Daniel Lazard

Last updated
Daniel Lazard
Born (1941-12-10) 10 December 1941 (age 82)
Nationality French
Alma mater
Scientific career
Fields Mathematics, computer science
Institutions Pierre and Marie Curie University
Thesis Autour de la platitude  (1968)
Doctoral advisor Pierre Samuel
Doctoral students Jean-Charles Faugère

Daniel Lazard (born December 10, 1941) is a French mathematician and computer scientist. He is emeritus professor at Pierre and Marie Curie University.

Contents

Career

Daniel Lazard was born in Carpentras, in southern France.[ citation needed ] His undergraduate education was at the École Normale Supérieure.[ citation needed ] Following graduate work at the École Normale Supérieure and the University of Paris, he was granted a doctorat d'état in 1968 by the University of Paris. His dissertation was supervised by the commutative algebraist Pierre Samuel, and was titled "Autour de la platitude" ("Around flatness", or literally "Around the platitude"). [1] [2]

After 1970, his main area of research changed to computer algebra, particularly multivariate polynomials, computational algebraic geometry and systems of polynomial equations. To mark his retirement at the end of 2004, there was a conference at Pierre and Marie Curie University devoted to his subject area. [3] In 2009, a special issue of the Journal of Symbolic Computation was published in his honor. [4] To date, Lazard has authored or co-authored more than 40 journal articles, book chapters, conference papers, and other publications. [5]

Selected articles

Related Research Articles

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In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm uses the same mathematical principles as the Buchberger algorithm, but computes many normal forms in one go by forming a generally sparse matrix and using fast linear algebra to do the reductions in parallel.

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FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora. They introduced their algorithm in 1993. The input of the algorithm is a Gröbner basis of a zero-dimensional ideal in the ring of polynomials over a field with respect to a monomial order and a second monomial order. As its output, it returns a Gröbner basis of the ideal with respect to the second ordering. The algorithm is a fundamental tool in computer algebra and has been implemented in most of the computer algebra systems. The complexity of FGLM is O(nD3), where n is the number of variables of the polynomials and D is the degree of the ideal. There are several generalization and various applications for FGLM.

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References

  1. Daniel Lazard at the Mathematics Genealogy Project.
  2. Lazard, Daniel. Autour de la platitude (Thèse de doctorat). École Normale Supérieure (library record). Retrieved March 10, 2023.
  3. "International Conference on Polynomial System Solving, Paris, November 24-25-26 2004, in honour of Daniel Lazard", LIP6, archived from the original on March 14, 2009.
  4. Faugère, Jean-Charles; Rouillier, Fabrice (2009-03-01). "Foreword". Journal of Symbolic Computation . Polynomial System Solving in honor of Daniel Lazard. 44 (3): 221. doi:10.1016/j.jsc.2008.08.004. ISSN   0747-7171.
  5. "LAZARD Daniel 1998-2021 Publications". Sorbonne Institute. Retrieved February 23, 2023.