Details:
Title  Local Bézout Theorem  Author(s)  M. Emilia Alonso, H. Lombardi  Type  Article in Journal  Abstract  We 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.  Keywords  Local Bézout Theorem, Henselian rings, Roots continuity, Stable computations  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110001021 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  10  Pages  975  985  Year  2010  Edition  0  Translation 
No  Refereed 
No 
