On Tue, Apr 22, 2008 at 11:51 AM, Leonardo Banchi <[EMAIL PROTECTED]> wrote: > Hi, i am a physics student and i have to find the *exact* eigenvector of a > large > (4000x4000, and more) integer valued symmetric matrix with many zeros and > probably relatively small elements. We have a conjecture about the minimum > eigenvalue and we need only to calculate the relative eigenvector. So our > problem can be reduced to calculate the solution of a homogeneous linear > system. > We know that eigenvector to have very large integer components. > I am not very expert in SAGE but i like its phylosophy of using best > opensource > mathematical program togheter. can be sage a good answer to my problem? or > may i > use one of the program composing sage for doing that? or something else? > the matrix is builded in a C program and so i would prefer interfacing all > with > C subroutines. > > thanks for the time and excuse my bad english.. > Leonardo Banchi
Wait, let me get this straight. Do you have a 4000x4000 matrix A with integer entries and your entire question reduces to finding a nonzero *exact* element in the kernel ker(A) of A? E.g., something like this? sage: a = matrix(QQ, 3, 3, [1,2,3, 4,5,6, 7,8,9]); a [1 2 3] [4 5 6] [7 8 9] sage: time a.kernel() Vector space of degree 3 and dimension 1 over Rational Field Basis matrix: [ 1 -2 1] CPU time: 0.02 s, Wall time: 0.02 s Anyway, if this is your problem then you're in luck, since Sage is very very good at that. -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
