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 ^{⊥} and the double tropical orthogonalization A ^{⊥ ⊥} of a subset A of the vector space (R∪ { ∞}) ^{n}. We also give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.
Original language  English 

Pages (fromto)  157174 
Number of pages  18 
Journal  Applicable Algebra in Engineering Communication and Computing 
Volume  32 
Issue number  2 
Early online date  29 Nov 2019 
DOIs  
Publication status  Published  31 Mar 2021 
Keywords
 Tropical algebra
 Computer algebra
 Complexity
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Nicolai Vorobjov
Person: Research & Teaching