.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
|
i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | 49 -40 -29 -45 |
| 37 -1 19 -10 |
| -16 7 -41 25 |
| 27 14 32 -39 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 32x - 44x + 17x + 50)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -32 1 0 0 |, | 0 -46 32 -19 |, | 4 -32 49 1 |)
| 44 0 1 0 | | 0 47 48 -21 | | -33 -10 37 0 |
| -17 0 0 1 | | 0 -1 -24 -39 | | -50 -2 -16 0 |
| -50 0 0 0 | | 1 20 -42 2 | | -15 -27 27 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
|