i1 : R = QQ o1 = QQ o1 : Ring |
i2 : A = random(R^2, R^5) o2 = | 2 4/5 10 4 7 | | 3/2 4/9 5/8 5/2 3/4 | 2 5 o2 : Matrix QQ <--- QQ |
i3 : B = random(R^2, R^5) o3 = | 4/3 4/3 2 3/2 4/3 | | 9 10 5/9 1/5 9/8 | 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 |, | -1/1413236 0 |, | 21072682 | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 -1/353309 | | -16032645 | 25438248 | -4820680 | -37774144 ------------------------------------------------------------------------ -413960 3115752 -295182 -82460 |) 398655 -2804220 258075 38700 | 0 0 0 0 | 261000 -1448280 -32040 44480 | -278320 257856 73152 -6280 | o4 : Sequence |
i5 : P*A*Q - A' == 0 o5 = true |
i6 : P*B*Q - B' == 0 o6 = true |