An algorithm for solving second order linear homogeneous differential equations
Journal of Symbolic Computation
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Journal of Symbolic Computation
Liouvillian and algebraic solutions of second and third order linear differential equations
Journal of Symbolic Computation
Journal of Symbolic Computation
Computing Galois groups of completely reducible differential equations
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Calculating the Galois group of Y' = AY + B, Y' = AY completely reducible
Journal of Symbolic Computation
First Integrals and Darboux Polynomials of Homogeneous Linear Differential Systems
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Closed form solutions of linear odes having elliptic function coefficients
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
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Let k be a differential field with algebraic closure k@?, and let [A]:Y^'=AY with A@?M"n(k) be a linear differential system. Denote by g the Lie algebra of the differential Galois group of [A]. We say that a matrix R@?M"n(k@?) is a reduced form of [A] if R@?g(k@?) and there exists P@?GL"n(k@?) such that R=P^-^1(AP-P^')@?g(k@?). Such a form is often the sparsest possible attainable through gauge transformations without introducing new transcendents. In this paper, we discuss how to compute reduced forms of some symplectic differential systems, arising as variational equations of Hamiltonian systems. We use this to give an effective form of the Morales-Ramis theorem on (non-)-integrability of Hamiltonian systems.