#15348: "R.<a> =" syntactic sugar incorrect for EquationOrder and ZZ.extension
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Reporter: emassop | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/15348 | e857c9a484132348092e21cd1de0711686b8b7f0
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
Replying to [comment:15 cremona]:
> We don't have unique representation for fields:
Well, it all boils down to the difference between "equal" and "isomorphic"
which is really a difference in how we use mathematics and not in
mathematics itself.
In your example with `K1` and `K2`, one could argue that those fields are
not equal because there is no canonical (again, this is not a
mathematically well-defined term) isomorphism.
For orders on the other hand, it makes a lot of sense to see orders as
subsets of a number field. Then obviously two orders are equal if they are
the same subset of the number field. That's the view that Sage uses. I
admit that it's all quite subtle.
Regardless, I don't think that this should hold back this ticket. I'm sure
that many people have stumbled on the bug on this ticket, so let's just
fix it. It also makes it possible to implement #7545. We can still look at
further subtleties later.
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Ticket URL: <http://trac.sagemath.org/ticket/15348#comment:18>
Sage <http://www.sagemath.org>
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