Numerical realization of the conditions of Max Nöther’s residual intersection theorem
| Autor: | Zhongxuan Luo, Jie-lin Zhang, Er-bao Feng |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Intersection theorem
Intersection theory medicine.medical_specialty Computational complexity theory Applied Mathematics Algebra Algebraic cycle ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Algebraic surface medicine Applied mathematics Algebraic function Algebraic curve Time complexity Mathematics |
| Zdroj: | Applied Mathematics-A Journal of Chinese Universities. 29:481-502 |
| ISSN: | 1993-0445 1005-1031 |
| DOI: | 10.1007/s11766-014-3242-y |
| Popis: | The aim of this paper is to study numerical realization of the conditions of Max Nother’s residual intersection theorem. The numerical realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink