Detecting tropical defects of polynomial equations

A fundamental notion in Tropical Geometry is that of a tropical basis: a set of polynomial equations whose associated tropical variety agrees with the intersection of the associated tropical hypersurfaces. We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide algorithms for finding them around affine spaces of complementary dimension to the zero set. This is joint work with Yue Ren and Jeff Sommars.