So I have been trying to implement the quadratic sieve and I did step 1 which is(in code):
f = 44
b = ceil(sqrt(n))
factorBase = [i for i in genPrimes(f) if jacobi(n, i) == 1]
t = [modInverse(n, p) for p in factorBase]
sol1 = [(t[i] - b) % factorBase[i] for i in range(len(t))]
sol2 = [(-t[i] - b) % factorBase[i] for i in range(len(t))]
l = [ln(p) for p in factorBase]
size = 60
Here genPrimes() is Sieve of Eratosthenes, jacobi checks if n is quadratic residue mod i, and modInverse is Tonelli-Shanks algorithm.
The next step in the quadratic sieve is this:
Initialize a sieve array to 0's. For each odd prime p in the factor
base, add l[p] to the locations sol1[p] + ip and soln[p] + ip of the sieve array, for
i = 0, 1, 2,... For the prime p = 2, sieve only with sol1.
Or as explained here:
Then I have to add values from to sieving array to positions 1[]+∗factor_base[j] and
1[]+∗ factor_base[j], where 0≤≤ size and 0≤≤|factor_base|. And for prime =2 add only to
positions with sol1.
Now say these were my lists:
sieveArray = [0 for i in range(60)]
factorBase = [2,3,7,17,23,29,37,41]
sol1 = [0,0,2,13,11,26,10,28]
sol2 = [0,1,5,14,8,10,17,26]
l = [0.69,1.1,1.95,2.83,3.14,3.37,3.61,3.71] # logs of factorbase rounded to 2 decimals
I should, following what was said above get this new list:
sieveArray = [1.79,1.1,2.64,1.1,1.79,1.95,1.79,1.1,3.83,3.05,8.77,3.14,3.74,3.93,3.52,1.1,3.74,3.61,1.79,3.0
5,0.69,1.1,1.79,1.95,1.79,1.1,9.72,1.1,5.5,0.0,6.57,7.07,0.69,3.05,4.93,0.0,1.79,3.05,0.69,4.47
,3.74,0.0,1.79,1.1,2.64,1.1,1.79,8.39,4.62,1.1,0.69,3.05,1.79,0.0,10.49,4.47,0.69,4.24,3.74,0.0]
However whenever I try to program I mess up horribly and index out of range errors. Here is my failed code:
for j in factorBase:
if j != 2:
for i in range(0, size):
try:
sieveArray[sol1[j] + (i * factorBase[j])] += l[j]
sieveArray[sol2[j] + (i * factorBase[j])] += l[j]
except:
continue
#Didn't implement case for 2 since I didn't know what I was doing.
Can someone please explain to me what I am doing wrong and how I can get expected results. Also If you want the actual explanation on what the step is go to https://pdfs.semanticscholar.org/5c52/8a975c1405bd35c65993abf5a4edb667c1db.pdf page 6(qs algorithm) step 2 or https://math.stackexchange.com/questions/183183/quadratic-sieve-algorithm?rq=1. Error when there are no try-except statements:
sieveArray[sol1[j] + (i * factorBase[j])] += j
IndexError: list index out of range
Note: No Index Out of Range error because of the try-except but the code doesn't work properly at all still.
