Number of common roots and resultant of two tropical univariate polynomials

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Authors
Hong, Hoon; Sendra Pons, Juan RafaelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49645
DOI: 10.1016/j.jalgebra.2018.06.027
ISSN: 0021-8693
Publisher
Elsevier
Date
2018-10-01
Academic Departments
Universidad de Alcalá. Departamento de Física y Matemáticas
Teaching unit
Unidad Docente Matemáticas
Funders
Ministerio de Economía y Competitividad
National Science Foundation
Bibliographic citation
Hong, H. & Sendra, J.R. 2018, “Number of common roots and resultant of two tropical univariate polynomials”, Journal of Algebra, vol. 511, pp. 420-439.
Keywords
Tropical semifield
Tropical resultant
Common roots
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/Construcciones algebro-geométricas: fundamentos, algoritmos y aplicaciones
info:eu-repo/grantAgreement/NSF//1319632/US
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.jalgebra.2018.06.027
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2018 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
It is well known that for two univariate polynomials over the complex number field the number of their common roots is equal to the order of their resultant. In this paper, we show that this fundamental relationship still holds for the tropical polynomials under suitable adaptation of the notion of order, if the roots are simple and non-zero.

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