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 …

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 …

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 first review the basic properties of the well known classes of Toeplitz, Hankel,
Vandermonde, and other related structured matrices and reexamine their correlation to …

Two novel 4-DOF very fast parallel robots were designed. This paper introduces the new
parallel mechanism designs which are named the Manta and the Kanuk. In order to reduce …

Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a
fundamental problem of computational real algebraic geometry. We propose an algorithm …

Finding one point on each semi-algebraically connected component of a real algebraic
variety, or at least deciding if such a variety is empty or not, is a fundamental problem of …

Apart from specific methods amenable to specific problems, symplectic Runge-Kutta
methods are necessarily implicit. The aim of this paper is to construct explicit Runge-Kutta …

This paper describes a new method for computing the normal form of a polynomial modulo a
zero-dimensional ideal I. We give a detailed description of the algorithm, a proof of its …