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Preprint Number 1346
1346. Alexey Ovchinnikov, Gleb Pogudin and Thomas Scanlon Effective difference elimination and Nullstellensatz E-mail: Submission date: 4 December 2017 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 x = (x_1, ... , x_n) and y = (y_1, ... , y_m), if these equations have any nontrivial consequences in the x variables, then such a consequence may be seen algebraically considering transforms up to the order of our bound. Specializing to the case of n = 0, we obtain an effective method to test whether a given system of difference equations is consistent. Mathematics Subject Classification: Keywords and phrases: |

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