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- Jean-Charles Faugère, Patrizia M. Gianni, Daniel Lazard, Teo Mora
- J. Symb. Comput.
- 1993

We present an efficient algorithm for the transformation of a Grobner basis of a zero-dimensional ideal with respect to any given ordering into a Grobner basis with respect to any other ordering.… (More)

- François Boulier, Daniel Lazard, François Ollivier, Michel Petitot
- ISSAC
- 1995

We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for… (More)

- François Boulier, Daniel Lazard, François Ollivier, Michel Petitot
- Applicable Algebra in Engineering, Communication…
- 1997

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an… (More)

- Daniel Lazard, Fabrice Rouillier
- J. Symb. Comput.
- 2007

We present a new algorithm for solving basic parametric constructible or semi-algebraic systems of the form C={x@?C^n,p"1(x)=0,...,p"s(x)=0,f"1(x) 0,...,f"l(x) 0} or… (More)

- Philippe Aubry, Daniel Lazard, Marc Moreno Maza
- J. Symb. Comput.
- 1999

Different notions of triangular sets are presented. The relationship between these notions are studied. The main result is that four different existing notions of good triangular sets are equivalent.

- Daniel Lazard
- Theor. Comput. Sci.
- 1981

Abstract Let f 1 ,…, f k be k multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field, counting the common zeros at infinity. An algorithm is… (More)

- Daniel Lazard
- EUROCAL
- 1983

In the past few years, two very different methods have been developed for solving systems of algebraic equations : the method of Gr6bner bases or standard bases [Buc I, Buc 2, Tri, P.Y] and the one… (More)

- Daniel Lazard
- J. Symb. Comput.
- 1992

It is shown that a good output for a solver of algebraic systems of dimension zero consists of a family of ''triangular sets of polynomials''. Such an output is simple, readable and contains all… (More)

- Daniel Lazard
- Discrete Applied Mathematics
- 1991

Abstract A new algorithm is presented for solving algebraic systems of equations, which is designed from the structure which is wanted for the result. This algorithm is not yet implemented; thus… (More)

- Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean
- Symposium on Computational Geometry
- 2003

In this paper, we present the first exact, robust and practical method for computing an explicit representation of the intersection of two arbitrary quadrics whose coefficients are rational.… (More)