#4525: [with patch, needs work] LLL-reduction of elliptic curve bases (with
resulting speed enhancement to integral_points())
----------------------------+-----------------------------------------------
Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: elliptic curve |
----------------------------+-----------------------------------------------
Changes (by was):
* summary: [with patch, needs review] LLL-reduction of elliptic curve
bases (with resulting speed enhancement to
integral_points()) => [with patch, needs work]
LLL-reduction of elliptic curve bases (with
resulting speed enhancement to
integral_points())
Comment:
OK, this looks good, but it introduces a *BUG*:
We have in sage-3.2 released:
{{{
[EMAIL PROTECTED]:~/www/talks$ sage
----------------------------------------------------------------------
| Sage Version 3.2, Release Date: 2008-11-20 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: EllipticCurve('91b1').integral_points()
[(-1 : 3 : 1), (1 : 0 : 1), (3 : 4 : 1)]
}}}
However, after applying these patches, I get:
{{{
EllipticCurve('91b1').integral_points()
Traceback (click to the left for traceback)
...
ValueError: No point with x-coordinate 0 on Elliptic Curve defined by
y^2 + y = x^3 + x^2 - 7*x + 5 over Rational Field
}}}
I found with the following handy script, which anybody who ever works on
the integral points code should always consider running:
{{{
for e in cremona_curves([1..100]):
t = cputime(); i = len(e.integral_points()); t = cputime(t)
t2 = magma.cputime(); j = len(magma(e).IntegralPoints()); t2 =
magma.cputime(t2)
print e.cremona_label(), i, j, t, t2
assert i == j
}}}
Also, the curve 112a2 also gives the same error.
** One weird thing I noticed using the script is that for the elliptic
curve 102b5, magma takes 3.88 seconds to find all the integral points, and
sage takes 0.004
102b5 0 0 0.004 3.88.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:7>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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