i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 1/2 2/5 4/3 3 5/6 | | 1 1/10 3/5 3/5 3/4 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 7/4 5/7 1 9/5 5/8 | | 1/2 3/8 8/7 2 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 -1/190903 |, | 295596 | 0 0 0 1 0 | | 0 0 0 0 1 | | -1/190903 0 | | 1648080 | -8914920 | 2420490 | 4581672 ------------------------------------------------------------------------ -174260 271824 -113520 -54740 |) 590800 -535080 421680 -305200 | -137655 -701820 395745 166110 | 11450 337960 -276825 -24010 | 0 0 0 0 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |