An Elementary Proof of the Fundamental Theorem of Tropical Algebra

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dc.creatorGrigg, Nathan
dc.creatorManwaring, Nathan
dc.date2007-07-17
dc.date.accessioned2026-07-07T08:18:48Z
dc.date.available2026-07-07T08:18:48Z
dc.descriptionIn 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0707.2591
dc.identifierhttp://arxiv.org/abs/0707.2591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134563
dc.subjectCombinatorics
dc.subject20M14 (Primary); 52B20 (Secondary)
dc.titleAn Elementary Proof of the Fundamental Theorem of Tropical Algebra
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