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arXiv · 1803.01068

Complexity of deciding whether a tropical linear prevariety is a tropical variety

Dima Grigoriev·Nicolai Vorobjov
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Abstract

We give an algorithm, with a singly exponential complexity, deciding whether a tropical linear prevariety is a tropical linear variety. The algorithm relies on a criterion to be a tropical linear variety in terms of a duality between the tropical orthogonalization $A^\perp$ and the double tropical orthogonalization $A^{\perp \perp}$ of a subset $A$ of the vector space $({\mathbb R} \cup \{ \infty \})^n$. We also give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.

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Dima Grigoriev, Nicolai Vorobjov. 2018-03-02. Complexity of deciding whether a tropical linear prevariety is a tropical variety. https://arxiv.org/abs/1803.01068

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