Tropical Implicitization Revisited

Abstract: Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton polytope of the implicit equation, without computing its coefficients. We present a new implementation of this procedure in Oscar.jl. It solves challenging instances, and can be used for classical implicitization as well. We also develop implicitization in higher codimension via Chow forms, and we pose several open questions.