Computation of unirational fields

One of the main contributions which Volker Weispfenning made to mathematics is related to Gröbner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Gröbner bases theory. Our algorithm also requires computing primitive elements and factoring over algebraic extensions. Moreover, the method can be extended to finitely generated K-algebras.