I did not know that. I tought that by the line: S = P.division_points(n_1), I would get a non-trivial point in that case witouh having to return all the points. Can I just chose a non-trivial random point on the curve or what is the best to choose a point without going on whole of unecessary things?
What I am trying to do is to find elliptic curves over F_p with with point of order 4. Idealy I need E( F_p ) = Z/4Z*Z/(big prime)Z. Best wishes, Adam On Wed, Jun 24, 2009 at 12:49 PM, John Cremona <john.crem...@gmail.com>wrote: > > Here is the problem Adam. You have a prime l which is about 2^165. > You construct random curves over the field GF(l) and count the number > of points n_1 on them. This is possible using Sage's use of an > efficient SEA algorithm. When the number n_1 is prime, you then ask > for all the points of order n_1 on the curve using the division_points > () function. This is crazy! For a start, all the points on the curve > will be returned; that is a list of points far too big to store. But > you will never get there anyway since the division_points() function > creates the division polynomial which has degree (n_1^2-1)/2, i.e. > about 2^330. > > It's hard to make a constructive suggestion without knowing what it is > you are trying to do. If you write that down clearly, I'll try to > help. I found that the abelian_group() function works fine > for curves of this size (which makes me pleased, since I wrote it), > whether or not the group is cyclic (which is > usually is), so it may be that you should first find the generator(s) > of the group and their orders, and work with that. > > John > > On Jun 23, 2:17 pm, adam mohamed <adam.hariv...@googlemail.com> wrote: > > Hi All, > > > > I solve the problem with the memory, thanks to William. But, now when I > > impose some strict conditions so that I have to toss say 100 times in > order > > to hope for some curves to pop up, I am getting different kind of > errors. I > > have attached the code and the error message I got hereby. Maybe my code > is > > too naive that why I am having this problem. > > > > What I don't get is why the code seems to do well when the conditions are > > less restrictive but once I change a little bit, them Sage is not happy! > > Maybe one has to implement Reinier algorithms in order to avoid these > kind > > of problems. Is this doable in Sage now? > > > > Best wishes, > > > > Adam > > > > On Tue, Jun 23, 2009 at 1:14 PM, John Cremona <john.crem...@gmail.com > >wrote: > > > > > > > > > On Jun 22, 7:59 pm, adam mohamed <adam.hariv...@googlemail.com> wrote: > > > > Hi, > > > > > > Thanks for the very quick response. I will try that tomorrow. Now I > > > > understand the problem that we met when running the same code in a > linux > > > > machine. > > > > I am doing this search for cryptographic applications, so I am > dealing > > > with > > > > primes from the size of 170 bit Length. > > > > I would like the 2-sylow of E( F_p) to be Z/4Z and #E( F_p) = 4*L > with > > > > L prime. > > > > > > Reinier Broker did his PhD about EC with prescribed order and we will > > > would > > > > like to find out if his algorithms have been implemented in Sage? > > > > > Hello Adam, > > > > > No, as far as I know Sage has nothing implemented for finding curves > > > with prescribed order or structure. > > > > > John > > > > > > Regards, > > > > > > Adam > > > > > > On Mon, Jun 22, 2009 at 6:31 PM, William Stein <wst...@gmail.com> > wrote: > > > > > > > On Mon, Jun 22, 2009 at 5:35 PM, harivola< > adam.hariv...@googlemail.com > > > > > > > wrote: > > > > > > > > Hi all, > > > > > > > > I am running a small script on a windows xp machine and some > time I > > > > > > am getting this error message: > > > > > > /usr/local/sage/local/bin/sage-sage: line 348: 19954 Killed > > > > > > python "$@" > > > > > > > You're probably running out of memory (=RAM). Try editing the file > > > > > sage_vmx.vmx and increase the amount of RAM that is made available > to > > > > > the vmware machine running Sage. The default amount is very small. > > > > > > > > I don't get the meaning of that. By the way, does someone know an > > > > > > efficient way in Sage to search for EC with prescribed order ( I > need > > > > > > curves over a big prime field with rational points of order 4 and > > > > > > cofactor 4 ). Thanks. > > > > > > > Be way more precise. How big is "big prime field"? Do you want > > > > > #E(F_p) = 4*n with n odd? Do you require that #E(E_p)[2] = 4 too? > > > > > > > William > > > > > > > > Best wishes > > > > > > > -- > > > > > William Stein > > > > > Associate Professor of Mathematics > > > > > University of Washington > > > > >http://wstein.org > > > > > > > > full_output.txt > > 42KViewDownload > > > > test_ell.sage > > 2KViewDownload > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
