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...@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, 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 \alpha, how can I get the generator matrix for
> the
> > ideal lattice (J,\alpha) using sage?
> >
> > Thanks a lot.
> >
> > Cindy
>
> The first thing I tried was this, and it seems to work fine:
>
> sage: K.<z> = NumberField(x^3 - x + 17)
> sage: I = K.primes_above(17)[1]
> sage: alpha = 13*z + 4
> sage: matrix([[(u*v*alpha).trace() for u in I.basis()] for v in
> I.basis()])
> [ 3468 646 -11339]
> [ 646 -591 -871]
> [-11339 -871 225]
>
> David
>
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