.
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 = | -31 11 -15 45 |
| -24 31 48 -37 |
| -2 4 -25 5 |
| 25 -41 17 8 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 17x - 8x - 16x - 5)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -17 1 0 0 |, | 0 -38 -1 20 |, | -50 34 -31 1 |)
| 8 0 1 0 | | 0 -22 39 -18 | | 18 -11 -24 0 |
| 16 0 0 1 | | 0 11 -6 -2 | | -45 40 -2 0 |
| 5 0 0 0 | | 1 -3 -47 35 | | 32 -29 25 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
|