Dear Cindy, Without wishing to cause offence, I think your problem isn't a Sage problem: it's that you don't understand the mathematical problem that you're trying to solve.
Firstly, if V is an inner product space with basis v_1, ..., v_n and M is its Gram matrix (the matrix whose i,j entry is v_i paired with v_j), then the norm of the vector with coordinates x_1, .., x_n is not the usual norm of (M * [x_1; ...; x_n]); it's [x_1, ..., x_n] * M * [x_1; ...; x_n]. Secondly, the matrix [1, 2; 3, 4] is not symmetric or Hermitian and its determinant is 0, so it is not the Gram matrix of a positive definite inner product space. Thirdly, the "minimize" function does what it says on the tin: it finds the minimum value of a function, and it does so by using calculus, assuming the function is differentiable. The minimum value of the norm of a vector in a positive definite inner product space is 0, the norm of the zero vector. You want the minimum value at a non-zero integer point and calculus is not going to help you with that. May I ask what motivates this long string of questions? Are you a student? If so, you should go back and read your undergraduate linear algebra notes a bit more carefully. Regards, David Loeffler On 6 September 2012 10:38, Cindy <[email protected]> wrote: > BTW, the generator matrix I used for the previous example is > [1 2] > [3 4] > > Thanks. > > Cindy > > > On Wednesday, September 5, 2012 7:31:48 PM UTC+8, David Loeffler wrote: >> >> > how can I get the minimum norm for the >> > ideal lattice (J,\alpha) using sage? >> >> What have you tried so far? >> >> 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. > > -- 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.
