Open rzil opened 8 years ago
octave:8> output_precision(1)
octave:9> A=[-1,1,0,0,0,0,0,0,1,1;1,-1,0,0,0,0,1,0,1,1;1,1,-1,0,0,0,0,1,0,1;0,0,1,-1,0,0,0,0,0,1;0,0,0,1,-1,1,0,0,0,1;0,0,0,0,0,-1,1,0,0,1;0,0,0,0,0,0,-1,0,1,1;0,0,0,0,0,0,0,-1,0,1;0,0,0,0,0,0,0,0,-1,1]
A =
-1 1 0 0 0 0 0 0 1 1
1 -1 0 0 0 0 1 0 1 1
1 1 -1 0 0 0 0 1 0 1
0 0 1 -1 0 0 0 0 0 1
0 0 0 1 -1 1 0 0 0 1
0 0 0 0 0 -1 1 0 0 1
0 0 0 0 0 0 -1 0 1 1
0 0 0 0 0 0 0 -1 0 1
0 0 0 0 0 0 0 0 -1 1
octave:10> rref(A)
ans =
1.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0
0.0 0.0 1.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 1.0 0.0 -0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 -0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0
Seems octave doesn't agree with sage. Reason is, what you provided is the echelon form; not the reduced echelon form. One can clearly see that in your matrix, the last column's elements of rows 1-9 can be easily eliminated by the last row multiplying by ?/6.
The following commands result in unexpected behaviour with matrix-0.3.5.1
NB: the correct row reduced form is given below (computed with sage)