Introduction to Algorithms for D-Modules with Quiver D-Modules

DOI10.1007/978-3-030-26454-3_3zbMath1453.14057OpenAlexW3008023506MaRDI QIDQ3294888

Hiromasa Nakayama, Nobuki Takayama

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_3

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) de Rham cohomology and algebraic geometry (14F40) Commutative rings of differential operators and their modules (13N10)

Related Items (1)

Noncommutative Gröbner Bases: Applications and Generalizations

Uses Software

• Risa/Asir

Cites Work

• An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation
• Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients
• Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules
• Gröbner Bases
• Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups
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