Re: Re : Field inclusion problem

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* Ewan Delanoy [2013-01-24 14:51]:
> > nffactor(B, A) would factor A(X) over the number field Q[b] / (B(b)).
>  > ( a few seconds on such small inputs )
> 
>  I tried that and obtained the following output :
> 
> 
>  ? nffactor(polynomial_called_b,polynomial_called_a)
>  *** at top-level: nffactor(polynomial_ca
>  *** ^--------------------
>  *** nffactor: incorrect polynomial in rnf function.
>  *** Break loop: type 'break' to go back to GP
> 
>  I suppose itâs no use to do a âmy_field=nfinit(polynomial_called_b)â first ? The computation would be prohibitively long.

The problem is variable priorities. The variable of the polynomial
defining the "base field" must have *lower* priority then the variable
of the polynomial to be factored. See ??nffactor

  ? A = x^2+1;
  ? B = y^2+1;
  ? nffactor(A,B)
  ***   at top-level: nffactor(A,B)
  ***                 ^-------------
  *** nffactor: incorrect priority in nffactor: variable y >= x
  ***   Break loop: type 'break' to go back to GP prompt
  ? nffactor(B,A)
  [x + Mod(-y, y^2 + 1) 1]

  [ x + Mod(y, y^2 + 1) 1]


N.B. This is 2.6.*, the error messages in 2.5.* are a little less helpful :-)

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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