On 2013-11-15 11:45, Georgi Guninski wrote:
sage: Kz.<t>=Qp(3,5)[];pol=(1 + O(3^5))*t^2 + (1 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4
+ O(3^5))*t + (1 + O(3^5))
sage: (pol(1),pol(1).is_zero())
(O(3^5), True)
There is some mathematical subtlety going on here: the value of that
polynomial at 1 equals O(3^5), but from this fact one cannot conclude
that the original polynomial has a p-adic zero. The problem is that your
zero modulo 3^5 is not Hensel-liftable to a 3-adic zero.
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