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Multivariate Difference-Differential Dimension Polynomials and New Invariants of Difference-Differential Field Extensions (1302.1505v1)
Published 6 Feb 2013 in math.AC
Abstract: In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of finitely generated difference-differential field extensions. Furthermore, we find new invariants of such extensions and show how the computation of multivariate difference-differential polynomials is applied to the equivalence problem for systems of algebraic difference-differential equations.