Tropical Homotopy Continuation

Understand

Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables.

• In particular, a tropicalisation of the numerical "regeneration" technique leads to a new method for enumerating the mixed cells of a mixed subdivision.
• This tropical approach shares some ideas with the recent algorithm by Malajovich.
• However, our algorithm has several advantages.