.
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 = | -7 -15 -15 50 |
| 43 -46 -27 33 |
| -1 -29 5 -29 |
| -46 -40 -38 9 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 41)(x - 2x - 49x + 20)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -7 47 -46 20 |, | 34 14 39 50 |)
| 0 2 1 0 | | -9 46 12 38 | | -12 -9 -17 1 |
| 0 49 0 1 | | -4 -2 10 -24 | | -13 47 22 0 |
| 0 -20 0 0 | | -38 -18 -17 -8 | | 32 18 -17 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
|