#11639: conductor of simple curve over Q(cube root 3) takes forever
-------------------------------+--------------------------------------------
Reporter: was | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
-------------------------------+--------------------------------------------
{{
sage: x=var('x'); K.<a> = NumberField(x^3 - 2);
EllipticCurve([0,a]).conductor()
[[ wait forever! ]]
}}}
The correct answer has norm 322486272, and should be instant:
{{{
sage: magma(E).Conductor()
Ideal
Basis:
[864 0 0]
[ 0 864 0]
[ 0 0 432]
sage: magma(E).Conductor().Norm()
322486272
}}}
Trying with {{{proof.all(False)}}} doesn't help, by the way, so I don't
think it is just some complexity issue... and yet, I just tried control-c
after letting "E.conductor()" sit there for a while, then typed "%debug",
then "u", then saw that two ideals of the integers of the cubic field were
being multiplied. I printed the gens of one ideal and got
{{{
ipdb> u
> /Users/wstein/sage/install/current/local/lib/python2.6/site-
packages/sage/rings/ideal.py(857)__mul__()
856 other = self.ring().ideal(other)
--> 857 return self.ring().ideal([x*y for x in self.gens() for y
in other.gens()])
858
ipdb> print self.gens()
(16384, 8192*a, 8192*a, 4096*a^2, 8192*a, 4096*a^2, ... goes on
redundantly for many pages!)
}}}
So, maybe ideals aren't being properly reduced, which is causing huge
trouble.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11639>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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