.
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 = | -38 -30 50 -30 |
| 12 0 20 -41 |
| 42 -36 -21 2 |
| 33 19 -1 -28 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 12)(x - 26x - 22x - 39)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | -29 48 23 10 |, | -21 -33 29 33 |)
| 0 26 1 0 | | -45 -30 -32 -9 | | 35 -1 -8 1 |
| 0 22 0 1 | | -30 -20 -24 -28 | | 7 16 37 0 |
| 0 39 0 0 | | -42 -27 43 28 | | 42 44 -3 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
|