i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 2 5/6 1/10 2/5 2 | | 7/10 1/2 4/7 7/6 9/4 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 4 1/2 9/8 7/4 1/5 | | 2/3 8/9 1/2 2/9 5/7 | 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 -1/5001572 |, | 44836875 | 0 0 0 1 0 | | 0 0 0 0 1 | | -1/1250393 0 | | -234976020 | 350110040 | -270670260 | 89698350 ------------------------------------------------------------------------ 1478740 1582665 -539875 -173300 |) 579120 -8125236 559230 33600 | 0 0 0 0 | -3427200 -1537200 1136580 -354300 | -1034600 2110290 -545650 230160 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |