Step 2: challenges and permutation

We now compute the challenges $\beta$ and $\gamma$ for the permutation argument from the transcript, one at a time and then push them to the transcript. With these values we can compute the $z$, $N$ and $D$ polynomials.

Exercise 20

Compute $\beta$ from the transcript and push this value to it. Then compute $\gamma$ and similarly, push it to the transcript. Finally interpolate values for $z,N,D$ and commit $z$ to the transcript.

#Solve here!
beta = #?
gamma = #?
# interpolate and commit z
z_poly, N_poly, D_poly = #?
c_z = #?