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.
Original language | English |
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Publication status | Published - 20 Sep 2024 |
Bibliographical note
36 pages, 6 figures. Improved exposition. Comments welcome!Keywords
- math.AG
- 14T90, 65H14, 13P15