2011/01/14 by Yen-Lung Tsai, Tsai, Yen-lung
Computer Science · Mathematics · #14A10 #30C15 #52B20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1101.2703
openalex publication_date 2011/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For instance, we introduce maximally represented tropical polynomials and tropical polynomials in compact forms to quickly find roots of given tropical polynomials. We also prove the existence and uniqueness of tropical theorems for meromorphic functions with prescribed roots and poles. Moreover, we explain the relations between classical and tropical meromorphic functions. Different definitions and applications of tropical meromorphic functions are discussed. Finally, we point out the properties of tropical meromorphic functions are very similar to complex ones and prove some tropical analogues of theorems in complex analysis.