Séminaire du 17 mai 04, Agnes Szanto.

Elimination Theory for Large Differential-Difference Polynomials

We present an elimination algorithm for differential-difference polynomial systems. We use the framework of a generalization of Ore algebras, where the independent variables are non-commutative. We prove that for certain term orderings, Buchberger's algorithm applied to differential difference systems terminates and produces a Groebner basis. Therefore, differential-difference algebras provide a new instance of non-commutative graded rings which are effective Groebner structures.