INTERNAL REPORT (Limited Distribution) International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS TRACING A PLANAR ALGEBRAIC CURVE

In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for the tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of zeros of several polynomials of one variable. MIRAMARE TRIESTE September 1994 Permanent Address: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.