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arXiv · 1312.5029

Hrushovski's Algorithm for Computing the Galois Group of a Linear Differential Equation

Ruyong Feng
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Abstract

We present a detailed and simplified version of Hrushovski's algorithm that determines the Galois group of a linear differential equation. There are three major ingredients in this algorithm. The first is to look for a degree bound for proto-Galois groups, which enables one to compute one of them. The second is to determine the identity component of the Galois group that is the pullback of a torus to the proto-Galois group. The third is to recover the Galois group from its identity component and a finite Galois group.

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Ruyong Feng. 2013-12-18. Hrushovski's Algorithm for Computing the Galois Group of a Linear Differential Equation. https://doi.org/10.1016/j.aam.2015.01.001

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