Some New Symbolic Algorithms for the Computation of Generalized Asymptotes

We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly parametrically defined. The g-asymptotes generalize classical concept asymptotes curve. Both notions have been previously studied analyzing geometry and topology curve at infinity points, as well to detect symmetries that can occur in coordinates far from origin. Thus, based on this research, order solve practical problems fields science engineering, we pseudocodes implementations Puiseux series expansion construct Additionally, propose some new methods their corresponding which improve efficiency preceding. These are computation limits derivatives; they show higher computational performance, demanding fewer hardware resources system requirements, reducing computer overload. Finally, novelty research area, comparative analysis all is carried out, considering properties input curves outcomes, analyze establish criteria between them.