Author:
Görlach Paul,Ren Yue,Zhang Leon
Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Computational Theory and Mathematics,General Mathematics,Theoretical Computer Science
Reference39 articles.
1. Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert & Michael Joswig (2018). Log-barrier interior point methods are not strongly polynomial. SIAM J. Appl. Algebra Geom. 2(1), 140–178. ISSN 2470-6566.
2. Federico Ardila & Caroline J. Klivans (2006). The Bergman complex of a matroid and phylogenetic trees. J. Combin. Theory Ser. B 96(1), 38–49. ISSN 0095-8956.
3. Elizabeth Baldwin & Paul Klemperer (2019). Understanding Preferences: Demand Types and the Existence of Equilibrium With Indivisibilities. Econometrica 87(3), 867–932.
4. L. Bernardin, P. Chin, P. DeMarco, K. O. Geddes, D. E. G. Hare, K. M. Heal, G. Labahn, J. P. May, J. McCarron, M. B. Monagan, D. Ohashi & S. M. Vorkoetter. (1996-2020). Maple Programming Guide. Maplesoft, a division of Waterloo Maple Inc., Waterloo ON, Canada
5. T. Bogart, A. N. Jensen, D. Speyer, B. Sturmfels & R. R. Thomas (2007). Computing tropical varieties. J. Symbolic Comput. 42(1-2), 54–73. ISSN 0747-7171.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献