.
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 = | 48 45 42 -17 |
| -8 18 34 -15 |
| -22 18 24 5 |
| 37 -37 19 43 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3
o4 = (x - 32x + 20x - 38)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 32 1 0 0 |, | 0 27 24 1 |, | 20 -13 48 1 |)
| 0 0 1 0 | | 0 17 38 29 | | 36 -13 -8 0 |
| -20 0 0 1 | | 0 18 21 -30 | | -50 -28 -22 0 |
| 38 0 0 0 | | 1 29 16 -21 | | 27 13 37 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = true
|