J. Berthomieu and M. Safey El Din. Guessing Gröbner Bases of Structured Ideals of Relations of Sequences. Preprint. [ HAL ]

J. Berthomieu and J.-Ch. Faugère. A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations. Preprint, extended version. [ HAL ]

J. Berthomieu, A. Ferguson, and M. Safey El Din. Towards fast one-block quantifier elimination through generalised critical values. To appear in ACM Communications in Computer Algebra. [ HAL ]

J. Berthomieu and J.-Ch. Faugère. In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: The adaptive variants. Journal of Symbolic Computation 101, 270–303. [ HAL | DOI ]

J. Berthomieu and J.-Ch. Faugère. A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations. In Proceedings of the 43rd International Symposium on Symbolic and Algebraic Computation, ISSAC '18, pages 79–86, New York, NY, USA, 2018. [ HAL | DOI ]

J. Berthomieu, B. Boyer, and J.-Ch. Faugère. Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences. Journal of Symbolic Computation 83 (Supplement C), 36–67, special issue on the con-

ference ISSAC 2015: Symbolic computation and computer algebra. [ HAL | DOI ]

J. Berthomieu and J.-Ch. Faugère. Guessing Linear Recurrence Relations of Sequence Tuples and P-recursive Sequences with Linear Algebra. In Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pages 95–102, Waterloo, ON, Canada, 2016. [ HAL | DOI ]

J. Berthomieu, B. Boyer, and J.-Ch. Faugère. Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences. In Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pages 61–68, Bath, United Kingdom, 2015. [ HAL | DOI ]

J. Berthomieu, J.-Ch. Faugère, and L. Perret. Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials. J. Complexity, 31(4):590–616, 2015. [ HAL | DOI ]

J. Berthomieu, G. Lecerf, and G. Quintin. Polynomial root finding over local rings and application to error correcting codes. Appl. Algebra Engrg. Comm. Comput., 24(6), 413–443, 2013. [ HAL | DOI ]

J. Berthomieu and R. Lebreton. Relaxed \(p\)-adic Hensel Lifting for Algebraic Systems. In Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pages 59–66, Grenoble, France, 2012. [ HAL | DOI ]

J. Berthomieu and G. Lecerf. Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations. Math. Comp., 81(279):1799–1821, 2012. [ HAL | DOI ]

J. Berthomieu and L. M. Pardo. Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian. J. Complexity, 28(3):388–421, 2012. [ HAL | DOI ]

J. van der Hoeven, G. Lecerf, B. Mourrain, P. Trébuchet, J. Berthomieu, D. N. Diatta, and A. Manzaflaris. Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation, ACM Commun. Comput. Algebra, 45(3):186–188, 2011. In Section "ISSAC 2011 Software Demonstrations", edited by M. Stillman, pages 166–188. [ DOI ]

J. Berthomieu. Contributions à la résolution des systèmes algébriques : réduction, localisation, traitement des singularités ; implantations. PhD thesis, École polytechnique, 2011. [ TEL ]

J. Berthomieu, J. van der Hoeven, and G. Lecerf. Relaxed algorithms for \(p\)-adic numbers. J. Théor. Nombres Bordeaux, 23(3):541–577, 2011. [ HAL | DOI ]

J. Berthomieu, P. Hivert, and H. Mourtada. Computing Hironaka's invariants: ridge and directrix. In Arithmetic, Geometry, Cryptography and Coding Theory 2009, volume 521 of Contemp. Math., pages 9–20. Amer. Math. Soc., Providence, RI, 2010. [ HAL | DOI ]

Conferences

2018

A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations, ISSAC 2018, New York City, New York, United States.

Guessing Linear Recurrence Relations of Sequence Tuples and P-recursive Sequences with Linear Algebra, ISSAC 2016, Waterloo, Ontario, Canada.

Algèbre linéaire pour le calcul de bases de Gröbner de suites multidimensionnelles récurrentes linéaires, Journées Nationales de Calcul Formel 2015, Cluny, France.

Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials: The Regular Case, ACA 2015, Kalamata, Greece.

Algorithmes en temps polynomial pour l'isomorphisme de polynômes quadratiques : le cas régulier, Journées Nationales de Calcul Formel 2014, Luminy, France.

2013

\(p\)-adics in Mathemagix, Sage Days: Arithmetics over discrete valuation rings, Rennes, France.

Résolution détendue sur les entiers \(p\)-adiques des systèmes algébriques, Journées Nationales de Calcul Formel 2013, Luminy, France.

Relaxed \(p\)-adic Hensel lifting for algebraic systems, ISSAC 2012, Grenoble, France.

Factorisation de polynômes à deux variables convexe-denses, Journées Nationales de Calcul Formel 2011, Luminy, France.

Integral geometry formulae motivated by real polynomial equation solving, MEGA 2011, Stockholm, Sweden.

Arithmétique détendue pour les nombres \(p\)-adiques, Journées Nationales de Calcul Formel 2010, Luminy, France.

Installation and first steps with Mathemagix, SAGA Winter School 2010, Auron, France.