Gröbner Bases in D-Modules: Application to Bernstein-Sato Polynomials

DOI10.1007/978-3-030-26454-3_2zbMath1442.14065OpenAlexW3008496111MaRDI QIDQ3294887

Rouchdi Bahloul

Publication date: 29 June 2020

Published in: Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-26454-3_2

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Commutative rings of differential operators and their modules (13N10)

Uses Software

• SINGULAR

Cites Work

• Idéaux de germes d'opérateurs différentiels à une variable
• Local Bernstein-Sato ideals: algorithm and examples
• B-functions and holonomic systems. Rationality of roots of B-functions
• An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation
• The complexity of the word problems for commutative semigroups and polynomial ideals
• Generalized functional equations: transversality and principality of the Bernstein-Sato ideal
• Meromorphic property of the functions \(P^ \lambda\)
• The Structure of Polynomial Ideals and Gröbner Bases
• La théorie du polynôme de Bernstein-Sato pour les algèbres de Tate et de Dwork-Monsky-Washnitzer
• Démonstration constructive de l'existence de polynômes de Bernstein–Sato pour plusieurs fonctions analytiques
• Ideals, Varieties, and Algorithms
• Resolution of Singularities and Division of Distributions
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