Computing the differential Galois group of a parameterized second-order linear differential equation

DOI10.1145/2608628.2608680zbMath1325.68263arXiv1401.5127OpenAlexW2065825720MaRDI QIDQ3452375

Carlos E. Arreche

Publication date: 11 November 2015

Published in: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5127

zbMATH Keywords

linear differential algebraic groupparameterized Picard-Vessiot theoryparameterized differential equation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear ordinary differential equations and systems (34A30) Geometric theory, characteristics, transformations in context of PDEs (35A30) Abstract differential equations (12H20)

Related Items (7)

On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters ⋮ Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence ⋮ Calculating Galois groups of third-order linear differential equations with parameters ⋮ Computing differential Galois groups of second-order linear \(q\)-difference equations ⋮ Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation ⋮ Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation ⋮ Almost-simple affine difference algebraic groups

Uses Software

• Jordan

Cites Work

• An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination
• Cylindrical algebraic decomposition using validated numerics
• The Jordan Curve Theorem, Formally and Informally
• On Computable Numbers, with an Application to the Entscheidungsproblem
• Definability and decision problems in arithmetic
• Unnamed Item
• Unnamed Item

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