2018/03/02 by Dima Grigoriev, Grigoriev, Dima, Nicolai Vorobjov +1
Computer Science · #14T05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1803.01068
openalex publication_date 2018/03/02 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
We give an algorithm, with a singly exponential complexity, deciding whether\na tropical linear prevariety is a tropical linear variety. The algorithm relies\non a criterion to be a tropical linear variety in terms of a duality between\nthe tropical orthogonalization A^\⊥ and the double tropical\northogonalization A\⊥ \⊥ of a subset A of the vector space\n( mathbb R \∪ \∞ )n. We also give an example of a countable\nfamily of tropical hyperplanes such that their intersection is not a tropical\nprevariety.\n