Hi, David,
Thanks a lot. I tried trace_dual_basis? to find out the meaning. I didn't
realize I should use K.trace_dual_basis?
Thanks. :)
Cindy
On Wednesday, September 5, 2012 5:15:19 PM UTC+8, David Loeffler wrote:
>
> On 5 September 2012 09:34, Cindy >
> wrote:
> > Hi, David,
> >
> > Coul
On 5 September 2012 09:34, Cindy wrote:
> Hi, David,
>
> Could you please explain a little bit about the code?
Sure, but you should make a little effort to play with it yourself for
a bit first.
> For the example you use, it seems I is an ideal above 17, what does [0]
> mean?
The command K.prim
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,
On 5 September 2012 02:41, Cindy wrote:
> Hi, David,
>
> Yes, that's what I mean. Can I find it using sage?
>
> Thanks.
>
> Cindy
sage: K. = 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
Hi,
BTW, the ideals I am dealing with are ideals of the ring of integers of a
number field.
Cindy
On Tuesday, September 4, 2012 3:12:25 PM UTC+8, David Loeffler wrote:
>
> What exactly do you mean by the dual of an ideal? Do you mean dual
> with respect to the trace pairing, so the dual of the
Hi, Vijay,
Let K be a number field and O_k be its ring of integers. Given an ideal J
of O_k, I want to find the dual of J, which is defined as the O_k-module:
J^*={x\in K| Tr(xJ)\subset Z}.
Thanks.
Cindy
On Tuesday, September 4, 2012 3:20:35 PM UTC+8, Vj wrote:
>
> Cindy,
>
> Could you elabor
Hi, David,
Yes, that's what I mean. Can I find it using sage?
Thanks.
Cindy
On Tuesday, September 4, 2012 3:12:25 PM UTC+8, David Loeffler wrote:
>
> What exactly do you mean by the dual of an ideal? Do you mean dual
> with respect to the trace pairing, so the dual of the ideal (1) is the
> i
Cindy,
Could you elaborate little more, what is precisely you need.
Regards,
Vijay
On Tue, Sep 4, 2012 at 12:42 PM, David Loeffler
wrote:
> What exactly do you mean by the dual of an ideal? Do you mean dual
> with respect to the trace pairing, so the dual of the ideal (1) is the
> inverse diffe
What exactly do you mean by the dual of an ideal? Do you mean dual
with respect to the trace pairing, so the dual of the ideal (1) is the
inverse different?
David
On 4 September 2012 04:15, Cindy wrote:
> Hi,
>
> How can I calculate the dual of an ideal using sage?
>
> Thanks.
>
> Cindy
>
> --
>
Hi,
How can I calculate the dual of an ideal using sage?
Thanks.
Cindy
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