.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
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i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | 6 2 30 -49 |
| -35 38 -6 16 |
| -10 3 -32 7 |
| 6 14 4 31 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 43x + 26x + 5x - 43)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 43 1 0 0 |, | 0 37 -4 24 |, | 23 -22 6 1 |)
| -26 0 1 0 | | 0 38 -28 -27 | | 42 30 -35 0 |
| -5 0 0 1 | | 0 25 -49 -3 | | 31 -5 -10 0 |
| 43 0 0 0 | | 1 37 -28 -17 | | 12 -5 6 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
|