Standard Bases in Finitely Generated Difference-Skew-Differential Modules and Their Application to Dimension Polynomials
نویسنده
چکیده
This thesis treats different kinds of standard bases in finitely generated modules over the ring of difference-skew-differential operators, their computation and their application to the computation of multivariate dimension (quasi-)polynomials. It consists of two parts. The first deals with standard bases in modules over the ring of difference-skew-differential operators. The second part deals with uniand multivariate dimension quasipolynomials associated with such modules. We start by recalling the notions of skew-differential, difference, and difference-skew-differential operators. Skew-differential operators are a generalization of commutative polynomials, differential operators, and difference operators. For the numeric solution of linear differential equations one often considers the associated difference scheme which can be described in terms of inversive difference operators. Combining the notions of skew-differential operators and dif-
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