25.2.5 Unramified Extensions

One can create unramified extensions of $ \mathbf{Z}_p$ and $ \mathbf{Q}_p$ using the functions Zq and Qq. These extensions are still in a relatively primitive state, so I would suggest the following options when creating such extensions (more are available but may not currently work as well).

In addition to requiring a prime power as the first argument, Zq also requires a name for the generator of the residue field. One can specify this name as follows:

sage: R.<c> = Zq(125, prec = 20); R
Unramified Extension of 5-adic Ring with capped absolute precision 20
in c defined by (1 + O(5^20))*x^3 + (3 + O(5^20))*x + (3 + O(5^20))

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