.
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 = | -48 6 -10 -13 |
| 8 -20 4 -36 |
| 26 -37 25 44 |
| 33 -8 13 -49 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 18)(x - 44)(x + 17x + 5)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 18 22 -31 -38 |, | 38 -13 11 31 |)
| 0 1 0 0 | | 20 -46 41 4 | | 32 42 -31 -1 |
| 0 0 -17 1 | | -13 -29 -30 4 | | -10 44 -41 1 |
| 0 0 -5 0 | | 28 -24 18 -33 | | 28 -39 34 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|