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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2008, Volume 20, Issue 5, Pages 41–82 (Mi aa530)

Research Papers

Complexity of the Standard Basis of a $D$-Module

D. Yu. Grigorieva, A. L. Chistovb

a CNRS, IRMAR, Université de Rennes, Rennes, France
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: A double-exponential upper bound is obtained for the degree and for the complexity of constructing a standard basis of a $D$-module. This generalizes a well-known bound for the complexity of a Gröbner basis of a module over the algebra of polynomials. It should be emphasized that the bound obtained cannot be deduced immediately from the commutative case. To get the bound in question, a new technique is elaborated for constructing all the solutions of a linear system over a homogeneous version of a Weyl algebra.

Keywords: Weyl algebra, Janet basis, Gröbner basis

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English version:
St. Petersburg Mathematical Journal, 2009, 20:5, 709–736

Bibliographic databases:

MSC: 16Z05

Citation: D. Yu. Grigoriev, A. L. Chistov, “Complexity of the Standard Basis of a $D$-Module”, Algebra i Analiz, 20:5 (2008), 41–82; St. Petersburg Math. J., 20:5 (2009), 709–736

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Shibuta T., Tajima Sh., “An Algorithm For Computing the Truncated Annihilating Ideals For An Algebraic Local Cohomology Class”, Computer Algebra in Scientific Computing, Casc 2014, Lecture Notes in Computer Science, 8660, eds. Gerdt V., Koepf W., Seiler W., Vorozhtsov E., Springer-Verlag Berlin, 2014, 447–459
2. Gustavson R., Sanchez O.L., “Effective Bounds For the Consistency of Differential Equations”, J. Symbolic Comput., 89 (2018), 41–72
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