.
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 = | -7 8 22 -20 |
| -5 25 -41 23 |
| -23 22 15 3 |
| -47 -18 33 -30 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 3x + 29x - 36x + 5)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 3 1 0 0 |, | 0 32 20 4 |, | -40 39 -7 1 |)
| -29 0 1 0 | | 0 -39 -31 -43 | | -12 -26 -5 0 |
| 36 0 0 1 | | 0 45 -8 12 | | -37 -31 -23 0 |
| -5 0 0 0 | | 1 -15 34 2 | | -47 -41 -47 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
|