Installation

Tutorials

  • Quick start: Learn how to use Hom4PS-3 on Linux in 5 minutes.
  • A longer tutorial: Learn how to use Hom4PS-3 to solve commonly encountered types of systems of polynomial equations.
  • Howtos: A list of short tutorials on how to perform specific tasks or deal with certain types of problems.
  • Parallel computation: Learn how to let Hom4PS-3 perform computation in parallel on modern computer systems.
  • Using Hom4PS-3 in Python
  • Using Hom4PS-3 in Sage

Mathematical background

  • Homotopy continuation methods
  • Mixed volume and the BKK
  • Polyhedral homotopy

Reference manual

  • The modular design
  • Interface to programming languages and mathematical software
  • Using hom4ps-core, the command line interface
  • Using libhom4ps, the C++ core library

Homotopies

  • Polyhedral homotopy
  • Total degree homotopy
  • m-Homogeneous homotopy
  • Cheater's homotopy
  • Coefficient parameter homotopy
  • Newton homotopy
  • User defined homotopies

Direct solvers

  • Binomial system solver

Endgames

  • Cauchy integral method
  • Puiseux series interpolation
  • Tropical endgame

Path trackers

  • Basic affine path tracking
  • Higher order affine path tracking
  • Advanced affine path tracking
  • Spherical projective path tracking
  • Toric path tracking

Related papers