Hm, interesting. The current code for ZZ.__getitem__ (i.e., ZZ[a]) does
this:
if isinstance(x, NumberFieldElement_base):
K, _ = parent(x).subfield(x)
return K.order(K.gen())
However, this functionality is also available in K.order:
sage: K.order(a,allow_subfield=
If you want the order generated by a, you can do
sage: K.=NumberField(x^2-10)
sage: OK=K.maximal_order()
sage: O = K.order(a)
sage: O.index_in(OK)
1
Note that this correctly fails in Nils' example:
sage: K.order(a^2)
...
ValueError: the rank of the span of gens is wrong
David
On Thu, Sep 7, 202
Hi Justin,
You can see the problem from:
sage: O.ambient()
Number Field in a0 with defining polynomial x^2 - 10 with a0 = a
As you can see, the ambient field of O is not identical to K (which is the
ambient field of OK). It is a field with an *embedding* into K, though, and
it happens to be an
