  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.
