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math.AG2024
A tropical method for solving parametrized polynomial systems
Paul Alexander Helminck, Oskar Henriksson, Yue Ren
We give a framework for constructing generically optimal homotopies for parametrized polynomial systems from tropical data. Here, generically optimal means that the number of paths…
math.AG2023
Generic root counts of tropically transverse systems -- An invitation to tropical geometry in OSCAR
Isaac Holt, Yue Ren
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 solutio…