PHoM: a polyhedral homotopy continuation method for polynomial systems

PHoM is a software package in C for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the rst module Start System constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations fx 0. The second module CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions of fx 0. The third module Verify checks whether all isolated solutions of fx 0 have been approximated correctly. We describe numerical methods used in each module and the usage of the package. Numerical results to demonstrate the performance of PHoM include some large polynomial systems that have not been solved previously. [PUBLICATION ABSTRACT]