On Computing Gröbner Bases in Rings of Differential Operators with Coefficients in a Ring |
| |
Authors: | Meng Zhou Franz Winkler |
| |
Institution: | (1) Department of Mathematics and LMIB, Beihang University, Xueyuan Road 37, Haidian District, Beijing, 100083, China;(2) RISC-Linz, J. Kepler University, A-4040 Linz, Austria |
| |
Abstract: | Following the definition of Gr?bner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some
computational properties of Gr?bner 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 Gr?bner 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 Gr?bner bases. The algorithm for computation of Gr?bner bases can thus be simplified.
Last we discuss the elimination property of Gr?bner bases in rings of differential operators and give some examples of solving
PDE by elimination using Gr?bner bases.
This work was supported by the NSFC project 60473019. |
| |
Keywords: | Gr?bner basis rings of differential operators G-S-polynomials |
本文献已被 SpringerLink 等数据库收录! |
|