Title  On computing Gröbner bases in rings of differential operators with coefficients in a ring 
Author(s)  Franz Winkler, Meng Zhou 
Type  Technical Report, Misc 
Abstract  Following 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 Spolynomials is necessary for computation
of Gröbner bases. Then we prove that under certain conditions the
GSpolynomials can be reduced to be simpler than the original one. Especially
for some simple case it is enough to consider Spolynomials 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. 
Keywords  Gröbner basis, rings of differential operators, generalized Spolynomials, elimination property 
Length  13 
File 

Language  English 
Number  0504 
Year  2005 
Month  September 
Translation 
No 
Refereed 
No 
Organization 
Johannes Kepler University Linz 
Institution 
RISC (Research Institute for Symbolic Computation) 
Sponsors  This work has been supported by the FWF project P16357N04 