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TitleConstructive $D$-module theory with tt Singular.
Author(s) Michael Brickenstein, Andres Daniel, Viktor Levandovskyy, J. Martín-Morales, Hans Schönemann
TypeArticle in Journal
AbstractWe overview numerous algorithms in computational D-module theory together with the theoretical background as well as the implementation in the computer algebra system Singular. We discuss new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of polynomials. We analyze algorithms for local Bernstein–Sato polynomials and also algorithms, recovering any kind of Bernstein–Sato polynomial from partial knowledge of its roots. We address a novel way to compute the Bernstein–Sato polynomial for an affine variety algorithmically. All the carefully selected nontrivial examples, which we present, have been computed with our implementation. We also address such applications as the computation of a zeta-function for certain integrals and revealing the algebraic dependence between pairwise commuting elements.
Keywords D-modules, Non-commutative Gröbner basis, Annihilator ideal, b-Function, Bernstein–Sato polynomial, Bernstein–Sato ideal
ISSN1661-8270; 1661-8289/e
URL http://link.springer.com/article/10.1007%2Fs11786-010-0058-x
JournalMath. Comput. Sci.
PublisherSpringer (Birkh\"auser), Basel
Translation No
Refereed No