#20749: Use PARI nfeltup() for inclusion of base field into relative number
field
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: number fields | Resolution:
Keywords: relative number | Merged in:
field pari | Reviewers: Stephan Ehlen
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 9f1d90be8d3f05b6d5de8ee75e36e6d17ad52095
u/pbruin/20749-pari_nfeltup | Stopgaps:
Dependencies: |
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Comment (by pbruin):
Replying to [comment:8 ehlen]:
> Replying to [comment:7 pbruin]:
> > See #20759; we can postpone the call to `_nf_nfzk`, but we should do
it at the latest when first mapping an element of the base field into the
relative field, since there is no way to predict how often this is going
to be done.
>
> OK, #20759 is a good idea and I really think that your changes are
great. However, the time spend in {{{nf_nfzk}}} is really a lot of time
when the degree of the extension increases (and maybe it depends on the
absolute degree in fact?).
Hmm, I agree that this is a lot of time. What `_nf_nfzk` does is
computing the images of a '''Q'''-basis of the base field ''K'' under the
inclusion map into the relative field (so mapping any element is reduced
to linear algebra). This means that `_nf_nfzk` should roughly perform
[''K'':'''Q'''] "slow" applications of this inclusion map; it is currently
much more. I am now trying to profile the computation directly in PARI.
--
Ticket URL: <http://trac.sagemath.org/ticket/20749#comment:10>
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