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 …

We present a new algorithm for solving basic parametric constructible or semi-algebraic
systems of the form C={x∈ Cn, p1 (x)= 0,…, ps (x)= 0, f1 (x)≠ 0,…, fl (x)≠ 0} or S={x∈ Rn …

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 …

Let A(x)=A_0+x_1A_1+⋯+x_nA_n be a linear matrix, or pencil, generated by given
symmetric matrices A_0,A_1,...,A_n of size m with rational entries. The set of real vectors x …

Let f,f_1,...,f_s be n-variate polynomials with rational coefficients of maximum degree D and
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …

We have developed in the past several algorithms with intrinsic complexity bounds for the
problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive …

We give a complete description of the Voronoi diagram of three lines in R3. In particular, we
show that the topology of the Voronoi diagram is invariant for three lines in general position …

We survey both old and new developments in the theory of algorithms in real algebraic
geometry--starting from effective quantifier elimination in the first order theory of reals due to …

Let f be a polynomial in Q X_1, ..., X_n of degree D. We focus on testing the emptiness and
computing at least one point in each connected component of the semi-algebraic set defined …

We consider the problem of computing critical points of the restriction of a polynomial map to
an algebraic variety. This is of first importance since the global minimum of such a map is …