diff --git a/permutation_algebra_examples.ipynb b/permutation_algebra_examples.ipynb
new file mode 100644
index 0000000..8376ee4
--- /dev/null
+++ b/permutation_algebra_examples.ipynb
@@ -0,0 +1,284 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:43:00.143871Z",
+     "start_time": "2024-07-03T14:43:00.105294Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from src.models import OuterKey, InnerKey, AlphabetKey"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "outputs": [],
+   "source": [
+    "height = 10\n",
+    "width = 7\n",
+    "\n",
+    "a0 = AlphabetKey.init_matrix(width, height, 255)\n",
+    "\n",
+    "o0 = OuterKey.init_matrix(height)\n",
+    "o1 = OuterKey.init_matrix(height)\n",
+    "o2 = OuterKey.init_matrix(height)\n",
+    "o3 = OuterKey.init_matrix(height)\n",
+    "\n",
+    "i0 = InnerKey.init_matrix(width, height)\n",
+    "i1 = InnerKey.init_matrix(width, height)\n",
+    "i2 = InnerKey.init_matrix(width, height)\n"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:43:11.536945Z",
+     "start_time": "2024-07-03T14:43:11.532046Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a0_i0_o0_v0 = a0 << (i0 < o0)\n",
+    "a0_i0_o0_v1 = ((a0 < ~o0) << i0) < o0\n",
+    "\n",
+    "a0_i0_o0_v0 == a0_i0_o0_v1"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:43:36.810538Z",
+     "start_time": "2024-07-03T14:43:36.805348Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n"
+     ]
+    }
+   ],
+   "source": [
+    "a0_o0_i0_v0 = (a0 < o0) << i0\n",
+    "a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
+    "a0_i0_o0_v0 == a0_i0_o0_v1"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:44:07.321778Z",
+     "start_time": "2024-07-03T14:44:07.318402Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a0_o0_i0_v0 = (a0 < o0) << i0\n",
+    "a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
+    "a0_o0_i0_v0 == a0_o0_i0_v1"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:44:48.380940Z",
+     "start_time": "2024-07-03T14:44:48.377032Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "n_i0_i1 = ~(i0 << i1)\n",
+    "ni1_ni0 = ~i1 << ~i0\n",
+    "ni1_ni0 == n_i0_i1"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:45:01.588349Z",
+     "start_time": "2024-07-03T14:45:01.584641Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "i0_i1_i2_v0 = i0 << i1 << i2\n",
+    "i0_i1_i2_v1 = i0 << (i1 << i2)\n",
+    "i0_i1_i2_v2 = (i0 << i1) << i2\n",
+    "i0_i1_i2_v0 == i0_i1_i2_v1 == i0_i1_i2_v2"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:45:41.860153Z",
+     "start_time": "2024-07-03T14:45:41.855897Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "i0_i2_i1 = i0 << i2 << i1\n",
+    "i0 == i0_i2_i1 << ~(i2 << i1) == i0_i2_i1 << ~i1 << ~i2"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:47:02.948800Z",
+     "start_time": "2024-07-03T14:47:02.944314Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "i0_o0_o1_o2_v1 = ((i0 < o0) < o1) < o2\n",
+    "i0_o0_o1_o2_v2 = (i0 < (o0 << o1)) < o2\n",
+    "i0_o0_o1_o2_v3 = ((i0 < o0) < (o1 << o2))\n",
+    "\n",
+    "i0_o0_o1_o2_v1 == i0_o0_o1_o2_v2 == i0_o0_o1_o2_v3"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:48:17.489611Z",
+     "start_time": "2024-07-03T14:48:17.485650Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "True"
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "i0 < (o0 << o1 << o2) != i0_o0_o1_o2_v1 # not equal"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T14:48:18.120561Z",
+     "start_time": "2024-07-03T14:48:18.116436Z"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "outputs": [],
+   "source": [],
+   "metadata": {
+    "collapsed": false
+   }
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/permutation_algebra_examples.py b/permutation_algebra_examples.py
deleted file mode 100644
index fb8a11b..0000000
--- a/permutation_algebra_examples.py
+++ /dev/null
@@ -1,47 +0,0 @@
-from src.models import OuterKey, InnerKey, AlphabetKey
-
-height = 10
-width = 7
-
-a0 = AlphabetKey.init_matrix(width, height, 255)
-
-o0 = OuterKey.init_matrix(height)
-
-i0 = InnerKey.init_matrix(width, height)
-i1 = InnerKey.init_matrix(width, height)
-i2 = InnerKey.init_matrix(width, height)
-
-a0_i0_o0_v0 = a0 << (i0 < o0)
-
-a0_i0_o0_v1 = ((a0 < ~o0) << i0) < o0
-
-print(a0_i0_o0_v0 == a0_i0_o0_v1)
-
-a0_o0_i0_v0 = (a0 < o0) << i0
-a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0
-print(a0_i0_o0_v0 == a0_i0_o0_v1)
-
-
-a0_o0_i0_v0 = (a0 < o0) << i0
-
-
-a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0
-print(a0_o0_i0_v0 == a0_o0_i0_v1)
-
-n_i0_i1 = ~(i0 << i1)
-
-ni1_ni0 = ~i1 << ~i0
-
-print(ni1_ni0 == n_i0_i1)
-
-i0_i1_i2_v0 = i0 << i1 << i2
-i0_i1_i2_v1 = i0 << (i1 << i2)
-i0_i1_i2_v2 = (i0 << i1) << i2
-
-print(i0_i1_i2_v0 == i0_i1_i2_v1 == i0_i1_i2_v2)
-
-i0_i2_i1 = i0 << i2 << i1
-#print(i0_i2_i1 == i0_i1_i2_v0)
-
-print(i0 == i0_i2_i1 << ~(i2 << i1))
-print(i0 == i0_i2_i1 << ~i1 << ~i2)
\ No newline at end of file