Generic root counts of tropically transverse systems -- An invitation to tropical geometry in OSCAR
Algebraic Geometry
2023-12-01 v1
Abstract
The main mathematical focus of this paper is a class of parametrised polynomial systems that we refer to as being tropically transverse. We show how their generic number of solutions can be expressed as the mixed volume of a modified system. We then provide an alternate proof of a recent result by Borovik et al, on the number of equilibria of coupled nonlinear oscillators using elementary tropical geometry. The proof draws upon a wide range of concepts across tropical geometry, which we will use as an opportunity to give a first overview over various tropical features in OSCAR.
Keywords
Cite
@article{arxiv.2311.18018,
title = {Generic root counts of tropically transverse systems -- An invitation to tropical geometry in OSCAR},
author = {Isaac Holt and Yue Ren},
journal= {arXiv preprint arXiv:2311.18018},
year = {2023}
}
Comments
33 pages, 2 figures, submitted as chapter for the upcoming book on the computer algebra system OSCAR