We present a p-adic algorithm to recover the lexicographic Gröbner basis of an ideal in with
a generating set in, with a complexity that is less than cubic in terms of the dimension of and …

We present an m-adic Newton iteration with quadratic convergence for lexicographic
Gröbner basis of zero dimensional ideals in two variables. We rely on a structural result …

We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite
field can be computed in quasi-linear expected time, using a randomized algorithm of Las …

Given a zero-dimensional polynomial system consisting of n integer polynomials in n
variables, we propose a certified and complete method to compute all complex solutions of …

We consider the problem of computing the topology and describing the geometry of a
parametric curve in R n. We present an algorithm, PTOPO, that constructs an abstract graph …

In this paper, we present a new method for isolating real roots of a bivariate nonlinear
system. It is a subdivision method based on analyzing the local geometrical properties of the …

Abstract Let P∈ Z [X, Y] be a given square-free polynomial of total degree d with integer
coefficients of bitsize less than τ, and let VR (P):={(x, y)∈ R 2∣ P (x, y)= 0} be the real planar …

We give an algorithm for the symbolic solution of polynomial systems in Z [X, Y]. Following
previous work with Lebreton, we use a combination of lifting and modular composition …

We present explicit worst case degree and height bounds for the rational univariate
representation of the isolated roots of polynomial systems based on mixed volume. We base …

Let P and Q be two polynomials in K [x, y] with degree at most d, where K is a field. Denoting
by R∈ K [x] the resultant of P and Q with respect to y, we present an algorithm to compute R …