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 for differentiable functions. > > > > For the stuff regarding lattice, I think there may be some > misunderstanding > > here. > > > > What I want is to find the minimum of a lattice. > > > > A lattice L can be defined as > > > > L={x=\lambda M| \lambda\in Z^m}, > > > > where M is the generator matrix of L and the gram matrix of L is equal > to > > MM^T. > > OK, I've never heard of this definition but if you want to take that > to be the definition that's up to you -- apparently for you all > lattices come with a fixed embedding into Euclidean space. But that > then changes the interpretation of your previous question, because in > your previous thread I assumed you wanted a Gram matrix, and that is > what the code I suggested calculates; the lattices coming from trace > pairings on number fields won't have any preferred embedding into > Euclidean space. To get *a* generator matrix (in your sense) from the > Gram matrix, you could use Cholesky decomposition, for example. But to > do this you will have to introduce square roots all over the place and > hence the computation becomes inexact; it is far simpler to just work > with the Gram matrix, which will be integer-valued in the examples > you've mentioned so far. > > To find the shortest vector, you might want to use some of the > routines in Sage's quadratic forms module. > > David > -- 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-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.