extension of ZZ gives wrong generator

[dkrenn]

Generating an extension in the way below gives back the wrong generator.

sage: Z.<z> = ZZ.extension(x^2+1); Z
Order in Number Field in z with defining polynomial x^2 + 1
sage: z
1

The output should be

sage: z
z

as, for example, in the case of an extension of QQ, which works correctly.

[davidloeffler]

Yup, this is annoying. The reason for this is that the X.<y> syntax defines y to be the first element of X.gens(), but gens for number field orders returns *module* generators, not *ring* generators (which don't always exist for general orders).

It would certainly be nice to fix this, but it's not clear to me what the best solution is.