Interfacing with the numerical homotopy algorithms in PHCpack

Abstract

PHCpack implements numerical algorithms for solving polynomial systems using homotopy continuation methods. In this paper we describe two types of interfaces to PHCpack. The first interface PHCmaple originally follows OpenXM, in the sense that the program (in our case Maple) that uses PHCpack needs only the executable version phc built by the package PHCpack. Following the recent development of PHCpack, PHCmaple has been extended with functions that deal with singular polynomial systems, in particular, the deflation procedures that guarantee the ability to refine approximations to an isolated solution even if it is multiple. The second interface to PHCpack was developed in conjunction with MPI (Message Passing Interface), needed to run the path trackers on parallel machines. This interface gives access to the functionality of PHCpack as a conventional software library. © Springer-Verlag Berlin Heidelberg 2006.