Iterated extensions of Qp

[Julian Rüth]

Hi,

I'm trying to do some computations with p-adics in sage but I'm running
into problems with iterated extensions of Qp.
Defining extensions of Qp works fine, but extensions of extensions never
worked for me.

As an example, I tried the following:

sage: K=Qp(3)
sage: R.<X>=K[]
sage: L.<xi>=K.extension(X^12 + 342/145*X^10 + 189/145*X^8 + 36/29*X^7 +
sage: 198/145*X^5 + 18/145*X^3 + 6/29*X^2 + 3/145)
sage: R.<T>=L[]
sage: f=1+3*T^3+3*T^5
sage: f2=f(T+xi)
sage: L.<y> = K.extension(T^3-f2.coeffs()[0])

The last line produces a lengthy stacktrace
(http://pastebin.com/xHmBPb0a) which ends in

sage.rings.padics.padic_ZZ_pX_CR_element.pAdicZZpXCRElement._integer_
ValueError: This element not well approximated by an integer.

Now I'm wondering, am I doing something wrong or are such
iterated extensions simply not supported?

Thanks,

julian

PS: I already did some sage hacking in the past, so if anybody had been
working on code that would make this work, I would be eager to help with the coding.