#13765: Cyclotomic embeddings should respect coercions.
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Reporter: robertwb | Owner: davidloeffler
Type: defect | Status: needs_work
Priority: critical | Milestone: sage-5.7
Component: number fields | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Robert Bradshaw | Merged in:
Dependencies: | Stopgaps:
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Changes (by ehlen):
* status: needs_review => needs_work
Comment:
* I tested the patch using Sage 5.5.
* It is well documented and it solves the bug as far as I can see.
* The documentation builds.
But I am not convinced that the implementation of
NumberField_cyclotomic._log_gen should stay like it is. It is a private
method but it might be used within the class for ther purposes later.
Therefore, I think the output should always make sense. But it doesn't
always and it is not completely consistent. Here is an Example.
This is what I expect from the documentation:
{{{
sage: K.<zeta>=CyclotomicField(5, embedding=CC(exp(2*pi*i/5)))
sage: K._log_gen(10)
sage: type(K._log_gen(10))
<type 'NoneType'>
}}}
So, this is o.k., but:
{{{
sage: K.<zeta>=CyclotomicField(5, embedding=CC(exp(2*pi*i/5)))
sage: K._log_gen(CDF(10))
sage: 0
sage: type(K._log_gen(CDF(10)))
sage: <type 'sage.rings.integer.Integer'>
}}}
This behaviour is more or less documented in the docstring. It says that
"If x is complex, returns the nearest such e whether or not the result is
exact.". But I don't agree that it should be this way.
But I think this is not consistent and it should be fixed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13765#comment:9>
Sage <http://www.sagemath.org>
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