On Saturday, July 13, 2013 1:40:53 PM UTC-7, Ursula Whitcher wrote:
>
> I would like to construct a ring over a p-adic field that includes a 
> (p-1)st root of -p.  I tried:
>
> R = Qp(5, 10)
> S.<v> = R[]
> piPoly = v^(5-1)+5
> T.<w> = R.ext(piPoly)
>
> But elements of T seem to be power series in w.  I would expect them to be 
> described using power series in p (up to O(p^10)) and w, w^2, ..., w^3.


OK, offline conversation has persuaded me that this is not unreasonable 
behaviour, given that we only know w up to a certain precision.

--Ursula. 

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