i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 2/5 9/2 7/4 7/4 6/5 | | 1/4 1/2 1/3 5/2 7/3 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 3/7 4/9 2/7 1/5 8/3 | | 5/2 1 1/2 4/5 1 | 2 5 o3 : Matrix QQ <--- QQ |
i4 : (A',B',P,Q) = kroneckerNormalForm(A,B) o4 = (| 0 1 0 0 0 |, | 0 0 1 0 0 |, | 0 -1/1148498 |, | -2962302 | 0 0 0 1 0 | | 0 0 0 0 1 | | -1/4593992 0 | | -35493759 | 96473832 | -1920870 | -3800706 ------------------------------------------------------------------------ 87402 -494578 374360 267498 |) 188145 34731 -1114740 -208971 | 0 0 0 0 | -498270 -28250 73400 1753290 | -8034 75816 120120 -1862406 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |