| and (2007) | |||||||||||||||
Abstract | |||||||||||||||
| The usual Galois theory of polynomial equations allows one to associate a group to a polynomial in such a way that the algebraic properties of the roots of the polynomial are reflected in properties of the group. More specifically, given a field k and a polynomial p(x) with coefficients in the field, one forms the splitting field K of p(x) by formally adjoining all the roots of p(x) to k. The Galois group G is defined to be the group of all automorphisms of K that leave each element of k fixed. A similar construction can be made for linear differential equations. One starts with a differential field k. This is a field 1 together with a map | |||||||||||||||
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