Computing zero-dimensional tropical varieties via projections

Görlach, Paul; Ren, Yue; Zhang, Leon

doi:10.1007/s00037-022-00222-9

Computing zero-dimensional tropical varieties via projections

Görlach, Paul; Ren, Yue; Zhang, Leon

Authors

Paul Görlach

Dr Yue Ren yue.ren2@durham.ac.uk
Assistant Professor

Leon Zhang

Abstract

We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast monomial transforms of triangular sets. Given a Gröbner basis, we prove that our algorithm requires only a polynomial number of arithmetic operations, and, for ideals in shape position, we show that its timings compare well against univariate factorization and backsubstitution. We conclude that the complexity of computing positive-dimensional tropical varieties via a traversal of the Gröbner complex is dominated by the complexity of the Gröbner walk.

Citation

Görlach, P., Ren, Y., & Zhang, L. (2022). Computing zero-dimensional tropical varieties via projections. Computational Complexity, 31(1), Article 5. https://doi.org/10.1007/s00037-022-00222-9

Journal Article Type	Article
Online Publication Date	May 20, 2022
Publication Date	2022-06
Deposit Date	Jul 14, 2022
Publicly Available Date	Jul 14, 2022
Journal	computational complexity
Print ISSN	1016-3328
Electronic ISSN	1420-8954
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	31
Issue	1
Article Number	5
DOI	https://doi.org/10.1007/s00037-022-00222-9

Files

Published Journal Article (739 Kb)
PDF

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.