[sage-support] Re: Notebook evaluate fails return: OSX 10.6.8

2012-09-04 Thread mazkime
I had the same problem and deleting the 'sage_notebook.sagenb' directory from '~/.sage/' resolved it. Thanks for the tip. -- 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

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

[sage-support] see field extensions as a vector space.

2012-09-04 Thread sha2nk
k=GF(2^11); K=GF(2^33) How to see K as a vector space over filed k ? How to form its basis ? How to construct tower of field extensions ? -- 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] Re: Notebook evaluate fails return: OSX 10.6.8

2012-09-04 Thread kcrisman
On Tuesday, September 4, 2012 2:52:29 AM UTC-4, mazkime wrote: I had the same problem and deleting the 'sage_notebook.sagenb' directory from '~/.sage/' resolved it. Thanks for the tip. But note that all of your notebook files are probably in there, so don't forget the I then just copied

[sage-support] Re: see field extensions as a vector space.

2012-09-04 Thread Maarten Derickx
Le mardi 4 septembre 2012 10:40:24 UTC+2, sha2nk a écrit : k=GF(2^11); K=GF(2^33) How to see K as a vector space over filed k ? How to form its basis ? How to construct tower of field extensions ? Hi, Sadly enough non of these three things are implemented in sage yet for finite fields.

[sage-support] Symmetric polynomials as composition of elementary SP

2012-09-04 Thread Jori Mantysalo
Some time ago I asked if Sage can solve something like If P(x)=x³+ax²+bx+c with roots r_1, r_2 and r_3, how to express ((r_1-r_2)(r_1-r_3)(r_2-r_3))^2 as a function of a, b and c? Because a, b and c are symmetric functions of roots, I guess I should read

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] Generator matrix of ideal lattice

2012-09-04 Thread Cindy
Hi, Let K be a number field and O_k denote its ring of integers. For an ideal, J of O_k, we can have an ideal lattice (I,b_\alpha), where b_\alpha: J\times J \to Z, b_\alpha(x,y)=Tr(\alpha xy), \forall x,y \in J and \alpha is a totally positive element of K\{0}. Suppose now I know J and

[sage-support] Re: see field extensions as a vector space.

2012-09-04 Thread sha2nk
Thanks Maarten for a quick reply. I tried to hack this functionality but as you pointed out sage does not treat L(below) as a field. sage: n=2 sage: m=3 sage: q=2; sage: k=GF(q); sage: K=GF(q^n,'w');K Finite Field in w of size 2^2 sage: P1.t = PolynomialRing(K,'t'); P1 Univariate Polynomial