i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 1/2 5/9 2 1/8 5/9 | | 1/2 5/3 4 10/3 4/9 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 7 9/5 8/7 3/5 6/7 | | 10 1 1/2 1 7/4 | 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 |, | -1/4145255 0 |, | 32529952 | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 -1/4145255 | | -91153944 | 58033570 | -9625728 | -144878076 ------------------------------------------------------------------------ 1231632 -319130 88398 -257136 |) -2126664 -2739765 -34866 2025912 | 0 0 0 0 | 1791432 1045520 -1271592 -757856 | -6846336 2791740 241416 -1623972 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |