Programs for the Study of Real Solutions of Semi-algebraic Systems

Bican Xia
Department of Mathematics, Peking University
Beijing 100871, China


Abstract. Based on our algorithms for the study of real solutions of semi-algebraic systems (SAS), two programs, called 'realzero' and 'discoverer', have been realized under Maple. With 'realzero', one can count and isolate the real solutions of a given SAS in which all the polynomials have integer (rational) coefficients. As for a SAS with parametric coefficients, one can use 'discoverer' to discover the necessary and sufficient condition for the SAS to have a given number of distinct real solutions.