  The divided cell algorithm was introduced by Delone in 1947 to calculate the
inhomogeneous minima of binary quadratic forms and developed further by E. S.
Barnes and H. P. F. Swinnerton-Dyer in the 1950s. We show how advances of the
past fifty years in both symbolic computation and our understanding of
homogeneous spectra can be combined to make divided cells more useful for
organizing information about inhomogeneous approximation problems. A crucial
part of our analysis relies on work of Jane Pitman, who related the divided
cell algorithm to the regular continued fraction algorithm. In particular, the
relation to continued fractions allows two divided cells for the same problem
to be compared without stepping through the chain of divided cells connecting
them.
