.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
|
i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | 37 36 11 40 |
| -35 -23 -30 46 |
| -7 -24 24 48 |
| 41 -33 -37 30 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 9)(x - 39)(x - 38x - 14)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 7 47 31 8 |, | 28 -45 34 -46 |)
| 0 1 0 0 | | 30 17 -49 15 | | -46 1 15 -11 |
| 0 0 38 1 | | 30 -30 40 -4 | | 41 20 4 1 |
| 0 0 14 0 | | -30 -39 10 -46 | | -45 -44 -45 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|