#10730: simon_two_descent -- reports points as being independent, but they are
not
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Reporter: was | Owner: davidloeffler
Type: defect | Status: closed
Priority: minor | Milestone: sage-duplicate/invalid/wontfix
Component: elliptic curves | Resolution: duplicate
Keywords: | Work_issues:
Upstream: N/A | Reviewer: Robert Miller
Author: | Merged:
Dependencies: |
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Changes (by jdemeyer):
* status: new => closed
* component: number fields => elliptic curves
* milestone: sage-4.7.2 => sage-duplicate/invalid/wontfix
* reviewer: => Robert Miller
* resolution: => duplicate
Old description:
> Check out this
> {{{
> sage: F.<a> = NumberField(x^2-x-1)
> sage: E = EllipticCurve([1,a+1,a,a,0])
> sage: E.simon_two_descent()
> (0, 1, [(-1 : -a + 1 : 1), (-a : 0 : 1)])
> }}}
>
> According to the docs:
> {{{
> Computes lower and upper bounds on the rank of the Mordell-Weil group,
> and a list of independent points.
> }}}
>
> It output a lower bound of 0, an upper bound of 1, and gave *two*
> independent points? Clearly something is wrong. In fact, the points
> output are all torsion and one is a multiple of the other:
> {{{
> sage: E.torsion_subgroup()
> Torsion Subgroup isomorphic to Z/8 associated to the Elliptic Curve
> defined by y^2 + x*y + a*y = x^3 + (a+1)*x^2 + a*x over Number Field in a
> with defining polynomial x^2 - x - 1
> sage: Q == 4*P
> True
> sage: v = E.simon_two_descent()
> sage: P,Q =v[2]
> sage: Q == 4*P
> True
> sage: P.order()
> 8
> sage: Q.order()
> 2
> }}}
>
> So instead of claiming the output points are independent, claim nothing
> about them?
New description:
Check out this
{{{
sage: F.<a> = NumberField(x^2-x-1)
sage: E = EllipticCurve([1,a+1,a,a,0])
sage: E.simon_two_descent()
(0, 1, [(-1 : -a + 1 : 1), (-a : 0 : 1)])
}}}
According to the docs:
{{{
Computes lower and upper bounds on the rank of the Mordell-Weil group, and
a list of independent points.
}}}
It output a lower bound of 0, an upper bound of 1, and gave *two*
independent points? Clearly something is wrong. In fact, the points
output are all torsion and one is a multiple of the other:
{{{
sage: E.torsion_subgroup()
Torsion Subgroup isomorphic to Z/8 associated to the Elliptic Curve
defined by y^2 + x*y + a*y = x^3 + (a+1)*x^2 + a*x over Number Field in a
with defining polynomial x^2 - x - 1
sage: Q == 4*P
True
sage: v = E.simon_two_descent()
sage: P,Q =v[2]
sage: Q == 4*P
True
sage: P.order()
8
sage: Q.order()
2
}}}
So instead of claiming the output points are independent, claim nothing
about them?
This is a duplicate of #5153.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10730#comment:4>
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