2011-2025 Publications

• 2025
  • D. Kaufmann, J. Berthomieu : “Extracting Linear Relations from Gröbner Bases for Formal Verification of And-Inverter Graphs”, Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2025, vol. 15696, Lecture Notes in Computer Science, Hamilton, Canada, pp. 355-374, (Springer Nature Switzerland), (ISBN: 978-3-031-90643-5) (2025)
  • J. Berthomieu, R. Lebreton, K. Tran : “Quasi-Linear Guessing of Minimal Lexicographic Gröbner Bases of Ideals of C-Relations of Random Bi-Indexed Sequences”, (2025)
  • J. Berthomieu, S. Graillat, D. Lesnoff, Th. Mary : “Multiword matrix multiplication over large finite fields in floating-point arithmetic”, (2025)
• 2024
  • J. Berthomieu, R. Mohr : “Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting”, 49^th International Symposium on Symbolic and Algebraic Computation, ISSAC '24, Raleigh, NC, United States, pp. 307-315, (ACM), (ISBN: 9798400706967) (2024)
• 2023
  • J. Berthomieu, Ch. Eder, M. Safey El Din : “New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)”, (2023)
  • J. Berthomieu, S. Graillat, D. Lesnoff, Th. Mary : “Modular matrix multiplication on GPU for polynomial system solving”, ACM Communications in Computer Algebra, vol. 57 (2), pp. 35-38, (Association for Computing Machinery (ACM)) (2023)
• 2022
  • J. Berthomieu, A. Bostan, A. Ferguson, M. Safey El Din : “Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems”, Journal of Algebra, vol. 602, pp. 154-180, (Elsevier) (2022)
  • J. Berthomieu, M. Safey El Din : “Guessing Gröbner Bases of Structured Ideals of Relations of Sequences”, Journal of Symbolic Computation, vol. 111, pp. 1-26, (Elsevier) (2022)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “Computing the set of asymptotic critical values of polynomial mappings from smooth algebraic sets”, (2022)
  • J. Berthomieu, J.‑Ch. Faugère : “Polynomial-Division-Based Algorithms for Computing Linear Recurrence Relations”, Journal of Symbolic Computation, vol. 109, pp. 1-30, (Elsevier) (2022)
  • J. Berthomieu, V. Neiger, M. Safey El Din : “Faster change of order algorithm for Gröbner bases under shape and stability assumptions”, 47^th International Symposium on Symbolic and Algebraic Computation, Lille, France (2022)
• 2021
  • J. Berthomieu, Ch. Eder, M. Safey El Din : “msolve: A Library for Solving Polynomial Systems”, ISSAC '21: Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, Saint Petersburg, Russian Federation, pp. 51-58 (2021)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “On the computation of asymptotic critical values of polynomial maps and applications”, (2021)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “Towards fast one-block quantifier elimination through generalised critical values”, ACM Communications in Computer Algebra, vol. 54 (3), Kalamata, Greece, pp. 109-113, (Association for Computing Machinery (ACM)) (2021)
• 2020
  • J. Berthomieu, J.‑Ch. Faugère : “In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: the adaptive variants”, Journal of Symbolic Computation, vol. 101, pp. 270-303, (Elsevier) (2020)
• 2018
  • J. Berthomieu, J.‑Ch. Faugère : “A polynomial-division-based algorithm for computing linear recurrence relations”, ISSAC '18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, New York, United States, pp. 79-86 (2018)
• 2017
  • J. Berthomieu, B. Boyer, J.‑Ch. Faugère : “Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences”, Journal of Symbolic Computation, vol. 83 (Supplement C), pp. 36-67, (Elsevier) (2017)
  • J. Berthomieu, J.‑Ch. Faugère : “In-depth comparison of the Berlekamp – Massey – Sakata and the Scalar-FGLM algorithms: the non adaptive variants”, (2017)
• 2016
  • J. Berthomieu, J.‑Ch. Faugère : “Guessing Linear Recurrence Relations of Sequence Tuples and P-recursive Sequences with Linear Algebra”, ISSAC '16: Proceedings of the 2016 on International Symposium on Symbolic and Algebraic Computation, Waterloo, ON, Canada, pp. 95-102 (2016)
• 2015
  • J. Berthomieu, J.‑Ch. Faugère, L. Perret : “Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials: The Regular Case”, Journal of Complexity, vol. 31 (4), pp. 590-616, (Elsevier) (2015)
  • J. Berthomieu, B. Boyer, J.‑Ch. Faugère : “Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences”, ISSAC '15: Proceedings of the 2015 on International Symposium on Symbolic and Algebraic Computation, Bath, United Kingdom, pp. 61-68 (2015)
• 2013
  • J. Berthomieu, G. Lecerf, G. Quintin : “Polynomial root finding over local rings and application to error correcting codes”, Applicable Algebra in Engineering, Communication and Computing, vol. 24 (6), pp. 413-443, (Springer Verlag) (2013)
  • J. Berthomieu : “Decomposition of multihomogeneous polynomials: minimal number of variables”, (2013)
• 2012
  • J. Van Der Hoeven, G. Lecerf, B. Mourrain, Ph. Trébuchet, J. Berthomieu, D. Diatta, A. Mantzaflaris : “Mathemagix”, ACM Communications in Computer Algebra, vol. 45 (3/4), pp. 186-188, (Association for Computing Machinery (ACM)) (2012)
• 2011
  • J. Van Der Hoeven, G. Lecerf, B. Mourrain, Ph. Trébuchet, J. Berthomieu, D. Diatta, A. Mantzaflaris : “Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation”, ACM Communications in Computer Algebra, vol. 45 (3), pp. 186-188, (Association for Computing Machinery (ACM)) (2011)