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

Zhongxuan Luo | Zendy; Erbao Feng | Zendy; Jielin Zhang | Zendy

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

Author(s) -

Zhongxuan Luo,

Erbao Feng,

Jielin Zhang

Publication year - 2014

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2014/230847

Subject(s) - mathematics , plane curve , algebraic curve , algebraic number , real algebraic geometry , singular point of an algebraic variety , degree (music) , computation , homotopy , continuation , polynomial , univariate , algebra over a field , pure mathematics , mathematical analysis , algorithm , computer science , differential algebraic equation , ordinary differential equation , statistics , physics , multivariate statistics , acoustics , programming language , differential equation

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 continuationmethods and a method of root computation of univariate polynomials. Numerical experiments show that our algorithm is feasible and efficient

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