The entropy of the radical ideal of a tropical curve

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-14 DOI:10.1016/j.aam.2023.102635

Dima Grigoriev

引用次数: 0

Abstract

The entropy of a semiring ideal of tropical polynomials is introduced. The radical of a semiring ideal consists of all tropical polynomials vanishing on the tropical prevariety determined by the ideal. We prove that the entropy of the radical of a tropical bivariate polynomial with zero coefficients vanishes. Also, we prove that the entropy of a zero-dimensional tropical prevariety vanishes. An example of a non-radical semiring ideal with a positive entropy is exhibited.

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热带曲线的基本理想的熵

介绍了热带多项式半环理想的熵。半环理想的根由消失在由理想确定的热带多项式上的所有热带多项式组成。证明了零系数热带二元多项式的根的熵消失。同时，我们也证明了零维热带变异的熵是消失的。给出了一个具有正熵的非自由基半环理想的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.