Max Alekseyev on Wed, 01 May 2013 17:18:45 +0200


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factoring polynomials modulo non-prime


The first result below is non-sense.
The second one seems to be the way how this situation should be
handled if PARI cannot factor a given polynomial.
Is this a bug?
Regards,
Max

? factor( (x^2 - 6*x + 1)*Mod(1,32) )
%1 =
[              Mod(1, 32)*x 1]

[Mod(1, 32)*x + Mod(26, 32) 1]


? factor( (x^2 - 6*x + 1)*Mod(1,64) )
  ***   at top-level: factor((x^2-6*x+1)*M
  ***                 ^--------------------
  *** factor: not a prime number in Fl_sqrt [modulus]: 64.
  ***   Break loop: type 'break' to go back to GP
break>