.
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 = | -26 45 -39 34 |
| -23 -42 48 4 |
| -28 38 6 -8 |
| -8 29 18 11 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 14)(x + 44)(x - 7x + 29)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 13 47 -14 -19 |, | 9 -12 -18 -41 |)
| 0 1 0 0 | | 8 18 39 27 | | -3 -11 -20 -12 |
| 0 0 7 1 | | -40 -18 -38 -47 | | -43 -32 -9 1 |
| 0 0 -29 0 | | 43 12 -11 -3 | | 39 36 -2 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
|