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TitleOn computing Gr\"obner bases in rings of differential operators with coefficients in a ring.
Author(s) Franz Winkler, Meng Zhou
TypeArticle in Journal
AbstractFollowing the definition of Gröbner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some computational properties of Gröbner bases arising when the coefficient set is a ring. First we give examples to show that the generalization of S-polynomials is necessary for computation of Gröbner bases. Then we prove that under certain conditions the G-S-polynomials can be reduced to be simpler than the original one. Especially for some simple case it is enough to consider S-polynomials in the computation of Gröbner bases. The algorithm for computation of Gröbner bases can thus be simplified. Last we discuss the elimination property of Gröbner bases in rings of differential operators and give some examples of solving PDE by elimination using Gröbner bases.
KeywordsGröbner basis, rings of differential operators, G-S-polynomials
ISSN1661-8270; 1661-8289/e
URL http://link.springer.com/article/10.1007%2Fs11786-007-0015-5
JournalMath. Comput. Sci.
PublisherSpringer (Birkh\"auser), Basel
Translation No
Refereed No