An effective algorithm for computing the asymptotes of an implicit curve

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Authors
Pérez Díaz, SoniaUniversity of Alcalá Author; Magdalena Benedicto, Rafael; Fernandez de Sevilla Vellon, Maria de los AngelesUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/57921
DOI: 10.1016/j.cam.2023.115468
ISSN: 0377-0427
Publisher
Elsevier
Date
2024-02-01
Academic Departments
Universidad de Alcalá. Departamento de Física y Matemáticas
Teaching unit
Unidad Docente Matemáticas
Funders
Agencia Estatal de Investigación
Bibliographic citation
Pérez Díaz, S., Magdalena Benedicto, R. & Fernández de Sevilla, M. 2024, "An effective algorithm for computing the asymptotes of an implicit curve", Journal of Computational and Applied Mathematics,vol. 437, art. no. 115468, pp. 1-15.
Keywords
Implicit algebraic plane curve
Infinity branches
Asymptotes
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023/PID2021-127946OB-100
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2023.115468
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
In this paper, we first summarize the algorithm presented in Blasco and Pérez-Díaz (2014) for computing the generalized asymptotes of algebraic curves implicitly defined. This algorithm is based on the computation of Puiseux series. The main and very important contribution of this paper is a new and efficient method that allows to easily compute all the generalized asymptotes of an algebraic plane curve implicitly defined by just solving a triangular system of equations. The method can be easily generalized to the case of algebraic curves implicitly defined in the n-dimensional space.

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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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