Jérémy Berthomieu

Research – Publications

My research domain is computer algebra and more precisely, I am mainly interested in algebraic algorithms for solving polynomial systems and guessing linear recurrence relations.

Submissions

  1. D. Kaufmann and J. Berthomieu.
    Extracting Linear Relations from Gröbner Bases for Formal Verification of And-Inverter Graphs
  2. J. Berthomieu, Ch. Eder and M. Safey El Din.
    New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)
  3. J. Berthomieu, A. Ferguson and M. Safey El Din.
    On the computation of asymptotic critical values of polynomial maps and applications.

Journal Papers

  1. J. Berthomieu, S. Graillat, D. Lesnoff and Th. Mary 2023.
    Modular matrix multiplication on GPU for polynomial system solving.
    ACM Communications in Computer Algebra 57 (2), 35–38.
  2. J. Berthomieu, A. Bostan, A. Ferguson and M. Safey El Din 2022.
    Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems.
    Journal of Algebra 602, 154–180.
  3. J. Berthomieu and M. Safey El Din 2022.
    Guessing Gröbner Bases of Structured Ideals of Relations of Sequences.
    Journal of Symbolic Computation 111, 1–26.
  4. J. Berthomieu and J.-Ch. Faugère 2022.
    Polynomial-Division-Based Algorithms for Computing Linear Recurrence Relations.
    Journal of Symbolic Computation 109, 1–30.
  5. J. Berthomieu, A. Ferguson and M. Safey El Din 2021.
    Towards fast one-block quantifier elimination through generalised critical values.
    ACM Communications in Computer Algebra 54 (3), 109–113.
  6. J. Berthomieu and J.-Ch. Faugère 2020.
    In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: The adaptive variants.
    Journal of Symbolic Computation 101, 270–303.
  7. J. Berthomieu, B. Boyer and J.-Ch. Faugère 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.
  8. J. Berthomieu, J.-Ch. Faugère, and L. Perret 2015.
    Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials.
    Journal of Complexity, 31 (4), 590–616.
  9. J. Berthomieu, G. Lecerf, and G. Quintin 2013.
    Polynomial root finding over local rings and application to error correcting codes.
    Applicable Algebra in Engineering, Communication and Computing, 24 (6), 413–443, 2013.
  10. J. Berthomieu and L. M. Pardo 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.
  11. J. Berthomieu and G. Lecerf 2012.
    Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations.
    Mathematics of Computation, 81 (279), 1799–1821.
  12. J. van der Hoeven, G. Lecerf, B. Mourrain, Ph. Trébuchet, J. Berthomieu, D. N. Diatta and A. Manzaflaris 2011.
    Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation.
    ACM Communications in Computer Algebra, 45 (3/4), 186–188.
  13. J. Berthomieu, J. van der Hoeven and G. Lecerf 2011.
    Relaxed algorithms for p-adic numbers.
    Journal de Théorie des Nombres de Bordeaux, 23 (3), 541–577.
  14. J. Berthomieu, P. Hivert, and H. Mourtada. 2010
    Computing Hironaka's invariants: ridge and directrix.
    Arithmetic, Geometry, Cryptography and Coding Theory 2009, Contemporary Mathemathics 521, 9–20.

Conferences Papers

  1. J. Berthomieu and R. Mohr 2024.
    Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
    Proceedings of the 49th International Symposium on Symbolic and Algebraic Computation, ISSAC '24, 307–315,
    Raleigh, NC, USA.
  2. J. Berthomieu, V. Neiger and M. Safey El Din 2022.
    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 '22, 409–418,
    Villeneuve-d'Ascq, France.
  3. J. Berthomieu, Ch. Eder and M. Safey El Din 2021.
    msolve: A Library for Solving Polynomial Systems.
    Proceedings of the 46th International Symposium on Symbolic and Algebraic Computation, ISSAC '21, 51–58,
    Saint Petersburg, Russia.
  4. J. Berthomieu and J.-Ch. Faugère 2018.
    A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations.
    Proceedings of the 43rd International Symposium on Symbolic and Algebraic Computation, ISSAC '18, 79–86,
    New York, NY, USA.
  5. J. Berthomieu and J.-Ch. Faugère 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 '16, 95–102,
    Waterloo, ON, Canada.
  6. J. Berthomieu, B. Boyer and J.-Ch. Faugère 2015.
    Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences.
    Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ISSAC '15, 61–68,
    Bath, United Kingdom.
  7. J. Berthomieu and R. Lebreton 2012.
    Relaxed p-adic Hensel Lifting for Algebraic Systems.
    Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, 59–66,
    Grenoble, France.

Theses

  1. J. Berthomieu 2023.
    Contributions to polynomial system solving: Recurrences and Gröbner bases.
    Habilitation thesis, Sorbonne Université.
  2. J. Berthomieu 2011.
    Contributions à la résolution des systèmes algébriques : réduction, localisation, traitement des singularités ; implantations.
    PhD thesis, École polytechnique.