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| Sage Version 3.4, Release Date: 2009-03-11                         |
| Type notebook() for the GUI, and license() for information.        |
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sage: M = matrix([[8585 + O(101^2), 5612 + O(101^2), 5359 + O(101^2)],
[1616 + O(101^2), 5283 + O(101^2), 2057 + O(101^2)], [8383 + O(101^2),
5843 + O(101^2), 7490 + O(101^2)]])
sage: M

[     85*101 + O(101^2) 57 + 55*101 + O(101^2)  6 + 53*101 + O(101^2)]
[     16*101 + O(101^2) 31 + 52*101 + O(101^2) 37 + 20*101 + O(101^2)]
[     83*101 + O(101^2) 86 + 57*101 + O(101^2) 16 + 74*101 + O(101^2)]
sage: M.charpoly()
(1 + O(101^2))*x^3 + (54 + O(101))*x^2 + (41 + O(101))*x + (95*101 + O
(101^2))

Why does my charpoly have some coefficients only mod 101^1?

david

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