Here the references which I know:
1. Elkies ANTS paper:
\bibitem{Elkies}
N. D. Elkies.
\newblock Rational points near curves and small nonzero $|x^3 - y^2|$
via lattice reduction.
\newblock In ANTS IV proceedings (W.~Bosma, ed.), LNCS
{\bf1838}. Springer-Verlag,
2000, pages 33--63.
2.
John,
Do you have a reference for p-adic Elkies? I would be interested in looking
at that, and possibly implementing it in as much generality as possible in
sage.
Ben
On Jan 16, 2008 3:15 AM, John Cremona <[EMAIL PROTECTED]> wrote:
>
> I assumed that Enrique wanted *all* integral points (in som
Hello,
Sorry for my late reply.
At this moment I am teaching Number Theory at the Mathematics degree and
a ("easy") project for students is to read a webpage
(http://www.alpertron.com.ar/METODOS.HTM - Sorry, it is only in
spanish) where it appears an algorithm to compute integer solutions o
I assumed that Enrique wanted *all* integral points (in some sense
when there are infinitely many).
For listing rational (or integral) points up to some height bound
there are methods which are vastly more efficient than the one being
proposed here, which does not even use a quadratic sieve. Opt
Enrique,
This can easily be done at the moment, assuming that you want to count
integral points up to a certain height N. If you are looking for all of the
points of something you know has only finitely many, I am not so sure.
I hope the following ramble helps.
sage: A,B,C,D,E,F=[1,0,0,0,0,-1] #
Finding integral points on an affine curve is not the same as finding
rational points on the projective model and then scaling!
Quick answer to William's question is "no", since my code always finds
rational points (and their parametrization). The same sort of thing
that Simon's gp program does
On 15-Jan-08, at 8:28 AM, William Stein wrote:
>
> On Jan 15, 2008 7:39 AM, Enrique Gonzalez Jimenez
> <[EMAIL PROTECTED]> wrote:
>>
>> Hi,
>>
>> Let C be a plane conic given by an equation of the form
>> C:Ax^2+Bxy+Cy^2+Dx+Ey+F=0 where A,B,C,D,E,F in ZZ.
>>
>> Is there a package or function
On Jan 15, 2008 7:39 AM, Enrique Gonzalez Jimenez
<[EMAIL PROTECTED]> wrote:
>
> Hi,
>
> Let C be a plane conic given by an equation of the form
> C:Ax^2+Bxy+Cy^2+Dx+Ey+F=0 where A,B,C,D,E,F in ZZ.
>
> Is there a package or function in SAGE that compute C(ZZ)?
John Cremona -- is there code in
