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arXiv · 1901.01180

Decomposing tropical rational functions

Dima Grigoriev
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Abstract

An algorithm is designed which decomposes 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).

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Dima Grigoriev. 2019-01-04. Decomposing tropical rational functions. https://arxiv.org/abs/1901.01180

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