Finite systems of equations and implicit functions
  The classical Ruckert-Lefschetz scheme of analysis of implicit functions (defined by finite systems of n analytical equations with n unknowns) is studied from the point of view of calculations with finite number coefficients in Taylor expansions for left hand parts of corresponding equations. It is proved that this scheme is not applicable in the general case. It is offered some modifications allowing to lead the analysis of implicit functions to the calculation with finite number of coefficients. 
P. P. Zabreiko, A. V. Krivko-Krasko
math.FA