PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems with as many equations as variables into providing tools for a numerical irreducible decomposition. This document provides the outline for a software demonstration highlighting recent additions to the software, such as accepting polynomials with negative exponents and sweeping for real points that lie isolated on complex solution curves.
ISSAC 2010 software demonstration, T.U. Munich, Germany, 25-28 July, 2010.