X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=hill-ciphers.ipynb;h=bd07c69ff5f08ec9421452aca4e35cb2b2b39e08;hb=HEAD;hp=2019dd5b600618d8d93d69e6ad5cf79b60aa45bf;hpb=14ac787d794684b5aceacb307d687597e464e7b4;p=cipher-tools.git

diff --git a/hill-ciphers.ipynb b/hill-ciphers.ipynb
index 2019dd5..bd07c69 100644
--- a/hill-ciphers.ipynb
+++ b/hill-ciphers.ipynb
@@ -1,1657 +1,1706 @@
 {
- "metadata": {
-  "name": "",
-  "signature": "sha256:112d1c84c318592f927e18c5b0f15ed60ac8418ca15cb79596ba6212ff2d7e3f"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
+ "cells": [
   {
-   "cells": [
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import matplotlib.pyplot as plt\n",
-      "import pandas as pd\n",
-      "import collections\n",
-      "import string\n",
-      "import numpy as np\n",
-      "from numpy import matrix\n",
-      "from numpy import linalg\n",
-      "%matplotlib inline\n",
-      "\n",
-      "from cipher import *\n",
-      "from cipherbreak import *\n",
-      "\n",
-      "c6a = open('2014/6a.ciphertext').read()\n",
-      "c6b = open('2014/6b.ciphertext').read()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 54
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "key_a, score = railfence_break(sanitise(c6a))\n",
-      "key_a, score"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 3,
-       "text": [
-        "(3, -2314.997881051078)"
-       ]
-      }
-     ],
-     "prompt_number": 3
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "' '.join(segment(railfence_decipher(sanitise(c6a), key_a)))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 4,
-       "text": [
-        "'mark the last message told usa lot the scuttling equipment is designed to pump water in and out of the vessel like a submarine dive control but clearly they werent planning to turn a container ship into a sub this ship is a largescale version of something i have seen in the caribbean drug runners use a similar technique to get below radar coverage for inshore runs sinking the vessel so that the deck remains just below the wave tops the fda pirates seem more interested in staying away from shore but getting close enough to track and record electronic communications without detection i am guessing this scuttling system is what they call nautilus in their log but i am still baffled by the references to seahorse the next page of the log looks harder to crack but the cipher clerk tells me it is a hill cipher and that they must have been in a hurry or have been enciphering by hand since they just used a two by two matrix actually we have been pretty lax with our security and i think the next message is end will use avi genere cipher given that we are using secure cables i dont think we have too much to worry about so i will keep the keyword short say three characters more later harry'"
-       ]
-      }
-     ],
-     "prompt_number": 4
-    },
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import pandas as pd\n",
+    "import collections\n",
+    "import string\n",
+    "import numpy as np\n",
+    "from numpy import matrix\n",
+    "from numpy import linalg\n",
+    "%matplotlib inline\n",
+    "\n",
+    "from cipher import *\n",
+    "from cipherbreak import *\n",
+    "\n",
+    "c6a = open('2014/6a.ciphertext').read()\n",
+    "c6b = open('2014/6b.ciphertext').read()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "c6bs = sanitise(c6b)\n",
-      "c6bs"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "(3, -2314.997881051078)"
+      ]
+     },
+     "execution_count": 3,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 7,
-       "text": [
-        "'hwssswxfewhhrfewpdrvttdhxbccleayphalnadhiehaoudrotwnrrvysabjlttbaytmelrkaidopthatlelrtwaamaneksvvzrvllatkcrjquicizgtoqcpnrrkttowandqehtqrvtbaydqealannohulanuzlwextlvjrvivhnohdqmgykaclmswrupdetfioftfelhzpxhaswftwprrsweiseohefpdrvttnvagdvswgoerbetnharvaeevtlltbmgaiatgelinmdawevhatterdhrznbnvoutnefoteveaehlaymhacglzeptvvdimworfisgtuzlwibeqohubtghamqornjnnrumqvjtxeltfovgawdaeevllgrtxibgtibevmpsaateoasevaeyqohameonncfuidoefafattemuimnflznbekofobrliaehhauihnnnwzaeevtlltpaalnanvtzlzuucptaelinanpaahewfthaosetaribnbnvhaevdhyytlmuxb'"
-       ]
-      }
-     ],
-     "prompt_number": 7
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "key_a, score = railfence_break(sanitise(c6a))\n",
+    "key_a, score"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "c6b_nums = [ord(c) - ord('a') for c in c6bs]\n",
-      "c6b_nums"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'mark the last message told usa lot the scuttling equipment is designed to pump water in and out of the vessel like a submarine dive control but clearly they werent planning to turn a container ship into a sub this ship is a largescale version of something i have seen in the caribbean drug runners use a similar technique to get below radar coverage for inshore runs sinking the vessel so that the deck remains just below the wave tops the fda pirates seem more interested in staying away from shore but getting close enough to track and record electronic communications without detection i am guessing this scuttling system is what they call nautilus in their log but i am still baffled by the references to seahorse the next page of the log looks harder to crack but the cipher clerk tells me it is a hill cipher and that they must have been in a hurry or have been enciphering by hand since they just used a two by two matrix actually we have been pretty lax with our security and i think the next message is end will use avi genere cipher given that we are using secure cables i dont think we have too much to worry about so i will keep the keyword short say three characters more later harry'"
+      ]
+     },
+     "execution_count": 4,
      "metadata": {},
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-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 17,
-       "text": [
-        "[7,\n",
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-       ]
-      }
-     ],
-     "prompt_number": 17
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "' '.join(segment(railfence_decipher(sanitise(c6a), key_a)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "m = np.matrix([[7,8], [11,11]])\n",
-      "m"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'hwssswxfewhhrfewpdrvttdhxbccleayphalnadhiehaoudrotwnrrvysabjlttbaytmelrkaidopthatlelrtwaamaneksvvzrvllatkcrjquicizgtoqcpnrrkttowandqehtqrvtbaydqealannohulanuzlwextlvjrvivhnohdqmgykaclmswrupdetfioftfelhzpxhaswftwprrsweiseohefpdrvttnvagdvswgoerbetnharvaeevtlltbmgaiatgelinmdawevhatterdhrznbnvoutnefoteveaehlaymhacglzeptvvdimworfisgtuzlwibeqohubtghamqornjnnrumqvjtxeltfovgawdaeevllgrtxibgtibevmpsaateoasevaeyqohameonncfuidoefafattemuimnflznbekofobrliaehhauihnnnwzaeevtlltpaalnanvtzlzuucptaelinanpaahewfthaosetaribnbnvhaevdhyytlmuxb'"
+      ]
+     },
+     "execution_count": 7,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 106,
-       "text": [
-        "matrix([[ 7,  8],\n",
-        "        [11, 11]])"
-       ]
-      }
-     ],
-     "prompt_number": 106
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c6bs = sanitise(c6b)\n",
+    "c6bs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
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+       " 1]"
+      ]
+     },
+     "execution_count": 17,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 107,
-       "text": [
-        "-11.000000000000002"
-       ]
-      }
-     ],
-     "prompt_number": 107
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c6b_nums = [ord(c) - ord('a') for c in c6bs]\n",
+    "c6b_nums"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "m.I"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 7,  8],\n",
+       "        [11, 11]])"
+      ]
+     },
+     "execution_count": 106,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 108,
-       "text": [
-        "matrix([[-1.        ,  0.72727273],\n",
-        "        [ 1.        , -0.63636364]])"
-       ]
-      }
-     ],
-     "prompt_number": 108
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m = np.matrix([[7,8], [11,11]])\n",
+    "m"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "v = np.matrix([[7], [22]])\n",
-      "v"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "-11.000000000000002"
+      ]
+     },
+     "execution_count": 107,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 37,
-       "text": [
-        "matrix([[ 7],\n",
-        "        [22]])"
-       ]
-      }
-     ],
-     "prompt_number": 37
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linalg.det(m)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "c = (m*v) % 26\n",
-      "c"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[-1.        ,  0.72727273],\n",
+       "        [ 1.        , -0.63636364]])"
+      ]
+     },
+     "execution_count": 108,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 46,
-       "text": [
-        "matrix([[9],\n",
-        "        [5]])"
-       ]
-      }
-     ],
-     "prompt_number": 46
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m.I"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "np.linalg.solve(m, c) % 26"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 7],\n",
+       "        [22]])"
+      ]
+     },
+     "execution_count": 37,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 48,
-       "text": [
-        "matrix([[  7.],\n",
-        "        [ 22.]])"
-       ]
-      }
-     ],
-     "prompt_number": 48
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v = np.matrix([[7], [22]])\n",
+    "v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "m*v"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[9],\n",
+       "        [5]])"
+      ]
+     },
+     "execution_count": 46,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 40,
-       "text": [
-        "matrix([[ 87],\n",
-        "        [109]])"
-       ]
-      }
-     ],
-     "prompt_number": 40
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c = (m*v) % 26\n",
+    "c"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "(m*v)%26"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[  7.],\n",
+       "        [ 22.]])"
+      ]
+     },
+     "execution_count": 48,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 41,
-       "text": [
-        "matrix([[9],\n",
-        "        [5]])"
-       ]
-      }
-     ],
-     "prompt_number": 41
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linalg.solve(m, c) % 26"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "np.linalg.solve(m, (m*v)%26)%26"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 87],\n",
+       "        [109]])"
+      ]
+     },
+     "execution_count": 40,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 42,
-       "text": [
-        "matrix([[  7.],\n",
-        "        [ 22.]])"
-       ]
-      }
-     ],
-     "prompt_number": 42
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m*v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "len(m)"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[9],\n",
+       "        [5]])"
+      ]
+     },
+     "execution_count": 41,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 51,
-       "text": [
-        "2"
-       ]
-      }
-     ],
-     "prompt_number": 51
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(m*v)%26"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def hill_encipher(matrix, message_letters, fillvalue='a'):\n",
-      "    n = len(matrix)\n",
-      "    sanitised_message = sanitise(message_letters)\n",
-      "    if len(sanitised_message) % n != 0:\n",
-      "        padding = fillvalue[0] * (n - len(sanitised_message) % n)\n",
-      "    else:\n",
-      "        padding = ''\n",
-      "    message = [ord(c) - ord('a') for c in sanitised_message + padding]\n",
-      "    message_chunks = [message[i:i+n] for i in range(0, len(message), n)]\n",
-      "    # message_chunks = chunks(message, len(matrix), fillvalue=None)\n",
-      "    enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0] for c in message_chunks]\n",
-      "    return ''.join([chr(int(round(l)) % 26 + ord('a')) for l in sum(enciphered_chunks, [])])"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[  7.],\n",
+       "        [ 22.]])"
+      ]
+     },
+     "execution_count": 42,
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 181
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linalg.solve(m, (m*v)%26)%26"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_encipher(m, 'hellothere')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "execution_count": 51,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 156,
-       "text": [
-        "'drjiqzdrvx'"
-       ]
-      }
-     ],
-     "prompt_number": 156
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(m)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 181,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def hill_encipher(matrix, message_letters, fillvalue='a'):\n",
+    "    n = len(matrix)\n",
+    "    sanitised_message = sanitise(message_letters)\n",
+    "    if len(sanitised_message) % n != 0:\n",
+    "        padding = fillvalue[0] * (n - len(sanitised_message) % n)\n",
+    "    else:\n",
+    "        padding = ''\n",
+    "    message = [ord(c) - ord('a') for c in sanitised_message + padding]\n",
+    "    message_chunks = [message[i:i+n] for i in range(0, len(message), n)]\n",
+    "    # message_chunks = chunks(message, len(matrix), fillvalue=None)\n",
+    "    enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0] for c in message_chunks]\n",
+    "    return ''.join([chr(int(round(l)) % 26 + ord('a')) for l in sum(enciphered_chunks, [])])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 156,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "msg = [ord(c) - ord('a') for c in 'hellothere']\n",
-      "msg"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'drjiqzdrvx'"
+      ]
+     },
+     "execution_count": 156,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 68,
-       "text": [
-        "[7, 4, 11, 11, 14, 19, 7, 4, 17, 4]"
-       ]
-      }
-     ],
-     "prompt_number": 68
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_encipher(m, 'hellothere')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
-      "msgc"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[7, 4, 11, 11, 14, 19, 7, 4, 17, 4]"
+      ]
+     },
+     "execution_count": 68,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 112,
-       "text": [
-        "[[7, 11], [14, 25], [21, 14], [7, 11], [11, 15], [0, 0]]"
-       ]
-      }
-     ],
-     "prompt_number": 112
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "msg = [ord(c) - ord('a') for c in 'hellothere']\n",
+    "msg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "((m*np.matrix(msgc[0]).T).T % 26).tolist()[0]"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[[7, 11], [14, 25], [21, 14], [7, 11], [11, 15], [0, 0]]"
+      ]
+     },
+     "execution_count": 112,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 87,
-       "text": [
-        "[7, 11]"
-       ]
-      }
-     ],
-     "prompt_number": 87
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
+    "msgc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def hill_decipher(matrix, message, fillvalue='a'):\n",
-      "    adjugate = linalg.det(matrix)*linalg.inv(matrix)\n",
-      "    inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]\n",
-      "    inverse_matrix = (inverse_determinant * adjugate) % 26\n",
-      "    return hill_encipher(inverse_matrix, message, fillvalue)                                                 "
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[7, 11]"
+      ]
+     },
+     "execution_count": 87,
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 195
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "((m*np.matrix(msgc[0]).T).T % 26).tolist()[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 195,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def hill_decipher(matrix, message, fillvalue='a'):\n",
+    "    adjugate = linalg.det(matrix)*linalg.inv(matrix)\n",
+    "    inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]\n",
+    "    inverse_matrix = (inverse_determinant * adjugate) % 26\n",
+    "    return hill_encipher(inverse_matrix, message, fillvalue)                                                 "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 161,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_decipher(m, 'drjiqzdrvx')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'hellothere'"
+      ]
+     },
+     "execution_count": 161,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 161,
-       "text": [
-        "'hellothere'"
-       ]
-      }
-     ],
-     "prompt_number": 161
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_decipher(m, 'drjiqzdrvx')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "msg = [ord(c) - ord('a') for c in 'drjiqzdrvxaa']\n",
-      "msg"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[3, 17, 9, 8, 16, 25, 3, 17, 21, 23, 0, 0]"
+      ]
+     },
+     "execution_count": 114,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 114,
-       "text": [
-        "[3, 17, 9, 8, 16, 25, 3, 17, 21, 23, 0, 0]"
-       ]
-      }
-     ],
-     "prompt_number": 114
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "msg = [ord(c) - ord('a') for c in 'drjiqzdrvxaa']\n",
+    "msg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
-      "msgc"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[[3, 17], [9, 8], [16, 25], [3, 17], [21, 23], [0, 0]]"
+      ]
+     },
+     "execution_count": 115,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 115,
-       "text": [
-        "[[3, 17], [9, 8], [16, 25], [3, 17], [21, 23], [0, 0]]"
-       ]
-      }
-     ],
-     "prompt_number": 115
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
+    "msgc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "(np.linalg.solve(m, np.matrix(msgc[0]).T).T % 26)"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[  9.36363636,  18.18181818]])"
+      ]
+     },
+     "execution_count": 116,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 116,
-       "text": [
-        "matrix([[  9.36363636,  18.18181818]])"
-       ]
-      }
-     ],
-     "prompt_number": 116
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(np.linalg.solve(m, np.matrix(msgc[0]).T).T % 26)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 142,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "m_adj = linalg.det(m)*linalg.inv(m)\n",
-      "m_adj"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 11.,  -8.],\n",
+       "        [-11.,   7.]])"
+      ]
+     },
+     "execution_count": 142,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 142,
-       "text": [
-        "matrix([[ 11.,  -8.],\n",
-        "        [-11.,   7.]])"
-       ]
-      }
-     ],
-     "prompt_number": 142
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m_adj = linalg.det(m)*linalg.inv(m)\n",
+    "m_adj"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 148,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "modular_division_table[int(round(linalg.det(m))) % 26][1]"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "7"
+      ]
+     },
+     "execution_count": 148,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 148,
-       "text": [
-        "7"
-       ]
-      }
-     ],
-     "prompt_number": 148
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "modular_division_table[int(round(linalg.det(m))) % 26][1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 150,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "m_inv = (modular_division_table[int(round(linalg.det(m))) % 26][1] * m_adj) % 26\n",
-      "m_inv"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 25.,  22.],\n",
+       "        [  1.,  23.]])"
+      ]
+     },
+     "execution_count": 150,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 150,
-       "text": [
-        "matrix([[ 25.,  22.],\n",
-        "        [  1.,  23.]])"
-       ]
-      }
-     ],
-     "prompt_number": 150
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m_inv = (modular_division_table[int(round(linalg.det(m))) % 26][1] * m_adj) % 26\n",
+    "m_inv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_encipher(m_inv, 'drjiqzdrvx')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'hellothere'"
+      ]
+     },
+     "execution_count": 157,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 157,
-       "text": [
-        "'hellothere'"
-       ]
-      }
-     ],
-     "prompt_number": 157
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_encipher(m_inv, 'drjiqzdrvx')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 120,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "np.dot(m , 1/linalg.det(m) * mc)"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 1.,  0.],\n",
+       "        [ 0.,  1.]])"
+      ]
+     },
+     "execution_count": 120,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 120,
-       "text": [
-        "matrix([[ 1.,  0.],\n",
-        "        [ 0.,  1.]])"
-       ]
-      }
-     ],
-     "prompt_number": 120
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.dot(m , 1/linalg.det(m) * mc)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 122,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "ml = np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]])\n",
-      "ml"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 6, 24,  1],\n",
+       "        [13, 16, 10],\n",
+       "        [20, 17, 15]])"
+      ]
+     },
+     "execution_count": 122,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 122,
-       "text": [
-        "matrix([[ 6, 24,  1],\n",
-        "        [13, 16, 10],\n",
-        "        [20, 17, 15]])"
-       ]
-      }
-     ],
-     "prompt_number": 122
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ml = np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]])\n",
+    "ml"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 137,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "ml_adj = linalg.det(ml)*linalg.inv(ml) % 26\n",
-      "ml_adj"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[ 18.,  21.,  16.],\n",
+       "        [  5.,  18.,   5.],\n",
+       "        [  5.,  14.,  18.]])"
+      ]
+     },
+     "execution_count": 137,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 137,
-       "text": [
-        "matrix([[ 18.,  21.,  16.],\n",
-        "        [  5.,  18.,   5.],\n",
-        "        [  5.,  14.,  18.]])"
-       ]
-      }
-     ],
-     "prompt_number": 137
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ml_adj = linalg.det(ml)*linalg.inv(ml) % 26\n",
+    "ml_adj"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 138,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "modular_division_table[int(linalg.det(ml) % 26)][1]"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "25"
+      ]
+     },
+     "execution_count": 138,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 138,
-       "text": [
-        "25"
-       ]
-      }
-     ],
-     "prompt_number": 138
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "modular_division_table[int(linalg.det(ml) % 26)][1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 139,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "ml_inv = (modular_division_table[int(linalg.det(ml) % 26)][1] * ml_adj) % 26\n",
-      "ml_inv"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "matrix([[  8.,   5.,  10.],\n",
+       "        [ 21.,   8.,  21.],\n",
+       "        [ 21.,  12.,   8.]])"
+      ]
+     },
+     "execution_count": 139,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 139,
-       "text": [
-        "matrix([[  8.,   5.,  10.],\n",
-        "        [ 21.,   8.,  21.],\n",
-        "        [ 21.,  12.,   8.]])"
-       ]
-      }
-     ],
-     "prompt_number": 139
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ml_inv = (modular_division_table[int(linalg.det(ml) % 26)][1] * ml_adj) % 26\n",
+    "ml_inv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 193,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_encipher(ml, 'hello there')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'tfjflpznvyac'"
+      ]
+     },
+     "execution_count": 193,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 193,
-       "text": [
-        "'tfjflpznvyac'"
-       ]
-      }
-     ],
-     "prompt_number": 193
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_encipher(ml, 'hello there')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 196,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_decipher(ml, 'tfjflpznvyac')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'hellothereaa'"
+      ]
+     },
+     "execution_count": 196,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 196,
-       "text": [
-        "'hellothereaa'"
-       ]
-      }
-     ],
-     "prompt_number": 196
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_decipher(ml, 'tfjflpznvyac')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 182,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_encipher(ml, 'act')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'poh'"
+      ]
+     },
+     "execution_count": 182,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 182,
-       "text": [
-        "'poh'"
-       ]
-      }
-     ],
-     "prompt_number": 182
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_encipher(ml, 'act')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 192,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_decipher(ml, 'poh')"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "[[  8.   5.  10.]\n",
-        " [ 21.   8.  21.]\n",
-        " [ 21.  12.   8.]]\n"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 192,
-       "text": [
-        "'act'"
-       ]
-      }
-     ],
-     "prompt_number": 192
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[  8.   5.  10.]\n",
+      " [ 21.   8.  21.]\n",
+      " [ 21.  12.   8.]]\n"
+     ]
     },
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "[chr(int(round(i)) % 26 + ord('a')) for i in (ml_inv * np.matrix([ord(c) - ord('a') for c in 'poh']).T).T.tolist()[0]]"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'act'"
+      ]
+     },
+     "execution_count": 192,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 180,
-       "text": [
-        "['a', 'c', 't']"
-       ]
-      }
-     ],
-     "prompt_number": 180
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_decipher(ml, 'poh')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 180,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "hill_encipher(ml_inv, 'poh')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "['a', 'c', 't']"
+      ]
+     },
+     "execution_count": 180,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 184,
-       "text": [
-        "'act'"
-       ]
-      }
-     ],
-     "prompt_number": 184
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[chr(int(round(i)) % 26 + ord('a')) for i in (ml_inv * np.matrix([ord(c) - ord('a') for c in 'poh']).T).T.tolist()[0]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 184,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "len([list(m) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=3)], repeat=3)])"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "'act'"
+      ]
+     },
+     "execution_count": 184,
      "metadata": {},
-     "outputs": [
-      {
-       "ename": "KeyboardInterrupt",
-       "evalue": "",
-       "output_type": "pyerr",
-       "traceback": [
-        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
-        "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
-       ]
-      }
-     ],
-     "prompt_number": 203
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hill_encipher(ml_inv, 'poh')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 203,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "(3**3)**3"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 202,
-       "text": [
-        "19683"
-       ]
-      }
-     ],
-     "prompt_number": 202
-    },
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
+     ]
+    }
+   ],
+   "source": [
+    "len([list(m) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=3)], repeat=3)])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 202,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "[np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(3), repeat=2)], repeat=2)]"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "19683"
+      ]
+     },
+     "execution_count": 202,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 206,
-       "text": [
-        "[matrix([[0, 0],\n",
-        "         [0, 0]]), matrix([[0, 0],\n",
-        "         [0, 1]]), matrix([[0, 0],\n",
-        "         [0, 2]]), matrix([[0, 0],\n",
-        "         [1, 0]]), matrix([[0, 0],\n",
-        "         [1, 1]]), matrix([[0, 0],\n",
-        "         [1, 2]]), matrix([[0, 0],\n",
-        "         [2, 0]]), matrix([[0, 0],\n",
-        "         [2, 1]]), matrix([[0, 0],\n",
-        "         [2, 2]]), matrix([[0, 1],\n",
-        "         [0, 0]]), matrix([[0, 1],\n",
-        "         [0, 1]]), matrix([[0, 1],\n",
-        "         [0, 2]]), matrix([[0, 1],\n",
-        "         [1, 0]]), matrix([[0, 1],\n",
-        "         [1, 1]]), matrix([[0, 1],\n",
-        "         [1, 2]]), matrix([[0, 1],\n",
-        "         [2, 0]]), matrix([[0, 1],\n",
-        "         [2, 1]]), matrix([[0, 1],\n",
-        "         [2, 2]]), matrix([[0, 2],\n",
-        "         [0, 0]]), matrix([[0, 2],\n",
-        "         [0, 1]]), matrix([[0, 2],\n",
-        "         [0, 2]]), matrix([[0, 2],\n",
-        "         [1, 0]]), matrix([[0, 2],\n",
-        "         [1, 1]]), matrix([[0, 2],\n",
-        "         [1, 2]]), matrix([[0, 2],\n",
-        "         [2, 0]]), matrix([[0, 2],\n",
-        "         [2, 1]]), matrix([[0, 2],\n",
-        "         [2, 2]]), matrix([[1, 0],\n",
-        "         [0, 0]]), matrix([[1, 0],\n",
-        "         [0, 1]]), matrix([[1, 0],\n",
-        "         [0, 2]]), matrix([[1, 0],\n",
-        "         [1, 0]]), matrix([[1, 0],\n",
-        "         [1, 1]]), matrix([[1, 0],\n",
-        "         [1, 2]]), matrix([[1, 0],\n",
-        "         [2, 0]]), matrix([[1, 0],\n",
-        "         [2, 1]]), matrix([[1, 0],\n",
-        "         [2, 2]]), matrix([[1, 1],\n",
-        "         [0, 0]]), matrix([[1, 1],\n",
-        "         [0, 1]]), matrix([[1, 1],\n",
-        "         [0, 2]]), matrix([[1, 1],\n",
-        "         [1, 0]]), matrix([[1, 1],\n",
-        "         [1, 1]]), matrix([[1, 1],\n",
-        "         [1, 2]]), matrix([[1, 1],\n",
-        "         [2, 0]]), matrix([[1, 1],\n",
-        "         [2, 1]]), matrix([[1, 1],\n",
-        "         [2, 2]]), matrix([[1, 2],\n",
-        "         [0, 0]]), matrix([[1, 2],\n",
-        "         [0, 1]]), matrix([[1, 2],\n",
-        "         [0, 2]]), matrix([[1, 2],\n",
-        "         [1, 0]]), matrix([[1, 2],\n",
-        "         [1, 1]]), matrix([[1, 2],\n",
-        "         [1, 2]]), matrix([[1, 2],\n",
-        "         [2, 0]]), matrix([[1, 2],\n",
-        "         [2, 1]]), matrix([[1, 2],\n",
-        "         [2, 2]]), matrix([[2, 0],\n",
-        "         [0, 0]]), matrix([[2, 0],\n",
-        "         [0, 1]]), matrix([[2, 0],\n",
-        "         [0, 2]]), matrix([[2, 0],\n",
-        "         [1, 0]]), matrix([[2, 0],\n",
-        "         [1, 1]]), matrix([[2, 0],\n",
-        "         [1, 2]]), matrix([[2, 0],\n",
-        "         [2, 0]]), matrix([[2, 0],\n",
-        "         [2, 1]]), matrix([[2, 0],\n",
-        "         [2, 2]]), matrix([[2, 1],\n",
-        "         [0, 0]]), matrix([[2, 1],\n",
-        "         [0, 1]]), matrix([[2, 1],\n",
-        "         [0, 2]]), matrix([[2, 1],\n",
-        "         [1, 0]]), matrix([[2, 1],\n",
-        "         [1, 1]]), matrix([[2, 1],\n",
-        "         [1, 2]]), matrix([[2, 1],\n",
-        "         [2, 0]]), matrix([[2, 1],\n",
-        "         [2, 1]]), matrix([[2, 1],\n",
-        "         [2, 2]]), matrix([[2, 2],\n",
-        "         [0, 0]]), matrix([[2, 2],\n",
-        "         [0, 1]]), matrix([[2, 2],\n",
-        "         [0, 2]]), matrix([[2, 2],\n",
-        "         [1, 0]]), matrix([[2, 2],\n",
-        "         [1, 1]]), matrix([[2, 2],\n",
-        "         [1, 2]]), matrix([[2, 2],\n",
-        "         [2, 0]]), matrix([[2, 2],\n",
-        "         [2, 1]]), matrix([[2, 2],\n",
-        "         [2, 2]])]"
-       ]
-      }
-     ],
-     "prompt_number": 206
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(3**3)**3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 206,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "all_matrices = [np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=2)], repeat=2)]\n",
-      "valid_matrices = [m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
-      "                  if d != 0\n",
-      "                  if d % 2 != 0\n",
-      "                  if d % 13 != 0 ]\n",
-      "len(valid_matrices)"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "[matrix([[0, 0],\n",
+       "         [0, 0]]), matrix([[0, 0],\n",
+       "         [0, 1]]), matrix([[0, 0],\n",
+       "         [0, 2]]), matrix([[0, 0],\n",
+       "         [1, 0]]), matrix([[0, 0],\n",
+       "         [1, 1]]), matrix([[0, 0],\n",
+       "         [1, 2]]), matrix([[0, 0],\n",
+       "         [2, 0]]), matrix([[0, 0],\n",
+       "         [2, 1]]), matrix([[0, 0],\n",
+       "         [2, 2]]), matrix([[0, 1],\n",
+       "         [0, 0]]), matrix([[0, 1],\n",
+       "         [0, 1]]), matrix([[0, 1],\n",
+       "         [0, 2]]), matrix([[0, 1],\n",
+       "         [1, 0]]), matrix([[0, 1],\n",
+       "         [1, 1]]), matrix([[0, 1],\n",
+       "         [1, 2]]), matrix([[0, 1],\n",
+       "         [2, 0]]), matrix([[0, 1],\n",
+       "         [2, 1]]), matrix([[0, 1],\n",
+       "         [2, 2]]), matrix([[0, 2],\n",
+       "         [0, 0]]), matrix([[0, 2],\n",
+       "         [0, 1]]), matrix([[0, 2],\n",
+       "         [0, 2]]), matrix([[0, 2],\n",
+       "         [1, 0]]), matrix([[0, 2],\n",
+       "         [1, 1]]), matrix([[0, 2],\n",
+       "         [1, 2]]), matrix([[0, 2],\n",
+       "         [2, 0]]), matrix([[0, 2],\n",
+       "         [2, 1]]), matrix([[0, 2],\n",
+       "         [2, 2]]), matrix([[1, 0],\n",
+       "         [0, 0]]), matrix([[1, 0],\n",
+       "         [0, 1]]), matrix([[1, 0],\n",
+       "         [0, 2]]), matrix([[1, 0],\n",
+       "         [1, 0]]), matrix([[1, 0],\n",
+       "         [1, 1]]), matrix([[1, 0],\n",
+       "         [1, 2]]), matrix([[1, 0],\n",
+       "         [2, 0]]), matrix([[1, 0],\n",
+       "         [2, 1]]), matrix([[1, 0],\n",
+       "         [2, 2]]), matrix([[1, 1],\n",
+       "         [0, 0]]), matrix([[1, 1],\n",
+       "         [0, 1]]), matrix([[1, 1],\n",
+       "         [0, 2]]), matrix([[1, 1],\n",
+       "         [1, 0]]), matrix([[1, 1],\n",
+       "         [1, 1]]), matrix([[1, 1],\n",
+       "         [1, 2]]), matrix([[1, 1],\n",
+       "         [2, 0]]), matrix([[1, 1],\n",
+       "         [2, 1]]), matrix([[1, 1],\n",
+       "         [2, 2]]), matrix([[1, 2],\n",
+       "         [0, 0]]), matrix([[1, 2],\n",
+       "         [0, 1]]), matrix([[1, 2],\n",
+       "         [0, 2]]), matrix([[1, 2],\n",
+       "         [1, 0]]), matrix([[1, 2],\n",
+       "         [1, 1]]), matrix([[1, 2],\n",
+       "         [1, 2]]), matrix([[1, 2],\n",
+       "         [2, 0]]), matrix([[1, 2],\n",
+       "         [2, 1]]), matrix([[1, 2],\n",
+       "         [2, 2]]), matrix([[2, 0],\n",
+       "         [0, 0]]), matrix([[2, 0],\n",
+       "         [0, 1]]), matrix([[2, 0],\n",
+       "         [0, 2]]), matrix([[2, 0],\n",
+       "         [1, 0]]), matrix([[2, 0],\n",
+       "         [1, 1]]), matrix([[2, 0],\n",
+       "         [1, 2]]), matrix([[2, 0],\n",
+       "         [2, 0]]), matrix([[2, 0],\n",
+       "         [2, 1]]), matrix([[2, 0],\n",
+       "         [2, 2]]), matrix([[2, 1],\n",
+       "         [0, 0]]), matrix([[2, 1],\n",
+       "         [0, 1]]), matrix([[2, 1],\n",
+       "         [0, 2]]), matrix([[2, 1],\n",
+       "         [1, 0]]), matrix([[2, 1],\n",
+       "         [1, 1]]), matrix([[2, 1],\n",
+       "         [1, 2]]), matrix([[2, 1],\n",
+       "         [2, 0]]), matrix([[2, 1],\n",
+       "         [2, 1]]), matrix([[2, 1],\n",
+       "         [2, 2]]), matrix([[2, 2],\n",
+       "         [0, 0]]), matrix([[2, 2],\n",
+       "         [0, 1]]), matrix([[2, 2],\n",
+       "         [0, 2]]), matrix([[2, 2],\n",
+       "         [1, 0]]), matrix([[2, 2],\n",
+       "         [1, 1]]), matrix([[2, 2],\n",
+       "         [1, 2]]), matrix([[2, 2],\n",
+       "         [2, 0]]), matrix([[2, 2],\n",
+       "         [2, 1]]), matrix([[2, 2],\n",
+       "         [2, 2]])]"
+      ]
+     },
+     "execution_count": 206,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 215,
-       "text": [
-        "157248"
-       ]
-      }
-     ],
-     "prompt_number": 215
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(3), repeat=2)], repeat=2)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 215,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "%%timeit\n",
-      "[m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
-      "                  if d != 0\n",
-      "                  if d % 2 != 0\n",
-      "                  if d % 13 != 0 ]\n",
-      "print('done')"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "157248"
+      ]
+     },
+     "execution_count": 215,
      "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "done\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "1 loops, best of 3: 10 s per loop\n"
-       ]
-      }
-     ],
-     "prompt_number": 216
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "all_matrices = [np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=2)], repeat=2)]\n",
+    "valid_matrices = [m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
+    "                  if d != 0\n",
+    "                  if d % 2 != 0\n",
+    "                  if d % 13 != 0 ]\n",
+    "len(valid_matrices)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 216,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "%%timeit\n",
-      "[m for m in all_matrices\n",
-      "                  if int(round(linalg.det(m))) != 0\n",
-      "                  if int(round(linalg.det(m))) % 2 != 0\n",
-      "                  if int(round(linalg.det(m))) % 13 != 0 ]\n",
-      "print('done')"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "done\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "done"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "\n",
-        "1 loops, best of 3: 20.4 s per loop\n"
-       ]
-      }
-     ],
-     "prompt_number": 217
-    },
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "done\n",
+      "done\n",
+      "done\n",
+      "done\n",
+      "1 loops, best of 3: 10 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "[m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
+    "                  if d != 0\n",
+    "                  if d % 2 != 0\n",
+    "                  if d % 13 != 0 ]\n",
+    "print('done')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 217,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": []
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "done\n",
+      "done\n",
+      "done\n",
+      "done\n",
+      "1 loops, best of 3: 20.4 s per loop\n"
+     ]
     }
    ],
-   "metadata": {}
+   "source": [
+    "%%timeit\n",
+    "[m for m in all_matrices\n",
+    "                  if int(round(linalg.det(m))) != 0\n",
+    "                  if int(round(linalg.det(m))) % 2 != 0\n",
+    "                  if int(round(linalg.det(m))) % 13 != 0 ]\n",
+    "print('done')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": []
   }
- ]
-}
\ No newline at end of file
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}