PHCpack: a general-purpose solver
for polynomial systems by homotopy continuation

Algorithm 795 in ACM Trans. Math. Softw.
Jan Verschelde

Abstract:

Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this paper the structure and design of the software package PHC is described. The main program operates in several modes, is menu-driven and file-oriented. This package features a great variety of root-counting methods among its tools. The outline of one black-box solver is sketched and a report is given on its performance on a large database of test problems. The software has been developed on four different machine architectures. Its portability is ensured by the gnu-ada compiler.

D.3.2 Programming Languages Language Classification [Ada] G.1.5 Numerical Analysis Roots of Nonlinear Equations [Systems of equations, Polynomials, methods for] G.2.1 Discrete Mathematics Combinatorics [Counting problems] G.4 Mathematics of Computing Mathematical Software Algorithms, Theory homotopy continuation, polynomial systems, start system, root count, Bézout number, mixed volume, Bernshtein's theorem, polyhedral homotopy, enumerative geometry, Schubert calculus.

Note: This document is a modified internet version of the paper that was submitted to ACM Transactions on Mathematical Software. This version also contains the reference manual, which could not be included in the publication of the paper.