Polynomial and rational solutions of holonomic systems

DOI10.1016/S0022-4049(00)00153-5zbMath0990.35031arXivmath/0001064MaRDI QIDQ5951565

Toshinori Oaku, Nobuki Takayama, Harrison Tsai

Publication date: 15 August 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0001064

zbMATH Keywords

algorithmdualityWeyl algebrarestrictions\(D\)-modules

Mathematics Subject Classification ID

Solutions to PDEs in closed form (35C05) Computational aspects in algebraic geometry (14Q99) Overdetermined systems of PDEs with variable coefficients (35N10) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

Factoring systems of linear PDEs with finite-dimensional solution spaces, Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals, A \(D\)-modules approach on the equations of the Rees algebra, AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS, Perfect bases for differential equations, Factoring and decomposing a class of linear functional systems, The computation of the logarithmic cohomology for plane curves, Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations, Linear differential operators for polynomial equations

Uses Software

• Macaulay2
• Kan

Cites Work

• Unnamed Item
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• On the holonomic systems of linear differential equations. II
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• A localization algorithm for \(D\)-modules
• Algorithmic computation of de Rham cohomology of complements of complex affine varieties
• The Gröbner fan of an \(A_n\)-module
• Testing reducibility of linear differential operators: A group theoretic perspective
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups
• Computing homomorphisms between holonomic \(D\)-modules