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arXiv · 2007.06195

Entropy of radical ideal of a tropical prevariety

Dima Grigoriev
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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.

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Dima Grigoriev. 2020-07-13. Entropy of radical ideal of a tropical prevariety. https://arxiv.org/abs/2007.06195

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