Computation of unirational fields (extended abstract)

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, see [BW93]. Our algorithm also requires computing computing primitive elements and factoring over algebraic extensions. Moreover, the method can be extended to finitely generated K-algebras.