#11836: gens_reduced() does not handle "large" ideals
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Reporter: mirela | Owner: jdemeyer
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: number fields | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Jeroen Demeyer
Merged: | Dependencies: #11130
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Description changed by jdemeyer:
Old description:
> PARI does not compute the reduced generators of the ideal below (even
> though the class number of `L` is 1, so the ideal is certainly
> principal):
>
> {{{
> sage: R.<x> = QQ['x']
> sage: L.<b3> = NumberField(x^10 - 10*x^8 - 20*x^7 + 165*x^6 - 12*x^5 -
> 760*x^3 + 2220*x^2 + 5280*x + 7744)
> sage: z_x = -96698852571685/2145672615243325696*b3^9 +
> 2472249905907/195061146840302336*b3^8 +
> 916693155514421/2145672615243325696*b3^7 +
> 1348520950997779/2145672615243325696*b3^6 -
> 82344497086595/12191321677518896*b3^5 +
> 2627122040194919/536418153810831424*b3^4 -
> 452199105143745/48765286710075584*b3^3 +
> 4317002771457621/536418153810831424*b3^2 +
> 2050725777454935/67052269226353928*b3 + 3711967683469209/3047830419379724
> sage: P = EllipticCurve(L, '57a1').lift_x(z_x) * 3
> sage: OL = L.OK()
> sage: ideal = L.OK().fractional_ideal(P[0], P[1])
> sage: ideal.gens_reduced(proof=False)[0]
> *** Warning: precision too low for generators, not given.
> ---------------------------------------------------------------------------
> Traceback
> ...
>
> PariError: (25)
>
> }}}
New description:
PARI does not compute the reduced generators of the ideal below (even
though the class number of `L` is 1, so the ideal is certainly principal):
{{{
sage: R.<x> = QQ['x']
sage: L.<b3> = NumberField(x^10 - 10*x^8 - 20*x^7 + 165*x^6 - 12*x^5 -
760*x^3 + 2220*x^2 + 5280*x + 7744)
sage: z_x = -96698852571685/2145672615243325696*b3^9 +
2472249905907/195061146840302336*b3^8 +
916693155514421/2145672615243325696*b3^7 +
1348520950997779/2145672615243325696*b3^6 -
82344497086595/12191321677518896*b3^5 +
2627122040194919/536418153810831424*b3^4 -
452199105143745/48765286710075584*b3^3 +
4317002771457621/536418153810831424*b3^2 +
2050725777454935/67052269226353928*b3 + 3711967683469209/3047830419379724
sage: P = EllipticCurve(L, '57a1').lift_x(z_x) * 3
sage: ideal = L.OK().fractional_ideal(P[0], P[1])
sage: ideal.gens_reduced(proof=False)
*** Warning: precision too low for generators, not given.
---------------------------------------------------------------------------
Traceback
...
PariError: (25)
}}}
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11836#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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