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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 230847, 9 pages
Research Article

Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Software, Dalian University of Technology, Dalian 116620, China

Received 10 April 2014; Accepted 8 May 2014; Published 5 June 2014

Academic Editor: Baodong Zheng

Copyright © 2014 Zhongxuan Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. The feasibility of the algorithm is analyzed. We prove that the algorithm has the polynomial time complexity on the degree of the algebraic curve. The algorithm involves the combined applications of homotopy continuation methods and a method of root computation of univariate polynomials. Numerical experiments show that our algorithm is feasible and efficient.