Orthogonal tropical linear prevarieties

Nicolai Vorobjov, Dima Grigoriev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

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
PublisherSpringer
Pages187-196
Number of pages10
Volume11077
ISBN (Electronic)9783319996394
ISBN (Print)9783319996387
DOIs
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

Keywords

  • Orthogonalization
  • Tropical linear prevarieties
  • Tropical linear varieties

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Vorobjov, N., & Grigoriev, D. (2018). Orthogonal tropical linear prevarieties. In W. Koepf, W. M. Seiler, V. P. Gerdt, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings (Vol. 11077, pp. 187-196). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11077 LNCS). Springer. https://doi.org/10.1007/978-3-319-99639-4_13