English

Computing branches and asymptotes of meromorphic functions

Algebraic Geometry 2023-02-14 v1

Abstract

In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily compute the whole branch and all the generalized asymptotes of a special curve defined in n-dimensional space by a parametrization that is not necessarily rational. So, some new concepts and methods are established for this type of curves. The approach is based on the notion of perfect curves introduced from the concepts and results presented in previous papers.

Keywords

Cite

@article{arxiv.2302.06190,
  title  = {Computing branches and asymptotes of meromorphic functions},
  author = {M. Fernandez de Sevilla and R. Magdalena Benedicto and S. Perez-Diaz},
  journal= {arXiv preprint arXiv:2302.06190},
  year   = {2023}
}

Comments

31 pages. arXiv admin note: text overlap with arXiv:1307.6153

R2 v1 2026-06-28T08:38:30.848Z