On the frontiers of polynomial computations in tropical geometry

Authors:
Thorsten Theobald
Affiliations:
Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany
Venue:
Journal of Symbolic Computation
Year:
2006

Citing 4
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Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients

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Abstract

We 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 NP-hardness and #P-hardness results under various strong restrictions of the input data, as well as providing polynomial time algorithms for various other restrictions.