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HomotopyContinuation2

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homotopycontinuation2.jl's Issues

ToDo

Missing features compared to HC 1.4

  • multi-homogeneous total degree homotopy

    • start solutions iterator
    • construct start system
  • Result

    • Aggregate informations (finite, singular, excess-solutions)
    • Multiplicity computation / information
  • Progress information

  • solve

    • polyhedral
    • total degree
    • parameter homotopy
    • homotopy
    • many parameter
    • homogeneous input
  • complexity calculator

    • mixed volume
    • bezout number
  • Unique Points

  • composition system

  • monodromy

    • automatically compute linear start pair
    • tracking
    • group actions
    • trace test
  • Allow to set start parameters, target parameters in track

  • parallelization

    • monodromy
    • path tracking
    • solve

Misc

  • automatically apply horner rewrite rule

Compability to 1.4 / Old Workflow

  • Avoid name clashes between DynamicPolynomials and ModelKit
  • @polyvar support

New Features / Improvements 2.0

Linear / Affine spaces

  • Affine subspaces
  • Affine subspace homotopy
  • Affine sliced system
  • Linear subspaces
  • Linear subspace homotopy
  • Linear sliced system

Misc

  • automatically compute monodromy start pair using Newton
  • usable Newton's method
  • excess solution check
  • progress: show compilation time
  • presolve
  • multiplicities: Avoid false clustering, only assign multipicities if singular

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