Partial accumulators

In the following, it will be useful to implement partial accumulators as a function of an upper bound index $i$, a given column number and its respective polynomial $f$ , the permutation $\sigma$ and the challenges $\beta$ and $\gamma$.

Exercise 16

Compute accumulator functions for the numerator and the accumulator respectively as:

$$\mathsf{\text{acc\_numerator}}(i,column,f,\sigma ,\beta ,\gamma )=\prod _{j=1}^{i-1}\mathsf{\text{numerator}}(j,column,f,\sigma ,\beta ,\gamma )$$$$\mathsf{\text{acc\_denominator}}(i,column,f,\sigma ,\beta ,\gamma )=\prod _{j=1}^{i-1}\mathsf{\text{denominator}}(j,column,f,\sigma ,\beta ,\gamma )$$

def acc_numerator(i, column,f,sigma,beta, gamma):
    value = 1 
    #Solve here!
    return value    

def acc_denominator(i, column,f,sigma,beta, gamma):
    value = 1 
    #Solve here!
    return value

If implemented correctly, the following check should pass.

N_n = acc_numerator(n+1,1,a,sigma,42,42)*acc_numerator(n+1,2,b,sigma,42,42)*acc_numerator(n+1,3,c,sigma,42,42)
D_n = acc_denominator(n+1,1,a,sigma,42,42)*acc_denominator(n+1,2,b,sigma,42,42)*acc_denominator(n+1,3,c,sigma,42,42)
print("When multiplying z for each column with the corresponding upper and lower bounds one should obtain 1:", N_n//D_n==1)