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