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TitleOn computing Gröbner bases in rings of differential operators with coefficients in a ring
Author(s) Franz Winkler, Meng Zhou
TypeTechnical Report, Misc
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, generalized S-polynomials, elimination property
Translation No
Refereed No
Organization Johannes Kepler University Linz
Institution RISC (Research Institute for Symbolic Computation)
SponsorsThis work has been supported by the FWF project P16357-N04