.
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 = | 5 16 1 12 |
| -24 9 40 8 |
| -43 -33 13 20 |
| -48 -3 -31 24 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 50x + 4x - 38x + 27)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -50 1 0 0 |, | 0 -25 -49 8 |, | 27 32 5 1 |)
| -4 0 1 0 | | 0 17 8 18 | | -7 -16 -24 0 |
| 38 0 0 1 | | 0 38 30 -48 | | -7 -33 -43 0 |
| -27 0 0 0 | | 1 42 8 -47 | | 49 13 -48 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
|