.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
|
i2 : M = R^4
4
o2 = R
o2 : R-module, free
|
i3 : A = random(M,M)
o3 = | -44 -44 -37 37 |
| -11 16 -47 25 |
| -7 28 36 -1 |
| 17 -45 -11 -36 |
4 4
o3 : Matrix R <--- R
|
i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 28x - 33x - 25x - 14)
o4 : Expression of class Product
|
i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -28 1 0 0 |, | 0 21 -5 -36 |, | 11 -25 -44 1 |)
| 33 0 1 0 | | 0 -20 -2 10 | | 9 -49 -11 0 |
| 25 0 0 1 | | 0 -4 14 27 | | 7 34 -7 0 |
| 14 0 0 0 | | 1 2 15 16 | | -21 20 17 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|