Daniel Lazard

Daniel Lazard (born December 10, 1941) is a French mathematician and computer scientist. He is emeritus professor at Université Pierre et Marie Curie.^[1]

Biography[]

Lazard was born in Carpentras. He obtained a PhD from the University of Paris in 1968 for a thesis entitled Autour de la platitude. His doctoral supervisor was Pierre Samuel.^[2]

Lazard began his academic career by working in commutative algebra, especially on flat modules. Around 1970, he began to work in computer algebra, which, soon after, became his main research area. In this field, he is specially interested in multivariate polynomials and more generally in computational algebraic geometry, with emphasis on polynomial system solving.^{[citation needed]}

Prior to Lazard's scheduled retirement at the end of 2004, a conference on polynomial system solving was held at Université Pierre et Marie Curie to celebrate his contributions to computer algebra, polynomial systems solving and applications.^[3]

Selected contributions[]

• Lazard (1969) noted that a module is flat if and only if it is a direct limit of finitely generated free modules. As a consequence, one can deduce that every finitely presented flat module is projective. (See flat module § Categorical colimits)
• In computer algebra, the resultant of two polynomials can be used to analyze modular images of the greatest common divisor of integer polynomials where the coefficients are taken modulo some prime number p. The resultant of two polynomials is frequently computed in the Lazard–Rioboo–Trager method of finding the integral of a ratio of polynomials.
• Lazard (1992) introduced the lextriangular algorithm to obtain the triangular decomposition of a polynomial system. See System of polynomial equations § Regular chains.

Bibliography[]

• Lazard, Daniel (1969), "Autour de la platitude", Bulletin de la Société Mathématique de France, 97: 81–128, doi:10.24033/bsmf.1675
• Faugère, Jean-Charles; Gianni, Patrizia; Lazard, Daniel; Mora, Teo (1993), "Efficient computation of zero-dimensional Gröbner bases by change of ordering", Journal of Symbolic Computation, 16 (4): 329–344, doi:10.1006/jsco.1993.1051, MR 1263871
• Lazard, Daniel (2009), "Thirty years of Polynomial System Solving, and now?", Journal of Symbolic Computation, 44 (3): 222–231, doi:10.1016/j.jsc.2008.03.004
• Lazard, Daniel (1981), "Résolution des systèmes d'équations algébriques", Theoretical Computer Science, 15: 77–110, doi:10.1016/0304-3975(81)90064-5
• Lazard, Daniel (1992), "Solving zero-dimensional algebraic systems", Journal of Symbolic Computation, 13 (2): 117–131, doi:10.1016/s0747-7171(08)80086-7.
• Abramson, Michael (2001), "Solving systems of algebraic equations, translation of (Lazard 1981)", ACM SIGSAM Bulletin, 35 (3): 11–37, doi:10.1145/569746.569750
• ICPSS, International Conference on Polynomial System Solving, and special issue of Journal of Symbolic Computation, in honor of Daniel Lazard, archived from the original on 2012-04-26

References[]

External links[]

• Daniel Lazard at the Mathematics Genealogy Project