.
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 = | 43 -32 41 -3 |
| -13 35 14 21 |
| -15 -19 42 23 |
| 49 -17 -12 -15 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 7)(x + 22)(x - 33x - 21)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -7 0 0 0 |, | -12 -43 38 -37 |, | 19 -18 -34 1 |)
| 0 -22 0 0 | | 3 -14 36 26 | | 33 12 48 10 |
| 0 0 33 1 | | -35 14 -4 -13 | | 47 -31 39 1 |
| 0 0 21 0 | | 2 31 -8 22 | | 1 1 -32 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = true
|