Paper 2: Applications of the class field theory of global fields by Claus Fieker The code for this paper takes around 100 seconds to run on a 64-bit 2.6GHz AMD processor. Changes since book release: V2.14: The intrinsic AbelianExtension(DivFunElt, GrpAb) now returns a FldFunAb. An extra call to FunctionField has been inserted to compensate.