Re: pari?
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William Stein
Nov 4, 2007, 5:03:58 PM11/4/07
to Robert Miller, uw-...@groups.google.com
On 11/4/07, Robert Miller <rlmil...@gmail.com> wrote:
> William,
>
> I must be misunderstanding something. In sage:
> sage: K.<a> = NumberField(x^2 + 23)
> sage: K.ring_of_integers().basis()
> [1/2*a + 1/2, a]
>
> In pari:
> sage: pari('w = quadgen(-23)')
> w
> sage: pari('w.zk')
> [1, x]
>
> But the documentation says that w.zk should be a ZZ-basis for the
> maximal order \O_K. Is this a pari bug, or am I misunderstanding 'x'?
> William,
>
> I must be misunderstanding something. In sage:
> sage: K.<a> = NumberField(x^2 + 23)
> sage: K.ring_of_integers().basis()
> [1/2*a + 1/2, a]
>
> In pari:
> sage: pari('w = quadgen(-23)')
> w
> sage: pari('w.zk')
> [1, x]
>
> But the documentation says that w.zk should be a ZZ-basis for the
> maximal order \O_K. Is this a pari bug, or am I misunderstanding 'x'?
You are making false assumptions:
? w = quadgen(-23)
mi%1 = w
? minpoly(w)
%2 = x^2 - x + 6
? w^2
%3 = -6 + w
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