Generating subfields

Authors:
Mark Van Hoeij;JüRgen KlüNers;Andrew Novocin
Affiliations:
Florida State University, Tallahassee, FL 32306, United States;Mathematisches Institut, der Universität Paderborn, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany;David R. Cheriton School of Computer Science, University of Waterloo, Ontario, N2L 3G1, Canada
Venue:
Journal of Symbolic Computation
Year:
2013

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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 in any extension of K. Implementations show that previously difficult cases can now be handled.