.
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 = | 25 -16 11 27 |
| 45 -34 6 -48 |
| -49 -2 -35 28 |
| -21 -41 -6 -23 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 34x + 10x - 2x - 45)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 34 1 0 0 |, | 0 48 -5 -49 |, | 45 11 25 1 |)
| -10 0 1 0 | | 0 -33 18 46 | | -22 6 45 0 |
| 2 0 0 1 | | 0 -17 -43 35 | | 7 14 -49 0 |
| 45 0 0 0 | | 1 42 -9 16 | | 21 23 -21 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = true
|