TY - JOUR
T1 - Computing Numerical Singular Points of Plane Algebraic Curves
AU - Luo , Zhongxuan
AU - Feng , Er-Bao
AU - Hu , Wenyu
JO - Communications in Mathematical Research 
VL - 2
SP - 146
EP - 158
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19057.html
KW - numerical singular point, multiplicity, ordinary, homotopy continuation.
AB - <p style="text-align: justify;">Given an irreducible plane algebraic curve of degree $d ≥ 3$, we compute
its numerical singular points, determine their multiplicities, and count the number
of distinct tangents at each to decide whether the singular points are ordinary. The
numerical procedures rely on computing numerical solutions of polynomial systems
by homotopy continuation method and a reliable method that calculates multiple
roots of the univariate polynomials accurately using standard machine precision. It is
completely different from the traditional symbolic computation and provides singular
points and their related properties of some plane algebraic curves that the symbolic
software Maple cannot work out. Without using multiprecision arithmetic, extensive
numerical experiments show that our numerical procedures are accurate, efficient and
robust, even if the coefficients of plane algebraic curves are inexact.</p>