#11836: PARI bug in gens_reduced()
-----------------------------------+----------------------------------------
Reporter: mirela | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: commutative algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
-----------------------------------+----------------------------------------
Description changed by jdemeyer:
Old description:
> Even with `proof.number_field(False)` PARI cannot compute the reduced
> generators of the ideal below.
>
> {{{
> sage: E = EllipticCurve('57a1')
> 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: E2 = E.change_ring(L)
> sage: z = E2.lift_x(z_x)
> sage: z3=3*z
> sage: OL = L.OK()
> sage: proof.number_field(False)
> sage: gcd3 = OL.fractional_ideal(z3[0], z3[1]).gens_reduced()[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: 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)
}}}
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11836#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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