We present an algorithm for isolating all roots of an arbitrary complex polynomial p that also
works in the presence of multiple roots provided that (1) the number of distinct roots is given …

In this paper, we give improved bounds for the computational complexity of computing with
planar algebraic curves. More specifically, for arbitrary coprime polynomials f, g∈ Z [x, y] …

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 address the problem of solving systems of bivariate polynomials with integer coefficients.
We first present an algorithm for computing a separating linear form of such systems, that is …

We present a certified and complete algorithm to compute arrangements of real planar
algebraic curves. It computes the decomposition of the plane induced by a finite number of …

We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …

We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …

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 …

Subdivision-based algorithms recursively subdivide an input region until the smaller
subregions can be processed. It is a challenge to analyze the complexity of such algorithms …