.
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 = | -13 -25 26 42 |
| -34 -19 -10 5 |
| 45 17 -30 -50 |
| -5 32 12 33 |
4 4
o3 : Matrix R <--- R
|
i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 29x - 19x - 15x + 24)
o4 : Expression of class Product
|
i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -29 1 0 0 |, | 0 26 -49 -32 |, | -48 -41 -13 1 |)
| 19 0 1 0 | | 0 19 11 -10 | | 47 7 -34 0 |
| 15 0 0 1 | | 0 22 -12 25 | | -12 -41 45 0 |
| -24 0 0 0 | | 1 -10 -37 -5 | | -35 -42 -5 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|