132069 20240301161205.0 doi 10.1007/s11786-010-0058-x sideral 70485 ART-2011-70485 eng Andres, D. Constructive D-Module Theory with Singular 2011 We 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. Access copy available to the general public Unrestricted info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Brickenstein, M. Levandovskyy, V. Martín-Morales, J. (orcid)0000-0002-6559-4722 Schanemann, H. 4 (2011), 359-383 Math. comput. sci. Mathematics in computer science 1661-8270 422100 http://zaguan.unizar.es/record/132069/files/texto_completo.pdf Postprint 1917779 http://zaguan.unizar.es/record/132069/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:132069 articulos driver 2024-03-01-14:36:57 ARTICLE