Computing zero-dimensional tropical varieties via projections

Paul Görlach, Yue Ren, and Leon Zhang

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Submission date: 26. Aug. 2019
Pages: 22
Bibtex
MSC-Numbers: 14T05, 13P10, 13P15, 68W30
Keywords and phrases: tropical geometry, tropical varieties, computer algebra
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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 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.