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Computing the Galois group of some parameterized linear differential equation of order two


Author: Thomas Dreyfus
Journal: Proc. Amer. Math. Soc. 142 (2014), 1193-1207
MSC (2010): Primary 34M15, 12H20, 34M03
DOI: https://doi.org/10.1090/S0002-9939-2014-11826-0
Published electronically: January 24, 2014
MathSciNet review: 3162242
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Abstract: We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition for the integrability of the system. We give various examples of computation.


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Additional Information

Thomas Dreyfus
Affiliation: Université Paris Diderot, Institut de mathématiques de Jussieu, Topologie et géométrie algébriques, 4, place Jussieu, 75005 Paris, France
Email: tdreyfus@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-11826-0
Received by editor(s): October 3, 2011
Received by editor(s) in revised form: October 11, 2011, and April 12, 2012
Published electronically: January 24, 2014
Additional Notes: Work partially supported by NFS CCF-0952591 and ANR-06-JCJC-0028
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.