Decomposing tropical rational functions
Algebraic Geometry
2019-03-04 v2 Discrete Mathematics
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).
Cite
@article{arxiv.1901.01180,
title = {Decomposing tropical rational functions},
author = {Dima Grigoriev},
journal= {arXiv preprint arXiv:1901.01180},
year = {2019}
}