Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
| Autor: | Er-bao Feng, Zhongxuan Luo, Jie-lin Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Pure mathematics Article Subject Plane curve lcsh:Mathematics Dimension of an algebraic variety lcsh:QA1-939 n-connected Modeling and Simulation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION A¹ homotopy theory Projective plane Algebraic curve Bézout's theorem Singular point of an algebraic variety Mathematics |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2014 (2014) |
| ISSN: | 1026-0226 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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