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TitleLocal Bézout Theorem
Author(s) M. Emilia Alonso, H. Lombardi
TypeArticle in Journal
AbstractWe give an elementary proof of what we call the Local Bézout Theorem. Given a system of n polynomials in n indeterminates with coefficients in a Henselian local domain, ( V , m , k ) , which residually defines an isolated point in k n of multiplicity r , we prove (under some additional hypothesis on V ) that there are finitely many zeroes of the system above the residual zero (i.e., with coordinates in m ), and the sum of their multiplicities is r . Our proof is based on techniques of computational algebra.
KeywordsLocal Bézout Theorem, Henselian rings, Roots continuity, Stable computations
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717110001021
LanguageEnglish
JournalJournal of Symbolic Computation
Volume45
Number10
Pages975 - 985
Year2010
Edition0
Translation No
Refereed No
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