.
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 = | -32 -28 -47 10 |
| 13 23 2 -41 |
| -7 11 -5 4 |
| 6 4 20 -1 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 15x - 34x - 20x - 38)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -15 1 0 0 |, | 0 22 10 -36 |, | -40 39 -32 1 |)
| 34 0 1 0 | | 0 -6 30 48 | | -30 27 13 0 |
| 20 0 0 1 | | 0 40 -47 27 | | -18 22 -7 0 |
| 38 0 0 0 | | 1 -30 49 -24 | | -43 17 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
|