Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients

DOI10.1007/BF03167233zbMath0811.35006MaRDI QIDQ1343501

Toshinori Oaku

Publication date: 1 May 1995

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Weyl algebracomputer algebrapolynomial coefficientscharacteristic variety

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Linear higher-order PDEs (35G05)

Related Items

An algorithm of computing \(b\)-functions, Algorithms for the \(b\)-function and \(D\)-modules associated with a polynomial, Gröbner bases for \(D\)-modules on a non-singular affine algebraic variety, Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules, Fuchsian systems for Dotsenko-Fateev multipoint correlation functions and similar integrals of hypergeometric type, Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra, A nullstellensatz for linear partial differential equations with polynomial coefficients, Introduction to Algorithms for D-Modules with Quiver D-Modules, Algorithmic stratification of \(\mathbb R\Hom_{\mathcal D}(\mathcal M, \mathcal N)\) for regular algebraic \(\mathcal D\)-modules on \(\mathbb C^n\), Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups, The singular locus of Lauricella's \(F_C\), Gröbner deformations of regular holonomic systems, A localization algorithm for \(D\)-modules, Kinematic singularities of Feynman integrals and principal \(A\)-determinants, Calculation of orthant probabilities by the holonomic gradient method

Uses Software

• Risa/Asir

Cites Work

• Unnamed Item
• Unnamed Item
• An approach to the zero recognition problem by Buchberger algorithm
• On the maximally overdetermined system of linear differential equations. I
• A Gröbner basis method for modules over rings of differential operators
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems