An Elementary Proof of the Fundamental Theorem of Tropical Algebra

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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.
8 pages

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Combinatorics, 20M14 (Primary); 52B20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/134563

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.2591
 http://arxiv.org/abs/0707.2591

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arXiv