Görlach, Paul and Ren, Yue and Zhang, Leon (2022) 'Computing zero-dimensional tropical varieties via projections.', computational complexity, 31 (1). p. 5.
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.
| Item Type: | Article |
|---|---|
| Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution 4.0. Download PDF (723Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1007/s00037-022-00222-9 |
| Publisher 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/. |
| Date accepted: | No date available |
| Date deposited: | 14 July 2022 |
| Date of first online publication: | 20 May 2022 |
| Date first made open access: | 14 July 2022 |
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