#18942: Weird bug in roots of a polynomial in relative number field extension
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Reporter: robharron | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: number | Keywords: Relative number field, roots
fields | Authors:
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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I have no idea what is going on.
{{{
sage: F.<omega> = NumberField(x^2+x+1)
sage: xx = polygen(F)
sage: ABs = []
sage: ps = [p for p, _ in F(7).factor()]
sage: for mu in ps:
K = F.extension(xx^3 - mu, 'alpha')
print K.defining_polynomial().roots(K)
sage: for mu in ps:
K = F.extension(xx^3 - mu, 'alpha')
print K.defining_polynomial().roots(K)
[(alpha, 1), ((-omega - 1)*alpha, 1), (omega*alpha, 1)]
[(alpha, 1), (omega*alpha, 1), ((-omega - 1)*alpha, 1)]
[]
[(alpha, 1), (omega*alpha, 1), ((-omega - 1)*alpha, 1)]
}}}
So, that's weird. But it gets worse! First do this
{{{
sage: fbar = xx^3 - ps[0]
sage: Kbar = F.extension(fbar, 'alpha')
sage: fbar.roots(Kbar)
[]
}}}
Okay, but then do fbar.roots?? to see the source code, then press 'q' to
exit that, then
{{{
sage: fbar.roots(Kbar)
[(alpha, 1), ((-omega - 1)*alpha, 1), (omega*alpha, 1)]
}}}
Huh?
(I'm doing this is sage 6.7 on the cloud.)
--
Ticket URL: <http://trac.sagemath.org/ticket/18942>
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