def pollards_pminus1_wrapper(N):
steps = Steps()
primes_list = get_primes()
unfactored, factors = [N], []
while len(unfactored) > 0:
n = unfactored.pop()
if n in primes_list:
factors.append(n)
elif n == 1:
continue
else:
steps.add_cuberoot(n)
B = math.pow(n, 1.0 / 3.0)
f1, f2, hsteps = pollards_pminus1(n, B)
steps.append(hsteps)
if f1 == None: # p-1 wont work, trial division
flist, tsteps, _ = trial_division(n)
steps.append(tsteps)
factors.extend(flist)
else:
unfactored.append(f1)
unfactored.append(f2)
return factors, steps, 0
def lehmans_var_of_fermat_prewrapper(N):
steps = Steps()
steps.add_cuberoot(N)
s3n = int(math.ceil(N**(1.0 / 3.0)))
factors, tsteps, num_unfactored = trial_division(N, s3n)
steps.append(tsteps)
unfactored = []
if num_unfactored == 1:
unfactored.append(factors[-1])
factors = factors[:-1]
return factors, steps, unfactored
def harts_one_line_prewrapper(N):
steps = Steps()
factors, unfactored = [], [N]
isq, isq_steps = is_square(N)
steps.append(isq_steps)
if not isq:
steps.add_cuberoot(N)
when_to_stop = math.pow(N, 1.0 / 3.0)
factors, tsteps, num_unfactored = trial_division(N, when_to_stop)
steps.append(tsteps)
unfactored = []
if num_unfactored == 1:
unfactored.append(factors[-1])
factors = factors[:-1]
return factors, steps, unfactored
def pollards_pminus1(N, B=None, steps=None):
if steps == None:
steps = Steps()
if B == None:
steps.add_cuberoot(N)
B = math.pow(N, 1.0 / 3.0)
primes_list = get_primes()
a, i = 2, 0
a_set = set([])
while True:
pi = primes_list[i]
if pi > B:
break
steps.add_log(B)
steps.add_log(pi)
e = int(math.floor(math.log(B) / math.log(pi)))
steps.add_exp(pi, e)
f = pi**e
steps.add_exp(a, f)
steps.add_mod()
a_hold = powering.power_mod(a, f, N) #(a**f) % N
if a_hold == 0:
break
a = a_hold
a_set.add(a)
i += 1
for a in a_set:
g, g_steps = gcd(a - 1, N)
steps.append(g_steps)
if 1 < g and g < N:
return g, N / g, steps
return None, None, steps