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

Orthogonal tropical linear prevarieties. / Vorobjov, Nicolai; Grigoriev, Dima.

Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings. ed. / Wolfram Koepf; Werner M. Seiler; Vladimir P. Gerdt; Evgenii V. Vorozhtsov. Vol. 11077 Springer, 2018. p. 187-196 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11077 LNCS).

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

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