English

Computing zero-dimensional tropical varieties via projections

Algebraic Geometry 2019-08-12 v1 Symbolic Computation

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.

Keywords

Cite

@article{arxiv.1908.03486,
  title  = {Computing zero-dimensional tropical varieties via projections},
  author = {Paul Görlach and Yue Ren and Leon Zhang},
  journal= {arXiv preprint arXiv:1908.03486},
  year   = {2019}
}