diff --git a/tests/python/parity.ipynb b/tests/python/parity.ipynb
index 2b860dd45..efd19e0f7 100644
--- a/tests/python/parity.ipynb
+++ b/tests/python/parity.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -15,80 +15,64 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Definitions and examples"
+    "# Definitions and examples for parity acceptance"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In Spot a **Parity acceptance** is defined by an **kind**, a **style** and a **numsets** (number of acceptance sets):\n",
+    "In Spot a **parity acceptance** is defined by a **kind**, a **style** and a **numsets**:\n",
+    "+ The **kind** can be either **max** or **min**.\n",
+    "+ The **style** can be either **odd** or **even**.\n",
     "+ The **numsets** is the number of acceptance sets used by the parity acceptance.\n",
-    "+ The **kind** can be either **max** or **min**. The parity kind is well defined only if the **numsets** is strictly greater than 1.\n",
-    "    - **max** odd 4: *Inf(3) | (Fin(2) & (Inf(1) | Fin(0)))*\n",
-    "    - **min** odd 4: *Fin(0) & (Inf(1) | (Fin(2) & Inf(3)))*\n",
-    "+ The **style** can be either **odd** or **even**. The parity style is well defined only if the **numsets** is non-null.\n",
-    "    - max **odd** 4: *Inf(3) | (Fin(2) & (Inf(1) | Fin(0)))*\n",
-    "    - min **even** 4: *Fin(3) & (Inf(2) | (Fin(1) & Inf(0)))*\n",
-    "\n"
+    "    \n",
+    "Here are some examples:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "parity min odd 1  = Fin(0)\n",
+      "parity min odd 2  = Fin(0) & Inf(1)\n",
+      "parity min odd 3  = Fin(0) & (Inf(1) | Fin(2))\n",
+      "parity min odd 4  = Fin(0) & (Inf(1) | (Fin(2) & Inf(3)))\n",
+      "parity min even 1 = Inf(0)\n",
+      "parity min even 2 = Inf(0) | Fin(1)\n",
+      "parity min even 3 = Inf(0) | (Fin(1) & Inf(2))\n",
+      "parity min even 4 = Inf(0) | (Fin(1) & (Inf(2) | Fin(3)))\n",
+      "parity max odd 1  = Fin(0)\n",
+      "parity max odd 2  = Inf(1) | Fin(0)\n",
+      "parity max odd 3  = Fin(2) & (Inf(1) | Fin(0))\n",
+      "parity max odd 4  = Inf(3) | (Fin(2) & (Inf(1) | Fin(0)))\n",
+      "parity max even 1 = Inf(0)\n",
+      "parity max even 2 = Fin(1) & Inf(0)\n",
+      "parity max even 3 = Inf(2) | (Fin(1) & Inf(0))\n",
+      "parity max even 4 = Fin(3) & (Inf(2) | (Fin(1) & Inf(0)))\n"
+     ]
+    }
+   ],
+   "source": [
+    "for kind in ['min', 'max']:\n",
+    "    for style in ['odd', 'even']:\n",
+    "        for sets in range(1, 5):\n",
+    "            name = 'parity {} {} {}'.format(kind, style, sets)\n",
+    "            print('{:17} = {}'.format(name, spot.acc_code(name)))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**Some parity acceptance examples:**\n",
-    "<div align=\"center\">\n",
-    "**numsets = 1:** \n",
-    "</div>\n",
+    "# Change parity\n",
     "\n",
-    "|           |    **max**     |     **min**    |\n",
-    "|:---------:|:--------------:|:--------------:|\n",
-    "|  **odd**  |     Fin(1)     |     Fin(1)     |      \n",
-    "|  **even** |     Inf(0)     |     Inf(0)     |\n",
-    "\n",
-    "<br>\n",
-    "<div align=\"center\">\n",
-    "**numsets = 2:** \n",
-    "</div>\n",
-    "\n",
-    "|           |       **max**        |        **min**       |\n",
-    "|:---------:|:--------------------:|:--------------------:|\n",
-    "|  **odd**  | Inf(1) &#124; Fin(0) | Fin(1) & Inf(0)      |      \n",
-    "|  **even** | Fin(0) & Inf(1)      | Inf(0) &#124; Fin(1) |\n",
-    "\n",
-    "\n",
-    "<br>\n",
-    "<div align=\"center\">\n",
-    "**numsets = 3:** \n",
-    "</div>\n",
-    " \n",
-    "|           |             **max**             |             **min**             |\n",
-    "|:---------:|:-------------------------------:|:-------------------------------:|\n",
-    "|  **odd**  | Fin(2) & (Inf(1) &#124; Fin(0)) | Inf(2) &#124; (Fin(1) & Inf(0)) |      \n",
-    "|  **even** | Fin(0) & (Inf(1) &#124; Fin(2)) | Inf(0) &#124; (Fin(1) & Inf(2)) |\n",
-    "\n",
-    "<br>\n",
-    "<div align=\"center\">\n",
-    "**numsets = 4:** \n",
-    "</div>\n",
-    "\n",
-    "|           |                      **max**                    |                      **min**                    |\n",
-    "|:---------:|:-----------------------------------------------:|:-----------------------------------------------:|\n",
-    "|  **odd**  | Inf(3) &#124; (Fin(2) & (Inf(1) &#124; Fin(0))) | Fin(3) & (Inf(2) &#124; (Fin(1) & Inf(0)))      |      \n",
-    "|  **even** | Fin(0) & (Inf(1) &#124; (Fin(2) & Inf(3)))      | Inf(0) &#124; (Fin(1) & (Inf(2) &#124; Fin(3))) |\n",
-    "\n",
-    "<br>\n",
-    "According to the given examples, we can remark that:\n",
-    "+ Given a parity **max**: Acceptance sets with greater indexes are more significant\n",
-    "+ Given a parity **min**: Acceptance sets with lower indexes are more significant"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Change parity"
+    "This section describes the `change_parity()` method, that allows switching between different kinds and styles."
    ]
   },
   {
@@ -103,7 +87,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -1381,7 +1365,13 @@
    "metadata": {},
    "source": [
     "# Colorize parity\n",
-    "An automaton with a parity acceptance is not necessarily a parity automaton. It must be colored to be qualified like this.\n",
+    "\n",
+    "People working with parity automata usually expect all states (or edges) to be part of some acceptance set.  This constraints, which come in addition to the use of a parity acceptance, is what the HOA format call \"colored\".\n",
+    "\n",
+    "A *parity automaton* is a *colored* automaton with *parity acceptance*.\n",
+    "\n",
+    "Coloring an automaton can be done with the `colorize_parity()` function.\n",
+    "\n",
     "## Parity max\n",
     "Transitions with multiple acceptance sets are purified by keeping only the set with the greatest index.\n",
     "<br>\n",
@@ -2093,7 +2083,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.3"
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  "nbformat": 4,