While preparing examples with Gaussian Integers for an undergraduate
course I discovered this terrible bug:

sage: Zi.<i> = ZZ.extension(x^2+1)
sage: (123+456*i)/3
193

I note that the type of Zi here is Order in Number Field in i with
defining polynomial x^2 + 1 (not "maximal order" which might be the
problem.  I was looking for the simplest way to define Z[i], the ring
of Gaussian integers, in one line which also assignes the variable i
and uses "i" for output, suitable for 2nd year undergraduates who do
not know about alegbraic number fields.  So I would prefer not to do
the following since it is supposed to be an example of a nice ring,
not a field

sage: Qi.<i> = QuadraticField(-1)
sage: (123+456*i)/3
152*i + 41

is fine.  But the first way should display the same, which is definitely a BUG.

John

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