i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 1 1/2 10/3 2/5 3/4 | | 2 7/10 3/2 5/8 3 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 4/9 7/2 5/3 10 1/2 | | 2/9 5/2 10 1/2 9/8 | 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 |, | -1/1022351 0 |, | -20541510 | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 -1/1022351 | | -31937620 | 6134106 | 10271800 | 15939440 ------------------------------------------------------------------------ -1835415 39663 374760 206622 |) -453800 22590 269120 -425160 | 0 0 0 0 | 175760 -111480 -79000 143040 | 1292880 -8488 -636960 -68344 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |