bertini_real - software for real algebraic sets.
solitude

Features:

  • Seamless interface to Bertini,
  • Decomposes implicitly defined curves and surfaces,
  • Systems may be defined in ANY number of variables,
  • MPI parallelization,
  • Automatic deflation of singular curves,
  • Interactive Matlab visualization,
  • Surfaces are simply exported to .stl file for 3d printing.

Thanks to the following collaborators:

  • Dan Bates (Mentoring, advising, idea generation)
  • Jon Hauenstein (Mentoring, advising, analysis)
  • Andrew Sommese (Advising)
  • Charles Wampler (Advising, great challenges)
  • Wenrui Hao (Not-self-conjugate case for curves)

and to these awesome students:

  • Briar Weston (Grasshopper, towards medial axes )
  • Caden Joergens, Danya Morman (Grasshopper)
  • Morgan Fiebig (Scaling number sampling of surfaces)
  • Morgan Fiebig, Caden Joegens (Skeletons in Grasshopper)
  • William O'Brien and Samantha Maurer (3d printed electronic interactive Barth Sextic)
  • Foong Min Wong (3d videos in Blender)
  • Dan Hessler and Foong Min Wong (Python surface plotting)
  • Samantha Sherman (Parallelization of sampling)
  • Nicolle Ho (Python curve plotting)
  • Travis Wert (Mobius strips, `ignore_sing`)
  • Sam Cavender (preventing substitution of subfunctions in Matlab symbolics)
  • Alec Sievern (Blender animations)
  • Chris Lembo (Users manual improvements, how-to videos, 3d printing)
  • Elizabeth Sudkamp (Python symbolic work, Windows install)
  • Pierce Cunneen (Python data gathering)
  • Michael Padala (Windows compatibility)
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We use Bertini

Bertini is a numerical solver. More specifically, it is a homotopy continuation solver, producing solutions to polynomial systems. Invoked from the command line, it uses a text file input, declaring functions, variables, constants, and a plethora of configuration parameters.