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 <[email protected] <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 > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
