2020/07/13 by Dima Grigoriev, Grigoriev, Dima
Computer Science · Mathematics · #14T05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #G.2.1 #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2007.06195
openalex publication_date 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The entropy of a tropical ideal is introduced. The radical of a tropical 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 vanishing coefficients equals zero. Also we prove that the entropy of a zero-dimensional tropical prevariety vanishes. An example of a non-radical tropical ideal having a positive entropy is exhibited.