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Indexed by:期刊论文

Date of Publication:2014-12-01

Journal:APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B

Included Journals:SCIE、CSCD、Scopus

Volume:29

Issue:4

Page Number:481-502

ISSN No.:1005-1031

Key Words:algebraic curve; Puiseux expansion; place; homotopy continuation; multiple root

Abstract: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.