomial-Division-Based Algorithms for Computing Linear Recurrence Relations.
Journal of Symbolic Computation 109, 1–30
Faster change of order algorithm for Gröbner bases under shape and stability assumptions.
Proceedings of the 47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022, 409–418, Villeneuve-d'Ascq, France
2021
On the computation of asymptotic critical values of polynomial maps and applications.
Preprint
Towards fast one-block quantifier elimination through generalised critical values.
ACM Communications in Computer Algebra 54 (3), 109–113
msolve: A Library for Solving Polynomial Systems.
Proceedings of the 46th International Symposium on Symbolic and Algebraic Computation, ISSAC 2021, 51–58, Saint Petersburg, Russia
2020
In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: The adaptive variants.
Journal of Symbolic Computation 101, 270–303
2018
A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations.
Proceedings of the 43rd International Symposium on Symbolic and Algebraic Computation, ISSAC 2018, 79–86, New York, NY, USA
2017
Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences.
Journal of Symbolic Computation 83, 36–67, Special issue on the conference ISSAC 2015: Symbolic computation and computer algebra
2016
Guessing Linear Recurrence Relations of Sequence Tuples and P-recursive Sequences with Linear Algebra.
Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation, ISSAC 2016, 95–102, Waterloo, ON, Canada
2015
Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials.
Journal of Complexity 31 (4), 590–616
Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences.
Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, 61–68, Bath, United Kingdom
2013
Polynomial root finding over local rings and application to error correcting codes.
Applicable Algebra in Engineering, Communication and Computing 24 (6), 413–443
2012
Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian.
Journal of Complexity 28 (3), 388–421
Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations.
Mathematics of Computation 81 (279), 1799–1821
Relaxed $p$-adic Hensel Lifting for Algebraic Systems.
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012, 59–66, Grenoble, France
2011
Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation.
ACM Communications in Computer Algebra 45 (3/4), 186–188
Relaxed algorithms for $p$-adic numbers.
Journal de Théorie des Nombres de Bordeaux 23 (3), 541–577
Contributions à la résolution des systèmes algébriques : réduction, localisation, traitement des singularités ; implantations.
PhD thesis, École polytechnique
2010
Computing Hironaka's invariants: ridge and directrix.
Arithmetic, Geometry, Cryptography and Coding Theory 2009, Contemporary Mathematics 521, 9–20