Hi, David,

Could you please explain a little bit about the code?

For the example you use, it seems I is an ideal above 17, what does [0] 
mean?

In the end do we get a basis of the dual of I? Why do we need to put 
I.basis() in the bracket of trace_dual_basis?

Thanks a lot.

Cindy

On Wednesday, September 5, 2012 4:21:22 PM UTC+8, David Loeffler wrote:
>
> On 5 September 2012 02:41, Cindy <cindy42...@gmail.com <javascript:>> 
> wrote: 
> > Hi, David, 
> > 
> > Yes, that's what I mean. Can I find it using sage? 
> > 
> > Thanks. 
> > 
> > Cindy 
>
> sage: K.<z> = NumberField(x^3 - x + 17) 
> sage: I = K.primes_above(17)[0] 
> sage: K.trace_dual_basis(I.basis()) 
> [4/132583*z^2 + 6/7799*z + 2597/132583, -153/7799*z^2 - 2/7799*z + 
> 102/7799, -6/7799*z^2 - 153/7799*z + 4/7799] 
>
> hth, David 
>

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