Introduction
Daniel Lazard (born December 10, 1941) is a French mathematician and computer scientist. He is emeritus professor at Université Pierre et Marie Curie.
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.
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.
Lazard retired from the Université Pierre et Marie Curie Paris 6 UFR in 2008. Prior to his retirement, a special 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.
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.