.
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 = | -37 41 -23 -27 |
| -48 -28 -42 -6 |
| 0 48 -22 7 |
| 8 -2 36 0 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 25)(x - 39x + 4x - 32)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -17 38 -42 -50 |, | -43 42 -12 26 |)
| 0 39 1 0 | | 23 8 2 -29 | | -37 25 37 1 |
| 0 -4 0 1 | | -41 -45 -11 -29 | | 44 41 48 0 |
| 0 32 0 0 | | 2 50 19 -28 | | 4 43 4 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 = false
|