Subdivision algorithms and the Continued Fraction expansion of real roots of polynomial systems.

We present an overview of subdivision algorithms for the isolation of the real roots of a system of multivariate polynomials. We introduce a new algorithm of this family which treats equations in the monomial basis and uses robust inclusion and exclusion criteria to reach the solutions. Enveloping functions and preconditioning techniques are also employed to reduce the domain of search. The resulting isolation boxes have optimized rational coordinates, corresponding to the first terms of the continued fraction expansion of the real roots. New complexity bounds are provided for a simplified version of the algorithm. This is joint work with B. Mourrain and E. Tsigaridas.