> An orthogonal lattice might not exist in general, but you can use LLL > to get close (and, perhaps, hit it right on). > > sage: m = matrix([[1,2,3],[2,3,4]]) > sage: m.LLL() > [-1 0 1] > [ 1 1 1]
You might also want to try BKZ algorithm too. sage: m [ 1 0 -1 -2 -1] [ 1 -2 0 1 0] [ 1 2 0 -1 2] [-1 1 -2 0 2] [-1 0 0 2 -1] sage: m.LLL() [ 2 0 -1 0 0] [ 1 -2 0 1 0] [-1 0 0 -2 -1] [ 1 0 0 -2 1] [-1 -1 -2 -1 1] sage: m.BKZ() [ 2 0 -1 0 0] [ 0 0 1 0 2] [-1 0 0 -2 -1] [ 1 -2 0 1 0] [-1 -1 -2 -1 1] sage: sorted(b.norm()**2 for b in m.LLL()) [5, 6, 6, 6, 8] sage: sorted(b.norm()**2 for b in m.BKZ()) [5, 5, 6, 6, 8] sage: (prod(b.norm() for b in m.LLL())/ (m*m.transpose()).det().sqrt()).n() 1.78753077517265 sage: (prod(b.norm() for b in m.BKZ())/ (m*m.transpose()).det().sqrt()).n() 1.63178487966126 -- 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 For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe from this group, send email to sage-support+unsubscribegooglegroups.com or reply to this email with the words "REMOVE ME" as the subject.
