PHoM (Polyhedral Homotopy Continuation Method for Polynomial Systems)

Important notice: Currently, we do not have any plan to release a new version of PHoM in the near future, and we will no longer provide service for PHoM package. This webpage will not be available from Dec. 31, 2008. For solving polynomial systems by the polyhedral homotopy method, we recommend HOME4PS-2.0.

PHoM is a software package for a polyhedral homotopy continuation method of finding all isolated solutions of a system of n polynomial equations f(x) = 0 in n-dimensional complex vector variable x. It is implemented in C++ language using the LAPACK for matrix computation. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations f(x) = 0. The second module CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions of f(x) = 0. The third module Verify checks whether all isolated solutions of f(x)=0 have been approximated correctly. For more details, see the paper below, which also serves as a user's guide of PHoM.

Takayuki Gunji, Sunyoung Kim, Masakazu Kojima, Akiko Takeda, Katsuki Fujisawa and Tomohiko Mizutani, PHoM -- a Polyhedral Homotopy Continuation Method for Polynomial Systems,'' Research Report B-386, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, December 2002, revised January 2003. ps file, ps.gz file, pdf file.

The C++ program source codes and numerical results below are available.

Each software of PHoM is distributed under the GNU GPL (General Public License).

Version Last update
Install guide (text file) 2002.12.21
PHoM source file (C++ file) consisting of three modules
Startsystem, CMPSc and Verify
Ver.1.1 2006.10.12
Numerical results by PHoM
economic 8-12, katsura 7-11, reimer 4-6, noon 5-8
Input data generator
for the economic , katsura, reimer, noon and cyclic polynomial systems
Ver.1.1 2006.10.12
Stand-alone program of CMPSc Ver.1.1 2002.12.21
Stand-alone program of Verify Ver.1.1 2002.12.21

Some Other Results on Polynomial Systems

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October 12, 2006