def recursion(k, fcoeff, re):
gcd = [1]
if k > 1:
gcd = quot_remain_p(ZZ.map(recursion((k - 2), fcoeff, re)), ZZ.map(recursion((k - 1), fcoeff, re)), p, ZZ)[1]
elif any(re) == False:
gcd = fcoeff
else:
if k == 0:
gcd = re
else:
gcd = quot_remain_p(ZZ.map(fcoeff), ZZ.map(re), p, ZZ)[1]
return [item % p for item in gcd]
def x_powermod(k, fcoeff, a1): # this function genrates x^(2^k) mod function f(x)
if (k > 0):
p1 = np.poly1d(x_powermod((k - 1), fcoeff, a1)) ** 2
result = quot_remain_p(ZZ.map(p1.coeffs), ZZ.map(fcoeff), p, ZZ)[1]
else:
result = a1
return [item % p for item in result]
def mod_xp(position, fcoeff, a1): # mod_xp(p) is x^p mod f(x)
# multiply elements one by one
result = np.poly1d(1)
for x in position:
result = np.poly1d((result * np.poly1d(x_powermod(x, fcoeff, a1)) ).coeffs % p)
result = quot_remain_p(ZZ.map(np.poly1d(result).coeffs), ZZ.map(fcoeff), p, ZZ)[1]
return result
def roots_f(startP, g_x, resss):
if np.poly1d(g_x).order == 1:
resss.append(monic(g_x))
return resss
else:
r = GCD(startP, P, Y, g_x)
if np.poly1d(r).order < np.poly1d(g_x).order and np.poly1d(r).order != 0:
resss.append(monic(r))
g_x = quot_remain_p(ZZ.map(g_x), ZZ.map(np.poly1d(monic(r))), p, ZZ)[0]
return roots_f(startP, g_x, resss)
else:
startP = rand_startP()
return roots_f(startP, g_x, resss)