In the mixed dimensional case, we consider polynomial systems which may have isolated solutions and solution sets of different dimensions. Solution sets are represented by power series expansions and computed by Newton's method. The reformulation of polyhedral homotopies with the application of a power series Newton's method will be sketched.
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.