MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Computing zero-dimensional tropical varieties via projections

Paul Görlach, Yue Ren and Leon Zhang


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.

MSC Codes:
14T05, 13P10, 13P15, 68W30
tropical geometry, tropical varieties, computer algebra

Related publications

2022 Journal Open Access
Paul Görlach, Yue Ren and Leon Zhang

Computing zero-dimensional tropical varieties via projections

In: Computational complexity, 31 (2022) 1, p. 5