On 7 October 2013 08:15, Jori Mantysalo <jori.mantys...@uta.fi> wrote:
> On Fri, 4 Oct 2013, Marco Streng wrote:
>
>> Just take the factorization over QQ, then for each factor, make it a
>> primitive integral polynomial, i.e., multiply by the lcm of the
>> denominators of the coefficients and divide by the gcd of the numerators
>> of
>> the coefficients. Then you have a factorization into irreducible integral
>> polynomials times some integer, factor that integer and you have the
>> complete factorization over ZZ.
>
>
> Isn't that what Sage already does? I mean
>
> R.<x> = QQ[];   print (4*x^2-1).factor()
> R.<x,y> = QQ[]; print (4*x^2-1).factor()
>
> prints
>
>
> (4) * (x - 1/2) * (x + 1/2)
> (2*x - 1) * (2*x + 1)

And also:

sage: R.<x> = ZZ[];   print (4*x^2-1).factor()
(2*x - 1) * (2*x + 1)
sage: R.<x,y> = ZZ[]; print (4*x^2-1).factor()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)

John

>
>
> --
> Jori Mäntysalo
>
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