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arXiv · 1904.07925

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

Thomas Dreyfus·Jacques-Arthur Weil
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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.

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Thomas Dreyfus, Jacques-Arthur Weil. 2019-04-16. Computing the Lie algebra of the differential Galois group: the reducible case. https://doi.org/10.1016/j.jsc.2022.01.006

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