.
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 = | -34 0 21 0 |
| -33 -29 -39 13 |
| 4 45 -28 34 |
| 27 -11 -30 28 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 25)(x + 30)(x + 8x + 28)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 34 13 -13 -12 |, | 40 33 7 42 |)
| 0 1 0 0 | | -13 -3 33 -3 | | -8 -27 -1 31 |
| 0 0 -8 1 | | -13 -11 -22 -43 | | 46 -37 20 1 |
| 0 0 -28 0 | | -43 17 -33 -15 | | 4 37 -45 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
|