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####TESTING######
'''
CRYPTO PROOFS
'''
    
'''
def SUB_PROOF(sub_set,theta_input):
    #This function is checking if each index location contained in subset is either
    #a set of 1's or 0's in theta's input.
    to_check=[]

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i = 2
n_0 = 4

while True==True:
    v_2 = (float(1)/float((i*4)-3))
    v_3 = (float(1)/float((i*4)-5))
    n_1 = float(n_0) + (4 * (v_2 - v_3))
    n_0 = float(n_1)
    i+=1
    print(n_1)

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def reverse(LIST):
    to_return=[]
    for i in range(1,len(LIST)+1):
        to_return.append(LIST[-i])
    return(to_return)

def initialized_set(n):
    set_multiple = int(0.5*(2**n))
    return([[0]]*set_multiple + [[1]]*set_multiple)

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import win32api

def name_return():
    #Will return computer str name
    return(win32api.GetComputerName())


def send_email():
    import smtplib
    from email.MIMEMultipart import MIMEMultipart

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'''
Tree decision method with != operator.
'''

def unique_variables(LIST):
    to_iter = len(LIST)
    total_items = []
    for i in range(to_iter):
        insert = LIST[i]
        total_items.append(insert)

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#from Primes_Under_1_000_000 import prime_list
#from random import randint
##from rsa_list import rsa
##
##from UNIQUE_VARIABLES import U_V


def gcd(x,y):
    while y!=0:
        (x,y)=(y,x%y)

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from Primes_Under_1_000_000 import prime_list

'''
To return the prime factorization of a number
'''

def is_div(v,n):
    if v%n==0:
        return(True)
    return(False)

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import numpy
import itertools
from GREY_CODE import G_C

def sb(size,num):
    to_return=[]
    for i in range(num):
        to_return.append(str_build(list(numpy.random.randint(2,size=(size,)))))
    return(to_return)

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from PIL import Image
import numpy as np
import hashlib
import scipy.misc
 

def S_L(string_name_list,LIST):
    f = open(string_name_list + '.py', 'w')
    simplejson.dump(LIST,f)
    f.close()

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def conversion(str_list):
    for i in range(len(str_list)):
        str_list[i]=int(str_list[i])
    return(str_list)

def trim_end(a_string):
    return(a_string[0:len(a_string)-1])

def dec_shift(a_string):
    to_build_0=''