On 08/17/10 09:26 AM, John Cremona wrote:
At last, a contributiuon to this thread which actually addresses my
original question!
In contrast, it seems sympow is not used by many people. The fact there are
no bug reports of it not working on the public servers shows how little it
is used. (If someone actually tried to run many of the examples, they will
find they don't work).
There is 1 "example" -- the modular degree function -- that is 1000
times more important than the rest. Here's me *using* sympow:
sage: E = EllipticCurve('5077a'); E
Elliptic Curve defined by y^2 + y = x^3 - 7*x + 6 over Rational Field
sage: E.modular_degree()
1984
This is what I thought. I could provide modular degree from eclib but
it would be *vastly* slower. I myself stopped using my own modular
degree function (despite publishing a paper describing the algorithm,
which I was rather proud of at the time) and started to use sympow
(which was then called ec) for the elliptic curve database, since my
own version took much too long. In fact it is fair to say that for
any elliptic curve not in the database (whose modular degrees are
known and in the database), my implementation would not finish in
reasonable time, which makes my "offer" worth little.
John,
I think if you are able to compute this with your package, it would be useful
addition to Sage. Having two independent algorithms, implemented by two
different people, could be useful, despite one being much slower than the other.
I think it's particularly so in this case, given the concerns some people have
about the code quality.
It would be a student project to reimplement Mark W's algorithm (Here:
http://www.emis.ams.org/journals/EM/expmath/volumes/11/11.4/pp487_502.pdf)
Yes, it would be useful. But even if someone did that and got it working fast,
having the choice of a second algorithms is useful IMHO.
John
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