PHCPACK is a general-purpose solver for polynomial systems by homotopy continuation. This package features a great variety of root-counting methods exploiting the structure in a polynomial system, in particular its sparsity.


The package is written in Ada.


PHCPACK is available in source form for research purposes only. You are free to copy, distribute, modify and extend this software, provided full credit is always given to this original and that this file and other information files are always included. You may not ignore the fact that what you see is the result of a very long term project.

Note that anything free comes without guarantee...


Go here to go to the download page.


This software was developed at the Department of Computer Science of the Katholieke Universiteit Leuven, between 1989 and 1997. It was completed as part of a project funded by the Fund for Scientific Research, Flanders with additional support from the Research Council of K.U.Leuven.

       Fund for Scientific Research, Flanders    (FWO-Vlaanderen)
       Project: G.0261.96    Period: January 1996 - December 1999
       Title: Counting and computing all  isolated  solutions  of
              systems of nonlinear equations
       Co-directed by: Prof. Ronald Cools and Prof. Ann Haegemans

       Research Council of K.U.Leuven            (Onderzoeksraad)
                             Period: September 1996 - August 1997
       Postdoctoral  fellowship  granted  to  Dr. Jan Verschelde,
       promoted by Prof. Ann Haegemans.
The project history and the FWO-project have their own pages.

Related publications

  1. J. Verschelde and R. Cools. An Ada Workbench for Homotopy Continuation for Solving Polynomial Systems. The Ada-Belgium Newsletter, 2:23-40, 1993.
  2. J. Verschelde and R. Cools. Polynomial Homotopy Continuation, A Portable Ada Software Package. The Ada-Belgium Newsletter, 4:59-83, 1996.
    Since copyright of this paper is not transfered, we can offer you the Postscript file.
In addition a tutorial
  1. J. Verschelde. PHCPACK: A general-purpose solver for polynomial systems by homotopy continuation. Report TW 265, Dept. of Computer Science, K.U.Leuven (August 1997).
is available as part of the distribution and also separately.
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This page was last modified on Monday 15 June 1998, 11:02:27 MET DST.