Computing Galois Groups of Completely Reducible Differential Equations

@article{Compoint1999ComputingGG,
  title={Computing Galois Groups of Completely Reducible Differential Equations},
  author={Elie Compoint and Michael F. Singer},
  journal={J. Symb. Comput.},
  year={1999},
  volume={28},
  pages={473-494}
}
We give an algorithm to calculate a presentation of the Picard?Vessiot extension associated to a completely reducible linear differential equation (i.e. an equation whose Galois group is reductive). Using this, we show how to compute the Galois group of such an equation as well as properties of the Galois groups of general equations. 
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