000132069 001__ 132069 000132069 005__ 20240301161205.0 000132069 0247_ $$2doi$$a10.1007/s11786-010-0058-x 000132069 0248_ $$2sideral$$a70485 000132069 037__ $$aART-2011-70485 000132069 041__ $$aeng 000132069 100__ $$aAndres, D. 000132069 245__ $$aConstructive D-Module Theory with Singular 000132069 260__ $$c2011 000132069 5060_ $$aAccess copy available to the general public$$fUnrestricted 000132069 5203_ $$aWe 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. 000132069 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000132069 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000132069 700__ $$aBrickenstein, M. 000132069 700__ $$aLevandovskyy, V. 000132069 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, J. 000132069 700__ $$aSchanemann, H. 000132069 773__ $$g4 (2011), 359-383$$pMath. comput. sci.$$tMathematics in computer science$$x1661-8270 000132069 8564_ $$s422100$$uhttps://zaguan.unizar.es/record/132069/files/texto_completo.pdf$$yPostprint 000132069 8564_ $$s1917779$$uhttps://zaguan.unizar.es/record/132069/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000132069 909CO $$ooai:zaguan.unizar.es:132069$$particulos$$pdriver 000132069 951__ $$a2024-03-01-14:36:57 000132069 980__ $$aARTICLE