> is this not just a curiosity? Maybe a useful one for teaching,
> though, and implementing this would certainly be possible.
Very useful. I had to resort to some annoying crutches (i.e., using
the theorem in the code instead of "discovering" the theorem via the
demonstration of the code) to do stuff with Gaussian integers last
spring in my undergraduate course. In particular,
(1 + I).is_prime()
would have been really useful, but was not available. I realize that
in the symbolic ring it is not clear what should be "prime", but then
again
sage: is_prime(SR(3))
True
yet in theory it might not be a generator of a prime ideal depending
on what else is in the symbolic ring:
sage: 1/3 in SR
True
So anything that gives easy access to this particular number field
*and* its elements being treated as generators of the ideals would be
very nice, for instance for things like Gaussian constellations etc.
If there are any other rings of integers of number fields that show up
a lot they could have shortcuts too, maybe Cyclotomic_Integers(n) or
something, in the way Javier points out.
- kcrisman
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