An effective algorithm for computing the asymptotes of an implicit curve

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...

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Detalles Bibliográficos
Autores: Pérez Díaz, Sonia|||0000-0002-0174-5325, Magdalena Benedicto, Rafael, Fernandez de Sevilla Vellon, Maria de los Angeles|||0000-0002-0630-1141
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/57921
Acceso en línea:http://hdl.handle.net/10017/57921
https://dx.doi.org/10.1016/j.cam.2023.115468
Access Level:acceso abierto
Palabra clave:Implicit algebraic plane curve
Infinity branches
Asymptotes
Matemáticas
Mathematics
Descripción
Sumario: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.