Re: [sage-support] Dual of an ideal

2012-09-05 Thread David Loeffler
On 5 September 2012 02:41, Cindy cindy425192...@gmail.com 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,

Re: [sage-support] Dual of an ideal

2012-09-05 Thread Cindy
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

Re: [sage-support] Dual of an ideal

2012-09-05 Thread David Loeffler
On 5 September 2012 09:34, Cindy cindy425192...@gmail.com 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?

Re: [sage-support] Dual of an ideal

2012-09-05 Thread Cindy
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 cindy42...@gmail.com javascript: wrote:

Re: [sage-support] Dual of an ideal

2012-09-04 Thread David Loeffler
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 cindy425192...@gmail.com wrote: Hi, How can I calculate the dual of an ideal using sage?

Re: [sage-support] Dual of an ideal

2012-09-04 Thread vijay sharma
Cindy, Could you elaborate little more, what is precisely you need. Regards, Vijay On Tue, Sep 4, 2012 at 12:42 PM, David Loeffler d.a.loeff...@warwick.ac.ukwrote: 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

Re: [sage-support] Dual of an ideal

2012-09-04 Thread Cindy
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

Re: [sage-support] Dual of an ideal

2012-09-04 Thread Cindy
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 elaborate

Re: [sage-support] Dual of an ideal

2012-09-04 Thread Cindy
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

[sage-support] Dual of an ideal

2012-09-03 Thread Cindy
Hi, How can I calculate the dual of an ideal using sage? Thanks. Cindy -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to