.
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 = | -22 12 33 -45 |
| 49 1 -4 27 |
| -28 15 16 -44 |
| -1 22 -22 33 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 28x - 17x + 17x - 50)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 28 1 0 0 |, | 0 37 -31 -46 |, | 37 -9 -22 1 |)
| 17 0 1 0 | | 0 49 24 12 | | -31 -35 49 0 |
| -17 0 0 1 | | 0 44 47 31 | | 13 38 -28 0 |
| 50 0 0 0 | | 1 40 -27 -33 | | 8 -34 -1 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
|