BIVARIATE DIFFERENCE-DIFFERENTIAL DIMENSION POLYNOMIALS AND THEIR COMPUTATION IN Maple
نویسنده
چکیده
We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gröbner 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 Gröbner 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.
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