@kurner/Permutations

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• main.py
main.py
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```
```# -*- coding: utf-8 -*-
"""
Created on Tue Nov 10 17:39:09 2015

@author: Kirby Urner

Fun for Group Theory + Python
https://github.com/4dsolutions/Python5/blob/master/px_class.py

"""

from random import shuffle
from string import ascii_lowercase  # all lowercase letters

class P:
"""
A Permutation

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

def __init__(self,
the_code = None,   # direct inject
inv_table = None,  # construct
iterable = ascii_lowercase + ' '): # default domain
"""
start out with Identity, or directly inject the mapping as
a dict or use an inversions table to construct the permutation
"""
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 other one
newP = P()
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 output

def decrypt(self, cypher):
"""
Turn cyphertext into plaintext using ~self
"""
reverse_P = ~self  # invert me!
output = ""
for c in cypher:
output = output + reverse_P._code.get(c, c)
return output

def __getitem__(self, key):
return self._code.get(key, None)

def __repr__(self):
return "P class: " + str(tuple(self._code.items())[:3]) + "..."

def cyclic(self):
"""
cyclic notation, a compact view of a group
"""
output = []
the_dict = self._code.copy()
while the_dict:
start = tuple(the_dict.keys())[0]
the_cycle = [start]
the_next = the_dict.pop(start)
while the_next != start:
the_cycle.append(the_next)
the_next = the_dict.pop(the_next)
output.append(tuple(the_cycle))
return tuple(output)

def __mul__(self, other):
"""
look up my keys to get values that serve
as keys to get others "target" values
"""
new_code = {}
for c in self._code:  # going through my keys
target = other._code[ self._code[c] ]
new_code[c] = target
new_P = P(' ')
new_P._code = new_code
return new_P

def __truediv__(self, other):
return self * ~other

def __pow__(self, exp):
"""
multiply self * self the right number of times
"""
if exp == 0:
output = P()
else:
output = self

for x in range(1, abs(exp)):
output *= self

if exp < 0:
output = ~output

return output

def __call__(self, s):
"""
another way to encrypt
"""
return self.encrypt(s)

def __invert__(self):
"""
create new P with reversed dict
"""
newP = P(' ')
newP._code = dict(zip(self._code.values(), self._code.keys()))
return newP

def __eq__(self, other):
"""
are these permutation the same?
Yes if self._cod==e  other._code
"""
return self._code == other._code

def inversion_table(self):
invs = {}
invP = ~self
keys = sorted(self._code)
for key in keys:
x = invP[key] # position of key
cnt = 0
for left_of_key in keys: # in order up to position
if left_of_key == x: # none more to left
break
if self._code[left_of_key] > key:
cnt += 1
invs[key] = cnt
return invs

def test_me():
p = P() # identity permutation
new_p = p.shuffle()
inv_p = ~new_p
try:
assert p == inv_p * new_p   # should be True
print("First Test Succeeds")
except AssertionError:
print("First Test Fails")
#==========
p = P().shuffle()
try:
assert p ** -1 == ~p
assert p ** -2 == ~(p * p)
assert p ** -2 == (~p * ~p)
print("Second Test Succeeds")
except AssertionError:
print("Second Test Fails")
#==========
p = P().shuffle()
s = "able was i ere i saw elba"
c = p(s)
print("Plain:  ", s)
print("Cipher: ", c)
try:
assert p.decrypt(c) == s
print("Third Test Succeeds")
except AssertionError:
print("Third Test Fails")
#==========
knuth = {1:5, 2:9, 3:1, 4:8, 5:2, 6:6, 7:4, 8:7, 9:3} # vol 3 pg. 12
expected = {1:2, 2:3, 3:6, 4:4, 5:0, 6:2, 7:2, 8:1, 9:0} # Ibid
k = P(the_code=knuth)
try:
assert k.inversion_table() == expected
print("Fourth Test Succeeds")
except AssertionError:
print("Fourth Test Fails")
#==========
p = P(inv_table = expected)
try:
assert p == k
print("Fifth Test Succeeds")
except AssertionError:
print("Fifth Test Fails")
#==========
p = P().shuffle()
inv = p.inversion_table()
print("Perm:", p._code)
print("Inv table:", inv)
new_p = P(inv_table = inv)
try:
assert p == new_p
print("Sixth Test Succeeds")
except AssertionError:
print("Sixth Test Fails")

test_me()

```
Python 3.6.1 (default, Dec 2015, 13:05:11) [GCC 4.8.2] on linux