.
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 = | -44 -10 7 -49 |
| -14 25 -36 -49 |
| 20 47 -28 -23 |
| 42 -27 -49 -37 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 17x - 31x - 33x - 31)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 17 1 0 0 |, | 0 36 -14 -15 |, | 6 -44 -44 1 |)
| 31 0 1 0 | | 0 35 -32 -26 | | -3 13 -14 0 |
| 33 0 0 1 | | 0 -33 31 44 | | -44 -34 20 0 |
| 31 0 0 0 | | 1 -27 40 -27 | | -47 36 42 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
|