Real Solution Classification for Parametric Semi-Algebraic Systems

Real solution classification of parametric polynomial systems is a crucial problem in real quantifier elimination which interests Volker Weispfenning and others. In this paper, we present a stepwise refinement algorithm for real solution classifications of a class of parametric systems consisting of polynomial equations, inequalities and inequations. For an input system, the algorithm outputs the necessary and sufficient conditions (in terms of quantifier-free formulae) on the parameters for the system to have a given number of real solutions. Although the algorithm makes use of a pcad algorithm, it is different from any existing methods.