#5178: [with patch; needs review] change LLL_gram to work with Gram matrices 
with
not-necessarily integer entries
----------------------------+-----------------------------------------------
 Reporter:  was             |        Owner:  was     
     Type:  enhancement     |       Status:  new     
 Priority:  major           |    Milestone:  sage-3.3
Component:  linear algebra  |   Resolution:          
 Keywords:                  |  
----------------------------+-----------------------------------------------
Comment (by was):

 Gonzalo Tornaria sent this review in email to me:
 {{{
 Looks good to me.

 However, it seems pari is hanging when using lllgram() on some
 matrices with rational or integer entries; maybe indefinite or
 semidefinite matrices are the issue.
 Moreover, sage hangs badly on this...

 E.g.

 sage: pari("[1,1;1,1/2]").qflllgram()

 (it also hangs when running equivalent command from gp, Ctrl-C stops
 gp but not sage).
 [equivalent command = qflllgram([1,1,1,1/2])

 However, using 0.5 instead of 1/2 works ok.

 Seems a bug in pari, but it was not exposed in sage's LLL_gram() before.

 Gonzalo
 }}}

 He does point out that bad things can happen, but that the bugs are in
 PARI, not the new code attached to this patch.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5178#comment:1>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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