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 classical procedure in Oscar.jl. It solves challenging instances, and can be used for classical implicitization as well. We discuss implicitization in higher codimension via Chow forms and pose several open questions.

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Tropical Implicitization Revisited

  • Kemal Rose,
  • Bernd Sturmfels,
  • Simon Telen

摘要

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 classical procedure in Oscar.jl. It solves challenging instances, and can be used for classical implicitization as well. We discuss implicitization in higher codimension via Chow forms and pose several open questions.