.
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 = | -11 34 -11 -42 |
| -4 -24 -37 39 |
| -36 -4 36 -8 |
| 24 46 45 -8 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3
o4 = (x + 7)(x - 20x + 30)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -7 0 0 0 |, | 2 17 11 -14 |, | -22 -21 -24 42 |)
| 0 0 1 0 | | 41 -5 42 -49 | | 26 -7 10 1 |
| 0 20 0 1 | | 12 1 -50 -43 | | -44 32 -1 0 |
| 0 -30 0 0 | | 14 19 3 47 | | 1 -8 44 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|