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I am trying to define the polynomial ring $\Bbb{Z}[j]$ where $j$ is the 3rd root of unity, i.e. $j = e^{\frac{2}{3} \pi i} \in \Bbb C$.

I tried this:

P.<x> = PolynomialRing(QQ)
j = exp((2/3)*pi*i)
P[j]

But I get the error:

NotImplementedError: ring extension with prescribed embedding is not implemented

I am trying to define the polynomial ring $\Bbb{Z}[j]$ where $j$ is the a primitive 3rd root of unity, i.e. $j = e^{\frac{2}{3} \pi i} \in \Bbb C$.

I tried this:

P.<x> = PolynomialRing(QQ)
j = exp((2/3)*pi*i)
P[j]

But I get the error:

NotImplementedError: ring extension with prescribed embedding is not implemented