#19288: Make real/complex number field embeddings more accurate
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Reporter: pbruin | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.9
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
I don't completely agree with re-purposing this ticket. In my opinion a
method `logabs()` would still be useful. It should implement ''x'' ↦ log
|''x''|,,v,, for any place ''v'': either an Archimedean place defined by a
real or complex embedding, or a non-Archimedean place defined by a prime
ideal of the ring of integers. For Archimedean places it would do this by
simply computing the embedding to sufficient precision and then taking the
logarithm of the absolute value. For non-Archimedean places it should
return `-x.valuation(p) * RR(p.norm()).log()`, which would presumably be
more efficient than `RR(p.norm()^-x.valuation(p)).log()`.
Anyway, I'm not going to do that now, so I don't mind too much if this
becomes the ticket for fixing the accuracy of real/complex embeddings.
Still, I would be in favour of having a `logabs()` method at some point
(on a different ticket).
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Ticket URL: <http://trac.sagemath.org/ticket/19288#comment:7>
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