minor improvements to examples, documentation, internally used variable names

examples/quimb_intro/quimb_introduction.ipynb

@@ -28,7 +28,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a009a5e0-cfd4-4a49-9f7c-e82f252c6147",
+   "id": "0c5a8939",
    "metadata": {},
    "source": [
     "#### Some hyper parameters"
@@ -36,24 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "b0a1da82",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import cotengra as ctg\n",
-    "ctg_opt = ctg.ReusableHyperOptimizer(\n",
-    "    max_time=10,\n",
-    "    minimize='combo',\n",
-    "    slicing_opts=None,\n",
-    "    parallel=True,\n",
-    "    progbar=True\n",
-    ")\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "64162116-1555-4a68-811c-01593739d622",
    "metadata": {},
    "outputs": [],
@@ -67,7 +50,39 @@
     "# set numpy random seed\n",
     "np.random.seed(42)\n",
     "\n",
-    "quimb_backend.setup_backend_specifics(quimb_backend=\"jax\")"
+    "quimb_backend.setup_backend_specifics(quimb_backend=\"jax\", contractions_optimizer='auto-hq')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "926cfea5",
+   "metadata": {},
+   "source": [
+    "Quimb accepts different methods for optimizing the way it does contractions, that we pass through \"contractions_optimizer\". \n",
+    "We could also define our own cotengra contraction optimizer! \n",
+    "\n",
+    "cotengra is a Python library designed for **optimising contraction trees** and performing efficient contractions of large tensor‐networks.\n",
+    "You can find it here: [https://github.com/jcmgray/cotengra](https://github.com/jcmgray/cotengra)\n",
+    "\n",
+    "For the sake of this tutorial however the default \"auto-hq\" will be fine :) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b0a1da82",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import cotengra as ctg\n",
+    "ctg_opt = ctg.ReusableHyperOptimizer(\n",
+    "    max_time=10,\n",
+    "    minimize='combo',\n",
+    "    slicing_opts=None,\n",
+    "    parallel=True,\n",
+    "    progbar=True\n",
+    ")\n",
+    "# quimb_backend.setup_backend_specifics(quimb_backend=\"jax\", contractions_optimizer='ctg_opt')"
    ]
   },
   {