John Cremona on Tue, 04 Sep 2012 10:17:19 +0200 |
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Re: New experimental GP interface for elliptic curves over finite fields |
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. >