vtopt / polsys_glp

a parallel general linear product homotopy code for solving polynomial systems of equations

ACM TOMS Algorithm 857: POLSYS_GLP: a parallel general linear product homotopy code for solving polynomial systems of equations

POLSYS_GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95-derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS_PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although finding the optimal GLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS_GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.

• This code has been re-uploaded with the permission of Dr. Layne Watson. All comments and questions should be directed to him (see contact info at the bottom of this file).

Structure and Usage

The original source code, exactly as distributed by ACM TOMS, is included in the src directory. The src directory also contains its own README, build instructions, and a test case. Comments at the top of each subroutine document their proper usage.

Reference and Contact

To cite this work, use:

    @article{algorithm857,
        author = {Su, Hai-Jun and McCarthy, J. Michael and Sosonkina, Masha and Watson, Layne T.},
        title = {Algorithm 857: POLSYS_GLP—a Parallel General Linear Product Homotopy Code for Solving Polynomial Systems of Equations},
        year = {2006},
        volume = {32},
        number = {4},
        journal = {ACM Trans. Math. Softw.},
        pages = {561–579},
        doi = {10.1145/1186785.1186789}
    }

Inquiries should be directed to

Layne T. Watson,
Department of Computer Science, VPI&SU,
Blacksburg, VA 24061-0106;
[phone];
[e-mail]