.
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 = | -11 -24 31 -5 |
| 21 -43 7 -13 |
| 41 -43 13 -17 |
| -7 -48 2 8 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
4 3 2
o4 = (x + 33x - 32x + 9x - 41)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| -33 1 0 0 |, | 0 -5 -6 22 |, | 46 14 -11 1 |)
| 32 0 1 0 | | 0 -41 36 -42 | | -40 -49 21 0 |
| -9 0 0 1 | | 0 -33 -14 -8 | | -49 5 41 0 |
| 41 0 0 0 | | 1 37 22 -7 | | -27 4 -7 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 = true
|