.
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 = | 17 -46 22 49 |
| -43 -12 42 -30 |
| -50 42 36 -4 |
| -32 30 12 -27 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 10)(x - 24x - 7x - 7)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -34 25 27 6 |, | -7 -35 17 -26 |)
| 0 24 1 0 | | -11 17 -27 -16 | | 36 38 -5 1 |
| 0 7 0 1 | | -4 -3 -44 -24 | | -44 -30 29 0 |
| 0 7 0 0 | | -25 -43 22 22 | | 10 14 -47 0 |
o5 : Sequence
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i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = false
|