Gilles VILLARD    Directeur de recherche CNRS/INS2I
AriC project-team

Laboratoire LIP   [CNRS  ENSL  INRIA  UCBL  U. Lyon ]
  46, Allée d'Italie F69364   Lyon   Cedex 07

Recent Trends in Computer Algebra 2023

PUBLICATIONS    Detailed list / co-authors.


  • C. Pernet, H. Signargout, G. Villard. High-order lifting for polynomial Sylvester matrices, pdf/hal-03740320, 2022.
  • V. Neiger, B. Salvy, É. Schost, G. Villard. Faster modular composition, arXiv:2110.08354, 2021.
  • P. Karpman, C. Pernet, H. Signargout, G. Villard. Computing the characteristic polynomial of generic Toeplitz-like and Hankel-like Matrices. ISSAC'21, Virtual Event, Russian Federation, 2021, pdf/doi.
  • C.-P. Jeannerod, V. Neiger, G. Villard. Fast computation of approximant bases in canonical form. Journal of Symbolic Computation, 98:192-224, 2020, pdf/doi.
  • G. Villard. On computing the resultant of generic bivariate polynomials. ISSAC'18, New York, USA, 2018, pdf/doi, and maple worksheets.
  • J.-G. Dumas, E.Kaltofen, G.Villard, L. Zhi. Polynomial time interactive proofs for linear algebra with exponential matrix dimensions and scalars given by polynomial time circuits. ISSAC'17, Kaiserslautern, Germany, 2017, pdf/doi.
  • C.-P. Jeannerod, V. Neiger, É. Schost, G. Villard. Computing minimal interpolation bases, J. of Symbolic Computation, 83:272-314, 2017, pdf/doi.
  • Saruchi, I. Morel, D. Stehlé, G. Villard. LLL reducing with the most significant bits. ISSAC'14, Kobe, Japan, 2014, pdf/doi.
  • X.-W. Chang, D. Stehlé, G. Villard. Perturbation analysis of the QR factor R in the context of LLL lattice basis reduction, Mathematics of Computation, 81(279):1487-1511, 2012, pdf/doi.
  • G. Villard. Recent progress in linear algebra and lattice basis reduction. ISSAC'11, San Jose, California, 2011, invited, pdf/doi.
  • A. Novocin, D. Stehlé, G. Villard. An LLL-reduction algorithm with quasi-linear time complexity, STOC, San Jose, California, 2011, pdf/doi.
  • E. Kaltofen, G. Villard. On the complexity of computing determinants. Computational Complexity, 13:91-130, 2005, pdf/doi.


  • Extended precision floating-point benchmarks.
  • Hplll software library home page,  GitHub repository.
  • LinBox joint CNRS/NSF project LinBox Team GitHub (
  • The Givaro page, a C++ library for computer algebra.
  • Current teaching: Modern algorithms for symbolic summation and integration, M2 ENS de Lyon.

    TO SEE

    International Linear Algebra Society         GDR CNRS Informatique Mathématique - GT Arithmétique - GT Calcul Formel

            JNCF 2023, Journées Nationales de Calcul Formel, CIRM, Luminy, 6-10 mars 2023.
            STACS 2023, Symposium on Theoretical Aspects of Computer Science, Hamburg, Germany, March 7-10, 2023.
            JNIM 2023, Journées Nationales du GdR IM, IRIF, Université Paris Cité, 4-7 avril 2023.
            FoCM 2023, Foundation of Computational Mathematics conference, Paris, France, June 12-21, 2023.
            ICALP 2023, EATCS International Colloquium on Automata, Languages and Programming, Paderborn, Germany, July 10-14, 2023.
            ISSAC 2023, International Symposium on Symbolic and Algebraic Computation, Tromsø, Norway, July 24-27, 2023.
            CASC 2023, 25th International Workshop on Computer Algebra in Scientific Computing, Aug. 28 - Sept. 1, Havana, Cuba.