1. Some New Symbolic Algorithms for the Computation of Generalized Asymptotes
- Author
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Elena Campo-Montalvo, Marián Fernández de Sevilla, J. Rafael Magdalena Benedicto, Sonia Pérez-Díaz, Universidad de Alcalá. Departamento de Automática, Universidad de Alcalá. Departamento de Ciencias de la Computación, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Infinity branches ,Physics and Astronomy (miscellaneous) ,Matemáticas ,Algebraic curves ,General Mathematics ,Algorithm performance ,Convergent branches ,algebraic curves ,infinity branches ,convergent branches ,approaching curves ,generalized asymptotes ,algorithm performance ,symbolic computation ,Generalized asymptotes ,Symbolic computation ,Chemistry (miscellaneous) ,Approaching curves ,Computer Science (miscellaneous) ,Mathematics - Abstract
We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly or parametrically defined. The g-asymptotes generalize the classical concept of asymptotes of a plane algebraic curve. Both notions have been previously studied for analyzing the geometry and topology of a curve at infinity points, as well as to detect the symmetries that can occur in coordinates far from the origin. Thus, based on this research, and in order to solve practical problems in the fields of science and engineering, we present the pseudocodes and implementations of algorithms based on the Puiseux series expansion to construct the g-asymptotes of a plane algebraic curve, implicitly or parametrically defined. Additionally, we propose some new symbolic methods and their corresponding implementations which improve the efficiency of the preceding. These new methods are based on the computation of limits and derivatives; they show higher computational performance, demanding fewer hardware resources and system requirements, as well as reducing computer overload. Finally, as a novelty in this research area, a comparative analysis for all the algorithms is carried out, considering the properties of the input curves and their outcomes, to analyze their efficiency and to establish comparative criteria between them., Agencia Estatal de Investigación
- Published
- 2022