i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 3/10 3/10 2 1/10 1 | | 5 1 1/5 3/2 7/3 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 5 2/3 5/7 2/5 5/3 | | 5/9 3/8 1 5 1/5 | 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 |, | -1/13138921 0 |, | 6756858 | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 -1/13138921 | | -543857568 | -19782385 | 36111680 | 197083815 ------------------------------------------------------------------------ 2368530 -6752970 4063770 -726264 |) -13461600 36283800 -36396720 8285544 | -4992750 -4374825 4783870 -985320 | 1745000 -1095990 1321450 -2971440 | 0 0 0 0 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |