  The aim of this paper is to give an effective version of the Strong Artin
Approximation Theorem for binomial equations. First we give an effective
version of the Greenberg Approximation Theorem for polynomial equations, then
using the Weierstrass Preparation Theorem, we apply this effective result to
binomial equations. We prove that the Artin function of a system of binomial
equations is bounded by a doubly exponential function in general and that it is
bounded by an affine function if the order of the approximated solutions is
bounded.
