COMPLEXITY OF DECIDING WHETHER A TROPICAL LINEAR PREVARIETY IS A TROPICAL VARIETY

Dima Grigoriev (1, 2) , Nicolai Vorobjov

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: Tropical linear prevariety; Tropical variety; Complexity

Domaines: Mathématiques [math]

Dima Grigoriev, Nicolai Vorobjov. COMPLEXITY OF DECIDING WHETHER A TROPICAL LINEAR PREVARIETY IS A TROPICAL VARIETY. Applicable Algebra in Engineering, Communication and Computing, 2019, ⟨10.1007/s00200-019-00407-w⟩. ⟨hal-03047290⟩