Quite apart from any problems there may be with the sympow
implementation, there is another bug here: for curves in the
database, the modular degree is known from the database, as you can
see here:
sage: E = EllipticCurve('11a1')
sage: E._EllipticCurve_rational_field__modular_degree
1
But for some reason the modular_degree function does not have an
option to use the database value (at all, not just not being the
default), and that should be fixed. The documentation does say that
the value is taken from the database when you have the optional large
database installed, so that is a workaround at least (as long as your
curve is in the database).
John
On Oct 20, 1:33 am, "Dr. David Kirkby" <david.kir...@onetel.net>
wrote:
> On 10/20/10 12:07 AM, Justin C. Walker wrote:
>
>
>
>
>
>
>
>
>
>
>
> > On Oct 17, 2010, at 17:50 , gagan wrote:
>
> >> sage: E=EllipticCurve('11a1');
> >> sage: E.modular_degree();
> >> /Applications/sage/local/bin/sympow: line 3: 9922 Segmentation
> >> fault ./sympow $*
>
> > I can't reproduce this problem (Mac OS X, 10.6.4, Dual Quad Xeon) using
> > 4.4, 4.5.2, 4.5.3, or 4.6.a3.
>
> > Justin
>
> > --
> > Justin C. Walker, Curmudgeon at Large
> > Director
> > Institute for the Enhancement of the Director's income
>
> Same here - I can't reproduce it (OpenSolaris on Xeon processor).
>
> Based on an inspection of the source code for SYMPOW, it is the worst I've
> seen
> in Sage. In fact, it's the worst code I have ever seen. So I personally would
> not be surprised if there are bugs in it.
>
> That said, both John and William use the code for computing the modular degree
> of elliptic curves.
>
> There is a trac ticket open for implementing the Watkins-Delaunay's algorithm
> for computing modular degrees in Sage
>
> http://trac.sagemath.org/sage_trac/ticket/9758
>
> If there is a bug in the code, good luck finding it, as the code is almost
> obfuscated.
>
> Dave
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