Since a real univariate polynomial does not always have real roots, a very natural
algorithmic problem, is to design a method to count the number of real roots of a given …

George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for
Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major …

This series of papers presents a complete development and complexity analysis of a
decision method, and a quantifier elimination method, for the first order theory of the reals …

In this paper, a new algorithm for performing quantifier elimination from first order formulas
over real closed fields in given. This algorithm improves the complexity of the asymptotically …

The arrangement of a finite collection of geometric objects is the decomposition of the space
into connected cells induced by them. We survey combinatorial and algorithmic properties of …

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 …

Optimization Theory is becoming a more and more important mathematical as well as
interdisciplinary area, especially in the interplay between mathematics and many other …

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 …

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 …