Artin approximation theorem: Difference between revisions

Revision as of 17:38, 22 March 2013

Revision as of 20:59, 7 January 2014

Line 16:

:''f''('''x''', '''y''') = 0

be a system of [[polynomial equation]]s in ''k''['''x''', '''y'''], and ''c'' a positive [[integer]]. Then given a formal power series solution '''ŷ'''('''x''') ∈ ''k'''''<nowiki>[[x]]</nowiki>''' there is an algebraic solution '''y'''('''x''') consisting of [[algebraic function]]s (more precisely, algebraic power series) such that

:'''ŷ'''('''x''') ≡ '''y'''('''x''') mod ('''x''')^''c''.