.
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 = | 35 -9 44 -50 |
| 46 -41 -43 7 |
| 33 -3 43 -8 |
| 21 3 7 7 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 5)(x + 23)(x + 39x + 18)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 15 -30 -11 -45 |, | -49 9 49 -42 |)
| 0 1 0 0 | | 35 48 11 44 | | -1 -16 -25 -18 |
| 0 0 -39 1 | | -48 11 0 10 | | -18 0 24 1 |
| 0 0 -18 0 | | -8 36 10 8 | | -22 -20 -20 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|