Generating subfields

Authors:
Mark van Hoeij;Jürgen Klüners;Andrew Novocin
Affiliations:
Florida State University, Tallahassee, FL, USA;Universität Paderborn, Paderborn, Germany;CNRS, ENS Lyon, INRIA, UCBL, U. Lyon, Lyon, France
Venue:
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Year:
2011

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Abstract

Given a field extension K/k of degree n we are interested in finding the subfields of K containing k. There can be more than polynomially many subfields. We introduce the notion of generating subfields, a set of up to n subfields whose intersections give the rest. We provide an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization. Our implementation shows that previously difficult cases can now be handled.