This paper is devoted to the resolution of zero-dimensional systems in K [X 1,… X n], where
K is a field of characteristic zero (or strictly positive under some conditions). We follow the …

Given a system of polynomial equations and inequations with coefficients in the field of
rational numbers, we show how to compute a geometric resolution of the set of common …

We present a new method for solving symbolically zero-dimensional polynomial equation
systems in the affine and toric case. The main feature of our method is the use of problem …

In this paper, we present a new approach for computing normal forms in the quotient algebra
A of a polynomial ring R by an ideal I. It is based on a criterion, which gives a necessary and …

Let f1, ldots, fs be polynomials in Q [X1,..., Xn] that generate a radical ideal and let V be their
complex zero-set. Suppose that V is smooth and equidimensional; then we show that …

The last decade has witnessed the rebirth of resultant methods as a powerful computational
tool for variable elimination and polynomial system solving. In particular, the advent of …

We introduce a subexponential algorithm for geometric solving of multivariate polynomial
equation systems whose bit complexity depends mainly on intrinsic geometric invariants of …

Given a polynomial system of n equations in n unknowns that depends on some parameters,
we define the notion of parametric geometric resolution as a means to represent some …

Multivariate resultants generalize the Sylvester resultant of two polynomials and
characterize the solvability of a polynomial system. They also reduce the computation of all …

A roadmap for a semi-algebraic set S is a curve which has a non-empty and connected
intersection with all connected components of S. Hence, this kind of object, introduced by …