.
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 = | 24 19 -8 -38 |
| -36 19 -22 -16 |
| -30 -10 -29 39 |
| -29 -29 -24 21 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2 2
o4 = (x + 39x - 10)(x + 27x - 27)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -27 1 0 0 |, | 15 -11 46 -1 |, | 50 13 7 -23 |)
| 27 0 0 0 | | 12 -46 -47 39 | | -37 -24 -41 -18 |
| 0 0 -39 1 | | -9 47 33 -2 | | 23 1 33 1 |
| 0 0 10 0 | | 41 -40 22 50 | | -8 0 -47 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = true
|