A Gröbner basis method for modules over rings of differential operators

DOI10.1006/jsco.1994.1046zbMath0820.13023OpenAlexW2168031759MaRDI QIDQ1346479

Toshinori Oaku, Takeshi Shimoyama

Publication date: 4 April 1995

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

Full work available at URL: https://doi.org/10.1006/jsco.1994.1046

zbMATH Keywords

linear differential equationscharacteristic variety\(F\)-Gröbner basis

Mathematics Subject Classification ID

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) Rings of differential operators (associative algebraic aspects) (16S32) Abstract differential equations (12H20)

Related Items (10)

Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients ⋮ Gröbner bases in difference-differential modules with coefficients in a commutative ring ⋮ Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra ⋮ Relative reduction and Buchberger's algorithm in filtered free modules ⋮ On computing Gröbner bases in rings of differential operators ⋮ Gröbner bases with respect to several orderings and multivariable dimension polynomials ⋮ Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules ⋮ Gröbner bases in difference-differential modules and difference-differential dimension polynomials ⋮ Degree bounds for Gröbner bases in algebras of solvable type ⋮ Termination of algorithm for computing relative Gröbner bases and difference differential dimension polynomials

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