Finding all real points of a complex curve

Abstract

An algorithm is given to compute the real points of the irreducible one-dimensional complex components of the solution sets of systems of polynomials with real coefficients. The algorithm is based on homo-topy continuation and the numerical irreducible decomposition. An extended application is made to Griffis-Duffy platforms, a class of Stewart-Gough platform robots. 2000 Mathematics Subject Classification. Primary 65H10; Sec-ondary 65H20, 14Q99. Key words and phrases. Homotopy continuation, numerical alge-braic geometry, real polynomial systems. In this article we give a numerical algorithm to find the real zero- and