Fast computations in the lattice of polynomial rational function fields
Franz Binder · 1996
By Luroth's theorem, all intermediate fields of the extension ---(x) : ---, --- an arbitrary field, are simple. Those that contain a nonconstant polynomial, the polynomial rational function fields, constitute a sublattice (with respect to set inclusion). We give a fast algorithm for computing a generator of ---(p; q), which is similar to the Euclidean algorithm, and also an extended version, that expresses this generator in terms of p and q. These algorithms work over any computable field, in particular, no assumption on the characteristic is needed.