.
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 = | 31 -47 2 4 |
| -44 12 -30 44 |
| 27 -43 45 -30 |
| 19 -16 39 48 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 35x - 32x - 34x - 14)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 35 1 0 0 |, | 0 28 35 47 |, | -23 28 31 1 |)
| 32 0 1 0 | | 0 28 30 -15 | | 25 -48 -44 0 |
| 34 0 0 1 | | 0 6 17 27 | | 47 41 27 0 |
| 14 0 0 0 | | 1 -23 44 -43 | | 6 26 19 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = true
|