Decomposing tropical rational functions. (November 2020)

• Record Type: Journal Article
• Authors: Grigoriev, Dima
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 61
• Page End: 72
• Publication Date: 2020-11
• Subjects: Decomposing a univariate tropical rational function -- Commuting composition of tropical polynomials; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: An algorithm is designed to decompose a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are designed for decomposing tropical algebraic rational functions being (in the classical language) piece-wise linear functions with rational slopes of their linear pieces. In addition, we provide a criterion when the composition of two tropical polynomials commutes (for classical polynomials a similar question was answered by J. Ritt).