Quadratic Number Fields

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.