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 …

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 …

Let T (x)∈ k [x] be a monic non-constant polynomial and write R= k [x]/< T> the quotient ring.
Consider two bivariate polynomials a (x, y), b (x, y)∈ R [y]. In a first part, T= pe is assumed to …

Given two coprime polynomials P and Q in Z [x, y] of degree at most d and coefficients of
bitsize at most τ, we address the problem of computing a triangular decomposition {(U i (x), V …

We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The
algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the …

In this paper, we present a new method for isolating real roots of a bivariate polynomial
system. Our method is a subdivision method which is based on real root isolation of …