.
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 -49 -42 42 |
| -49 -15 -25 29 |
| 9 5 -38 -49 |
| -21 19 -43 -25 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 21)(x + 19)(x - 16x + 7)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -21 0 0 0 |, | 41 -1 -16 -12 |, | -42 -50 45 39 |)
| 0 -19 0 0 | | 26 -47 -40 29 | | 35 43 -27 -33 |
| 0 0 16 1 | | -22 -37 41 46 | | 3 1 47 1 |
| 0 0 -7 0 | | -24 -29 -20 -34 | | 1 1 26 0 |
o5 : Sequence
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i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = true
|