On Feb 6, 6:49 am, Rob Beezer <goo...@beezer.cotse.net> wrote:
> William, Volker,
>
> Thanks for the replies. Kernels for the rationals go to IML and for
> number fields they go to PARI. Does either of those rely on linbox?
>
> Here's the requested output - three different number fields are
> evident. Thanks for the help.
>
> Rob
>
The defining polynomials of the number fields might be different, but
the numberfields themselves are actually isomorphic. The squarefree
part of the discriminant of the polynomial is 3 in all cases so the
numberfield obtained is just adjoining the square root of 3. The code
below shows that the three awnsers generated by the code are at least
up to isomorphims the same:
K.<x>=QQ[]
for a,f in [(-x-1,x^2 + 4*x + 1),(1/2*x+1/2,x^2 - 2*x - 11),
(-1/2*x-1/2,x^2 + 6*x - 3)]:
f.discriminant().squarefree_part()
K.<b>=QQ.extension(f)
K(a).minpoly()
3
x^2 - 2*x - 2
3
x^2 - 2*x - 2
3
x^2 - 2*x - 2
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