On Computing Grobner Bases in Rings of Differential Operators with Coefficients in a Ring

被引：0
|
作者：
Zhou, Meng [1 ]
Winkler, Franz [2 ]
机构：
[1] Beihang Univ, Dept Math & LMIB, Xueyuan Rd 37, Beijing 100083, Peoples R China
[2] J Kepler Univ, RISC Linz, A-4040 Linz, Austria
来源：
MATHEMATICS IN COMPUTER SCIENCE | 2007年 / 1卷 / 02期
关键词：
Grobner basis; rings of differential operators; G-S-polynomials;
D O I：
10.1007/s11786-007-0015-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Following the definition of Grobner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some computational properties of Grobner 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 Grobner 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 Grobner bases. The algorithm for computation of Grobner bases can thus be simplified. Last we discuss the elimination property of Grobner bases in rings of differential operators and give some examples of solving PDE by elimination using Grobner bases.
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页码：211 / 223
页数：13
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