A Tropical F5 algorithm - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ISSAC'17-Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation Year : 2017

A Tropical F5 algorithm

Abstract

Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gröbner bases taking into account the valuation of K. While generalizing the classical theory of Gröbner bases, it is not clear how modern algorithms for computing Gröbner bases can be adapted to the tropical case. Among them, one of the most efficient is the celebrated F5 Algorithm of Faugère. In this article, we prove that, for homogeneous ideals, it can be adapted to the tropical case. We prove termination and correctness. Because of the use of the valuation, the theory of tropical Gröb-ner bases is promising for stable computations over polynomial rings over a p-adic field. We provide numerical examples to illustrate time-complexity and p-adic stability of this tropical F5 algorithm.
Fichier principal
Vignette du fichier
F5trop_arxiv.pdf (280.94 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01521865 , version 1 (12-05-2017)

Licence

Attribution - CC BY 4.0

Identifiers

Cite

Tristan Vaccon, Kazuhiro Yokoyama. A Tropical F5 algorithm. ISSAC'17-Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, 2017, ⟨10.1145/3087604.3087630⟩. ⟨hal-01521865⟩
303 View
112 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More