#11770: Add ability to detect CM number fields and take complex conjugate of
their
elements
---------------------------------+------------------------------------------
Reporter: robharron | Owner: tba
Type: enhancement | Status: closed
Priority: minor | Milestone: sage-5.4
Component: number fields | Resolution: fixed
Keywords: CM field | Work issues:
Report Upstream: N/A | Reviewers: Francis Clarke
Authors: Robert Harron | Merged in: sage-5.4.beta0
Dependencies: | Stopgaps:
---------------------------------+------------------------------------------
Comment (by fwclarke):
Replying to [comment:19 jdemeyer]:
> My additional patch [attachment:11770_long_time.patch] needs review
I don't think this does the job. The second example
{{{
sage: d = a^253
sage: (d+d.conjugate()).is_real_positive()
}}}
will take just as long if the first one isn't executed. It's only
quicker after the first because conjugation has been cached.
But computation of the conjugation automorphism can be greatly speeded up
by a minor change. What's taking the time is the following step:
{{{
sage: %timeit K.hom([a^-1])
5 loops, best of 3: 29 s per loop
}}}
But checking can be turned off, since we know that this does define an
automorphism. Thus
{{{
sage: %timeit K.hom([a^-1], check=False)
125 loops, best of 3: 3.28 ms per loop
}}}
Several speed-ups of this kind occur in the patch to #10843 (still waiting
a review).
So I conclude that the long-time patch is unnecessary, but that a minor
change should be made in the new line 1926 of the definition of
complex_conjugation.
> (just mention the review in the comments, don't change the status).
I haven't changed the status, but I believe that "needs work" is where it
should be.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11770#comment:23>
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