2021/10/15 by JuAe Song, Song, JuAe
Computer Science · Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cancer Treatment and Pharmacology #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2110.08091
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a semiring isomorphism between the rational function semifields of two tropical curves induces an expansive map between those tropical curves. This semiring isomorphism and the expansive map respect zeros and poles of rational functions with their degrees. As a corollary, we show that the automorphism group of a tropical curve is isomorphic to the \boldsymbolT-algebra automorphism group of its rational function semifield, where \boldsymbolT := (\boldsymbolR ∪ \ -∞ \, max, +) is the tropical semifield. Finally, we describe all semiring automorphisms of rational function semifields of all tropical curves.