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

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 al...

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Main Authors:	Zhongxuan Luo, Erbao Feng, Jielin Zhang
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2014/230847

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spelling	doaj-3e11249704d84b958a3f76de3eba38d62020-11-25T00:49:54ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/230847230847Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation MethodsZhongxuan Luo0Erbao Feng1Jielin Zhang2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe 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.http://dx.doi.org/10.1155/2014/230847
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zhongxuan Luo Erbao Feng Jielin Zhang
spellingShingle	Zhongxuan Luo Erbao Feng Jielin Zhang Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods Discrete Dynamics in Nature and Society
author_facet	Zhongxuan Luo Erbao Feng Jielin Zhang
author_sort	Zhongxuan Luo
title	Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
title_short	Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
title_full	Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
title_fullStr	Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
title_full_unstemmed	Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
title_sort	computing singular points of projective plane algebraic curves by homotopy continuation methods
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2014-01-01
description	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.
url	http://dx.doi.org/10.1155/2014/230847
work_keys_str_mv	AT zhongxuanluo computingsingularpointsofprojectiveplanealgebraiccurvesbyhomotopycontinuationmethods AT erbaofeng computingsingularpointsofprojectiveplanealgebraiccurvesbyhomotopycontinuationmethods AT jielinzhang computingsingularpointsofprojectiveplanealgebraiccurvesbyhomotopycontinuationmethods
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Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods

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