Computation of unirational fields (extended abstract)

TL;DR

This paper introduces an algorithm leveraging Groebner bases to compute all algebraic intermediate subfields in separably generated unirational field extensions, with extensions to finitely generated algebras.

Contribution

The paper presents a novel algorithm for computing algebraic intermediate subfields in unirational fields, incorporating primitive element computation and factoring over algebraic extensions.

Findings

Algorithm successfully computes all algebraic intermediate subfields.

Method extends to finitely generated K-algebras.

Utilizes Groebner bases and primitive element techniques.

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 Groebner bases theory. Our algorithm also requires computing computing primitive elements and factoring over algebraic extensions. Moreover, the method can be extended to finitely generated K-algebras.