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arXiv · 2311.18018

Generic root counts of tropically transverse systems -- An invitation to tropical geometry in OSCAR

Isaac Holt·Yue Ren
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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.

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Isaac Holt, Yue Ren. 2023-11-29. Generic root counts of tropically transverse systems -- An invitation to tropical geometry in OSCAR. https://arxiv.org/abs/2311.18018

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