Polynomial homotopy continuation with PHCpack

Abstract

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.