An Elementary Proof of the Fundamental Theorem of Tropical Algebra
An Elementary Proof of the Fundamental Theorem of Tropical Algebra
复制标题
热带代数基本定理的初步证明
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
N. Manwaring
中科院分区：
文献类型：
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作者：
Nathan Grigg;N. Manwaring
本文给出了有理热带半环上多项式代数基本定理的一个初等证明。我们证明了，热带，有理数代数闭。我们提供了一个简单的算法分解热带多项式的一个单一的变量。一个中心思想是最小系数多项式的概念作为代表类的功能等价多项式。这一思想的重要性远远超过了热带代数基本定理的证明。
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.