id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
18942 Weird bug in roots of a polynomial in relative number field extension robharron "I have no idea what is going on.
{{{
sage: F. = 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.)" defect closed major sage-7.3 number fields fixed Relative number field, roots misjafasteinmetz Kiran Kedlaya Peter Bruin N/A 4c52f08b74a2883ce23ba82a5ef8bda4b37e5f04