Details:
Title  On a generalization of Stickelberger’s Theorem  Author(s)  Peter Scheiblechner  Type  Article in Journal  Abstract  We prove two versions of Stickelberger’s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree ≤ d in n variables, then our algorithms run in parallel (sequential) time ( n log d )^O ( 1 ) ( d^O ( n^4 ) ). In the case of a hypersurface, the complexity drops to O ( n^2 log^2 d ) ( d O ( n ) ). In the proof of the last result we use the effective Nullstellensatz for two polynomials, which we also prove by very elementary methods.  Keywords  Stickelberger’s Theorem, Connected components, Irreducible components, Effective Nullstellensatz  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110001008 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  12  Pages  1459  1470  Year  2010  Note  MEGA’2009  Edition  0  Translation 
No  Refereed 
No 
