.
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 = | 29 30 32 -26 |
| 25 -42 13 -6 |
| 48 -31 -24 35 |
| -42 22 -48 38 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 27)(x - 10)(x + 36x + 11)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -23 26 35 9 |, | 5 -28 -22 -32 |)
| 0 1 0 0 | | 19 -40 -11 3 | | -24 -4 -31 -18 |
| 0 0 -36 1 | | 22 -24 -31 -10 | | -17 24 8 1 |
| 0 0 -11 0 | | -36 30 -5 -31 | | -10 15 -9 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|