human
What is a the Python program you requested given the following:
I am working on the file "Permutations.ipynb".
The first task is:
Before diving deeper into Permutations, a couple helper functions will come in handy, that of gcd (greatest common divisor) and lcm (lowest common multiple).  These two are related.  Furthermore, we would like versions which tackle any number of integer inputs, which we'll call GCD and LCD respectively.
Can you write Python program for it?
assistant
#Here is the Python program you requested.

def gcd(a, b):
    while b:
        b, a = a % b, b
    return a

def lcm(a, b):
    return int((a * b)/gcd(a, b))

def GCD(*terms):
    return reduce(gcd, terms)

def LCM(*terms):
    return reduce(lcm, terms)

GCD(25, 50, 15)

LCM(25, 50, 15)

class P:
    """
    A Permutation
    
    self._code: a dict, is a mapping of iterable elements 
    to themselves in any order.

    start out with Identity, or directly inject the mapping as
    a dict or use an inversions table to construct the permutation
    """   

    def __init__(self, 
        the_code = None,   # direct inject
        inv_table = None,  # construct 
        iterable = ascii_lowercase + ' '): # default domain

        if the_code:
            self._code = the_code
            
        elif inv_table:
            values = []
            for key in sorted(inv_table, reverse=True):
                if inv_table[key] >= len(values):
                    values.append(key)
                else:
                    values.insert(inv_table[key], key)
            self._code = dict(zip(sorted(inv_table), values))
            
        elif iterable:    
            try:
              # create two iterators for zipping together
              iter1 = iter(iterable)
              iter2 = iter(iterable)
            except:
                raise TypeError
                
            self._code = dict(zip(iter1, iter2))
        
    def shuffle(self):
        """
        return a random permutation of this permutation
        """
        # use shuffle
        # something like
        the_keys = list(self._code.keys()) # grab keys
        shuffle(the_keys)  # shuffles copied one
        newP = P()
        # old keys point to new ones
        newP._code = dict(zip(self._code.keys(), the_keys))
        return newP
        
    def encrypt(self, plain):
        """
        turn plaintext into cyphertext using self._code
        """
        output = ""  # empty string
        for c in plain:
            output = output + self._code.get(c, c) 
        return...