i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 5/8 1 10/9 1/2 8 | | 9/7 2/3 1/9 1/3 1/2 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 6 1/3 4/5 1/9 3/8 | | 2/5 5 2/5 9/2 3/4 | 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 |, | 0 -1/5236165 |, | 38251920 | 0 0 0 1 0 | | 0 0 0 0 1 | | -1/5236165 0 | | -151084467 | -268764840 | 181380114 | 41889320 ------------------------------------------------------------------------ -389760 -23800 664440 -856800 |) -18158784 1418970 -1544304 3957435 | 7778295 -32850 -4627080 -1182600 | 19519668 -2735190 2068128 -4215870 | 0 0 0 0 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |