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arXiv · 1908.03486

Computing zero-dimensional tropical varieties via projections

Paul Görlach·Yue Ren·Leon Zhang
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Abstract

We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gr\"obner bases. We prove that our algorithm requires only a polynomial number of arithmetic operations if given a Gr\"obner 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 Gr\"obner walk.

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Paul Görlach, Yue Ren, Leon Zhang. 2019-08-09. Computing zero-dimensional tropical varieties via projections. https://arxiv.org/abs/1908.03486

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