i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 9/5 7/9 10 4/3 1/5 | | 1/7 1/2 3 4/7 5/4 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 10/7 10/3 5/3 9/5 8/3 | | 3 8 2/3 8/7 4/7 | 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 -1/2970062 |, | 1129202270 | 0 0 0 1 0 | | 0 0 0 0 1 | | -1/2970062 0 | | -284386080 | -24112515 | -1271244275 | 623713020 ------------------------------------------------------------------------ 6061860 84980 -1704990 -715400 |) -2219016 -542478 601290 603480 | -941178 -111867 -78525 427980 | 169750 1040725 312375 -2596090 | 0 0 0 0 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |