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

Zhongxuan Luo, Erbao Feng and Jielin Zhang

Discrete Dynamics in Nature and Society, 2014, vol. 2014, 1-9

Abstract:

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:230847

DOI: 10.1155/2014/230847

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