[with patch, positive review] bug in integral_points when rank is large

[was]

I don't know if this would ever finish, but it probably shouldn't stop with the following error! (this is in sage-4.0.2 on sage.math):

wstein@sage:~/build/sage-4.0.2$ ./sage
----------------------------------------------------------------------
| Sage Version 4.0.2, Release Date: 2009-06-18                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: D=6611719866; E = EllipticCurve([0,0,0,-D^2,0])
sage: time E.integral_points()
---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)

/scratch/wstein/sage/temp/sage.math.washington.edu/21323/_scratch_wstein_sage_init_sage_0.py in <module>()

/scratch/wstein/build/sage-4.0.2/local/lib/python2.5/site-packages/IPython/iplib.pyc in ipmagic(self, arg_s)
    951         else:
    952             magic_args = self.var_expand(magic_args,1)
--> 953             return fn(magic_args)
    954 
    955     def ipalias(self,arg_s):

/scratch/wstein/build/sage-4.0.2/local/lib/python2.5/site-packages/IPython/Magic.pyc in magic_time(self, parameter_s)
   1905         if mode=='eval':
   1906             st = clk()
-> 1907             out = eval(code,glob)
   1908             end = clk()
   1909         else:

/scratch/wstein/sage/temp/sage.math.washington.edu/21323/_scratch_wstein_sage_init_sage_0.py in <module>()

/scratch/wstein/build/sage-4.0.2/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_rational_field.pyc in integral_points(self, mw_base, both_signs, verbose)
   5801         if disc > 0:
   5802             ##Points in egg have X(P) between e1 and e2 [X(P)=x(P)+b2/12]:
-> 5803             x_int_points = self.integral_x_coords_in_interval((e1-b2_12).ceil(), (e2-b2_12).floor()+1)
   5804             if verbose:
   5805                 print 'x-coords of points on compact component with ',(e1-b2_12).ceil(),'<=x<=',(e2-b2_12).floor()

/scratch/wstein/build/sage-4.0.2/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_rational_field.pyc in integral_x_coords_in_interval(self, xmin, xmax)
   5466         `x`-coordinates of points on this curve.
   5467         """
-> 5468         return set([x for x  in range(xmin,xmax) if self.is_x_coord(x)])
   5469 
   5470     def integral_points(self, mw_base='auto', both_signs=False, verbose=False):

OverflowError: range() result has too many items

It might be better to use xrange, or say that the rank is too big, so the computation would never finish or something meaningful.

On 32-bit it fails in the same place but with a different error:

...
TypeError: range() integer start argument expected, got sage.rings.integer.Integer.

[cremona]

It should be pretty easy since the rank and gens are found very quickly. The failure is simply that range() is used to loop over the integers between -D and 0 (to find the integral points on the egg) and D is too big.

[cremona]

Applies to 4.0.2

[cremona]

Patch fixes the problem. I wrote a longer comment but it was lost when I added the patch and I'm not going to type it again!

[was]

Looks good to me. Thanks!

[mvngu]

When using Mercurial queue, one has to be careful about the commit message. I would manually edit the commit message of a patch before uploading it to the trac server. A number of folks who use Mercurial queue upload patches that have nonsensical commit messages.

[cremona]

Replying to mvngu:

When using Mercurial queue, one has to be careful about the commit message. I would manually edit the commit message of a patch before uploading it to the trac server. A number of folks who use Mercurial queue upload patches that have nonsensical commit messages.

Very sorry, I am one of these culprits. I'll try to remember!