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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