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Orthogonal Tropical Linear Prevarieties

  • Dima Grigoriev
  • Nicolai VorobjovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11077)

Abstract

We study the operation \(A^\perp \) of tropical orthogonalization, applied to a subset A of a vector space \(({\mathbb R}\cup \{ \infty \})^n\), and iterations of this operation. Main results include a criterion and an algorithm, deciding whether a tropical linear prevariety is a tropical linear variety formulated in terms of a duality between \(A^\perp \) and \(A^{\perp \perp }\). We give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.

Keywords

Tropical linear prevarieties Tropical linear varieties Orthogonalization 

Notes

Acknowledgments

We thank M. Joswig, N. Kalinin, H. Markwig, and T. Theobald for useful discussions. Part of this research was carried out during our joint visit in September 2017 to the Hausdorff Research Institute for Mathematics at Bonn University, under the program Applied and Computational Algebraic Topology, to which we are very grateful. D. Grigoriev was partly supported by the RSF grant 16-11-10075.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.CNRS, Mathématiques, Université de LilleVilleneuve d’AscqFrance
  2. 2.Department of Computer ScienceUniversity of BathBathEngland, UK

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