#10076: Bug in is_divisible_by on elliptic curves
-------------------------------+--------------------------------------------
Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.6
Component: elliptic curves | Keywords: torsion point division
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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James Parson writes on sage-support:
{{{
I was playing with some elliptic-curves calculations in Sage 4.5.3,
and I came across (or, rather, cooked up) the following, which puzzled
me:
sage: K = QuadraticField(8,'a')
sage: E = EllipticCurve([K(0),0,0,-1,0])
sage: P = E([-1,0])
sage: P.division_points(2)
[]
sage: P.is_divisible_by(2)
True
Is this the intended behavior? From the source code, it looks as if
P.is_divisible_by(2) just checks whether the x-coordinate of the
system of equations for dividing P by 2 can be solved over K. The
division_points method does the full check of whether the system has a
solution over K. Shouldn't is_divisible_by do the same thing?
}}}
to which John Cremona replied
{{{
It is a bug -- well spotted. In this case the x-coordinates of the
points Q such that 2*Q=P are the roots of x^2 + 2*x - 1 which are a/
2-1 and -a/2-1, but the y-coordinates are not in the field.
}}}
Patch coming up.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10076>
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