Re: New experimental GP interface for elliptic curves over finite fields

[John Cremona <john.cremona@gmail.com>]

On 3 September 2012 22:42, Bill Allombert
<Bill.Allombert@math.u-bordeaux1.fr> wrote:
> On Thu, Jul 26, 2012 at 08:33:37PM +0200, Bill Allombert wrote:
>> On Thu, Jul 12, 2012 at 07:47:37PM +0200, Bill Allombert wrote:
>> > On Thu, Jun 07, 2012 at 12:16:11PM +0200, Bill Allombert wrote:
>> > > Dear PARI developers,
>> > >
>> > > I have added a new experimental interface for elliptic curves over finite
>> > > fields.
>> > > A new function ellffinit is provided to create curves over finite fields:
>> > >
>> > > Create a curves over F_7:
>> > > ? E=ellffinit([1,3],7);
>> > >
>> > > Create a curves over F_101^3:
>> > > ? a=ffgen(ffinit(101,3),'a);
>> > > ? E=ellffinit([1,a^3],a);
>> > >
>> > > (for technical reasons, the characteristic must be >3. This will be fixed eventually.)
>> >
>> > I have just added support for ordinary curves over finite field of characteristic 2.
>>
>> I have added support for supersingular curves over finite field of characteristic 2,
>> and corrected a lot of bugs.
>
> I have reimplemented the support for ordinary curves over finite field of characteristic 2
> to use Harley algorithm. This is much faster now.
>
> ? a=ffgen(ffinit(2,1024),'a);ellffinit([1,0,0,0,a],a,1);
> ? ##
>   ***   last result computed in 11,482 ms.
>
> (I like the ellffinit interface less and less. Indeed, why wasting time computing
> the group structure if you are looking for curves of prime order ?)

Of course.  When I first wrote the ellzpinit from which I suspect your
ellffinit has evolved, I did want the group structure, and I also
found that in most cases one obtains the group structure along the way
to getting the group order (using the BSGS method, which I was).

I would expect that users would not expect a constructor such as
ellffinit to do any non-trivial work, either group order (except when
the field is very small) or structure (ditto).  They mayjust want to e
playing around with addition of points, say.  In the same way that one
should be allowed to construct a number field without automatically
computing class group & units.

John

>
> Cheers,
> Bill.
>