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

26 Sep 2019 Grigoriev Dima Vorobjov Nicolai

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 $({\mathbb R} \cup \{ \infty \})^n$... (read more)

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• ALGEBRAIC GEOMETRY