WORKING WITH TROPICAL MEROMORPHIC FUNCTIONS OF ONE VARIABLE

Abstract

In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical mero-morphic functions, emphasizing practical techniques that can really carry out computations. For instance, we introduce maximally represented tropical poly-nomials 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 meromor-phic functions. Different definitions and applications of tropical meromorphic functions are discussed. Finally, we point out the properties of tropical mero-morphic functions are very similar to complex ones and prove some tropical analogues of theorems in complex analysis.