On 5 September 2012 02:56, Cindy <[email protected]> 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.
