Orthogonal tropical linear prevarieties

Nicolai Vorobjov; Dima Grigoriev

doi:10.1007/978-3-319-99639-4_13

Orthogonal tropical linear prevarieties

Nicolai Vorobjov, Dima Grigoriev

Université de Lille

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

2 Citations (SciVal)

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 language	English
Title of host publication	Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings
Editors	Wolfram Koepf, Werner M. Seiler, Vladimir P. Gerdt, Evgenii V. Vorozhtsov
Publisher	Springer
Pages	187-196
Number of pages	10
Volume	11077
ISBN (Electronic)	9783319996394
ISBN (Print)	9783319996387
DOIs	https://doi.org/10.1007/978-3-319-99639-4_13
Publication status	Published - 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11077 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Orthogonalization
Tropical linear prevarieties
Tropical linear varieties

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-99639-4_13

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 or section in a book/report/conference proceeding › Chapter in a published conference proceeding

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)). Epub 2018 Aug 23. doi: 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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Orthogonal tropical linear prevarieties

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