Asymptotes and Perfect Curves

TL;DR

This paper presents a novel method for computing all generalized asymptotes of real plane algebraic curves, enhancing understanding of their asymptotic behavior using the concept of perfect curves.

Contribution

It introduces a new approach based on perfect curves to determine all generalized asymptotes of algebraic curves, extending previous theoretical frameworks.

Findings

Method successfully computes all asymptotes for given curves.

Enhances understanding of asymptotic behavior of algebraic curves.

Builds on and extends prior theoretical work on perfect curves.

Abstract

We develop a method for computing all the {\it generalized asymptotes} of a real plane algebraic curve $\cal C$ over $\Bbb C$ implicitly defined by an irreducible polynomial $f(x,y)\in {\Bbb R}[x,y]$. The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco, A., P\'erez-D\'{\i}az, S. (2013). {\it Asymptotic Behavior of an Implicit Algebraic Plane Curve}. arxiv.org/abs/1302.2522v2.