Currently, elements in different number fields cannot be compared. As a consequence, we cannot compare equivalence classes of surfaces in libflatsurf if the surfaces are defined over different number fields.
There are several ways to solve this. All of which are quite a bit of work:
First we should of course compare the Arb approximations of elements up to some precision and special case for when the elements are actually rational.
We could embed one element in the other parent by determining a root of its minpoly.
Or, more generally but less efficient, compute the compositum of the parents, lift the elements and compare them.