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