.
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 = | 25 -27 -23 9 |
| 21 23 -50 30 |
| 20 -27 -18 -23 |
| -19 -29 -24 -24 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2 2
o4 = (x + 4x + 12)(x - 10x - 7)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -4 1 0 0 |, | 36 -39 -43 -7 |, | 49 44 -25 -9 |)
| -12 0 0 0 | | 3 46 -27 -20 | | 14 -33 -10 -12 |
| 0 0 10 1 | | 26 -45 -3 33 | | 36 1 25 1 |
| 0 0 7 0 | | -30 -42 35 -48 | | -4 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
|