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 …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

We present sharp estimates for the degree and the height of the polynomials in the
Nullstellensatz over the integer ring ℤ. The result improves previous work of P. Philippon, C …

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 …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

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 …

Let S_0 be a smooth and compact real variety given by a reduced regular sequence of
polynomials f_1,...,f_p. This paper is devoted to the algorithmic problem of finding efficiently …

We present a new probabilistic method for solving systems of polynomial equations and
inequations. Our algorithm computes the equidimensional decomposition of the Zariski …

In this paper we apply for the first time a new method for multivariate equation solving which
was developed in\cite {gh1},\cite {gh2},\cite {gh3} for complex root determination to the {\em …

We study the triangular representation of zero-dimensional varieties defined over the
rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic …