Daniel Lazard

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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 testing membership in J . This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been(More)
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 information which may be wanted, Different algorithms are described for handling triangular systems and obtaining them from Gr/Sbner bases. These algorithms are(More)
Triangular sets appear under various names in many papers concerning systems of polynomial equations. Ritt (1932) introduced them as characteristic sets. He described also an algorithm for solving polynomial systems by computing characteristic sets of prime ideals and factorizing in field extensions. Characteristic sets of prime ideals have good properties(More)
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like C = {x ∈ C, p1(x) = 0, , ps(x) = 0, f1(x) 0, , fl(x) 0} or S = {x ∈ R, p1(x) = 0, , ps(x) = 0, f1(x)> 0, , fl(x)> 0}, where pi, fi ∈Q[U , X], U = [U1, , Ud] is the set of parameters and X = [Xd+1, , Xn] the set of unknowns. If ΠU denotes the canonical(More)
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. Combining results from the theory of quadratic forms, linear algebra and number theory, we show how to obtain parametric intersection curves that are near-optimal in(More)