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

✍ Scribed by Meng Zhou; Franz Winkler

Book ID
107508826
Publisher
Springer-Verlag
Year
2007
Tongue
English
Weight
209 KB
Volume
1
Category
Article
ISSN
1661-8270

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In this paper we will define analogs of Gröbner bases for R-subalgebras and their ideals in a polynomial ring R[x 1 , . . . , xn] where R is a noetherian integral domain with multiplicative identity and in which we can determine ideal membership and compute syzygies. The main goal is to present and

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We study modules over the ring \(\mathcal{D}_{0}\) of differential operators with power series coeffcients. For \(\mathcal{D}_{0}\)-modules, we introduce a new notion of \(F\)-Gröbner basis and present an algorithmic method to compute it. Our method is more algebraic than that of Castro \((1986,1987