Local Bernstein-Sato ideals: algorithm and examples

DOI10.1016/j.jsc.2009.06.004zbMath1184.14030arXiv0806.4869OpenAlexW2031528609MaRDI QIDQ1034547

Toshinori Oaku, Rouchdi Bahloul

Publication date: 6 November 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4869

zbMATH Keywords

decomposition\(D\)-moduleBernstein-Sato idealGröbner base

Mathematics Subject Classification ID

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10)

Related Items (13)

Bernstein-Sato Polynomials in Commutative Algebra ⋮ Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic \(D\)-modules ⋮ ON A BERNSTEIN–SATO POLYNOMIAL OF A MEROMORPHIC FUNCTION ⋮ A note on Bernstein-Sato varieties for tame divisors and arrangements ⋮ Algorithms for checking rational roots of \(b\)-functions and their applications ⋮ Combinatorially determined zeroes of Bernstein--Sato ideals for tame and free arrangements ⋮ Gröbner Bases in D-Modules: Application to Bernstein-Sato Polynomials ⋮ Bernstein–Sato varieties and annihilation of powers ⋮ Constructive \(D\)-module theory with \texttt{Singular} ⋮ Stratification associated with local \(b\)-functions ⋮ Local systems on analytic germ complements ⋮ Zero loci of Bernstein-Sato ideals ⋮ Bernstein-Sato ideals and local systems

Uses Software

• Risa/Asir
• SINGULAR
• Kan

Cites Work

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• Algorithm computing the local \(b\) function by an approximate division algorithm in \(\widehat{\mathcal D}\)
• An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation
• An algorithm of computing \(b\)-functions
• Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules
• Generalized functional equations: transversality and principality of the Bernstein-Sato ideal
• Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials
• On the computation of Bernstein-Sato ideals.
• Démonstration constructive de l'existence de polynômes de Bernstein–Sato pour plusieurs fonctions analytiques
• Computational D-module theory with singular, comparison with other systems and two new algorithms
• CONSTRUCTION D'UN ÉLÉMENT REMARQUABLE DE L'IDÉAL DE BERNSTEIN-SATO ASSOCIÉ À DEUX COURBES PLANES ANALYTIQUES
• Algorithm for computing Bernstein-Sato ideals associated with a polynomial mapping.

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