.
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 = | 21 -5 -24 2 |
| -9 -49 -23 8 |
| -43 -5 7 15 |
| 24 -15 21 -36 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x - 46)(x + 2x + 6x + 34)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 12 -37 12 -43 |, | 24 -42 -16 -39 |)
| 0 -2 1 0 | | 50 31 8 -50 | | -11 -17 -1 1 |
| 0 -6 0 1 | | 34 13 38 47 | | -26 -50 -45 0 |
| 0 -34 0 0 | | -13 -1 -16 -38 | | 11 -4 -42 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
|