.
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 = | -13 18 23 10 |
| -26 -11 -7 -22 |
| 39 7 35 35 |
| -35 -46 -44 -7 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 4x + 27x + 9x + 33)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 4 1 0 0 |, | 0 36 -18 34 |, | -34 46 -13 1 |)
| -27 0 1 0 | | 0 -8 17 22 | | -9 10 -26 0 |
| -9 0 0 1 | | 0 -35 5 20 | | -42 -44 39 0 |
| -33 0 0 0 | | 1 26 -16 0 | | 20 -22 -35 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
|