sage: M = matrix([[1,1,1,1,1,1],[1,1,-2,1,1,-2],[-2,1,1,-2,1,1], [1,-2,1,1,-2,1]]) sage: M [ 1 1 1 1 1 1] [ 1 1 -2 1 1 -2] [-2 1 1 -2 1 1] [ 1 -2 1 1 -2 1] sage: M.row_space() Free module of degree 6 and rank 3 over Integer Ring Echelon basis matrix: [1 1 1 1 1 1] [0 3 0 0 3 0] [0 0 3 0 0 3] sage: M.row_space().zero() (0, 0, 0, 0, 0, 0) sage: vector([1,0,0,1,0,0]) in M.row_space() False sage: vector(ZZ,[1,0,0,1,0,0]) (1, 0, 0, 1, 0, 0) sage: vector(ZZ,[1,0,0,1,0,0]) in M.row_space() False
I guess I'm a little surprised that even the 'vector' explicitly designated to be over ZZ isn't in there. I think I'm mathematically ok, too - taking the echelon matrix, isn't my vector e_1-(1/3)*e_2- (1/3)*e_3 ? Anyway, I hope that I'm just misusing free modules and vectors - though since my vector isn't really one, it would seem reasonable to let it live in the free module. Thanks for any assistance, - kcrisman -- 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
