English

Entropy of radical ideal of a tropical prevariety

Algebraic Geometry 2020-12-01 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2007.06195,
  title  = {Entropy of radical ideal of a tropical prevariety},
  author = {Dima Grigoriev},
  journal= {arXiv preprint arXiv:2007.06195},
  year   = {2020}
}