On 6 September 2012 13:28, Cindy <[email protected]> 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 [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.
