.
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 = | -34 -3 -35 30 |
| -15 50 1 14 |
| -50 -49 30 15 |
| 23 -16 24 -31 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 49)(x + 39)(x - 2x + 16)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 44 19 47 4 |, | -13 -25 39 39 |)
| 0 1 0 0 | | -27 -32 24 5 | | 45 6 -14 -29 |
| 0 0 2 1 | | 18 10 -8 -45 | | 32 -2 6 1 |
| 0 0 -16 0 | | -19 23 -5 25 | | 44 -33 -29 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|