#8344: Factor constant polynomials over QQbar
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Reporter: boothby | Owner: AlexGhitza
Type: defect | Status: needs_info
Priority: critical | Milestone: sage-4.3.4
Component: basic arithmetic | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
Very sorry, it was a cut-and-paste error. The lines defining f1 and f2
should read
{{{
sage: f1 = Factorization([(x-r,e) for r,e in f.roots() if
r.imag().is_zero()],unit=f.leading_coefficient())
sage: f2 = Factorization([(x^2-(r+r.conjugate()).real()*x+r.norm(),e) for
r,e in fr if r.imag()>0])
}}}
(there was a typo in the second one too).
The trick of testing r.imag()>0 was just a way of picking exactly one
conjugate of each pair of non-real conjugate roots. I think that is quite
cheap. But a better way would be, for each element of AA or QQbar to have
a function returning its minpoly over RR (currently the minpoly() function
returns its minpoly over QQ). And we have the norm of an element of QQbar
which is the product of it with its CC/RR-conjugate (and not its norm down
to QQ), but we do not have a trace: another function I would like to add!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8344#comment:14>
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