Title: Effective difference elimination and Nullstellensatz,
Abstract: We prove effective Nullstellensatz and elimination theorems for difference
equations in sequence rings. More precisely, we compute an explicit function of
geometric quantities associated to a system of difference equations (and these
geometric quantities may themselves be bounded by a function of the number of
variables, the order of the equations, and the degrees of the equations) so
that for any system of difference equations in variables $\mathbf{x} = (x_1,
\ldots, x_m)$ and $\mathbf{u} = (u_1, \ldots, u_r)$, if these equations have
any nontrivial consequences in the $\mathbf{x}$ variables, then such a
consequence may be seen algebraically considering transforms up to the order of
our bound. Specializing to the case of $m = 0$, we obtain an effective method
to test whether a given system of difference equations is consistent.