  We show that the S-Euclidean minimum of an ideal class is a rational number,
generalizing a result of Cerri. We also give some corollaries which explain the
relationship of our results with Lenstra's notion of a norm-Euclidean ideal
class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. The
proof is self-contained but uses ideas from ergodic theory and topological
dynamics, particularly those of Berend.
