Re: [sage-support] Minimum norm of an ideal lattice

Let M denote the generator matrix of the lattice. Suppose M is a 2 by 2 matrix. sage: var('x', domain=ZZ); sage: var('y', domain=ZZ); sage: v=vector((x,y)); sage: f=(M*v).norm();minimize(f,[1,1]) But the output is Warning: Maximum number of iterations has been exceeded Current

Re: [sage-support] Minimum norm of an ideal lattice

BTW, the generator matrix I used for the previous example is [1 2] [3 4] Thanks. Cindy On Wednesday, September 5, 2012 7:31:48 PM UTC+8, David Loeffler wrote: how can I get the minimum norm for the ideal lattice (J,\alpha) using sage? What have you tried so far? David -- You

Re: [sage-support] Minimum norm of an ideal lattice

of this vector in L. What I need is the minimum of this value. Did I get the wrong definition of the minimum of lattice? Best Regards, Xiaolu On Thursday, September 6, 2012 6:50:00 PM UTC+8, David Loeffler wrote: Dear Cindy, Without wishing to cause offence, I think your problem isn't a Sage problem

Re: [sage-support] Minimum norm of an ideal lattice

of this vector in L. What I need is the minimum of this value. Did I get the wrong definition of the minimum of lattice? Best Regards, Cindy On Thursday, September 6, 2012 6:50:00 PM UTC+8, David Loeffler wrote: Dear Cindy, Without wishing to cause offence, I think your problem isn't a Sage problem

Re: [sage-support] Minimum norm of an ideal lattice

Thanks. Cindy On Thursday, September 6, 2012 9:03:47 PM UTC+8, David Loeffler wrote: On 6 September 2012 13:28, Cindy cindy42...@gmail.com javascript: wrote: Hi, David, Thanks for your explanation about the minimize function in sage. I didn't realize it's only

Re: [sage-support] Dual of an ideal

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

Re: [sage-support] Dual of an ideal

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] Generator matrix of ideal lattice

Hi, David, Thanks a lot! It works.^^ Cindy On Wednesday, September 5, 2012 4:30:40 PM UTC+8, David Loeffler wrote: On 5 September 2012 02:56, Cindy cindy42...@gmail.com javascript: wrote: Hi, Let K be a number field and O_k denote its ring of integers. For an ideal, J of O_k

[sage-support] Minimum norm of an ideal lattice

and \alpha, how can I get the minimum norm for the ideal lattice (J,\alpha) using sage? Thanks a lot. 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

Re: [sage-support] Generator matrix of ideal lattice

Hi, David, BTW, do you know how to find the minimum norm of the lattice? I posted a question regarding this in this group. Do you know which function I should use? Thanks. Cindy On Wednesday, September 5, 2012 4:30:40 PM UTC+8, David Loeffler wrote: On 5 September 2012 02:56, Cindy cindy42

Re: [sage-support] Dual of an ideal

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

Re: [sage-support] Dual of an ideal

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

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

[sage-support] Generator matrix of ideal lattice

and \alpha, how can I get the generator matrix for the ideal lattice (J,\alpha) using sage? Thanks a lot. 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

[sage-support] Dual of an ideal

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 sage

Re: [sage-support] Calculate discrimanent of relative number fields

Thanks a lot David! It works ^^ Cindy On Thursday, August 30, 2012 4:39:36 PM UTC+8, David Loeffler wrote: On 29 August 2012 12:54, Cindy cindy42...@gmail.com javascript: wrote: Hi, Given a cyclotomic field Q(zeta_n), where zeta_n is a primitive nth root of unity

[sage-support] Calculate discrimanent of relative number fields

Hi, Given a cyclotomic field Q(zeta_n), where zeta_n is a primitive nth root of unity, with maximal real subfield F, how can I calculate the discriminant of K/F? Thanks. Cindy -- You received this message because you are subscribed to the Google Groups sage-support group. To post

[sage-support] Find the generator matrix and minimum norm of ideal lattice

Hi, Given an ideal I, I want to find the following properties of the ideal lattice (I,b), where b is the trace form. 1. generator matrix 2. minimum norm How can I do this in Sage? Thanks. Cindy -- You received this message because you are subscribed to the Google Groups sage-support group