Computing the Lie algebra of the differential Galois group: the reducible case
Algebraic Geometry
2024-10-22 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.1904.07925,
title = {Computing the Lie algebra of the differential Galois group: the reducible case},
author = {Thomas Dreyfus and Jacques-Arthur Weil},
journal= {arXiv preprint arXiv:1904.07925},
year = {2024}
}