Consider the extension $\mathbb{Q}(\zeta_p)/\mathbb{Q}$, where $\zeta_p$ is a primitive $p^{\text{th}}$ root of unity (and $p$ is a prime number). Form the ring of integers $\mathbb{Z}[\zeta_p]$. Now, invert the prime $p$, to obtain the ring $R=\mathbb{Z}[\zeta_p,1/p]$. I want to compute $\operatorname{Pic}(R)$.
Is this possible to do using sagemath? If so, how? How do I construct the ring $R$ using sagemath?
