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Computing zero-dimensional tropical varieties via projections

Görlach, Paul; Ren, Yue; Zhang, Leon

Computing zero-dimensional tropical varieties via projections Thumbnail


Paul Görlach

Leon Zhang


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.


Görlach, P., Ren, Y., & Zhang, L. (2022). Computing zero-dimensional tropical varieties via projections. Computational Complexity, 31(1), Article 5.

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


Published Journal Article (739 Kb)

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