Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations

  • Authors:

  • Steven M. Wise;Andrew J. Sommese;Layne T. Watson

  • Affiliations:

  • Virginia Polytechnic Institute and State Univ., Blacksburg;Univ. of Notre Dame, Notre Dame, IN;Virginia Polytechnic Institute and State Univ., Blacksburg

  • Venue:
  • ACM Transactions on Mathematical Software (TOMS)
  • Year:
  • 2000

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Abstract

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS_PLP consists of Fortran 90 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP) polynomial system structure. PLP structure is a generalization of m-homogeneous structure, whereby each component of the system can have a different m-homogeneous structure. The code requires a PLP structure as input, and although finding the optimal PLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good structure. POLSYS_PLP 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 PLP structures and their corresponding Bezout