Working with Tropical Meromorphic Functions of One Variable

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 polyno...

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Bibliographic Details
Published inarXiv.org
Main Author Yen-lung Tsai
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.01.2011
Subjects
Existence theorems
Meromorphic functions
Polynomials
Rational functions
Roots
Uniqueness theorems
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Summary: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.
ISSN:2331-8422