.
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 = | -47 -27 30 15 |
| 20 34 11 -35 |
| 41 -32 -3 -24 |
| -19 21 50 -42 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 43x - 15x + 2x - 34)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 43 1 0 0 |, | 0 11 -8 -11 |, | 16 -12 -47 1 |)
| 15 0 1 0 | | 0 27 40 35 | | -46 48 20 0 |
| -2 0 0 1 | | 0 6 27 22 | | -48 -12 41 0 |
| 34 0 0 0 | | 1 26 -42 14 | | -2 20 -19 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|