.
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 = | 17 -32 39 16 |
| 37 9 39 2 |
| -10 -44 38 -26 |
| -43 35 -9 3 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 24)(x - 18)(x - 25x - 10)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -31 2 -3 38 |, | -36 -21 17 1 |)
| 0 1 0 0 | | 45 47 -36 -18 | | -37 44 27 17 |
| 0 0 25 1 | | -11 12 9 50 | | 21 -41 -13 1 |
| 0 0 10 0 | | 9 -1 9 29 | | -21 -28 38 0 |
o5 : Sequence
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i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|