I have a finite dimensional vector space V/k, and various automorphisms (i.e. members of GL(V)). I would like to construct the field k(X), where the variables in X correspond to a basis of V, along with the operation of GL(V) on k(X). Is there some existing way to do this in SAGE, or do I need to write new classes? In addition I have a map, h, from the basis of V to another field L, so that h is extended in the obvious way k(X) --> L.
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