.
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 = | 34 16 49 10 |
| 48 8 -14 41 |
| 4 -6 35 50 |
| 6 -38 -1 32 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2 2
o4 = (x - 3x + 11)(x - 5x + 34)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 5 1 0 0 |, | -50 -3 5 -40 |, | -18 -20 -9 -17 |)
| -34 0 0 0 | | 4 -26 4 -39 | | -11 32 36 -18 |
| 0 0 3 1 | | 48 15 -25 2 | | -35 1 -26 1 |
| 0 0 -11 0 | | -1 8 27 4 | | -24 0 -25 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
|