.
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 = | -10 33 18 17 |
| 23 -45 24 16 |
| -31 -33 -13 -35 |
| 13 17 20 47 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2 2
o4 = (x + 49x + 42)(x - 28x - 4)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -49 1 0 0 |, | 28 3 29 -48 |, | -38 -31 -26 49 |)
| -42 0 0 0 | | 42 -29 -47 -49 | | -43 44 47 38 |
| 0 0 28 1 | | 12 -42 -2 -25 | | 1 1 42 1 |
| 0 0 4 0 | | 32 -28 2 36 | | -39 0 -10 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
|