PHCpack is a software package to solve polynomial systems by homotopy continuation methods.

A polynomial system is given as a sequence of polynomials in several variables. Homotopy continuation methods operate in two stages. In the first stage, a family of polynomial systems (the so-called homotopy) is constructed. This homotopy contains a polynomial system with known solutions. In the second stage, numerical continuation methods are applied to track the solution paths defined by the homotopy, starting at the known solutions and leading to the solutions of the given polynomial system.

Version 1.0 of PHCpack has been archived by ACM Transactions of Mathematical Software (ACM TOMS) as Algorithm 795. PHCpack incorporates MixedVol (Algorithm 846 of ACM TOMS by T. Gao, T.Y. Li, and M. Wu) to compute mixed volumes fast. For its double double and quad double arithmetic, PHCpack contains QDlib of Y. Hida, X.S. Li, and D.H. Bailey.

This material is based upon work supported by the National Science Foundation under Grants No. 9804846, 0105739, 0134611, 0410036, 0713018, 1115777, and 1440534. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.