We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Some New Symbolic Algorithms for the Computation of Generalized Asymptotes.
- Authors
Campo-Montalvo, Elena; Fernández de Sevilla, Marián; Magdalena Benedicto, J. Rafael; Pérez-Díaz, Sonia
- 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.
- Subjects
SYMBOLIC computation; PLANE curves; ALGEBRAIC curves; ASYMPTOTES; TOPOLOGY; GEOMETRY
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 1, p69
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15010069