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TitleGröbner bases and logarithmic -modules
Author(s) Francisco Jesus Castro-Jimenez, Jose Maria Ucha-Enriquez
TypeArticle in Journal
AbstractLet C[x] = C[x_1, ,x_n] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C[x] f of rational functions with poles along f has a natural structure of a left A n -module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f . In this paper we use Gröbner base theory in the non-commutative frame of the ring A n to compare M to some other A n -modules arising in Singularity Theory as the so-called logarithmic A n -modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial.
KeywordsGröbner bases, Weyl algebra, D -modules, Free divisors, Spencer divisors
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717105001355
LanguageEnglish
JournalJournal of Symbolic Computation
Volume41
Number34
Pages317 - 335
Year2006
NoteLogic, Mathematics and Computer Science: Interactions in honor of Bruno Buchberger (60th birthday)
Edition0
Translation No
Refereed No
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