.
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 3 49 -38 |
| -25 50 28 42 |
| 9 -22 22 36 |
| 0 23 -22 -13 |
4 4
o3 : Matrix R <--- R
|
i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 2x + 8x + 12x + 14)
o4 : Expression of class Product
|
i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 2 1 0 0 |, | 0 -32 -44 25 |, | 38 -21 44 1 |)
| -8 0 1 0 | | 0 7 -3 30 | | 29 23 -25 0 |
| -12 0 0 1 | | 0 42 27 -4 | | -22 33 9 0 |
| -14 0 0 0 | | 1 20 17 -43 | | -46 35 0 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|