#18036: I should not be symbolic
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Reporter: vdelecroix | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:1 nbruin]:
> I'm not so sure it should. Which quadratic field is the appropriate one?
There are many, distinguishable by the name of their generator (that would
be 'I') for this one, but also by their specified embeddings, and it's not
clear which one to choose.
I also thought of this in the train... and I do not see much possible
choices. I found two rather natural choices for the adoption of `I`:
- the ring of integers `Z[sqrt(-1)]` with its natural embedding in `QQbar`
- `QQbar` itself
> Is there an argument for doing this? Ticket #17860 referenced in the
description makes no mention of it. I'd imagine there might be evaluation
reasons that might make it attractive. Perhaps those also give an
indication of which quadratic field would be the appropriate one.
Some reasons (in favor of the first choice):
- `I + 1.0` and `1.0 * I` should be complex numbers
- `factor((I+3))` should be the factorization over the Gaussian integers
(i.e. `(-I) * (I + 1) * (2*I + 1)`)
- `abs(I)` should be the integer `1`
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18036#comment:2>
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