.
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 = | 27 37 46 15 |
| -1 -8 -6 -45 |
| -23 22 23 20 |
| 44 42 -6 20 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x - 42)(x - 4)(x - 16x + 7)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -32 30 -31 8 |, | 7 -49 -8 -14 |)
| 0 1 0 0 | | -9 -19 24 26 | | 38 -2 -2 -24 |
| 0 0 16 1 | | -39 8 50 24 | | -9 -36 19 1 |
| 0 0 -7 0 | | -26 -32 -20 50 | | -12 -25 -14 0 |
o5 : Sequence
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i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|