Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving

In this paper we present a framework for the cooperation of symbolic and propagation-based numerical solvers over the real numbers. This cooperation is expressed in terms of fixed points of closure operators over a complete lattice of constraint systems. In a second part we instantiate this framework to a particular cooperation scheme, where propagation is associated to pruning operators implementing interval algorithms enclosing the possible solutions of constraint systems, whereas symbolic methods are mainly devoted to generate redundant constraints. When carefully chosen, it is well known that the addition of redundant constraint drastically improve the performances of systems based on local consistency (e.g. Prolog IV or Newton). We propose here a method which computes sets of redundant polynomials called partial Gröbner bases and show on some benchmarks the advantages of such computations.