.
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 = | -30 -17 12 7 |
| 3 -27 41 -5 |
| 27 20 8 11 |
| 12 -23 -7 -25 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 47)(x - 10)(x + 30x - 12)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 10 0 0 0 |, | -47 -39 6 50 |, | -21 26 -8 7 |)
| 0 47 0 0 | | -21 2 3 -41 | | -18 -14 37 -29 |
| 0 0 -30 1 | | -20 1 -33 38 | | 47 37 21 1 |
| 0 0 12 0 | | -28 21 -2 -15 | | 1 1 37 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|