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  • @techreport{RISC3935,
    author = {Christian Doench},
    title = {{Bivariate difference-differential dimension polynomials and their computation in Maple}},
    language = {english},
    abstract = {We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gr�bner basis of a finitely generated difference-differential module and we use this to compute the bivariate difference-differential dimension polyomial of the module with respect to the natural bifiltration of the ring of difference-differential operators. An overview regarding affine Hilbert polynomials, Kolchin�s differential dimension polynomials and difference-differential dimension polynomials is given. Then the notion of relative Gr�bner basis and its use for computing bivariate difference-differential dimension polynomials is explained. After this the implementations of the two algorithms are illustrated by a couple of examples.},
    number = {09-19},
    year = {2009},
    keywords = {Groebner basis; Differential ring; Differential module; Differencedifferential module; Difference differential dimension polynomial.},
    sponsor = {This work has been supported by the Austrian FWF project P20336-N18.},
    length = {29},
    type = {RISC Report Series},
    institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
    address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
    }