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Article Dans Une Revue Journal of Symbolic Computation Année : 2022

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

Résumé

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.

Dates et versions

hal-02408036 , version 1 (12-12-2019)

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Thomas Dreyfus, Jacques-Arthur Weil. Computing the Lie algebra of the differential Galois group: the reducible case. Journal of Symbolic Computation, 2022, ⟨10.1016/j.jsc.2022.01.006⟩. ⟨hal-02408036⟩
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