In the zero dimensional case, polyhedral homotopies compute approximations for all isolated solutions of a polynomial system. The tropical variety provides candidate tropisms for the leading exponents of the power series expansions at the positive solution sets. Our methods are illustrated on the cyclic n-roots problem.
This talk is based on joint work with Danko Adrovic, Nathan Bliss, Anders Jensen, and Jeff Sommars.
Tropical Algebra and Applications workshop, Institut Mittag-Leffler, 22--26 January 2018, Djursholm, Sweden.