### 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 | |

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
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Orthogonal tropical linear prevarieties

AU - Vorobjov, Nicolai

AU - Grigoriev, Dima

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Orthogonalization

KW - Tropical linear prevarieties

KW - Tropical linear varieties

UR - http://www.scopus.com/inward/record.url?scp=85053995028&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99639-4_13

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

M3 - Conference contribution

SN - 9783319996387

VL - 11077

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 187

EP - 196

BT - Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings

A2 - Koepf, Wolfram

A2 - Seiler, Werner M.

A2 - Gerdt, Vladimir P.

A2 - Vorozhtsov, Evgenii V.

PB - Springer

ER -