RT info:eu-repo/semantics/article
T1 Asymptotes and perfect curves
A1 Blasco Lorenzo, Ángel
A1 Pérez Díaz, Sonia
K1 Implicit algebraic plane curve
K1 Infinity branches
K1 Asymptotes
K1 Perfect curves
K1 Matemáticas
K1 Mathematics
AB We develop a method for computing all the generalized asymptotes of a real plane algebraic curve C implicitly defined by an irreducible polynomial f(x, y) ∈ R[x, y]. The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and P´erez-D´ıaz (2013). In addition, we study some properties concerning perfect curves and in particular, we provide a necessary and sufficient condition for a plane curve to be perfect. Finally, we show that the equivalent class of generalized asymptotes for a branch of a plane curve can be described as an affine space R m for a certain m.
PB Elsevier
SN 0167-8396
YR 2014
FD 2014-02
LK http://hdl.handle.net/10017/49575
UL http://hdl.handle.net/10017/49575
LA eng
DS MINDS@UW
RD 09-feb-2023