Note on Kovacic's algorithm

DOI10.1006/jsco.1996.0047zbMath0871.12008OpenAlexW1987322017MaRDI QIDQ674766

Felix Ulmer, Jacques-Arthur Weil

Publication date: 24 September 1997

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

Full work available at URL: https://doi.org/10.1006/jsco.1996.0047

zbMATH Keywords

differential Galois theorysemi-invariantsrational solutionLiouvillian solutionPicard-Vessiot extensiondifferential Galois groupsdifferential fieldrationality problemsecond order equationalgebraic solutionsKovacic's algorithmLiouvillian extensionRiccati invariants

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear ordinary differential equations and systems (34A30) Differential algebra (12H05) Abstract differential equations (12H20)

Related Items (28)

A note on $G$-operators of order $2$ ⋮ Linear differential equations and products of linear forms ⋮ A modular algorithm for computing the exponential solutions of a linear differential operator ⋮ Algebraic invariant curves and first integrals for Riccati polynomial differential systems ⋮ On second order homogeneous linear differential equations with Liouvillian solutions ⋮ On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole ⋮ Non-integrability of some few body problems in two degrees of freedom ⋮ A reduced form for linear differential systems and its application to integrability of Hamiltonian systems ⋮ Galoisian approach to integrability of Schrödinger equation ⋮ Liouvillian solutions of third order differential equations ⋮ Picard-Vessiot theory and integrability ⋮ On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory ⋮ Liouvillian solutions of linear differential equations of order three and higher ⋮ Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations ⋮ Extensions of differential representations of SL₂ and tori ⋮ Computing the Galois group of some parameterized linear differential equation of order two ⋮ Differential Galois approach to the non-integrability of the heavy top problem ⋮ Zariski closures of reductive linear differential algebraic groups ⋮ Nonintegrability of Bianchi VIII Hamiltonian system ⋮ Irreducibility criteria for skew polynomials. ⋮ Differential equations and finite groups ⋮ Classes of elementary function solutions to the CEV model I ⋮ Nonintegrability of the Suslov problem ⋮ Nonintegrability of the Dragt-Finn model of magnetic confinement: A Galoisian-group approach ⋮ Note on algebraic solutions of differential equations with known finite Galois group ⋮ Equivalence of differential equations of order one ⋮ Differential Galois Theory and Integration ⋮ Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators

This page was built for publication: Note on Kovacic's algorithm