On Computing Gröbner Bases in Rings of Differential Operators with Coefficients in a Ring
نویسندگان
چکیده
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 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.
منابع مشابه
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ورودعنوان ژورنال:
- Mathematics in Computer Science
دوره 1 شماره
صفحات -
تاریخ انتشار 2007