2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100924We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a tropical variety, and whether it is connected, as well as counting the number of connected components. We characterize the borderline between tractable and hard computations by proving $\mathcal{NP}$-hardness and #$\mathcal{P}$-hardness results under various strong restrictions of the input data, as well as providing polynomial time algorithms for various other restrictions.17 pages, 5 figures. To appear in Journal of Symbolic ComputationCombinatorics52B70; 68W30text