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Hi,
Currently you can create such a field
sage: K.<x> = FunctionField(QQ, 'x')
sage: R.<y> = PolynomialRing(K)
sage: p = y^7 - x
sage: K2 = K.extension(p)
sage: K2
Function field in y defined by y^7 - x
But, sadly, there is no such feature as computing the Galois closure...
Vincent
