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**Differential Galois theory.**
*(English)*
Zbl 0813.12001

Waldschmidt, Michel (ed.) et al., From number theory to physics. Lectures of a meeting on number theory and physics held at the Centre de Physique, Les Houches (France), March 7-16, 1989. Berlin: Springer-Verlag. 413-439 (1992).

A basic introduction to Galois theory of ordinary differential equations is given. Differential Galois groups are introduced and their basic properties are described. The definitions and theorems are formulated in a fairly general form using differential fields of characteristic zero and algebraically closed constant field. Some background on linear algebraic groups is given. The technique for the computation of differential Galois groups is illustrated by computing them for the generalized hypergeometric equation in one variable. The proofs of the main theorem are absent, however, the references are given.

For the entire collection see [Zbl 0784.00021].

For the entire collection see [Zbl 0784.00021].

Reviewer: E.V.Pankrat’ev (Moskva)

### MSC:

12H05 | Differential algebra |

12F10 | Separable extensions, Galois theory |

34A30 | Linear ordinary differential equations and systems |

12F20 | Transcendental field extensions |