Hom4PS-3

Hom4PS-3 is a parallel software package specialized for solving system of polynomial equations using efficient and reliable numerical methods.
Solving systems of polynomial equations is an important problem in mathematics. It has a wide range of applications in many fields of mathematics, sciences, and engineering. By the Abel's impossibility theorem and the Galois theory, explicit formulae for solutions to such systems by radicals are unlikely to exist, as a result, numerical computation arises naturally in the solution to such systems. Homotopy continuation methods represent a major class of numerical methods for solving systems of polynomial equations. Hom4PS-3 is a software package that implement many homotopy continuation algorithms with which it could numerically approximate, identify, and classify solutions to systems of polynomial equations. For more information, please checkout the Documentation and F.A.Q. pages or email us at mailto:info@hom4ps3.org.
Hom4PS-3 is capable of performing parallel computation on a wide range of parallel computer architectures with great efficiency and scalability, including
  • Multi-core architecture
  • Computer clusters
  • Distributed environments
Hom4PS-3 works nicely with other mathematical software and programming languages such as
  • Python
  • Sage
  • Octave
  • Matlab

The Hom4PS family

The Hom4PS family is a family of numerical solvers for systems of polynomial equations using homotopy continuation method. Hom4PS-3 is our current experimental project within this family which contains latest features. Other projects in the Hom4PS family are
  • Hom4PS: The original Hom4PS developed in the 1990s implementing the Polyhedral Homotopy.
  • Hom4PS-2.0: Our most mature and stable implementation written in Fortran. It implements both the Total Degree Homotopy and the Polyhedral Homotopy, and we encourage users to use it for important computations.
  • Hom4PS-2.0para: Parallel version of the Hom4PS-2.0 package, developed using MPI, suitable for computer clusters.

News

  • Jun. 20, 2014: The real homotopy portion of Hom4PS-3 is now a separated project.
  • Jun. 12, 2014: A bug in handling binomial systems has been fixed. Details can be found here. 
  • Apr. 10, 2014  Two real homotopies (Newton homotopy and fixed point homotopy) has been added for finding real solutions.
  • Jan. 1, 2014  New toric path tracking algorithm has been added to track solution paths inside certain toric varieties.
  • Nov 13, 2013 Real curve following algorithms for traditional homotopy constructions over the real numbers has been added.

Contact us

Quick links

  • Homotopy continuation method
  • Polyhedral homotopy
  • Mixed volume computation

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