Nrthugu

The following function gives the correct result for me. But for a large number of q's, it very difficult to handle this program. So, I would like to iterate q's via a loop or some other manner. How can I do this?

def sgf(a): # here a is a list of two numbers

    import random

    a2=random.randint(1,1068)

    p=1069

    q1=(a[0]+a[1]*1+a2*1**2)%p

    q2=(a[0]+a[1]*2+a2*2**2)%p

    q3=(a[0]+a[1]*3+a2*3**2)%p

    q4=(a[0]+a[1]*4+a2*4**2)%p

    q5=(a[0]+a[1]*5+a2*5**2)%p

    q6=(a[0]+a[1]*6+a2*6**2)%p

    q7=(a[0]+a[1]*7+a2*7**2)%p

    q8=(a[0]+a[1]*8+a2*8**2)%p

    q9=(a[0]+a[1]*9+a2*9**2)%p

    while ((q1>1060) or (q2>1060) or (q3>1060) or (q4>1060) or (q5>1060) or (q6>1060) or (q7>1060) or (q8>1060) or (q9>1060)):

        a2=random.randint(1,1068)

        q1=(a[0]+a[1]*1+a2*1**2)%p

        q2=(a[0]+a[1]*2+a2*2**2)%p

        q3=(a[0]+a[1]*3+a2*3**2)%p

        q4=(a[0]+a[1]*4+a2*4**2)%p

        q5=(a[0]+a[1]*5+a2*5**2)%p

        q6=(a[0]+a[1]*6+a2*6**2)%p

        q7=(a[0]+a[1]*7+a2*7**2)%p

        q8=(a[0]+a[1]*8+a2*8**2)%p

        q9=(a[0]+a[1]*9+a2*9**2)%p

        if ((q1<=1060) and (q2<=1060) and (q3<=1060) and (q4<=1060) and (q5<=1060) and (q6<=1060) and (q7<=1060) and (q8<=1060) and (q9<=1060)):

            break  

    return q1,q2,q3,q4,q5,q6,q7,q8,q9

For simplicity,

f(x)=(a0+a1*x+a2*x**2)%p

where a0,a1 are in [0,1060] and a2 chosen randomly from [0,1068]
if all f(x)<=1060, accept f(x) otherwise regenerate f(x)

It looks like the only variables in your generation of qs are the integers that you multiple a[1] and a2 by.

You could alter your function to accept the total number of qs as a second parameter (e.g. total_q), then iterate over range(1, total_q+1) and append each new q to a Python list, returning the list at the end.

Try something like:

def sgf(a, total_q):

    import random

    a2=random.randint(1,1068)

    p=1069

    q_list = 

    for i in range(0,total_q+1):

        q = (a[0]+a[1]*i+a2*i**2)%p

        q_list.append(q)

    while any(q > 1060 for q in q_list):

        a2=random.randint(1,1068)

        q_list = 

        for i in range(0,total_q+1):

            q =(a[0]+a[1]*i+a2*i**2)%p

            q_list.append(q)



        if all(q <= 1060 for q in q_list):

            break 

    return q_list

Your q should probably be a list. That way you can use a for loop with range to perform your calculation:

for ind in range(len(q)):

    q[ind]=(a[0]+a[1]*(ind + 1)+a2*(ind + 1)**2)%p

You can also represent your condition as an iteration, but the simplest way would probably be to use the any function and write your condition as a generator:

while any(qx > 1060 for qx in q):

def sgf(a):

    import random

    a2=random.randint(1,1068)

    p=1069

    items = 

    # if items is empty, or any element is greater than 1060, keep looping

    while not items or any(item > 1060 for item in items):

        items = [(a[0]+a[1]*i+a2*i**2)%p for i in range(1,10)]

    return items