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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.07925
- arXiv:
- arXiv:1904.07925
- Bibcode:
- 2019arXiv190407925D
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra;
- 34A05;
- 68W30;
- 34M03;
- 34M15;
- 34M25;
- 17B45