.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
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i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | 17 -41 11 50 |
| 19 19 -28 -37 |
| -44 27 -34 28 |
| -11 31 -23 23 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x - 25x - 30x - 15x - 44)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 25 1 0 0 |, | 0 -7 -16 6 |, | 3 -9 17 1 |)
| 30 0 1 0 | | 0 -2 -8 1 | | -21 0 19 0 |
| 15 0 0 1 | | 0 -13 -23 -4 | | -3 44 -44 0 |
| 44 0 0 0 | | 1 22 -37 -42 | | 35 50 -11 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
|