Christian Eckhardt Karl-H Dönch,
"Bivariate difference-differential dimension polynomials and their computation in Maple"
, Serie RISC Report Series, Nummer 09-19, RISC, JKU Linz, Schloss Hagenberg, 4232 Hagenberg, 2009
Original Titel:
Bivariate difference-differential dimension polynomials and their computation in Maple
Sprache des Titels:
Englisch
Original Kurzfassung:
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.