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 > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/notebook/sage_notebook/worksheets/admin/1/code/6.py", line 9, in
<module>
A.append(elliptic_curves_search(_sage_const_100 ))
File "/home/notebook/sage_notebook/worksheets/admin/1/code/5.py", line 27, in
elliptic_curves_search
S = P.division_points(n_1)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_point.py",
line 820, in division_points
g = E.division_polynomial(m)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1835, in division_polynomial
f = self.division_polynomial_0(m,x)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1646, in division_polynomial_0
g_mplus3 = self.division_polynomial_0(m+3, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1655, in division_polynomial_0
g_mplus2 = self.division_polynomial_0(m+2, x, cache)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1661, in division_polynomial_0
answer = B6_sqr * g_mplus2 * g_m**3 - \
File "polynomial_element.pyx", line 1328, in
sage.rings.polynomial.polynomial_element.Polynomial.__pow__
(sage/rings/polynomial/polynomial_element.c:12454)
File "element.pyx", line 2842, in sage.structure.element.generic_power
(sage/structure/element.c:20872)
File "element.pyx", line 2894, in sage.structure.element.generic_power_c
(sage/structure/element.c:21559)
File "element.pyx", line 1152, in sage.structure.element.RingElement.__mul__
(sage/structure/element.c:9796)
File "polynomial_modn_dense_ntl.pyx", line 213, in
sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n._mul_
(sage/rings/polynomial/polynomial_modn_dense_ntl.cpp:5624)
RuntimeError: Polynomial too big for FFT
test_ell.sage
Description: Binary data
