Worked on Enigma, mainly changing how the notch positions are handled
[cipher-training.git] / enigma-old.ipynb
diff --git a/enigma-old.ipynb b/enigma-old.ipynb
new file mode 100644 (file)
index 0000000..a9e832d
--- /dev/null
@@ -0,0 +1,2639 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Enigma machine\n",
+    "Specification from [Codes and Ciphers](http://www.codesandciphers.org.uk/enigma/rotorspec.htm) page.\n",
+    "\n",
+    "Example Enigma machines from [Louise Dale](http://enigma.louisedade.co.uk/enigma.html) (full simulation) and [EnigmaCo](http://enigmaco.de/enigma/enigma.html) (good animation of the wheels, but no ring settings).\n",
+    "\n",
+    "There's also the nice Enigma simulator for Android by [Franklin Heath](https://franklinheath.co.uk/2012/02/04/our-first-app-published-enigma-simulator/), available on the [Google Play store](https://play.google.com/store/apps/details?id=uk.co.franklinheath.enigmasim&hl=en_GB)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import string\n",
+    "import collections\n",
+    "\n",
+    "cat = ''.join\n",
+    "\n",
+    "def clean(text): return cat(l.lower() for l in text if l in string.ascii_letters)\n",
+    "\n",
+    "def pos(letter): \n",
+    "    if letter in string.ascii_lowercase:\n",
+    "        return ord(letter) - ord('a')\n",
+    "    elif letter in string.ascii_uppercase:\n",
+    "        return ord(letter) - ord('A')\n",
+    "    else:\n",
+    "        return ''\n",
+    "    \n",
+    "def unpos(number): return chr(number % 26 + ord('a'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "wheel_i_spec = 'ekmflgdqvzntowyhxuspaibrcj'\n",
+    "wheel_ii_spec = 'ajdksiruxblhwtmcqgznpyfvoe'\n",
+    "wheel_iii_spec = 'bdfhjlcprtxvznyeiwgakmusqo'\n",
+    "wheel_iv_spec = 'esovpzjayquirhxlnftgkdcmwb'\n",
+    "wheel_v_spec = 'vzbrgityupsdnhlxawmjqofeck'\n",
+    "wheel_vi_spec = 'jpgvoumfyqbenhzrdkasxlictw'\n",
+    "wheel_vii_spec = 'nzjhgrcxmyswboufaivlpekqdt'\n",
+    "wheel_viii_spec = 'fkqhtlxocbjspdzramewniuygv'\n",
+    "beta_wheel_spec = 'leyjvcnixwpbqmdrtakzgfuhos'\n",
+    "gamma_wheel_spec = 'fsokanuerhmbtiycwlqpzxvgjd'\n",
+    "\n",
+    "wheel_i_pegs = ['q']\n",
+    "wheel_ii_pegs = ['e']\n",
+    "wheel_iii_pegs = ['v']\n",
+    "wheel_iv_pegs = ['j']\n",
+    "wheel_v_pegs = ['z']\n",
+    "wheel_vi_pegs = ['z', 'm']\n",
+    "wheel_vii_pegs = ['z', 'm']\n",
+    "wheel_viii_pegs = ['z', 'm']\n",
+    "\n",
+    "reflector_b_spec = 'ay br cu dh eq fs gl ip jx kn mo tz vw'\n",
+    "reflector_c_spec = 'af bv cp dj ei go hy kr lz mx nw tq su'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class LetterTransformer(object):\n",
+    "    def __init__(self, specification, raw_transform=False):\n",
+    "        if raw_transform:\n",
+    "            transform = specification\n",
+    "        else:\n",
+    "            transform = self.parse_specification(specification)\n",
+    "        self.validate_transform(transform)\n",
+    "        self.make_transform_map(transform)\n",
+    "    \n",
+    "    def parse_specification(self, specification):\n",
+    "        return list(zip(string.ascii_lowercase, clean(specification)))\n",
+    "        # return specification\n",
+    "    \n",
+    "    def validate_transform(self, transform):\n",
+    "        \"\"\"A set of pairs, of from-to\"\"\"\n",
+    "        if len(transform) != 26:\n",
+    "            raise ValueError(\"Transform specification has {} pairs, requires 26\".\n",
+    "                format(len(transform)))\n",
+    "        for p in transform:\n",
+    "            if len(p) != 2:\n",
+    "                raise ValueError(\"Not all mappings in transform \"\n",
+    "                    \"have two elements\")\n",
+    "        if len(set([p[0] for p in transform])) != 26:\n",
+    "            raise ValueError(\"Transform specification must list 26 origin letters\") \n",
+    "        if len(set([p[1] for p in transform])) != 26:\n",
+    "            raise ValueError(\"Transform specification must list 26 destination letters\") \n",
+    "\n",
+    "    def make_empty_transform(self):\n",
+    "        self.forward_map = [0] * 26\n",
+    "        self.backward_map = [0] * 26\n",
+    "            \n",
+    "    def make_transform_map(self, transform):\n",
+    "        self.make_empty_transform()\n",
+    "        for p in transform:\n",
+    "            self.forward_map[pos(p[0])] = pos(p[1])\n",
+    "            self.backward_map[pos(p[1])] = pos(p[0])\n",
+    "        return self.forward_map, self.backward_map\n",
+    "    \n",
+    "    def forward(self, letter):\n",
+    "        if letter in string.ascii_lowercase:\n",
+    "            return unpos(self.forward_map[pos(letter)])\n",
+    "        else:\n",
+    "            return ''\n",
+    "                \n",
+    "    def backward(self, letter):\n",
+    "        if letter in string.ascii_lowercase:\n",
+    "            return unpos(self.backward_map[pos(letter)])\n",
+    "        else:\n",
+    "            return ''"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[('z', 'a'),\n",
+       " ('a', 'b'),\n",
+       " ('b', 'c'),\n",
+       " ('c', 'd'),\n",
+       " ('d', 'e'),\n",
+       " ('e', 'f'),\n",
+       " ('f', 'g'),\n",
+       " ('g', 'h'),\n",
+       " ('h', 'i'),\n",
+       " ('i', 'j'),\n",
+       " ('j', 'k'),\n",
+       " ('k', 'l'),\n",
+       " ('l', 'm'),\n",
+       " ('m', 'n'),\n",
+       " ('n', 'o'),\n",
+       " ('o', 'p'),\n",
+       " ('p', 'q'),\n",
+       " ('q', 'r'),\n",
+       " ('r', 's'),\n",
+       " ('s', 't'),\n",
+       " ('t', 'u'),\n",
+       " ('u', 'v'),\n",
+       " ('v', 'w'),\n",
+       " ('w', 'x'),\n",
+       " ('x', 'y'),\n",
+       " ('y', 'z')]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tmap = [('z', 'a')] + [(l, string.ascii_lowercase[i+1]) for i, l in enumerate(string.ascii_lowercase[:-1])]\n",
+    "tmap"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zyxwcabdefghijklmnopqrstuv'"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(collections.OrderedDict.fromkeys('zyxwc' + string.ascii_lowercase))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "tmap2 = list(zip(string.ascii_lowercase, cat(collections.OrderedDict.fromkeys('zyxwc' + string.ascii_lowercase))))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([1,\n",
+       "  2,\n",
+       "  3,\n",
+       "  4,\n",
+       "  5,\n",
+       "  6,\n",
+       "  7,\n",
+       "  8,\n",
+       "  9,\n",
+       "  10,\n",
+       "  11,\n",
+       "  12,\n",
+       "  13,\n",
+       "  14,\n",
+       "  15,\n",
+       "  16,\n",
+       "  17,\n",
+       "  18,\n",
+       "  19,\n",
+       "  20,\n",
+       "  21,\n",
+       "  22,\n",
+       "  23,\n",
+       "  24,\n",
+       "  25,\n",
+       "  0],\n",
+       " [25,\n",
+       "  0,\n",
+       "  1,\n",
+       "  2,\n",
+       "  3,\n",
+       "  4,\n",
+       "  5,\n",
+       "  6,\n",
+       "  7,\n",
+       "  8,\n",
+       "  9,\n",
+       "  10,\n",
+       "  11,\n",
+       "  12,\n",
+       "  13,\n",
+       "  14,\n",
+       "  15,\n",
+       "  16,\n",
+       "  17,\n",
+       "  18,\n",
+       "  19,\n",
+       "  20,\n",
+       "  21,\n",
+       "  22,\n",
+       "  23,\n",
+       "  24])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lt = LetterTransformer(tmap, raw_transform = True)\n",
+    "assert(lt.forward_map == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0])\n",
+    "assert(lt.backward_map == [25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24])\n",
+    "lt.forward_map, lt.backward_map"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([25,\n",
+       "  24,\n",
+       "  23,\n",
+       "  22,\n",
+       "  2,\n",
+       "  0,\n",
+       "  1,\n",
+       "  3,\n",
+       "  4,\n",
+       "  5,\n",
+       "  6,\n",
+       "  7,\n",
+       "  8,\n",
+       "  9,\n",
+       "  10,\n",
+       "  11,\n",
+       "  12,\n",
+       "  13,\n",
+       "  14,\n",
+       "  15,\n",
+       "  16,\n",
+       "  17,\n",
+       "  18,\n",
+       "  19,\n",
+       "  20,\n",
+       "  21],\n",
+       " [5,\n",
+       "  6,\n",
+       "  4,\n",
+       "  7,\n",
+       "  8,\n",
+       "  9,\n",
+       "  10,\n",
+       "  11,\n",
+       "  12,\n",
+       "  13,\n",
+       "  14,\n",
+       "  15,\n",
+       "  16,\n",
+       "  17,\n",
+       "  18,\n",
+       "  19,\n",
+       "  20,\n",
+       "  21,\n",
+       "  22,\n",
+       "  23,\n",
+       "  24,\n",
+       "  25,\n",
+       "  3,\n",
+       "  2,\n",
+       "  1,\n",
+       "  0])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lt = LetterTransformer(cat(collections.OrderedDict.fromkeys('zyxwc' + string.ascii_lowercase)))\n",
+    "assert(lt.forward_map == [25, 24, 23, 22, 2, 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21])\n",
+    "assert(lt.backward_map == [5, 6, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 3, 2, 1, 0])\n",
+    "assert(cat(lt.forward(l) for l in string.ascii_lowercase) == 'zyxwcabdefghijklmnopqrstuv')\n",
+    "assert(cat(lt.backward(l) for l in string.ascii_lowercase) == 'fgehijklmnopqrstuvwxyzdcba')\n",
+    "lt.forward_map, lt.backward_map"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zyxwcabdefghijklmnopqrstuv'"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(lt.forward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'fgehijklmnopqrstuvwxyzdcba'"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(lt.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Plugboard(LetterTransformer):\n",
+    "    def parse_specification(self, specification):\n",
+    "        return [tuple(clean(p)) for p in specification.split()]\n",
+    "    \n",
+    "    def validate_transform(self, transform):\n",
+    "        \"\"\"A set of pairs, of from-to\"\"\"\n",
+    "        for p in transform:\n",
+    "            if len(p) != 2:\n",
+    "                raise ValueError(\"Not all mappings in transform\"\n",
+    "                    \"have two elements\")\n",
+    "    \n",
+    "    def make_empty_transform(self):\n",
+    "        self.forward_map = list(range(26))\n",
+    "        self.backward_map = list(range(26))\n",
+    "        \n",
+    "    def make_transform_map(self, transform):\n",
+    "        expanded_transform = transform + [tuple(reversed(p)) for p in transform]\n",
+    "        return super(Plugboard, self).make_transform_map(expanded_transform)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pb = Plugboard([('a', 'z'), ('b', 'y')], raw_transform=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zycdefghijklmnopqrstuvwxba'"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(pb.forward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zycdefghijklmnopqrstuvwxba'"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(pb.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pb = Plugboard('az by')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('zycdefghijklmnopqrstuvwxba', 'zycdefghijklmnopqrstuvwxba')"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(pb.forward(l) for l in string.ascii_lowercase), cat(pb.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('ugcdypblnzkhmisfrqoxavwtej', 'ugcdypblnzkhmisfrqoxavwtej')"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pb = Plugboard('ua pf rq so ni ey bg hl tx zj'.upper())\n",
+    "assert(pb.forward_map == pb.backward_map)\n",
+    "assert(pb.forward_map == [20, 6, 2, 3, 24, 15, 1, 11, 13, 25, 10, 7, 12, 8, 18, 5, 17, 16, 14, 23, 0, 21, 22, 19, 4, 9])\n",
+    "assert(cat(pb.forward(l) for l in string.ascii_lowercase) == 'ugcdypblnzkhmisfrqoxavwtej')\n",
+    "assert(cat(pb.backward(l) for l in string.ascii_lowercase) == 'ugcdypblnzkhmisfrqoxavwtej')\n",
+    "cat(pb.forward(l) for l in string.ascii_lowercase), cat(pb.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Reflector(Plugboard):\n",
+    "    def validate_transform(self, transform):\n",
+    "        if len(transform) != 13:\n",
+    "            raise ValueError(\"Reflector specification has {} pairs, requires 13\".\n",
+    "                format(len(transform)))\n",
+    "        if len(set([p[0] for p in transform] + \n",
+    "                    [p[1] for p in transform])) != 26:\n",
+    "            raise ValueError(\"Reflector specification does not contain 26 letters\")\n",
+    "        try:\n",
+    "            super(Reflector, self).validate_transform(transform)\n",
+    "        except ValueError as v:\n",
+    "            raise ValueError(\"Not all mappings in reflector have two elements\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[('a', 'y'),\n",
+       " ('b', 'r'),\n",
+       " ('c', 'u'),\n",
+       " ('d', 'h'),\n",
+       " ('e', 'q'),\n",
+       " ('f', 's'),\n",
+       " ('g', 'l'),\n",
+       " ('i', 'p'),\n",
+       " ('j', 'x'),\n",
+       " ('k', 'n'),\n",
+       " ('m', 'o'),\n",
+       " ('t', 'z'),\n",
+       " ('v', 'w')]"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# reflector_b_text = '(AY) (BR) (CU) (DH) (EQ) (FS) (GL) (IP) (JX) (KN) (MO) (TZ) (VW)'\n",
+    "reflector_b_l = [tuple(clean(p)) for p in reflector_b_spec.split()]\n",
+    "reflector_b_l"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "reflector_b = Reflector(reflector_b_spec)\n",
+    "assert(reflector_b.forward_map == reflector_b.backward_map)\n",
+    "assert(reflector_b.forward_map == [24, 17, 20, 7, 16, 18, 11, 3, 15, 23, 13, 6, 14, 10, 12, 8, 4, 1, 5, 25, 2, 22, 21, 9, 0, 19])\n",
+    "assert(cat(reflector_b.forward(l) for l in string.ascii_lowercase) == 'yruhqsldpxngokmiebfzcwvjat')\n",
+    "assert(cat(reflector_b.backward(l) for l in string.ascii_lowercase) == 'yruhqsldpxngokmiebfzcwvjat')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'yruhqsldpxngokmiebfzcwvjat'"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(reflector_b.forward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "reflector_c = Reflector(reflector_c_spec)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'fvpjiaoyedrzxwgctkuqsbnmhl'"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(reflector_c.forward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class SimpleWheel(LetterTransformer):\n",
+    "    def __init__(self, transform, position='a', raw_transform=False):\n",
+    "        super(SimpleWheel, self).__init__(transform, raw_transform)\n",
+    "        self.set_position(position)\n",
+    "        \n",
+    "    def __getattribute__(self,name):\n",
+    "        if name=='position_l':\n",
+    "            return unpos(self.position)\n",
+    "        else:\n",
+    "            return object.__getattribute__(self, name)\n",
+    "    \n",
+    "    def set_position(self, position):\n",
+    "        self.position = ord(position) - ord('a')\n",
+    "    \n",
+    "    def forward(self, letter):\n",
+    "        if letter in string.ascii_lowercase:\n",
+    "            return unpos((self.forward_map[(pos(letter) + self.position) % 26] - self.position))\n",
+    "        else:\n",
+    "            return ''\n",
+    "                \n",
+    "    def backward(self, letter):\n",
+    "        if letter in string.ascii_lowercase:\n",
+    "            return unpos((self.backward_map[(pos(letter) + self.position) % 26] - self.position))\n",
+    "        else:\n",
+    "            return ''\n",
+    "        \n",
+    "    def advance(self):\n",
+    "        self.position = (self.position + 1) % 26\n",
+    "        return self.position"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[('a', 'e'),\n",
+       " ('b', 'k'),\n",
+       " ('c', 'm'),\n",
+       " ('d', 'f'),\n",
+       " ('e', 'l'),\n",
+       " ('f', 'g'),\n",
+       " ('g', 'd'),\n",
+       " ('h', 'q'),\n",
+       " ('i', 'v'),\n",
+       " ('j', 'z'),\n",
+       " ('k', 'n'),\n",
+       " ('l', 't'),\n",
+       " ('m', 'o'),\n",
+       " ('n', 'w'),\n",
+       " ('o', 'y'),\n",
+       " ('p', 'h'),\n",
+       " ('q', 'x'),\n",
+       " ('r', 'u'),\n",
+       " ('s', 's'),\n",
+       " ('t', 'p'),\n",
+       " ('u', 'a'),\n",
+       " ('v', 'i'),\n",
+       " ('w', 'b'),\n",
+       " ('x', 'r'),\n",
+       " ('y', 'c'),\n",
+       " ('z', 'j')]"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rotor_1_transform = list(zip(string.ascii_lowercase, 'EKMFLGDQVZNTOWYHXUSPAIBRCJ'.lower()))\n",
+    "rotor_1_transform"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "rotor_1_transform = list(zip(string.ascii_lowercase, 'EKMFLGDQVZNTOWYHXUSPAIBRCJ'.lower()))\n",
+    "wheel_1 = SimpleWheel(rotor_1_transform, raw_transform=True)\n",
+    "assert(cat(wheel_1.forward(l) for l in string.ascii_lowercase) == 'ekmflgdqvzntowyhxuspaibrcj')\n",
+    "assert(cat(wheel_1.backward(l) for l in string.ascii_lowercase) == 'uwygadfpvzbeckmthxslrinqoj')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('ekmflgdqvzntowyhxuspaibrcj', 'uwygadfpvzbeckmthxslrinqoj')"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(wheel_1.forward(l) for l in string.ascii_lowercase), cat(wheel_1.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a'"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wheel_1.position_l"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "wheel_2 = SimpleWheel(wheel_ii_spec)\n",
+    "assert(cat(wheel_2.forward(l) for l in string.ascii_lowercase) == 'ajdksiruxblhwtmcqgznpyfvoe')\n",
+    "assert(cat(wheel_2.backward(l) for l in string.ascii_lowercase) == 'ajpczwrlfbdkotyuqgenhxmivs')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('ajdksiruxblhwtmcqgznpyfvoe', 'ajpczwrlfbdkotyuqgenhxmivs')"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(wheel_2.forward(l) for l in string.ascii_lowercase), cat(wheel_2.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('bdfhjlcprtxvznyeiwgakmusqo', 'tagbpcsdqeufvnzhyixjwlrkom')"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wheel_3 = SimpleWheel(wheel_iii_spec)\n",
+    "wheel_3.set_position('a')\n",
+    "wheel_3.advance()\n",
+    "assert(cat(wheel_3.forward(l) for l in string.ascii_lowercase) == 'cegikboqswuymxdhvfzjltrpna')\n",
+    "assert(cat(wheel_3.backward(l) for l in string.ascii_lowercase) == 'zfaobrcpdteumygxhwivkqjnls')\n",
+    "assert(wheel_3.position == 1)\n",
+    "assert(wheel_3.position_l == 'b')\n",
+    "\n",
+    "for _ in range(24): wheel_3.advance()\n",
+    "assert(wheel_3.position == 25)\n",
+    "assert(wheel_3.position_l == 'z')\n",
+    "assert(cat(wheel_3.forward(l) for l in string.ascii_lowercase) == 'pcegikmdqsuywaozfjxhblnvtr')\n",
+    "assert(cat(wheel_3.backward(l) for l in string.ascii_lowercase) == 'nubhcqdterfvgwoaizjykxmslp')\n",
+    "\n",
+    "wheel_3.advance()\n",
+    "assert(wheel_3.position == 0)\n",
+    "assert(wheel_3.position_l == 'a')\n",
+    "assert(cat(wheel_3.forward(l) for l in string.ascii_lowercase) == 'bdfhjlcprtxvznyeiwgakmusqo')\n",
+    "assert(cat(wheel_3.backward(l) for l in string.ascii_lowercase) == 'tagbpcsdqeufvnzhyixjwlrkom')\n",
+    "\n",
+    "cat(wheel_3.forward(l) for l in string.ascii_lowercase), cat(wheel_3.backward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Wheel(SimpleWheel):\n",
+    "    def __init__(self, transform, ring_peg_letters, ring_setting=1, position='a', raw_transform=False):\n",
+    "        self.ring_peg_letters = ring_peg_letters\n",
+    "        self.ring_setting = ring_setting\n",
+    "        super(Wheel, self).__init__(transform, position=position, raw_transform=raw_transform)\n",
+    "        self.set_position(position)\n",
+    "        \n",
+    "    def __getattribute__(self,name):\n",
+    "        if name=='position_l':\n",
+    "            return unpos(self.position + self.ring_setting - 1)\n",
+    "        else:\n",
+    "            return object.__getattribute__(self, name)\n",
+    "\n",
+    "    def set_position(self, position):\n",
+    "        self.position = (pos(position) - self.ring_setting + 1) % 26\n",
+    "        # self.position_l = position\n",
+    "        self.peg_positions = [(pos(p) - pos(position)) % 26  for p in self.ring_peg_letters]\n",
+    "        \n",
+    "    def advance(self):\n",
+    "        super(Wheel, self).advance()\n",
+    "        self.peg_positions = [(p - 1) % 26 for p in self.peg_positions]\n",
+    "        # self.position_l = unpos(self.position + self.ring_setting - 1)\n",
+    "        return self.position"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "wheel_3 = Wheel(wheel_iii_spec, wheel_iii_pegs, position='b', ring_setting=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1, [20])"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wheel_3.position, wheel_3.peg_positions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(25, [24, 11])"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wheel_6 = Wheel(wheel_vi_spec, wheel_vi_pegs, position='b', ring_setting=3)\n",
+    "wheel_6.position, wheel_6.peg_positions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 [23, 10]\n",
+      "1 [22, 9]\n",
+      "2 [21, 8]\n",
+      "3 [20, 7]\n",
+      "4 [19, 6]\n",
+      "5 [18, 5]\n",
+      "6 [17, 4]\n",
+      "7 [16, 3]\n",
+      "8 [15, 2]\n",
+      "9 [14, 1]\n",
+      "10 [13, 0]\n",
+      "11 [12, 25]\n",
+      "12 [11, 24]\n",
+      "13 [10, 23]\n",
+      "14 [9, 22]\n",
+      "15 [8, 21]\n",
+      "16 [7, 20]\n",
+      "17 [6, 19]\n",
+      "18 [5, 18]\n",
+      "19 [4, 17]\n",
+      "20 [3, 16]\n",
+      "21 [2, 15]\n",
+      "22 [1, 14]\n",
+      "23 [0, 13]\n",
+      "24 [25, 12]\n",
+      "25 [24, 11]\n",
+      "0 [23, 10]\n"
+     ]
+    }
+   ],
+   "source": [
+    "for _ in range(27):\n",
+    "    wheel_6.advance()\n",
+    "    print(wheel_6.position, wheel_6.peg_positions)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "wheel_3 = Wheel(wheel_iii_spec, wheel_iii_pegs, position='b', ring_setting=1)\n",
+    "assert(wheel_3.position == 1)\n",
+    "assert(wheel_3.peg_positions == [20])\n",
+    "assert(wheel_3.position_l == 'b')\n",
+    "wheel_3.advance()\n",
+    "assert(wheel_3.position == 2)\n",
+    "assert(wheel_3.peg_positions == [19])\n",
+    "assert(wheel_3.position_l == 'c')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "wheel_6 = Wheel(wheel_vi_spec, wheel_vi_pegs, position='b', ring_setting=3)\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'xkqhwpvngzrcfoiaselbtymjdu')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'ptlyrmidoxbswhnfckquzgeavj')\n",
+    "assert(wheel_6.position == 25)\n",
+    "assert(11 in wheel_6.peg_positions)\n",
+    "assert(24 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'b')\n",
+    "\n",
+    "wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'jpgvoumfyqbenhzrdkasxlictw')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'skxqlhcnwarvgmebjptyfdzuio')\n",
+    "assert(wheel_6.position == 0)\n",
+    "assert(10 in wheel_6.peg_positions)\n",
+    "assert(23 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'c')\n",
+    "\n",
+    "for _ in range(22): wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'mgxantkzsyqjcufirldvhoewbp')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'dymswobuplgraevzkqifntxcjh')\n",
+    "assert(wheel_6.position == 22)\n",
+    "assert(1 in wheel_6.peg_positions)\n",
+    "assert(14 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'y')\n",
+    "\n",
+    "wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'fwzmsjyrxpibtehqkcugndvaol')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'xlrvnatokfqzduyjphemswbigc')\n",
+    "assert(wheel_6.position == 23)\n",
+    "assert(0 in wheel_6.peg_positions)\n",
+    "assert(13 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'z')\n",
+    "\n",
+    "wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'vylrixqwohasdgpjbtfmcuznke')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'kqumzsnjepyctxiogdlrvahfbw')\n",
+    "assert(wheel_6.position == 24)\n",
+    "assert(25 in wheel_6.peg_positions)\n",
+    "assert(12 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'a')\n",
+    "\n",
+    "wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'xkqhwpvngzrcfoiaselbtymjdu')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'ptlyrmidoxbswhnfckquzgeavj')\n",
+    "assert(wheel_6.position == 25)\n",
+    "assert(24 in wheel_6.peg_positions)\n",
+    "assert(11 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'b')\n",
+    "\n",
+    "wheel_6.advance()\n",
+    "assert(cat(wheel_6.forward(l) for l in string.ascii_lowercase) == 'jpgvoumfyqbenhzrdkasxlictw')\n",
+    "assert(cat(wheel_6.backward(l) for l in string.ascii_lowercase) == 'skxqlhcnwarvgmebjptyfdzuio')\n",
+    "assert(wheel_6.position == 0)\n",
+    "assert(23 in wheel_6.peg_positions)\n",
+    "assert(10 in wheel_6.peg_positions)\n",
+    "assert(wheel_6.position_l == 'c')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0, 'c', [23, 10])"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wheel_6.position, wheel_6.position_l, wheel_6.peg_positions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Enigma(object):\n",
+    "    def __init__(self, reflector_spec,\n",
+    "                 left_wheel_spec, left_wheel_pegs,\n",
+    "                 middle_wheel_spec, middle_wheel_pegs,\n",
+    "                 right_wheel_spec, right_wheel_pegs,\n",
+    "                 left_ring_setting, middle_ring_setting, right_ring_setting,\n",
+    "                 plugboard_setting):\n",
+    "        self.reflector = Reflector(reflector_spec)\n",
+    "        self.left_wheel = Wheel(left_wheel_spec, left_wheel_pegs, ring_setting=left_ring_setting)\n",
+    "        self.middle_wheel = Wheel(middle_wheel_spec, middle_wheel_pegs, ring_setting=middle_ring_setting)\n",
+    "        self.right_wheel = Wheel(right_wheel_spec, right_wheel_pegs, ring_setting=right_ring_setting)\n",
+    "        self.plugboard = Plugboard(plugboard_setting)\n",
+    "        \n",
+    "    def __getattribute__(self,name):\n",
+    "        if name=='wheel_positions':\n",
+    "            return self.left_wheel.position, self.middle_wheel.position, self.right_wheel.position \n",
+    "        elif name=='wheel_positions_l':\n",
+    "            return self.left_wheel.position_l, self.middle_wheel.position_l, self.right_wheel.position_l \n",
+    "        elif name=='peg_positions':\n",
+    "            return self.left_wheel.peg_positions, self.middle_wheel.peg_positions, self.right_wheel.peg_positions\n",
+    "        else:\n",
+    "            return object.__getattribute__(self, name)\n",
+    "\n",
+    "    \n",
+    "    def set_wheels(self, left_wheel_position, middle_wheel_position, right_wheel_position):\n",
+    "        self.left_wheel.set_position(left_wheel_position)\n",
+    "        self.middle_wheel.set_position(middle_wheel_position)\n",
+    "        self.right_wheel.set_position(right_wheel_position)\n",
+    "        \n",
+    "    def lookup(self, letter):\n",
+    "        a = self.plugboard.forward(letter)\n",
+    "        b = self.right_wheel.forward(a)\n",
+    "        c = self.middle_wheel.forward(b)\n",
+    "        d = self.left_wheel.forward(c)\n",
+    "        e = self.reflector.forward(d)\n",
+    "        f = self.left_wheel.backward(e)\n",
+    "        g = self.middle_wheel.backward(f)\n",
+    "        h = self.right_wheel.backward(g)\n",
+    "        i = self.plugboard.backward(h)\n",
+    "        return i\n",
+    "    \n",
+    "    def advance(self):\n",
+    "        advance_middle = False\n",
+    "        advance_left = False\n",
+    "        if 0 in self.right_wheel.peg_positions:\n",
+    "            advance_middle = True\n",
+    "        if 0 in self.middle_wheel.peg_positions:\n",
+    "            advance_left = True\n",
+    "            advance_middle = True\n",
+    "        self.right_wheel.advance()\n",
+    "        if advance_middle: self.middle_wheel.advance()\n",
+    "        if advance_left: self.left_wheel.advance()\n",
+    "            \n",
+    "    def encipher_letter(self, letter):\n",
+    "        self.advance()\n",
+    "        return self.lookup(letter)\n",
+    "    \n",
+    "    def encipher(self, message, debug=False):\n",
+    "        enciphered = ''\n",
+    "        for letter in clean(message):\n",
+    "            enciphered += self.encipher_letter(letter)\n",
+    "            if debug:\n",
+    "                print('Wheels now', list(self.wheel_positions_l), 'enciphering {} -> {}'.format(letter, self.lookup(letter)))\n",
+    "        return enciphered"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\"('a', 'b', 'c')\""
+      ]
+     },
+     "execution_count": 82,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sfsdf = ('a', 'b', 'c')\n",
+    "str(sfsdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "enigma = Enigma(reflector_b_spec, \n",
+    "                wheel_i_spec, wheel_i_pegs,\n",
+    "                wheel_ii_spec, wheel_ii_pegs,\n",
+    "                wheel_iii_spec, wheel_iii_pegs,\n",
+    "                1, 1, 1,\n",
+    "                '')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'u'"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.lookup('a')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a'"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.lookup('u')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'uejobtpzwcnsrkdgvmlfaqiyxh'"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(enigma.lookup(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 :: a a a ; [16] [4] [21] uejobtpzwcnsrkdgvmlfaqiyxh\n",
+      "1 :: a a b ; [16] [4] [20] baqmfexihswpdytlcvjozrkgnu\n",
+      "2 :: a a c ; [16] [4] [19] djralkwpobfeyqihncxzvugsmt\n",
+      "3 :: a a d ; [16] [4] [18] zlejcuitgdmbkonsvxphfqyrwa\n",
+      "4 :: a a e ; [16] [4] [17] gcblwtakqzhdosmxiunfryepvj\n",
+      "5 :: a a f ; [16] [4] [16] osnirgfmdpvuhcajwebxlkqtzy\n",
+      "6 :: a a g ; [16] [4] [15] wymvnqzjlhoicekuftxrpdasbg\n",
+      "7 :: a a h ; [16] [4] [14] cjafkdztpbeuormiwnvhlsqyxg\n",
+      "8 :: a a i ; [16] [4] [13] xijuyslvbczgnmqwotfrdhpaek\n",
+      "9 :: a a j ; [16] [4] [12] lfzrwbytjisaovmuxdkhpneqgc\n",
+      "10 :: a a k ; [16] [4] [11] tkezcqynuwbpvhslfxoaimjrgd\n",
+      "11 :: a a l ; [16] [4] [10] kiwfnduxbsaotelqpvjmgrchzy\n",
+      "12 :: a a m ; [16] [4] [9] sfkutbpoxycrnmhgwlaedzqijv\n",
+      "13 :: a a n ; [16] [4] [8] baqwlkhgrsfextpocijnvudmzy\n",
+      "14 :: a a o ; [16] [4] [7] teofbdzxqkjyrscvimnawpuhlg\n",
+      "15 :: a a p ; [16] [4] [6] mhypswrbzxqvaondkgeutlfjci\n",
+      "16 :: a a q ; [16] [4] [5] cpasnrhgkuixzevbyfdwjotlqm\n",
+      "17 :: a a r ; [16] [4] [4] dlfatcjwygvbnmzrxpueskhqio\n",
+      "18 :: a a s ; [16] [4] [3] lxymzjuqtfpadsrkhonigwvbce\n",
+      "19 :: a a t ; [16] [4] [2] puvioztjdhxmlyeawsrgbcqknf\n",
+      "20 :: a a u ; [16] [4] [1] baigpldqcowfyzjehvtsxrkumn\n",
+      "21 :: a a v ; [16] [4] [0] mnvfydiwgzsoablrxpkutchqej\n",
+      "22 :: a b w ; [16] [3] [25] ulfopcykswhbzvderqixanjtgm\n",
+      "23 :: a b x ; [16] [3] [24] qmwftdyovursbzhxaklejicpgn\n",
+      "24 :: a b y ; [16] [3] [23] oljmzxrvucybdqasngpwihtfke\n",
+      "25 :: a b z ; [16] [3] [22] fwevcalzxutgysrqponkjdbimh\n"
+     ]
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('a', 'a', 'a')\n",
+    "for i in range(26):\n",
+    "    print(i, '::', \n",
+    "          enigma.left_wheel.position_l, enigma.middle_wheel.position_l, enigma.right_wheel.position_l, ';',\n",
+    "          enigma.left_wheel.peg_positions, enigma.middle_wheel.peg_positions, enigma.right_wheel.peg_positions, \n",
+    "         cat(enigma.lookup(l) for l in string.ascii_lowercase))\n",
+    "    enigma.advance()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "enigma.set_wheels('a', 'a', 't')\n",
+    "assert(enigma.wheel_positions == (0, 0, 19))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'aat')\n",
+    "assert(enigma.peg_positions == ([16], [4], [2]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'puvioztjdhxmlyeawsrgbcqknf')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 0, 20))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'aau')\n",
+    "assert(enigma.peg_positions == ([16], [4], [1]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'baigpldqcowfyzjehvtsxrkumn')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 0, 21))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'aav')\n",
+    "assert(enigma.peg_positions == ([16], [4], [0]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'mnvfydiwgzsoablrxpkutchqej')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 1, 22))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'abw')\n",
+    "assert(enigma.peg_positions == ([16], [3], [25]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ulfopcykswhbzvderqixanjtgm')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 1, 23))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'abx')\n",
+    "assert(enigma.peg_positions == ([16], [3], [24]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qmwftdyovursbzhxaklejicpgn')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 1, 24))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'aby')\n",
+    "assert(enigma.peg_positions == ([16], [3], [23]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'oljmzxrvucybdqasngpwihtfke')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(1, 5, 24) ('b', 'f', 'y') ([15], [25], [23]) baknstqzrmcxjdvygiefwoulph\n"
+     ]
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('a', 'd', 't')\n",
+    "assert(enigma.wheel_positions == (0, 3, 19))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'adt')\n",
+    "assert(enigma.peg_positions == ([16], [1], [2]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'zcbpqxwsjiuonmldethrkygfva')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 3, 20))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'adu')\n",
+    "assert(enigma.peg_positions == ([16], [1], [1]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ehprawjbngotxikcsdqlzyfmvu')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 3, 21))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'adv')\n",
+    "assert(enigma.peg_positions == ([16], [1], [0]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'eqzxarpihmnvjkwgbfuyslodtc')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (0, 4, 22))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'aew')\n",
+    "assert(enigma.peg_positions == ([16], [0], [25]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qedcbtpluzmhkongavwfirsyxj')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (1, 5, 23))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'bfx')\n",
+    "assert(enigma.peg_positions == ([15], [25], [24]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'iwuedhsfazqxytvrkpgncoblmj')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (1, 5, 24))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'bfy')\n",
+    "assert(enigma.peg_positions == ([15], [25], [23]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'baknstqzrmcxjdvygiefwoulph')\n",
+    "\n",
+    "print(enigma.wheel_positions, enigma.wheel_positions_l, enigma.peg_positions, \n",
+    "         cat(enigma.lookup(l) for l in string.ascii_lowercase))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'olpfhnvflyn'"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('a', 'a', 'a')\n",
+    "ct = enigma.encipher('testmessage')\n",
+    "assert(ct == 'olpfhnvflyn')\n",
+    "ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'lawnjgpwjik'"
+      ]
+     },
+     "execution_count": 49,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('a', 'd', 't')\n",
+    "ct = enigma.encipher('testmessage')\n",
+    "assert(ct == 'lawnjgpwjik')\n",
+    "ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 5))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bff')\n",
+      "assert(enigma.peg_positions == ([15], [25], [16]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'zpqiogfsdlmjkyebcvhxwrutna')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 6))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfg')\n",
+      "assert(enigma.peg_positions == ([15], [25], [15]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'fjmnwayslbxicdpouthrqzekgv')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 7))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfh')\n",
+      "assert(enigma.peg_positions == ([15], [25], [14]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'csafzdyloxuhnmitwvbpkrqjge')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 8))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfi')\n",
+      "assert(enigma.peg_positions == ([15], [25], [13]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'kihyvulcbtagwrqzonxjfemsdp')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 9))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfj')\n",
+      "assert(enigma.peg_positions == ([15], [25], [12]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'pgzrytbksqhwxvuajdifonlmec')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 10))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfk')\n",
+      "assert(enigma.peg_positions == ([15], [25], [11]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'fkirsazncwbvyhpoudexqljtmg')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 11))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfl')\n",
+      "assert(enigma.peg_positions == ([15], [25], [10]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'mhkronubsvctafeqpdilgjxwzy')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 12))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfm')\n",
+      "assert(enigma.peg_positions == ([15], [25], [9]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'gnkuoxarzycmlbetvhwpdqsfji')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 13))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfn')\n",
+      "assert(enigma.peg_positions == ([15], [25], [8]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'bainslqkcxhfudpogtermwvjzy')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 14))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfo')\n",
+      "assert(enigma.peg_positions == ([15], [25], [7]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'xemfbdnwjitycgzusvqkprhalo')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 15))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfp')\n",
+      "assert(enigma.peg_positions == ([15], [25], [6]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qixksmhgbtdvfonrapejwluczy')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 16))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfq')\n",
+      "assert(enigma.peg_positions == ([15], [25], [5]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cgaulmbskwiefrtzynhodxjvqp')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 17))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfr')\n",
+      "assert(enigma.peg_positions == ([15], [25], [4]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'iwqfldszaxvenmyrcpgutkbjoh')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 18))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfs')\n",
+      "assert(enigma.peg_positions == ([15], [25], [3]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'vxykrjilgfdhqtusmepnoazbcw')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 19))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bft')\n",
+      "assert(enigma.peg_positions == ([15], [25], [2]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ieysbvkjahgmlpxnwtdrzfqocu')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 20))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfu')\n",
+      "assert(enigma.peg_positions == ([15], [25], [1]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'baihkjvdcfepywsltxoqzgnrmu')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 5, 21))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bfv')\n",
+      "assert(enigma.peg_positions == ([15], [25], [0]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'bayjtrilgdshvzuwxfkeompqcn')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 22))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgw')\n",
+      "assert(enigma.peg_positions == ([15], [24], [25]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'rszqohpfxyutvwegdablkmnijc')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 23))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgx')\n",
+      "assert(enigma.peg_positions == ([15], [24], [24]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'nfoxhbzeyrwqpacmljtsvukdig')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 24))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgy')\n",
+      "assert(enigma.peg_positions == ([15], [24], [23]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'czaogmeihtuqfsdxlwnjkyrpvb')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 25))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgz')\n",
+      "assert(enigma.peg_positions == ([15], [24], [22]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'omwgysdjkhizbxarupfvqtcnel')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 0))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bga')\n",
+      "assert(enigma.peg_positions == ([15], [24], [21]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cxafmdrzoqutepinjgvlksybwh')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 1))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgb')\n",
+      "assert(enigma.peg_positions == ([15], [24], [20]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'jymvnrxkoahwceiuzftspdlgbq')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 2))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgc')\n",
+      "assert(enigma.peg_positions == ([15], [24], [19]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'uzlyiqwrestcnmxvfhjkapgodb')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 3))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bgd')\n",
+      "assert(enigma.peg_positions == ([15], [24], [18]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'veosbuhgpzqynmcikwdxfartlj')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (1, 6, 4))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'bge')\n",
+      "assert(enigma.peg_positions == ([15], [24], [17]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ydhbmtrclxsiezpougkfqwvjan')\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "for i in range(26):\n",
+    "    enigma.advance()\n",
+    "    print('enigma.advance()')\n",
+    "    print(\"assert(enigma.wheel_positions == {})\".format(enigma.wheel_positions))\n",
+    "    print(\"assert(cat(enigma.wheel_positions_l) == '{}')\".format(cat(enigma.wheel_positions_l)))\n",
+    "    print(\"assert(enigma.peg_positions == {})\".format(enigma.peg_positions))\n",
+    "    print(\"assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == '{}')\".format(cat(enigma.lookup(l) for l in string.ascii_lowercase)))\n",
+    "    print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'bahxvfrpdc'"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('a', 'd', 't')\n",
+    "ct = enigma.encipher('hellothere')\n",
+    "assert(ct == 'bahxvfrpdc')\n",
+    "ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'kvmmwrlqlqsqpeugjrcxzwpfyiyybwloewrouvkpoztceuwtfjzqwpbqldttsr'"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('b', 'd', 'q')\n",
+    "ct = enigma.encipher('aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa')\n",
+    "assert(ct == 'kvmmwrlqlqsqpeugjrcxzwpfyiyybwloewrouvkpoztceuwtfjzqwpbqldttsr')\n",
+    "assert(enigma.left_wheel.position_l == 'c')\n",
+    "assert(enigma.middle_wheel.position_l == 'h')\n",
+    "assert(enigma.right_wheel.position_l == 'a')\n",
+    "ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'c'"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.left_wheel.position_l"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Setting sheet line 31 from http://www.codesandciphers.org.uk/enigma/enigma3.htm\n",
+    "# Enigma simulation settings are \n",
+    "# http://enigma.louisedade.co.uk/enigma.html?m3;b;b153;AFTX;AJFE;AU-BG-EY-FP-HL-IN-JZ-OS-QR-TX\n",
+    "w_enigma = Enigma(reflector_b_spec, \n",
+    "                wheel_i_spec, wheel_i_pegs,\n",
+    "                wheel_v_spec, wheel_v_pegs,\n",
+    "                wheel_iii_spec, wheel_iii_pegs,\n",
+    "                6, 20, 24,\n",
+    "                'ua pf rq so ni ey bg hl tx zj')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Setting sheet line 31 from http://www.codesandciphers.org.uk/enigma/enigma3.htm\n",
+    "# Enigma simulation settings are \n",
+    "# http://enigma.louisedade.co.uk/enigma.html?m3;b;b153;AFTX;AJFE;AU-BG-EY-FP-HL-IN-JZ-OS-QR-TX\n",
+    "enigma = Enigma(reflector_b_spec, \n",
+    "                wheel_i_spec, wheel_i_pegs,\n",
+    "                wheel_v_spec, wheel_v_pegs,\n",
+    "                wheel_iii_spec, wheel_iii_pegs,\n",
+    "                6, 20, 24,\n",
+    "                'ua pf rq so ni ey bg hl tx zj')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "enigma.set_wheels('j', 'e', 'u')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (4, 11, 24))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'jev')\n",
+    "assert(enigma.peg_positions == ([7], [21], [0]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'mvqjlyowkdieasgzcunxrbhtfp')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (4, 12, 25))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'jfw')\n",
+    "assert(enigma.peg_positions == ([7], [20], [25]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'sjolzuyvrbwdpxcmtiaqfhknge')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (4, 12, 0))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'jfx')\n",
+    "assert(enigma.peg_positions == ([7], [20], [24]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qrxedkoywufmlvgsabpzjnicht')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (4, 12, 1))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'jfy')\n",
+    "assert(enigma.peg_positions == ([7], [20], [23]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'hpsukliagqefwvtbjxcodnmrzy')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (4, 12, 2))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'jfz')\n",
+    "assert(enigma.peg_positions == ([7], [20], [22]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'zevnbpyqowrtxdifhkulscjmga')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "enigma.set_wheels('i', 'd', 'z')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 3))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'ida')\n",
+    "assert(enigma.peg_positions == ([8], [22], [21]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ikhpqrvcambzjondefwyxgsutl')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 4))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idb')\n",
+    "assert(enigma.peg_positions == ([8], [22], [20]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cdabskhgzwfmlqvunyexpojtri')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 5))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idc')\n",
+    "assert(enigma.peg_positions == ([8], [22], [19]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'pcbwiqhgemyvjsuaftnroldzkx')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 6))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idd')\n",
+    "assert(enigma.peg_positions == ([8], [22], [18]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'xcbfvdnouptmlghjzwykierasq')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 7))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'ide')\n",
+    "assert(enigma.peg_positions == ([8], [22], [17]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'xfvglbdynuseriwqpmkzjcoaht')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 8))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idf')\n",
+    "assert(enigma.peg_positions == ([8], [22], [16]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'tfpqlbouynsewjgcdxkahzmriv')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 9))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idg')\n",
+    "assert(enigma.peg_positions == ([8], [22], [15]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cjaunvlwtbygzexrspqidfhokm')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 10))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idh')\n",
+    "assert(enigma.peg_positions == ([8], [22], [14]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'yltxkrqvowebzpingfucshjdam')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 11))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idi')\n",
+    "assert(enigma.peg_positions == ([8], [22], [13]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'myktluzrnxceaiqsohpdfwvjbg')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 12))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idj')\n",
+    "assert(enigma.peg_positions == ([8], [22], [12]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'pynjrmiugdqxfcvakewzhoslbt')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 13))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idk')\n",
+    "assert(enigma.peg_positions == ([8], [22], [11]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'mwvedyplnoxhaijgrqtszcbkfu')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 14))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idl')\n",
+    "assert(enigma.peg_positions == ([8], [22], [10]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qcbrfeutvoxpnmjladzhgiykws')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 15))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idm')\n",
+    "assert(enigma.peg_positions == ([8], [22], [9]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'dnoahryetsmukbcvwfjilpqzgx')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 16))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idn')\n",
+    "assert(enigma.peg_positions == ([8], [22], [8]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'nidcfehgbqsovalyjzkxwmutpr')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 17))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'ido')\n",
+    "assert(enigma.peg_positions == ([8], [22], [7]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'joifxdulcarhzpbntkwqgysevm')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 18))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idp')\n",
+    "assert(enigma.peg_positions == ([8], [22], [6]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ptnlsxvozmwdjchayuebrgkfqi')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 19))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idq')\n",
+    "assert(enigma.peg_positions == ([8], [22], [5]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'slwopzqnmxybihdeguavrtcjkf')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 20))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idr')\n",
+    "assert(enigma.peg_positions == ([8], [22], [4]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'hcbedwlamzogixkytsrqvufnpj')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 21))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'ids')\n",
+    "assert(enigma.peg_positions == ([8], [22], [3]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'odxbjwzrmelkisavuhnyqpfctg')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 22))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idt')\n",
+    "assert(enigma.peg_positions == ([8], [22], [2]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'udgbfeclrwnhxksvtioqapjmzy')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 23))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idu')\n",
+    "assert(enigma.peg_positions == ([8], [22], [1]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'nrdczqxmowvshaiufblypkjgte')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 10, 24))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'idv')\n",
+    "assert(enigma.peg_positions == ([8], [22], [0]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'hkifjdoacebqtzgulyvmpsxwrn')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 11, 25))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'iew')\n",
+    "assert(enigma.peg_positions == ([8], [21], [25]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'yptzuhofqvnmlkgbixwcejsrad')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 11, 0))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'iex')\n",
+    "assert(enigma.peg_positions == ([8], [21], [24]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'vkdcwhqfjibzsptngumoraeyxl')\n",
+    "\n",
+    "enigma.advance()\n",
+    "assert(enigma.wheel_positions == (3, 11, 1))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'iey')\n",
+    "assert(enigma.peg_positions == ([8], [21], [23]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'wenpbqrouxlkychdfgzvitajms')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('verylongtestmessagewithanextrabitofmessageforgoodmeasure',\n",
+       " (3, 12, 6),\n",
+       " ('i', 'f', 'd'),\n",
+       " ([8], [20], [18]),\n",
+       " 'urygzpdmxtwshqvfnbljaokice')"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('i', 'd', 'z')\n",
+    "ct = enigma.encipher('verylongtestmessagewithanextrabitofmessageforgoodmeasure')\n",
+    "assert(ct == 'gstsegeqdrthkfwesljjomfvcqwcfspxpfqqmewvddybarzwubxtpejz')\n",
+    "assert(enigma.wheel_positions == (3, 12, 6))\n",
+    "assert(cat(enigma.wheel_positions_l) == 'ifd')\n",
+    "assert(enigma.peg_positions == ([8], [20], [18]))\n",
+    "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'urygzpdmxtwshqvfnbljaokice')\n",
+    "\n",
+    "enigma.set_wheels('i', 'd', 'z')\n",
+    "pt = enigma.encipher('gstsegeqdrthkfwesljjomfvcqwcfspxpfqqmewvddybarzwubxtpejz')\n",
+    "assert(pt == 'verylongtestmessagewithanextrabitofmessageforgoodmeasure')\n",
+    "\n",
+    "pt, enigma.wheel_positions, enigma.wheel_positions_l, enigma.peg_positions, cat(enigma.lookup(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 3))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'ida')\n",
+      "assert(enigma.peg_positions == ([8], [22], [21]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ikhpqrvcambzjondefwyxgsutl')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 4))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idb')\n",
+      "assert(enigma.peg_positions == ([8], [22], [20]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cdabskhgzwfmlqvunyexpojtri')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 5))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idc')\n",
+      "assert(enigma.peg_positions == ([8], [22], [19]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'pcbwiqhgemyvjsuaftnroldzkx')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 6))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idd')\n",
+      "assert(enigma.peg_positions == ([8], [22], [18]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'xcbfvdnouptmlghjzwykierasq')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 7))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'ide')\n",
+      "assert(enigma.peg_positions == ([8], [22], [17]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'xfvglbdynuseriwqpmkzjcoaht')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 8))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idf')\n",
+      "assert(enigma.peg_positions == ([8], [22], [16]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'tfpqlbouynsewjgcdxkahzmriv')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 9))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idg')\n",
+      "assert(enigma.peg_positions == ([8], [22], [15]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'cjaunvlwtbygzexrspqidfhokm')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 10))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idh')\n",
+      "assert(enigma.peg_positions == ([8], [22], [14]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'yltxkrqvowebzpingfucshjdam')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 11))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idi')\n",
+      "assert(enigma.peg_positions == ([8], [22], [13]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'myktluzrnxceaiqsohpdfwvjbg')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 12))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idj')\n",
+      "assert(enigma.peg_positions == ([8], [22], [12]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'pynjrmiugdqxfcvakewzhoslbt')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 13))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idk')\n",
+      "assert(enigma.peg_positions == ([8], [22], [11]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'mwvedyplnoxhaijgrqtszcbkfu')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 14))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idl')\n",
+      "assert(enigma.peg_positions == ([8], [22], [10]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'qcbrfeutvoxpnmjladzhgiykws')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 15))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idm')\n",
+      "assert(enigma.peg_positions == ([8], [22], [9]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'dnoahryetsmukbcvwfjilpqzgx')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 16))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idn')\n",
+      "assert(enigma.peg_positions == ([8], [22], [8]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'nidcfehgbqsovalyjzkxwmutpr')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 17))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'ido')\n",
+      "assert(enigma.peg_positions == ([8], [22], [7]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'joifxdulcarhzpbntkwqgysevm')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 18))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idp')\n",
+      "assert(enigma.peg_positions == ([8], [22], [6]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'ptnlsxvozmwdjchayuebrgkfqi')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 19))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idq')\n",
+      "assert(enigma.peg_positions == ([8], [22], [5]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'slwopzqnmxybihdeguavrtcjkf')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 20))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idr')\n",
+      "assert(enigma.peg_positions == ([8], [22], [4]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'hcbedwlamzogixkytsrqvufnpj')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 21))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'ids')\n",
+      "assert(enigma.peg_positions == ([8], [22], [3]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'odxbjwzrmelkisavuhnyqpfctg')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 22))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idt')\n",
+      "assert(enigma.peg_positions == ([8], [22], [2]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'udgbfeclrwnhxksvtioqapjmzy')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 23))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idu')\n",
+      "assert(enigma.peg_positions == ([8], [22], [1]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'nrdczqxmowvshaiufblypkjgte')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 10, 24))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'idv')\n",
+      "assert(enigma.peg_positions == ([8], [22], [0]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'hkifjdoacebqtzgulyvmpsxwrn')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 11, 25))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'iew')\n",
+      "assert(enigma.peg_positions == ([8], [21], [25]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'yptzuhofqvnmlkgbixwcejsrad')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 11, 0))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'iex')\n",
+      "assert(enigma.peg_positions == ([8], [21], [24]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'vkdcwhqfjibzsptngumoraeyxl')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 11, 1))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'iey')\n",
+      "assert(enigma.peg_positions == ([8], [21], [23]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'wenpbqrouxlkychdfgzvitajms')\n",
+      "\n",
+      "enigma.advance()\n",
+      "assert(enigma.wheel_positions == (3, 11, 2))\n",
+      "assert(cat(enigma.wheel_positions_l) == 'iez')\n",
+      "assert(enigma.peg_positions == ([8], [21], [22]))\n",
+      "assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == 'szgyqvclkoihurjwenaxmfptdb')\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "enigma.set_wheels('i', 'd', 'z')\n",
+    "\n",
+    "for i in range(26):\n",
+    "    enigma.advance()\n",
+    "    print('enigma.advance()')\n",
+    "    print(\"assert(enigma.wheel_positions == {})\".format(enigma.wheel_positions))\n",
+    "    print(\"assert(cat(enigma.wheel_positions_l) == '{}')\".format(cat(enigma.wheel_positions_l)))\n",
+    "    print(\"assert(enigma.peg_positions == {})\".format(enigma.peg_positions))\n",
+    "    print(\"assert(cat(enigma.lookup(l) for l in string.ascii_lowercase) == '{}')\".format(cat(enigma.lookup(l) for l in string.ascii_lowercase)))\n",
+    "    print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Reflector B\n",
+    "# Rotors III, I, II with rings 17, 11, 19\n",
+    "# Plugboard pairs GU FZ BD LK TC PS HV WN JE AM\n",
+    "\n",
+    "tbt_enigma = Enigma(reflector_b_spec, \n",
+    "                wheel_iii_spec, wheel_iii_pegs,\n",
+    "                wheel_i_spec, wheel_i_pegs,\n",
+    "                wheel_ii_spec, wheel_ii_pegs,\n",
+    "                17, 11, 19,\n",
+    "                'GU FZ BD LK TC PS HV WN JE AM'.lower())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'jbvbwwzfslhxnhzzccsngebmrnswgjonwbjnzcfgadeuoyameylmpvny'"
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'q', 'v')\n",
+    "ct = tbt_enigma.encipher('verylongtestmessagewithanextrabitofmessageforgoodmeasure')\n",
+    "ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'slgncszxltkzebghstgywdmpr'"
+      ]
+     },
+     "execution_count": 62,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "target_ct = ''.join(c.lower() for c in 'SLGNC SZXLT KZEBG HSTGY WDMPR' if c in string.ascii_letters)\n",
+    "target_ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'theyweredetectebybritishshipsinclud'"
+      ]
+     },
+     "execution_count": 63,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "target_pt = ''.join(c.lower() for c in 'Theyw erede tecte byBri tishs hipsi nclud' if c in string.ascii_letters)\n",
+    "target_pt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'theyweredetectedbybritishshipsinclud'"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "target_pt = ''.join(c.lower() for c in 'Theyw erede tecte d byBri tishs hipsi nclud' if c in string.ascii_letters)\n",
+    "target_pt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(25, 35)"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(target_ct), len(target_pt)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "slgncszxltkzebghstgywdmpr\n",
+      "theyweredetectebybritishshipsinclud\n"
+     ]
+    }
+   ],
+   "source": [
+    "print('{}\\n{}'.format(target_ct, target_pt))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "theyweredetectedbybritishshipsinclud\n",
+      "slgncszxltkzebghstgywdmpr\n",
+      "slgncszxltkzebghstgywdmprucuzqdqzpve\n",
+      "theyweredetectedbybritish\n"
+     ]
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "this_pt = tbt_enigma.encipher(target_ct)\n",
+    "\n",
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "this_ct = tbt_enigma.encipher(target_pt)\n",
+    "\n",
+    "\n",
+    "print('{}\\n{}\\n{}\\n{}'.format(target_pt, target_ct, this_ct, this_pt))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import itertools"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def str_ham(s1, s2):\n",
+    "    \"\"\"Hamming distance for strings\"\"\"\n",
+    "    return sum(1 for c1, c2 in zip(s1, s2) if c1 == c2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 68,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "str_ham('hello', 'hello')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "best ('a', 'a', 'a') 25\n",
+      "best ('a', 'a', 'a') 25\n",
+      "best ('a', 'a', 'a') 25\n",
+      "best ('a', 'a', 'a') 25\n",
+      "1 loop, best of 3: 17.6 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "best = ('a', 'a', 'a')\n",
+    "best_hd = 0\n",
+    "for w1, w2, w3 in itertools.product(string.ascii_lowercase, repeat=3):\n",
+    "    tbt_enigma.set_wheels(w1, w2, w3)\n",
+    "    this_ct = tbt_enigma.encipher(target_pt)\n",
+    "    if this_ct == target_ct:\n",
+    "        print(w1, w2, w3)\n",
+    "    if str_ham(this_ct, target_ct) > best_hd:\n",
+    "        best = (w1, w2, w3)\n",
+    "        best_hd = str_ham(this_ct, target_ct)\n",
+    "print('best', best, best_hd)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Wheels now ['a', 'a', 'b'] enciphering t -> s\n",
+      "Wheels now ['a', 'a', 'c'] enciphering h -> l\n",
+      "Wheels now ['a', 'a', 'd'] enciphering e -> g\n",
+      "Wheels now ['a', 'a', 'e'] enciphering y -> n\n",
+      "Wheels now ['a', 'b', 'f'] enciphering w -> c\n",
+      "Wheels now ['a', 'b', 'g'] enciphering e -> s\n",
+      "Wheels now ['a', 'b', 'h'] enciphering r -> z\n",
+      "Wheels now ['a', 'b', 'i'] enciphering e -> x\n",
+      "Wheels now ['a', 'b', 'j'] enciphering d -> l\n",
+      "Wheels now ['a', 'b', 'k'] enciphering e -> t\n",
+      "Wheels now ['a', 'b', 'l'] enciphering t -> k\n",
+      "Wheels now ['a', 'b', 'm'] enciphering e -> z\n",
+      "Wheels now ['a', 'b', 'n'] enciphering c -> e\n",
+      "Wheels now ['a', 'b', 'o'] enciphering t -> b\n",
+      "Wheels now ['a', 'b', 'p'] enciphering e -> g\n",
+      "Wheels now ['a', 'b', 'q'] enciphering d -> h\n",
+      "Wheels now ['a', 'b', 'r'] enciphering b -> s\n",
+      "Wheels now ['a', 'b', 's'] enciphering y -> t\n",
+      "Wheels now ['a', 'b', 't'] enciphering b -> g\n",
+      "Wheels now ['a', 'b', 'u'] enciphering r -> y\n",
+      "Wheels now ['a', 'b', 'v'] enciphering i -> w\n",
+      "Wheels now ['a', 'b', 'w'] enciphering t -> d\n",
+      "Wheels now ['a', 'b', 'x'] enciphering i -> m\n",
+      "Wheels now ['a', 'b', 'y'] enciphering s -> p\n",
+      "Wheels now ['a', 'b', 'z'] enciphering h -> r\n",
+      "Wheels now ['a', 'b', 'a'] enciphering s -> u\n",
+      "Wheels now ['a', 'b', 'b'] enciphering h -> c\n",
+      "Wheels now ['a', 'b', 'c'] enciphering i -> u\n",
+      "Wheels now ['a', 'b', 'd'] enciphering p -> z\n",
+      "Wheels now ['a', 'b', 'e'] enciphering s -> q\n",
+      "Wheels now ['a', 'c', 'f'] enciphering i -> d\n",
+      "Wheels now ['a', 'c', 'g'] enciphering n -> q\n",
+      "Wheels now ['a', 'c', 'h'] enciphering c -> z\n",
+      "Wheels now ['a', 'c', 'i'] enciphering l -> p\n",
+      "Wheels now ['a', 'c', 'j'] enciphering u -> v\n",
+      "Wheels now ['a', 'c', 'k'] enciphering d -> e\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "('slgncszxltkzebghstgywdmprucuzqdqzpve', 'slgncszxltkzebghstgywdmpr')"
+      ]
+     },
+     "execution_count": 94,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "tbt_enigma.encipher(target_pt, debug=True), target_ct"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Wheels now ['a', 'a', 'b'] enciphering s -> t\n",
+      "Wheels now ['a', 'a', 'c'] enciphering l -> h\n",
+      "Wheels now ['a', 'a', 'd'] enciphering g -> e\n",
+      "Wheels now ['a', 'a', 'e'] enciphering n -> y\n",
+      "Wheels now ['a', 'b', 'f'] enciphering c -> w\n",
+      "Wheels now ['a', 'b', 'g'] enciphering s -> e\n",
+      "Wheels now ['a', 'b', 'h'] enciphering z -> r\n",
+      "Wheels now ['a', 'b', 'i'] enciphering x -> e\n",
+      "Wheels now ['a', 'b', 'j'] enciphering l -> d\n",
+      "Wheels now ['a', 'b', 'k'] enciphering t -> e\n",
+      "Wheels now ['a', 'b', 'l'] enciphering k -> t\n",
+      "Wheels now ['a', 'b', 'm'] enciphering z -> e\n",
+      "Wheels now ['a', 'b', 'n'] enciphering e -> c\n",
+      "Wheels now ['a', 'b', 'o'] enciphering b -> t\n",
+      "Wheels now ['a', 'b', 'p'] enciphering g -> e\n",
+      "Wheels now ['a', 'b', 'q'] enciphering h -> d\n",
+      "Wheels now ['a', 'b', 'r'] enciphering s -> b\n",
+      "Wheels now ['a', 'b', 's'] enciphering t -> y\n",
+      "Wheels now ['a', 'b', 't'] enciphering g -> b\n",
+      "Wheels now ['a', 'b', 'u'] enciphering y -> r\n",
+      "Wheels now ['a', 'b', 'v'] enciphering w -> i\n",
+      "Wheels now ['a', 'b', 'w'] enciphering d -> t\n",
+      "Wheels now ['a', 'b', 'x'] enciphering m -> i\n",
+      "Wheels now ['a', 'b', 'y'] enciphering p -> s\n",
+      "Wheels now ['a', 'b', 'z'] enciphering r -> h\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "('theyweredetectedbybritish', 'theyweredetectedbybritishshipsinclud')"
+      ]
+     },
+     "execution_count": 95,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "tbt_enigma.encipher(target_ct, debug=True), target_pt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('theyweredetectedbybritish', 'theyweredetectedbybritishshipsinclud')"
+      ]
+     },
+     "execution_count": 96,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "tbt_enigma.encipher(target_ct), target_pt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'mdtbjzuvielkawosqrpcghnxyf'"
+      ]
+     },
+     "execution_count": 97,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cat(tbt_enigma.plugboard.forward(l) for l in string.ascii_lowercase)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 99,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tbt_enigma.set_wheels('a', 'a', 'a')\n",
+    "tbt_enigma.left_wheel.position"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.5.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}