On Thursday, October 18, 2018 at 11:55:14 AM UTC-7, Simon Brandhorst wrote:
> I would say because there is no canonically defined embedding as one can
> send i to -i as well.
>
> That's in principle true, but in sage names of generators carry essential
information. For instance:
sage: parent(QQ['x'].0+ZZ['x,y'].1)
Multivariate Polynomial Ring in x, y over Rational Field
so there's an argument to be made that the "natural" map in this case would
be to map i to i. I think that choice could be justifiable in sage, but I
also expect it will be too expensive to support properly in this case: One
would also need to check that the minimal polynomials of the different "i"s
are compatible. They are in this case, but that requires quite a bit of
work to figure out.
> On Thursday, October 18, 2018 at 1:38:24 PM UTC+2, Daniel Krenn wrote:
>>
>> sage: CyclotomicField(3).extension(x^2+1, 'i')(QQ.extension(x^2+1,
>> 'i').gen())
>>
>> returns
>>
>> TypeError: Cannot coerce element into this number field
>>
>> Does anyone have some idea why this is not working?
>>
>> (This is https://trac.sagemath.org/ticket/26443)
>>
>> Best, Daniel
>>
>
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