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(Not a solution). The problem comes from the fact that sage is not able to derive enough information on Zpi
sage: ZZq.<xi> = Qq(3^1)
sage: R.<x_pi> = ZZq[]
sage: Zpi.<pi> = QuotientRing(R, R.ideal(x_pi^(p-1)+p))
sage: print(Zpi.is_field())
True
sage: ZZq.<xi> = Qq(3^2)
sage: R.<x_pi> = ZZq[]
sage: Zpi.<pi> = QuotientRing(R, R.ideal(x_pi^(p-1)+p))
sage: print(Zpi.is_field())
Traceback (most recent call last):
...
NotImplementedError
