.
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 = | 25 5 -5 46 |
| -29 5 -1 -14 |
| -46 -16 -29 -48 |
| -5 7 -11 -9 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 12)(x - 39)(x - 42x - 29)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 39 0 0 0 |, | -22 44 30 -5 |, | -36 4 -13 0 |)
| 0 12 0 0 | | 10 -41 -5 27 | | -17 -49 -9 -42 |
| 0 0 42 1 | | -6 -49 -38 -40 | | -8 11 37 1 |
| 0 0 29 0 | | 37 -10 -15 32 | | 1 1 -2 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 = true
|