.
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 = | -41 6 -29 45 |
| -36 15 39 -16 |
| -42 -17 -3 -33 |
| -32 -39 14 34 |
4 4
o3 : Matrix R <--- R
|
i4 : factor det(x*id_M - A)
3 2
o4 = (x + 48)(x + 48x + 41x + 18)
o4 : Expression of class Product
|
i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -40 -28 -24 29 |, | -17 45 -36 -31 |)
| 0 -48 1 0 | | -27 -29 22 -50 | | -48 2 20 1 |
| 0 -41 0 1 | | 16 -9 43 -22 | | 4 6 -28 0 |
| 0 -18 0 0 | | -16 10 -47 -20 | | -40 -39 44 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|