I think it is essential (speaking priority) to have a parallel to
Magam

"
RationalExtensionRepresentation(F) : FldFunG -> FldFun

The function field F represented as an extension of a rational
function field. This function gives the representation of function
fields F/k as finite extensions.
"
 This basically collapses the extension tower to one extension. It
significantly speeds up any computation which happens at the top of
the tower. If sage has such a method for number fields, it should be
fairly straight forward to  recycle for the function field class. Does
anybody knows if we have such a method for number fields?

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