The entropy of the radical ideal of a tropical curve

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics 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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.