Orthogonal tropical linear prevarieties

Nicolai Vorobjov, Dima Grigoriev

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)


We study the operation A of tropical orthogonalization, applied to a subset A of a vector space (R U) 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 and A. We give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.

Original languageEnglish
Title of host publicationComputer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings
EditorsWolfram Koepf, Werner M. Seiler, Vladimir P. Gerdt, Evgenii V. Vorozhtsov
Number of pages10
ISBN (Electronic)9783319996394
ISBN (Print)9783319996387
Publication statusPublished - 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11077 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Orthogonalization
  • Tropical linear prevarieties
  • Tropical linear varieties

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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