.
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 = | 41 46 38 -26 |
| 47 3 -38 21 |
| -10 42 5 48 |
| -14 23 34 43 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
o4 = (x + 11)(x + 20)(x + 40)(x + 39)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -22 -43 3 38 |, | -18 -14 -11 10 |)
| 0 1 0 0 | | 30 28 -50 -43 | | 17 39 41 47 |
| 0 0 1 0 | | 7 41 47 48 | | -27 -13 6 -17 |
| 0 0 0 1 | | -15 -26 0 -42 | | 44 -48 5 -46 |
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
|