#4249: [with patch] Inconsistency in number field integral bases
---------------------------+------------------------------------------------
 Reporter:  cremona        |        Owner:  was       
     Type:  defect         |       Status:  new       
 Priority:  major          |    Milestone:  sage-3.2.1
Component:  number theory  |   Resolution:            
 Keywords:  number fields  |  
---------------------------+------------------------------------------------
Comment (by cremona):

 I applied my patch to 3.2.alpha3 on two machines, a 32-bit Suse linux and
 a 64-bit ubuntu.
 On both machines two files failed doctests:

    1.  sage -t  devel/sage-intpts/sage/rings/number_field/number_field.py
    2.  sage -t  devel/sage-
 intpts/sage/rings/number_field/totallyreal_rel.py

 In totallrel_rel.py we get this:
 {{{
 sage -t  devel/sage-
 
intpts/sage/rings/number_field/totallyreal_rel.py**********************************************************************
 File "/home/jec/sage-3.2.alpha3/tmp/totallyreal_rel.py", line 658:
     sage: [ f[0] for f in ls ]
 Expected:
     [725, 1125, 1600, 2000, 2225, 2525, 3600, 4225, 4400, 4525, 5125,
 5225, 5725, 6125, 7225, 7600, 7625, 8000, 8525, 8725, 9225]
 Got:
     [725, 1125, 1600, 2000, 2225, 2525, 3600, 4225, 4400, 4525, 5125,
 5225, 5725, 6125, 7600, 7625, 8000, 8525, 8725, 9225]
 **********************************************************************
 File "/home/jec/sage-3.2.alpha3/tmp/totallyreal_rel.py", line 661:
     sage: [NumberField(ZZx(x[1]), 't').is_galois() for x in ls]
 Expected:
     [False, True, True, True, False, False, True, True, False, False,
 False, False, False, True, True, False, False, True, False, False, False]
 Got:
     [False, True, True, True, False, False, True, True, False, False,
 False, False, False, True, False, False, True, False, False, False]
 **********************************************************************
 }}}
 which looks like what I got before.  In number_field.py we get this:
 {{{
 sage -t  local/sage-3.2.alpha3/devel/sage-
 
intbasis/sage/rings/number_field//number_field.py**********************************************************************
 File "/local/jec/sage-3.2.alpha3/tmp/number_field.py", line 2742:
     sage: F.reduced_gram_matrix(prec=128)
 Expected:
     [   4.0000000000000000000000000000000000000
 0.00000000000000000000000000000000000000
 1.9999999999999999999999999999999999037
 -1.0684680000000000000000000000000000000e6]
     [  0.00000000000000000000000000000000000000
 46721.539331563218381658483353092335550
 11488.910026551724275122749703614966768
 -1.1228558200864828963821803781091898982e7]
     [   1.9999999999999999999999999999999999037
 11488.910026551724275122749703614966768
 5.5658915310500611768713076521847709187e8
 8.0619179090987317435751641503958312826e9]
     [-1.0684680000000000000000000000000000000e6
 -1.1228558200864828963821803781091898982e7
 8.0619179090987317435751641503958312826e9
 5.8711879006497804783677635022079228656e12]
 Got:
     [   4.0000000000000000000000000000000000000
 0.00000000000000000000000000000000000000
 -2.1369320000000000000000000000000000000e6
 -3.3122478000000000000000000000000000000e7]
     [  0.00000000000000000000000000000000000000
 46721.539331563218381658483353092335550
 -2.2467769057394530109094755223395819322e7
 -3.4807276041138450473611629088647496430e8]
     [-2.1369320000000000000000000000000000000e6
 -2.2467769057394530109094755223395819322e7
 7.0704243186034907491782135494859351061e12
 1.1256636615786237006027526953641297995e14]
     [-3.3122478000000000000000000000000000000e7
 -3.4807276041138450473611629088647496430e8
 1.1256636615786237006027526953641297995e14
 1.7923838231014970520503146603069479547e15]

 }}}
 which is new.  I find it slightly encouraging that my 32- and 64-bit tests
 both give exactly the same above (as each other).  I guess that this
 second discrepancy will be fixed by just changing the Expected doctest
 output, but the first one really is a bug since a field which should be
 returned is not.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4249#comment:14>
Sage <http://sagemath.org/>
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