diff --git a/computations/C_L_as_products.ipynb b/computations/C_L_as_products.ipynb
index 08b9ab1..a23dd71 100644
--- a/computations/C_L_as_products.ipynb
+++ b/computations/C_L_as_products.ipynb
@@ -440,6 +440,95 @@
    "source": [
     "lookup_table_lengths"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVQoFXWSCw0CQQxEb0/BBRyAAzQg4bCABBIkIAEN4AAsIAEc8HFwvLe0BBJoMnTbznan5cowDI1WSulwa3AFY2C8o37EN43EIG/znF4i6Gs9SEsSyySkJ2fXk3HLQZuCRT39+4mOc+qKPYDuo+OWuL70qVE9ksUKSKr6arO8HZ03QZR8ApOsp0bX01PQ1OtKZuBMXlmv9eCc+ms9xF608x10ucMa5DPpIUyC3Lfxjzjpg+SXkbuQ2INRG4QHF7z9y1z6MZ9WsFO+d+jzmNpXnksknNop/ShuIO39UTwBncWwmlIdE58AAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$\\displaystyle 8$"
+      ],
+      "text/plain": [
+       "8"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "get_product_index(siZ)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAOCAYAAADNGCeJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVQ4EaWTDQ3CQAxGbwQBCxLAAQkOkAAWwAFoAAdgAQnMAjgACQwH471ll1z4ywZNvlzba7/r2jVUVRUiQghjcAF59KUn/iHYNThxHsE4xqCHHByAQQZU4IUMn0SHmOiJbIDKtLafLlfN5TsyH3znL/GX8vRQ2sqUwDLLMr8klQIjxz/sQmbSlQruKVOi5/3E+KpCMv8Q4NAc4rlLZS9cfJpEDmbt5V9k5DuUPVVt/yKjKn+lAqKlRMpPlUG0MDkl0m49AIMViGYco5QIn33rVhlJNnwCUd1wCRrxgVvryprXbXiBbr+iDFDcz2295BgGubSuhrvmsutbERRj4t56/4yTcQ/S5q0FawIcEQAAAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$\\displaystyle 12$"
+      ],
+      "text/plain": [
+       "12"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "get_product_index(smiX)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def str2vops(s):\n",
+    "    c2v = {'s': 8, 'x': 12}\n",
+    "    result = [c2v[c] for c in s]\n",
+    "    return result + ([0] * (5 - len(result)))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[ \\left[ 8, \\  12, \\  12, \\  12, \\  8\\right], \\  \\left[ 8, \\  8, \\  8, \\  0, \\  0\\right], \\  \\left[ 8, \\  8, \\  8, \\  8, \\  0\\right], \\  \\left[ 12, \\  12, \\  12, \\  8, \\  0\\right], \\  \\left[ 8, \\  12, \\  12, \\  12, \\  0\\right], \\  \\left[ 8, \\  8, \\  0, \\  0, \\  0\\right], \\  \\left[ 8, \\  8, \\  12, \\  8, \\  8\\right], \\  \\left[ 8, \\  8, \\  8, \\  12, \\  8\\right], \\  \\left[ 8, \\  0, \\  0, \\  0, \\  0\\right], \\  \\left[ 8, \\  8, \\  12, \\  8, \\  0\\right], \\  \\left[ 8, \\  8, \\  8, \\  12, \\  0\\right], \\  \\left[ 8, \\  8, \\  12, \\  0, \\  0\\right], \\  \\left[ 8, \\  8, \\  8, \\  8, \\  12\\right], \\  \\left[ 8, \\  12, \\  8, \\  8, \\  8\\right], \\  \\left[ 8, \\  12, \\  12, \\  8, \\  0\\right], \\  \\left[ 12, \\  8, \\  8, \\  8, \\  0\\right], \\  \\left[ 8, \\  8, \\  8, \\  12, \\  12\\right], \\  \\left[ 8, \\  12, \\  8, \\  8, \\  0\\right], \\  \\left[ 8, \\  8, \\  12, \\  12, \\  8\\right], \\  \\left[ 8, \\  8, \\  12, \\  12, \\  12\\right], \\  \\left[ 8, \\  12, \\  8, \\  0, \\  0\\right], \\  \\left[ 8, \\  8, \\  12, \\  12, \\  0\\right], \\  \\left[ 12, \\  8, \\  0, \\  0, \\  0\\right], \\  \\left[ 8, \\  12, \\  0, \\  0, \\  0\\right]\\right]$"
+      ],
+      "text/plain": [
+       "[[8, 12, 12, 12, 8], [8, 8, 8, 0, 0], [8, 8, 8, 8, 0], [12, 12, 12, 8, 0], [8,\n",
+       " 12, 12, 12, 0], [8, 8, 0, 0, 0], [8, 8, 12, 8, 8], [8, 8, 8, 12, 8], [8, 0, 0\n",
+       ", 0, 0], [8, 8, 12, 8, 0], [8, 8, 8, 12, 0], [8, 8, 12, 0, 0], [8, 8, 8, 8, 12\n",
+       "], [8, 12, 8, 8, 8], [8, 12, 12, 8, 0], [12, 8, 8, 8, 0], [8, 8, 8, 12, 12], [\n",
+       "8, 12, 8, 8, 0], [8, 8, 12, 12, 8], [8, 8, 12, 12, 12], [8, 12, 8, 0, 0], [8, \n",
+       "8, 12, 12, 0], [12, 8, 0, 0, 0], [8, 12, 0, 0, 0]]"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[str2vops(s) for s in lookup_table]"
+   ]
   }
  ],
  "metadata": {