Papers › A tropical method for solving parametrized polynomial systems

A tropical method for solving parametrized polynomial systems

20 Sep 2024arXiv:2409.13288links table onlyarchive 2025-07-28

Paul Alexander Helminck, Oskar Henriksson, Yue Ren

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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 tracked is equal to the generic number of solutions. We focus on two types of parametrized systems -- vertically parametrized and horizontally parametrized systems -- and discuss techniques for computing the tropical data efficiently. We end the paper with several case studies, where we analyze systems arising from chemical reaction networks, coupled oscillators, and rigid graphs.

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