Thank you for your answer. Unfortunately did not work for me. But I did the 
following. I copy paste the code from the patch in matrix.pyx and run 
$./sage -b. It seems that the patch is installed!

On Saturday, March 21, 2015 at 6:59:18 PM UTC+2, vdelecroix wrote:
>
> The following worked for me: 
>
> 1. download the patch 
> 2. run 
>
>    $ sage -dev import-patch --local=/tmp/12051_LLL_QQ.patch 
>
> where "/tmp/12051_LLL_QQ.patch" has to be replaced with the name of 
> the file you just downloaded. 
>
> And then, after 
>
>     $ sage -b 
>
> you can do in a Sage console 
>
> sage: m = matrix(QQ, [[1/2,3],[7,2/5]]) 
> sage: m.LLL() 
> [  1/2     3] 
> [ 13/2 -13/5] 
>
> Vincent 
>
> On 21/03/2015, [email protected] <javascript:> <[email protected] 
> <javascript:>> wrote: 
> > Thank you for your answer. The thing is that I have some old sage's code 
> > that uses this patch and seem useless in the recent version of sage. 
> > Your idea is not bad, about adding this function in the source code and 
> > patch sage,  but not easy for me do it. Maybe I try it. 
> > Some "simple" things in sage, sometimes are too complicated for simple 
> > users. 
> > Costas 
> > 
> > 
> > On Saturday, March 21, 2015 at 6:02:39 PM UTC+2, John Cremona wrote: 
> >> 
> >> The patch on that ticket was written in 2011 so there is little hope 
> >> that it will apply to the most recent version of Sage.  Also, it is 
> >> old enough that it predates Sage's current git-based revision system 
> >> so would need to be applied manually anyway. 
> >> 
> >> The patch on that ticket was never reviewed (or ever set to "needs 
> >> review", it seems).  But since all it does is to add one function to 
> >> one class, it should be hard to add the function yourself.  This would 
> >> be a good way into Sage development, if you have not done any before, 
> >> especially since you clearly have some motivation for it! 
> >> 
> >> If you are going to patch a local version of Sage then you will need 
> >> to make your own clone of the full source distribution first -- see 
> >> the developers' manual.  I note that you were trying to use "sudo", 
> >> but note that you should never build or run Sage as root.  Build it in 
> >> your own directory. 
> >> 
> >> John Cremona 
> >> 
> >> On 21 March 2015 at 15:54,  <[email protected] <javascript:>> wrote: 
> >> > I have the most recent version of sage. I want to ask 
> >> > how to add the patch for the ticket 
> >> http://trac.sagemath.org/ticket/12051. 
> >> > I tried $sudo ./sage --dev import-patch --url 
> >> > http://trac.sagemath.org/attachment/ticket/12051/12051_LLL_QQ.patch 
> >> > but it failed to added. 
> >> > I am sure that to previous versions (I don't remember exactly the 
> >> versions!) 
> >> > of sage it worked. 
> >> > Also, why this patch did not applied to the recent versions of sage? 
> >> > It would be nice to have LLL for rational (not integers) matrices. 
> >> > thank you 
> >> > Costas 
> >> > 
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