.
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 = | -3 20 24 12 |
| -50 -18 -3 2 |
| 38 18 11 12 |
| -40 37 -8 28 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 27)(x + 47)(x + 9x - 31)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -22 -21 38 34 |, | 7 12 47 13 |)
| 0 1 0 0 | | -47 -26 25 50 | | 20 -44 -22 -7 |
| 0 0 -9 1 | | -40 -17 -3 -28 | | -33 -48 -25 1 |
| 0 0 31 0 | | 0 -20 -38 30 | | -15 -43 21 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|