Computing the Lie algebra of the differential Galois group: the reducible case

Abstract

In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a block-triangular linear differential system into a Kolchin-Kovacic reduced form. We combine this with other reduction results to propose a general algorithm for computing a reduced form of a general linear differential system. In particular, this provides directly the Lie algebra of the differential Galois group without an a priori computation of this Galois group.

References in corpus (4)

• Globally nilpotent differential operators and the square Ising model
• Differential Galois Theory of Algebraic Lie-Vessiot Systems
• A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems
• A New Bound on Hrushovski's Algorithm for Computing the Galois Group of a Linear Differential Equation

Cited by in corpus (1)

• Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz