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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/230847 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |