.
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 = | 49 -13 4 42 |
| 32 -3 -38 -26 |
| -25 -12 49 -16 |
| 2 -49 -17 -24 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 4)(x + 26x - 29x - 8)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -30 21 -17 -6 |, | -17 -43 -9 31 |)
| 0 -26 1 0 | | 47 -43 -49 50 | | 15 -48 -21 1 |
| 0 29 0 1 | | 40 -28 24 37 | | -39 -15 21 0 |
| 0 8 0 0 | | -17 23 -40 -11 | | 25 39 13 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 = false
|