I get this also with PARI-2.7.1:

sage: test1()
ERROR (after 708 iterations):
 polynomial   : 2*T^8 + 2*T^7 + 2*T^5 + T^3 + 2*T^2 + 2
 factorization: (2) * (T + 2*z^4 + z^3 + 2*z^2...
 product      : 2*T^8 + (2*z^6 + z^4 + 2*z^2 +...
calling once more p.factor().prod() gives back the polynomial!!

sage: %pari
/home/release/Sage/local/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2126:
 
DeprecationWarning: Use %gp instead of %pari.
See http://trac.sagemath.org/6288 for details.
  result = fn(*args,**kwargs)

  --> Switching to PARI/GP interpreter <--

pari: version()
[2, 7, 1]



On Wednesday, August 27, 2014 11:29:00 AM UTC+1, Jeroen Demeyer wrote:
>
> On 2014-08-27 00:25, Vincent Delecroix wrote: 
> > So I suspect something is wrong in between Sage and pari about 
> > conversions between finite fields. 
> Did you try with #15767? 
>
>

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