Computing zero-dimensional tropical varieties via projections

08/09/2019

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by   Paul Görlach, et al.

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We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gröbner bases. We prove that our algorithm requires only a polynomial number of arithmetic operations if given a Gröbner basis, and we demonstrate that our implementation compares favourably to other existing implementations. Applying it to the computation of general positive-dimensional tropical varieties, we argue that the complexity for calculating tropical links is dominated by the complexity of the Gröbner walk.