Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Helminck, Paul Alexander, Henriksson, Oskar, Ren, Yue
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403755246