An Elementary Proof of the Fundamental Theorem of Tropical Algebra
Combinatorics
2007-07-18 v1
Abstract
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm for factoring tropical polynomials of a single variable. A central idea is the concept of least-coefficient polynomials as representatives for classes of functionally equivalent polynomials. This idea has importance far beyond the proof of the Fundamental Theorem of Tropical Algebra.
Keywords
Cite
@article{arxiv.0707.2591,
title = {An Elementary Proof of the Fundamental Theorem of Tropical Algebra},
author = {Nathan Grigg and Nathan Manwaring},
journal= {arXiv preprint arXiv:0707.2591},
year = {2007}
}
Comments
8 pages