diff --git a/example/example_analysis.ipynb b/example/example_analysis.ipynb
index 1a9e76c..29ad395 100644
--- a/example/example_analysis.ipynb
+++ b/example/example_analysis.ipynb
@@ -72,28 +72,33 @@
     }
    ],
    "source": [
-    "# Json data model \n",
-    "df_country = { \n",
-    "    'country and region:$erDiagram' : { \n",
-    "        'entity': {\n",
-    "            'COUNTRY':  [ \n",
-    "                ['string', 'country',  'PK' ], \n",
-    "                ['string', 'code', 'unique'] \n",
-    "            ], \n",
-    "            'REGION': [ \n",
-    "                ['string', 'region',  'PK'],\n",
-    "                ['number',    'population'] \n",
-    "            ]\n",
+    "# Json data model\n",
+    "df_country = {\n",
+    "    \"country and region:$erDiagram\": {\n",
+    "        \"entity\": {\n",
+    "            \"COUNTRY\": [[\"string\", \"country\", \"PK\"], [\"string\", \"code\", \"unique\"]],\n",
+    "            \"REGION\": [[\"string\", \"region\", \"PK\"], [\"number\", \"population\"]],\n",
     "        },\n",
-    "        'relationship': [ \n",
-    "            [ 'REGION', 'exactly one', 'identifying', 'one or more', 'COUNTRY',     'brings_together']\n",
+    "        \"relationship\": [\n",
+    "            [\n",
+    "                \"REGION\",\n",
+    "                \"exactly one\",\n",
+    "                \"identifying\",\n",
+    "                \"one or more\",\n",
+    "                \"COUNTRY\",\n",
+    "                \"brings_together\",\n",
+    "            ]\n",
     "        ],\n",
-    "\n",
-    "     } }\n",
+    "    }\n",
+    "}\n",
     "\n",
     "# It is converted in Mermaid structure and then displayed\n",
     "diag = MermaidConnec.diagram(df_country)\n",
-    "display(Image(url=\"https://mermaid.ink/img/\" + b64encode(diag.encode(\"ascii\")).decode(\"ascii\")))"
+    "display(\n",
+    "    Image(\n",
+    "        url=\"https://mermaid.ink/img/\" + b64encode(diag.encode(\"ascii\")).decode(\"ascii\")\n",
+    "    )\n",
+    ")"
    ]
   },
   {
@@ -176,8 +181,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import pandas as pd\n",
-    "import ntv_pandas as npd"
+    "import pandas as pd"
    ]
   },
   {
@@ -187,10 +191,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "example1 = {'country' :   ['France', 'Spain', 'Estonia', 'Nigeria'],\n",
-    "            'region':     ['European Union', 'European Union', 'European Union', 'Africa'],\n",
-    "            'code':       ['FR', 'ES', 'ES', 'NI'],\n",
-    "            'population': [449, 48, 449, 1460]}\n",
+    "example1 = {\n",
+    "    \"country\": [\"France\", \"Spain\", \"Estonia\", \"Nigeria\"],\n",
+    "    \"region\": [\"European Union\", \"European Union\", \"European Union\", \"Africa\"],\n",
+    "    \"code\": [\"FR\", \"ES\", \"ES\", \"NI\"],\n",
+    "    \"population\": [449, 48, 449, 1460],\n",
+    "}\n",
     "pd_ex1 = pd.DataFrame(example1)"
    ]
   },
@@ -222,11 +228,19 @@
    ],
    "source": [
     "ana1 = pd_ex1.npd.analysis()\n",
-    "print(\"country - code (must be coupled): \", ana1.get_relation('country', 'code').typecoupl)\n",
-    "print(\"region - population (must be derived True): \", ana1.get_relation('region', 'population').typecoupl, \n",
-    "      ana1.get_relation('region', 'population').parent_child)\n",
-    "print(\"country - region (must be derived True): \", ana1.get_relation('country', 'region').typecoupl,\n",
-    "     ana1.get_relation('country', 'region').parent_child)"
+    "print(\n",
+    "    \"country - code (must be coupled): \", ana1.get_relation(\"country\", \"code\").typecoupl\n",
+    ")\n",
+    "print(\n",
+    "    \"region - population (must be derived True): \",\n",
+    "    ana1.get_relation(\"region\", \"population\").typecoupl,\n",
+    "    ana1.get_relation(\"region\", \"population\").parent_child,\n",
+    ")\n",
+    "print(\n",
+    "    \"country - region (must be derived True): \",\n",
+    "    ana1.get_relation(\"country\", \"region\").typecoupl,\n",
+    "    ana1.get_relation(\"country\", \"region\").parent_child,\n",
+    ")"
    ]
   },
   {
@@ -253,8 +267,8 @@
     }
    ],
    "source": [
-    "print(pd_ex1.npd.check_relation('country', 'code', 'coupled', value=True))\n",
-    "print(pd_ex1.npd.check_relation('region', 'population', 'derived', value=True))"
+    "print(pd_ex1.npd.check_relation(\"country\", \"code\", \"coupled\", value=True))\n",
+    "print(pd_ex1.npd.check_relation(\"region\", \"population\", \"derived\", value=True))"
    ]
   },
   {
@@ -294,10 +308,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "example2 = {'country' :   ['France', 'Spain', 'Estonia', 'Nigeria'],\n",
-    "            'region':     ['European Union', 'European Union', 'European Union', 'Africa'],\n",
-    "            'code':       ['FR', 'ES', 'EE', 'NI'],\n",
-    "            'population': [449, 449, 449, 1460]}\n",
+    "example2 = {\n",
+    "    \"country\": [\"France\", \"Spain\", \"Estonia\", \"Nigeria\"],\n",
+    "    \"region\": [\"European Union\", \"European Union\", \"European Union\", \"Africa\"],\n",
+    "    \"code\": [\"FR\", \"ES\", \"EE\", \"NI\"],\n",
+    "    \"population\": [449, 449, 449, 1460],\n",
+    "}\n",
     "pd_ex2 = pd.DataFrame(example2)"
    ]
   },
@@ -321,11 +337,19 @@
    ],
    "source": [
     "ana2 = pd_ex2.npd.analysis()\n",
-    "print(\"country - code (must be coupled): \", ana2.get_relation('country', 'code').typecoupl)\n",
-    "print(\"region - population (must be derived True): \", ana2.get_relation('region', 'population').typecoupl, \n",
-    "      ana2.get_relation('region', 'population').parent_child)\n",
-    "print(\"country - region (must be derived True): \", ana2.get_relation('country', 'region').typecoupl,\n",
-    "     ana2.get_relation('country', 'region').parent_child)"
+    "print(\n",
+    "    \"country - code (must be coupled): \", ana2.get_relation(\"country\", \"code\").typecoupl\n",
+    ")\n",
+    "print(\n",
+    "    \"region - population (must be derived True): \",\n",
+    "    ana2.get_relation(\"region\", \"population\").typecoupl,\n",
+    "    ana2.get_relation(\"region\", \"population\").parent_child,\n",
+    ")\n",
+    "print(\n",
+    "    \"country - region (must be derived True): \",\n",
+    "    ana2.get_relation(\"country\", \"region\").typecoupl,\n",
+    "    ana2.get_relation(\"country\", \"region\").parent_child,\n",
+    ")"
    ]
   },
   {
diff --git a/example/example_json_pandas.ipynb b/example/example_json_pandas.ipynb
index 6d846d7..baa41dd 100644
--- a/example/example_json_pandas.ipynb
+++ b/example/example_json_pandas.ipynb
@@ -36,11 +36,9 @@
    "outputs": [],
    "source": [
     "import math\n",
-    "from pprint import pprint\n",
     "from io import StringIO\n",
     "\n",
     "import pandas as pd\n",
-    "from shapely.geometry import Point\n",
     "from datetime import date, datetime, time"
    ]
   },
@@ -119,7 +117,7 @@
     }
    ],
    "source": [
-    "df  = pd.DataFrame(pd.Series([10,20], name='test int32', dtype='Int32'))\n",
+    "df = pd.DataFrame(pd.Series([10, 20], name=\"test int32\", dtype=\"Int32\"))\n",
     "\n",
     "# dtype is not included in usual json interface\n",
     "df.to_json()"
@@ -153,9 +151,9 @@
    ],
    "source": [
     "# 'int32' is lost in json-table interface\n",
-    "df2 = pd.read_json(StringIO(df.to_json(orient='table')), orient='table')\n",
+    "df2 = pd.read_json(StringIO(df.to_json(orient=\"table\")), orient=\"table\")\n",
     "print(df2.dtypes)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(df2))"
+    "print(\"\\nis Json translation reversible ? \", df.equals(df2))"
    ]
   },
   {
@@ -187,11 +185,11 @@
     }
    ],
    "source": [
-    "df = pd.DataFrame(pd.Series([10,20], name='test float64', dtype='float64'))\n",
-    "print(df.dtypes, '\\n')\n",
-    "df2 = pd.read_json(StringIO(df.to_json(orient='records')), orient='records')\n",
+    "df = pd.DataFrame(pd.Series([10, 20], name=\"test float64\", dtype=\"float64\"))\n",
+    "print(df.dtypes, \"\\n\")\n",
+    "df2 = pd.read_json(StringIO(df.to_json(orient=\"records\")), orient=\"records\")\n",
     "print(df2.dtypes)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(df2))"
+    "print(\"\\nis Json translation reversible ? \", df.equals(df2))"
    ]
   },
   {
@@ -215,11 +213,11 @@
     }
    ],
    "source": [
-    "sr = pd.Series([math.nan,math.nan], name='nan')\n",
-    "print(sr.dtype, '\\n')\n",
-    "sr2 = pd.read_json(StringIO(sr.to_json()), typ='series')\n",
+    "sr = pd.Series([math.nan, math.nan], name=\"nan\")\n",
+    "print(sr.dtype, \"\\n\")\n",
+    "sr2 = pd.read_json(StringIO(sr.to_json()), typ=\"series\")\n",
     "print(sr2)\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(sr2))"
+    "print(\"\\nis Json translation reversible ? \", sr.equals(sr2))"
    ]
   },
   {
@@ -253,15 +251,15 @@
     }
    ],
    "source": [
-    "dfd = pd.DataFrame({'test dates': [date(2021, 3, 1), date(2021, 3, 3)]})\n",
+    "dfd = pd.DataFrame({\"test dates\": [date(2021, 3, 1), date(2021, 3, 3)]})\n",
     "\n",
-    "print(dfd.to_json(default_handler=date.isoformat), '\\n')\n",
-    "print(dfd.to_json(orient='table'), '\\n')\n",
+    "print(dfd.to_json(default_handler=date.isoformat), \"\\n\")\n",
+    "print(dfd.to_json(orient=\"table\"), \"\\n\")\n",
     "\n",
-    "dfd2 = pd.read_json(StringIO(dfd.to_json(orient='table')), orient='table')\n",
+    "dfd2 = pd.read_json(StringIO(dfd.to_json(orient=\"table\")), orient=\"table\")\n",
     "print(dfd2)\n",
     "\n",
-    "print('\\nis Json translation reversible ? ', dfd.equals(dfd2))"
+    "print(\"\\nis Json translation reversible ? \", dfd.equals(dfd2))"
    ]
   },
   {
@@ -291,13 +289,13 @@
     }
    ],
    "source": [
-    "dfd = pd.DataFrame({'test tuple': [(2021, 3, 1), (2021, 3, 3)]})\n",
-    "print(dfd, '\\n')\n",
-    "print(dfd.to_json(), '\\n')\n",
-    "print(dfd.to_json(orient='table'), '\\n')\n",
-    "dfd2 = pd.read_json(StringIO(dfd.to_json(orient='table')), orient='table')\n",
+    "dfd = pd.DataFrame({\"test tuple\": [(2021, 3, 1), (2021, 3, 3)]})\n",
+    "print(dfd, \"\\n\")\n",
+    "print(dfd.to_json(), \"\\n\")\n",
+    "print(dfd.to_json(orient=\"table\"), \"\\n\")\n",
+    "dfd2 = pd.read_json(StringIO(dfd.to_json(orient=\"table\")), orient=\"table\")\n",
     "print(dfd2)\n",
-    "print('\\nis Json translation reversible ? ', dfd.equals(dfd2))"
+    "print(\"\\nis Json translation reversible ? \", dfd.equals(dfd2))"
    ]
   },
   {
@@ -323,8 +321,10 @@
     }
    ],
    "source": [
-    "df = pd.DataFrame(pd.Series([10,20], name='test float', dtype='float32'), dtype='category')\n",
-    "print(df.to_json(orient='table'))"
+    "df = pd.DataFrame(\n",
+    "    pd.Series([10, 20], name=\"test float\", dtype=\"float32\"), dtype=\"category\"\n",
+    ")\n",
+    "print(df.to_json(orient=\"table\"))"
    ]
   },
   {
@@ -358,11 +358,15 @@
     }
    ],
    "source": [
-    "df = pd.DataFrame({'test dates' : [date(2021, 10, 2), date(2021, 10, 4)],\n",
-    "                   'test times' : [time(10, 10, 2), time(11, 10, 4)]})\n",
-    "print('CSV data :\\n', df.to_csv())\n",
-    "print('JSON data :\\n', df.to_json())\n",
-    "print('JSON data :\\n', df.to_json(date_format='iso'))"
+    "df = pd.DataFrame(\n",
+    "    {\n",
+    "        \"test dates\": [date(2021, 10, 2), date(2021, 10, 4)],\n",
+    "        \"test times\": [time(10, 10, 2), time(11, 10, 4)],\n",
+    "    }\n",
+    ")\n",
+    "print(\"CSV data :\\n\", df.to_csv())\n",
+    "print(\"JSON data :\\n\", df.to_json())\n",
+    "print(\"JSON data :\\n\", df.to_json(date_format=\"iso\"))"
    ]
   },
   {
@@ -404,21 +408,30 @@
    "source": [
     "import ntv_pandas as npd\n",
     "\n",
-    "tab_data = {'dates':           ['1964-01-01', '1985-02-05', '2022-01-21', '1964-01-01', '1985-02-05', '2022-01-21'], \n",
-    "            'value':           [10, 10, 20, 20, 30, 30],\n",
-    "            'names':           ['john', 'eric', 'judith', 'mila', 'hector', 'maria'],\n",
-    "            'unique':          [True, True, True, True, True, True] }\n",
+    "tab_data = {\n",
+    "    \"dates\": [\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "    ],\n",
+    "    \"value\": [10, 10, 20, 20, 30, 30],\n",
+    "    \"names\": [\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"],\n",
+    "    \"unique\": [True, True, True, True, True, True],\n",
+    "}\n",
     "\n",
-    "df = pd.DataFrame(tab_data, dtype='category')\n",
-    "print(df, '\\n')\n",
+    "df = pd.DataFrame(tab_data, dtype=\"category\")\n",
+    "print(df, \"\\n\")\n",
     "\n",
     "# length with compact interface : 240\n",
     "print(npd.to_json(df, text=True))\n",
-    "print(len(npd.to_json(df, text=True)), '\\n')\n",
+    "print(len(npd.to_json(df, text=True)), \"\\n\")\n",
     "\n",
     "# length with actual interface : 946\n",
-    "print(df.to_json(orient='table'))\n",
-    "print(len(df.to_json(orient='table')), '\\n')"
+    "print(df.to_json(orient=\"table\"))\n",
+    "print(len(df.to_json(orient=\"table\")), \"\\n\")"
    ]
   },
   {
@@ -580,33 +593,38 @@
    "source": [
     "import json\n",
     "\n",
-    "data = [[{'test': [1,2,3]}, {'dtype': 'int32'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'int'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'int64'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'Int64'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'UInt64'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'float'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'Float32'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'float32'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'float64'}],\n",
-    "        [{'test': [1,2,3]}, {'dtype': 'Sparse[float64]'}],\n",
-    "        # [{'test': [pd.Interval(1,2), pd.Interval(2,3), pd.Interval(3,4)]}], # read_json ko\n",
-    "        [{'test': ['2020-01-01']}, {'dtype': 'datetime64[ns]'}],\n",
-    "        [{'test': ['2020-01-01']}, {'dtype': 'datetime64[ns, UTC]'}],\n",
-    "        [{'test': ['2020-01-01']}, {'dtype': 'category'}],\n",
-    "        [{'test': [datetime(2020, 1, 1)]}, {'dtype': 'category'}],         \n",
-    "        [{'test': [True, False]}, {'dtype': 'boolean'}],\n",
-    "        [{'test': [True, False]}, {'dtype': 'bool'}],\n",
-    "        # [{'test': ['1 days', '2 days']}, {'dtype': 'timedelta64[ns]'}], # read_json not yet implemented\n",
-    "        # [{'test': ['2020-01-01', '2020-02-01', '2020-03-01']}, {'dtype': 'period[M]'}], # read_json not available\n",
-    "         [{'test': [True, 1, 'er', datetime(2020, 1, 1)]}, {'dtype': 'object'}],\n",
-    "       ]\n",
-    "print('reverse (True, False), json table-schema object, reverse dtype:\\n')\n",
+    "data = [\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"int32\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"int\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"int64\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"Int64\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"UInt64\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"float\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"Float32\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"float32\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"float64\"}],\n",
+    "    [{\"test\": [1, 2, 3]}, {\"dtype\": \"Sparse[float64]\"}],\n",
+    "    # [{'test': [pd.Interval(1,2), pd.Interval(2,3), pd.Interval(3,4)]}], # read_json ko\n",
+    "    [{\"test\": [\"2020-01-01\"]}, {\"dtype\": \"datetime64[ns]\"}],\n",
+    "    [{\"test\": [\"2020-01-01\"]}, {\"dtype\": \"datetime64[ns, UTC]\"}],\n",
+    "    [{\"test\": [\"2020-01-01\"]}, {\"dtype\": \"category\"}],\n",
+    "    [{\"test\": [datetime(2020, 1, 1)]}, {\"dtype\": \"category\"}],\n",
+    "    [{\"test\": [True, False]}, {\"dtype\": \"boolean\"}],\n",
+    "    [{\"test\": [True, False]}, {\"dtype\": \"bool\"}],\n",
+    "    # [{'test': ['1 days', '2 days']}, {'dtype': 'timedelta64[ns]'}], # read_json not yet implemented\n",
+    "    # [{'test': ['2020-01-01', '2020-02-01', '2020-03-01']}, {'dtype': 'period[M]'}], # read_json not available\n",
+    "    [{\"test\": [True, 1, \"er\", datetime(2020, 1, 1)]}, {\"dtype\": \"object\"}],\n",
+    "]\n",
+    "print(\"reverse (True, False), json table-schema object, reverse dtype:\\n\")\n",
     "for df_data in data:\n",
-    "    df = pd.DataFrame(df_data[0], **df_data[1]) if len(df_data) == 2 else pd.DataFrame(df_data[0])\n",
-    "    js = df.to_json(orient='table')\n",
-    "    df2 = pd.read_json(StringIO(js), orient='table')\n",
-    "    print(df.equals(df2), json.loads(js)['schema']['fields'][1], df2.dtypes.iloc[0])"
+    "    df = (\n",
+    "        pd.DataFrame(df_data[0], **df_data[1])\n",
+    "        if len(df_data) == 2\n",
+    "        else pd.DataFrame(df_data[0])\n",
+    "    )\n",
+    "    js = df.to_json(orient=\"table\")\n",
+    "    df2 = pd.read_json(StringIO(js), orient=\"table\")\n",
+    "    print(df.equals(df2), json.loads(js)[\"schema\"][\"fields\"][1], df2.dtypes.iloc[0])"
    ]
   }
  ],
diff --git a/example/example_multidimensional.ipynb b/example/example_multidimensional.ipynb
index b4b0177..d1b52af 100644
--- a/example/example_multidimensional.ipynb
+++ b/example/example_multidimensional.ipynb
@@ -36,19 +36,48 @@
    "outputs": [],
    "source": [
     "import pandas as pd\n",
-    "import ntv_pandas as npd # activate pandas npd accessor\n",
+    "import ntv_pandas as npd  # activate pandas npd accessor\n",
     "\n",
-    "fruits = {'plants':      ['fruit', 'fruit', 'fruit', 'fruit', 'vegetable', 'vegetable', 'vegetable', 'vegetable'],\n",
-    "          'plts':        ['fr', 'fr', 'fr', 'fr', 've', 've', 've', 've'], \n",
-    "          'quantity':    ['1 kg', '10 kg', '1 kg', '10 kg', '1 kg', '10 kg', '1 kg', '10 kg'],\n",
-    "          'product':     ['apple', 'apple', 'orange', 'orange', 'peppers', 'peppers', 'carrot', 'carrot'],\n",
-    "          'price':       [1, 10, 2, 20, 1.5, 15, 1.5, 20],\n",
-    "          'price level': ['low', 'low', 'high', 'high', 'low', 'low', 'high', 'high'],\n",
-    "          'group':       ['fruit 1', 'fruit 10', 'fruit 1', 'veget', 'veget', 'veget', 'veget', 'veget'],\n",
-    "          'id':          [1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008],\n",
-    "          'supplier':    [\"sup1\", \"sup1\", \"sup1\", \"sup2\", \"sup2\", \"sup2\", \"sup2\", \"sup1\"],\n",
-    "          'location':    [\"fr\", \"gb\", \"es\", \"ch\", \"gb\", \"fr\", \"es\", \"ch\"],\n",
-    "          'valid':       [\"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\"]}\n",
+    "fruits = {\n",
+    "    \"plants\": [\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"vegetable\",\n",
+    "        \"vegetable\",\n",
+    "        \"vegetable\",\n",
+    "        \"vegetable\",\n",
+    "    ],\n",
+    "    \"plts\": [\"fr\", \"fr\", \"fr\", \"fr\", \"ve\", \"ve\", \"ve\", \"ve\"],\n",
+    "    \"quantity\": [\"1 kg\", \"10 kg\", \"1 kg\", \"10 kg\", \"1 kg\", \"10 kg\", \"1 kg\", \"10 kg\"],\n",
+    "    \"product\": [\n",
+    "        \"apple\",\n",
+    "        \"apple\",\n",
+    "        \"orange\",\n",
+    "        \"orange\",\n",
+    "        \"peppers\",\n",
+    "        \"peppers\",\n",
+    "        \"carrot\",\n",
+    "        \"carrot\",\n",
+    "    ],\n",
+    "    \"price\": [1, 10, 2, 20, 1.5, 15, 1.5, 20],\n",
+    "    \"price level\": [\"low\", \"low\", \"high\", \"high\", \"low\", \"low\", \"high\", \"high\"],\n",
+    "    \"group\": [\n",
+    "        \"fruit 1\",\n",
+    "        \"fruit 10\",\n",
+    "        \"fruit 1\",\n",
+    "        \"veget\",\n",
+    "        \"veget\",\n",
+    "        \"veget\",\n",
+    "        \"veget\",\n",
+    "        \"veget\",\n",
+    "    ],\n",
+    "    \"id\": [1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008],\n",
+    "    \"supplier\": [\"sup1\", \"sup1\", \"sup1\", \"sup2\", \"sup2\", \"sup2\", \"sup2\", \"sup1\"],\n",
+    "    \"location\": [\"fr\", \"gb\", \"es\", \"ch\", \"gb\", \"fr\", \"es\", \"ch\"],\n",
+    "    \"valid\": [\"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\", \"ok\"],\n",
+    "}\n",
     "df_fruits = pd.DataFrame(fruits)"
    ]
   },
@@ -169,7 +198,7 @@
     }
    ],
    "source": [
-    "ana_fruits.field_partition() # first partition"
+    "ana_fruits.field_partition()  # first partition"
    ]
   },
   {
@@ -200,7 +229,7 @@
     }
    ],
    "source": [
-    "ana_fruits.relation_partition() # first partition"
+    "ana_fruits.relation_partition()  # first partition"
    ]
   },
   {
@@ -227,7 +256,7 @@
     }
    ],
    "source": [
-    "ana_fruits.field_partition(partition=['product', 'quantity'])"
+    "ana_fruits.field_partition(partition=[\"product\", \"quantity\"])"
    ]
   },
   {
@@ -258,7 +287,7 @@
     }
    ],
    "source": [
-    "ana_fruits.relation_partition(partition=['product', 'quantity'])"
+    "ana_fruits.relation_partition(partition=[\"product\", \"quantity\"])"
    ]
   },
   {
@@ -296,7 +325,15 @@
    "source": [
     "from base64 import b64encode\n",
     "from IPython.display import Image, display\n",
-    "display(Image(url=\"https://mermaid.ink/img/\" + b64encode(open('fruits.mmd', 'r', encoding=\"utf-8\").read().encode(\"ascii\")).decode(\"ascii\")))"
+    "\n",
+    "display(\n",
+    "    Image(\n",
+    "        url=\"https://mermaid.ink/img/\"\n",
+    "        + b64encode(\n",
+    "            open(\"fruits.mmd\", \"r\", encoding=\"utf-8\").read().encode(\"ascii\")\n",
+    "        ).decode(\"ascii\")\n",
+    "    )\n",
+    ")"
    ]
   },
   {
@@ -740,7 +777,11 @@
     }
    ],
    "source": [
-    "kwargs = {'dims':['plants', 'quantity', 'price level'], 'info': False, 'ntv_type': False}\n",
+    "kwargs = {\n",
+    "    \"dims\": [\"plants\", \"quantity\", \"price level\"],\n",
+    "    \"info\": False,\n",
+    "    \"ntv_type\": False,\n",
+    "}\n",
     "\n",
     "xd_fruits_1 = df_fruits.npd.to_xarray(**kwargs)\n",
     "xd_fruits_1"
@@ -752,9 +793,7 @@
    "id": "46ae0c11-2612-42e4-b6ab-135647762cf9",
    "metadata": {},
    "outputs": [],
-   "source": [
-    "import ntv_numpy  # activate xarray nxr accessor"
-   ]
+   "source": []
   },
   {
    "cell_type": "code",
@@ -774,9 +813,15 @@
     }
    ],
    "source": [
-    "df_fruits_xd = xd_fruits_1.nxr.to_dataframe(ntv_type=False) # identical as: df_fruits_xd = npd.from_xarray(ntv_type=False)\n",
+    "df_fruits_xd = xd_fruits_1.nxr.to_dataframe(\n",
+    "    ntv_type=False\n",
+    ")  # identical as: df_fruits_xd = npd.from_xarray(ntv_type=False)\n",
     "\n",
-    "df_fruits_xd_sort = df_fruits_xd.reset_index()[list(df_fruits.columns)].sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
+    "df_fruits_xd_sort = (\n",
+    "    df_fruits_xd.reset_index()[list(df_fruits.columns)]\n",
+    "    .sort_values(list(df_fruits.columns))\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "df_fruits_sort = df_fruits.sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
     "\n",
     "df_fruits_xd_sort.equals(df_fruits_sort)"
@@ -867,7 +912,11 @@
    "source": [
     "df_fruits_sc = npd.from_scipp(sc_fruits_1, ntv_type=False)\n",
     "\n",
-    "df_fruits_sc_sort = df_fruits_sc.reset_index()[list(df_fruits.columns)].sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
+    "df_fruits_sc_sort = (\n",
+    "    df_fruits_sc.reset_index()[list(df_fruits.columns)]\n",
+    "    .sort_values(list(df_fruits.columns))\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "df_fruits_sort = df_fruits.sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
     "\n",
     "df_fruits_sc_sort.equals(df_fruits_sort)"
@@ -1308,7 +1357,7 @@
     }
    ],
    "source": [
-    "kwargs = {'dims':['product', 'quantity'], 'info': False, 'ntv_type': False}\n",
+    "kwargs = {\"dims\": [\"product\", \"quantity\"], \"info\": False, \"ntv_type\": False}\n",
     "\n",
     "xd_fruits_2 = df_fruits.npd.to_xarray(**kwargs)\n",
     "xd_fruits_2"
@@ -1332,9 +1381,15 @@
     }
    ],
    "source": [
-    "df_fruits_xd = xd_fruits_2.nxr.to_dataframe(ntv_type=False) # or npd.from_xarray(xd_fruits_2, ntv_type=False)\n",
+    "df_fruits_xd = xd_fruits_2.nxr.to_dataframe(\n",
+    "    ntv_type=False\n",
+    ")  # or npd.from_xarray(xd_fruits_2, ntv_type=False)\n",
     "\n",
-    "df_fruits_xd_sort = df_fruits_xd.reset_index()[list(df_fruits.columns)].sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
+    "df_fruits_xd_sort = (\n",
+    "    df_fruits_xd.reset_index()[list(df_fruits.columns)]\n",
+    "    .sort_values(list(df_fruits.columns))\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "df_fruits_sort = df_fruits.sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
     "\n",
     "df_fruits_xd_sort.equals(df_fruits_sort)"
@@ -1423,7 +1478,11 @@
    "source": [
     "df_fruits_sc = npd.from_scipp(sc_fruits_2, ntv_type=False)\n",
     "\n",
-    "df_fruits_sc_sort = df_fruits_sc.reset_index()[list(df_fruits.columns)].sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
+    "df_fruits_sc_sort = (\n",
+    "    df_fruits_sc.reset_index()[list(df_fruits.columns)]\n",
+    "    .sort_values(list(df_fruits.columns))\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "df_fruits_sort = df_fruits.sort_values(list(df_fruits.columns)).reset_index(drop=True)\n",
     "\n",
     "df_fruits_sc_sort.equals(df_fruits_sort)"
@@ -1466,9 +1525,9 @@
     }
    ],
    "source": [
-    "print(ana_fruits.get_relation('plants', 'plts').typecoupl)\n",
-    "print(ana_fruits.get_relation('plants', 'product').typecoupl)\n",
-    "print(ana_fruits.get_relation('quantity', 'product').typecoupl)\n"
+    "print(ana_fruits.get_relation(\"plants\", \"plts\").typecoupl)\n",
+    "print(ana_fruits.get_relation(\"plants\", \"product\").typecoupl)\n",
+    "print(ana_fruits.get_relation(\"quantity\", \"product\").typecoupl)"
    ]
   },
   {
@@ -1499,11 +1558,11 @@
     }
    ],
    "source": [
-    "print('minimum distance: ', ana_fruits.get_relation('plants', 'plts').distance)\n",
-    "print('maximum distance: ', ana_fruits.get_relation('id', 'valid').distance)\n",
-    "print('intermediate distance: ', ana_fruits.get_relation('plants', 'product').distance)\n",
-    "# The 'plants' - 'product' relationship will be 'coupled' if we change, for example, \n",
-    "#'fruit-orange' in 'citrus-orange' and 'carrot-vegetable' in 'carrot-root vegetable' (2 changes)  "
+    "print(\"minimum distance: \", ana_fruits.get_relation(\"plants\", \"plts\").distance)\n",
+    "print(\"maximum distance: \", ana_fruits.get_relation(\"id\", \"valid\").distance)\n",
+    "print(\"intermediate distance: \", ana_fruits.get_relation(\"plants\", \"product\").distance)\n",
+    "# The 'plants' - 'product' relationship will be 'coupled' if we change, for example,\n",
+    "#'fruit-orange' in 'citrus-orange' and 'carrot-vegetable' in 'carrot-root vegetable' (2 changes)"
    ]
   },
   {
@@ -1538,7 +1597,12 @@
    ],
    "source": [
     "# list of categories for each Field\n",
-    "print({field.idfield: category for field, category in zip(ana_fruits.fields, ana_fruits.category)})"
+    "print(\n",
+    "    {\n",
+    "        field.idfield: category\n",
+    "        for field, category in zip(ana_fruits.fields, ana_fruits.category)\n",
+    "    }\n",
+    ")"
    ]
   },
   {
diff --git a/example/example_ntv_pandas.ipynb b/example/example_ntv_pandas.ipynb
index 99eed8a..1052360 100644
--- a/example/example_ntv_pandas.ipynb
+++ b/example/example_ntv_pandas.ipynb
@@ -52,7 +52,7 @@
     "\n",
     "import pandas as pd\n",
     "import ntv_pandas as npd\n",
-    "from shapely.geometry import Point, Polygon\n",
+    "from shapely.geometry import Point\n",
     "from json_ntv import Ntv\n",
     "from datetime import date, datetime, time"
    ]
@@ -201,16 +201,31 @@
     }
    ],
    "source": [
-    "tab_data = {'index':           [100, 200, 300, 400, 500, 600],\n",
-    "            'dates::date':     pd.Series([date(1964,1,1), date(1985,2,5), date(2022,1,21), date(1964,1,1), \n",
-    "                                          date(1985,2,5), date(2022,1,21)], dtype='category'), \n",
-    "            'valid':           [True, False, True, True, False, True],\n",
-    "            'value32':         pd.Series([12, 12, 22, 22, 32, 32], dtype='int32'),\n",
-    "            '::month':         [1, 2, 1, 1, 2, 1],\n",
-    "            'coord::point':    pd.Series([Point(1,2), Point(3,4), Point(5,6), Point(7,8), Point(3,4), Point(5,6)]),\n",
-    "            'names':           pd.Series(['john', 'eric', 'judith', 'mila', 'hector', 'maria'], dtype='string'),\n",
-    "            'unique::year':     2021 }\n",
-    "df = pd.DataFrame(tab_data).set_index('index')\n",
+    "tab_data = {\n",
+    "    \"index\": [100, 200, 300, 400, 500, 600],\n",
+    "    \"dates::date\": pd.Series(\n",
+    "        [\n",
+    "            date(1964, 1, 1),\n",
+    "            date(1985, 2, 5),\n",
+    "            date(2022, 1, 21),\n",
+    "            date(1964, 1, 1),\n",
+    "            date(1985, 2, 5),\n",
+    "            date(2022, 1, 21),\n",
+    "        ],\n",
+    "        dtype=\"category\",\n",
+    "    ),\n",
+    "    \"valid\": [True, False, True, True, False, True],\n",
+    "    \"value32\": pd.Series([12, 12, 22, 22, 32, 32], dtype=\"int32\"),\n",
+    "    \"::month\": [1, 2, 1, 1, 2, 1],\n",
+    "    \"coord::point\": pd.Series(\n",
+    "        [Point(1, 2), Point(3, 4), Point(5, 6), Point(7, 8), Point(3, 4), Point(5, 6)]\n",
+    "    ),\n",
+    "    \"names\": pd.Series(\n",
+    "        [\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"], dtype=\"string\"\n",
+    "    ),\n",
+    "    \"unique::year\": 2021,\n",
+    "}\n",
+    "df = pd.DataFrame(tab_data).set_index(\"index\")\n",
     "df"
    ]
   },
@@ -381,7 +396,7 @@
    ],
    "source": [
     "df_from_json = npd.read_json(df_to_json)\n",
-    "print('df created from JSON-NTV is equal to initial df ? ', df_from_json.equals(df))\n",
+    "print(\"df created from JSON-NTV is equal to initial df ? \", df_from_json.equals(df))\n",
     "df_from_json"
    ]
   },
@@ -427,13 +442,16 @@
     }
    ],
    "source": [
-    "field_data = {'value': [1, 2, 3]}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\"value\": [1, 2, 3]}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))\n",
-    "print('\\nis pandas translation reversible ? ', json.dumps(sr.npd.to_json()) == json.dumps({':field': field_data}))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))\n",
+    "print(\n",
+    "    \"\\nis pandas translation reversible ? \",\n",
+    "    json.dumps(sr.npd.to_json()) == json.dumps({\":field\": field_data}),\n",
+    ")"
    ]
   },
   {
@@ -468,12 +486,12 @@
     }
    ],
    "source": [
-    "field_data = {'dates::datetime': ['1964-01-01', '1985-02-05', '2022-01-21']}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\"dates::datetime\": [\"1964-01-01\", \"1985-02-05\", \"2022-01-21\"]}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))"
    ]
   },
   {
@@ -510,13 +528,16 @@
     }
    ],
    "source": [
-    "field_data = {'dates::date': ['1964-01-01', '1985-02-05', '2022-01-21']}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\"dates::date\": [\"1964-01-01\", \"1985-02-05\", \"2022-01-21\"]}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))\n",
-    "print('\\nis pandas translation reversible ? ', json.dumps(sr.npd.to_json()) == json.dumps({':field': field_data}))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))\n",
+    "print(\n",
+    "    \"\\nis pandas translation reversible ? \",\n",
+    "    json.dumps(sr.npd.to_json()) == json.dumps({\":field\": field_data}),\n",
+    ")"
    ]
   },
   {
@@ -543,12 +564,12 @@
     }
    ],
    "source": [
-    "field_data = {'coord::point':    [[1,2], [3,4], [5,6]]}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\"coord::point\": [[1, 2], [3, 4], [5, 6]]}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))"
    ]
   },
   {
@@ -589,12 +610,15 @@
    ],
    "source": [
     "field_data = {\"integer\": [[1, 2], [0, 1, 1, 0]]}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))\n",
-    "print('\\nis pandas translation reversible ? ', json.dumps(sr.npd.to_json()) == json.dumps({':field': field_data}))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))\n",
+    "print(\n",
+    "    \"\\nis pandas translation reversible ? \",\n",
+    "    json.dumps(sr.npd.to_json()) == json.dumps({\":field\": field_data}),\n",
+    ")"
    ]
   },
   {
@@ -623,12 +647,14 @@
     }
    ],
    "source": [
-    "field_data = {'dates': [{'::date': ['1964-01-01', '1985-02-05', '2022-01-21']}, [0, 1, 0, 2]]}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\n",
+    "    \"dates\": [{\"::date\": [\"1964-01-01\", \"1985-02-05\", \"2022-01-21\"]}, [0, 1, 0, 2]]\n",
+    "}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))"
    ]
   },
   {
@@ -659,13 +685,16 @@
     }
    ],
    "source": [
-    "field_data = {'test_array': [{'::array': [[1,2], [3,4], [5,6]]}, [0, 1, 0, 2]]}\n",
-    "sr = npd.read_json({':field': field_data})\n",
+    "field_data = {\"test_array\": [{\"::array\": [[1, 2], [3, 4], [5, 6]]}, [0, 1, 0, 2]]}\n",
+    "sr = npd.read_json({\":field\": field_data})\n",
     "# pandas dtype conform to Ntv type\n",
-    "print('pandas object :\\n' + str(sr))\n",
-    "print('\\nJson representation : \\n    ', sr.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', sr.equals(npd.read_json(sr.npd.to_json())))\n",
-    "print('\\nis pandas translation reversible ? ', json.dumps(sr.npd.to_json()) == json.dumps({':field': field_data}))"
+    "print(\"pandas object :\\n\" + str(sr))\n",
+    "print(\"\\nJson representation : \\n    \", sr.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", sr.equals(npd.read_json(sr.npd.to_json())))\n",
+    "print(\n",
+    "    \"\\nis pandas translation reversible ? \",\n",
+    "    json.dumps(sr.npd.to_json()) == json.dumps({\":field\": field_data}),\n",
+    ")"
    ]
   },
   {
@@ -716,10 +745,10 @@
    "source": [
     "df = pd.DataFrame({\"A\": list(\"abca\"), \"B\": list(\"bccd\")})\n",
     "\n",
-    "print('pandas dtype :\\n' + str(df.dtypes))\n",
-    "print('\\npandas object :\\n' + str(df))\n",
-    "print('\\nJson representation : \\n    ', df.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json())))"
+    "print(\"pandas dtype :\\n\" + str(df.dtypes))\n",
+    "print(\"\\npandas object :\\n\" + str(df))\n",
+    "print(\"\\nJson representation : \\n    \", df.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", df.equals(npd.read_json(df.npd.to_json())))"
    ]
   },
   {
@@ -778,20 +807,29 @@
     }
    ],
    "source": [
-    "tab_data = {'index':           [100, 200, 300, 400, 500, 600],\n",
-    "            'dates::date':     ['1964-01-01', '1985-02-05', '2022-01-21', '1964-01-01', '1985-02-05', '2022-01-21'], \n",
-    "            'value':           [10, 10, 20, 20, 30, 30],\n",
-    "            'value32::int32':  [12, 12, 22, 22, 32, 32],\n",
-    "            'res':             [10, 20, 30, 10, 20, 30],\n",
-    "            'coord::point':    [[1,2], [3,4], [5,6], [7,8], [3,4], [5,6]],\n",
-    "            'names::string':   ['john', 'eric', 'judith', 'mila', 'hector', 'maria'],\n",
-    "            'unique':          True }\n",
-    "df = npd.read_json({':tab': tab_data})\n",
-    "print('pandas dtype :\\n' + str(df.dtypes))\n",
-    "print('\\npandas object :\\n' + str(df))\n",
-    "print('\\nJson representation :')\n",
+    "tab_data = {\n",
+    "    \"index\": [100, 200, 300, 400, 500, 600],\n",
+    "    \"dates::date\": [\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "    ],\n",
+    "    \"value\": [10, 10, 20, 20, 30, 30],\n",
+    "    \"value32::int32\": [12, 12, 22, 22, 32, 32],\n",
+    "    \"res\": [10, 20, 30, 10, 20, 30],\n",
+    "    \"coord::point\": [[1, 2], [3, 4], [5, 6], [7, 8], [3, 4], [5, 6]],\n",
+    "    \"names::string\": [\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"],\n",
+    "    \"unique\": True,\n",
+    "}\n",
+    "df = npd.read_json({\":tab\": tab_data})\n",
+    "print(\"pandas dtype :\\n\" + str(df.dtypes))\n",
+    "print(\"\\npandas object :\\n\" + str(df))\n",
+    "print(\"\\nJson representation :\")\n",
     "pprint(df.npd.to_json(), width=140)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json())))"
+    "print(\"\\nis Json translation reversible ? \", df.equals(npd.read_json(df.npd.to_json())))"
    ]
   },
   {
@@ -817,17 +855,33 @@
     }
    ],
    "source": [
-    "tab_data = {'index':           [100, 200, 300, 400, 500, 600],\n",
-    "            'dates::date':     ['1964-01-01', '1985-02-05', '2022-01-21', '1964-01-01', '1985-02-05', '2022-01-21'], \n",
-    "            'value':           [10, 10, 20, 20, {'valid?': 30}, 30],\n",
-    "            'value32::int32':  [12, 12, 22, 22, 32, 32],\n",
-    "            'res':             {'res1': 10, 'res2': 20, 'res3': 30, 'res4': 10, 'res5': 20, 'res6': 30},\n",
-    "            'coord::point':    [[1,2], [3,4], [5,6], [7,8], {'same as 2nd point': [3,4]}, [5,6]],\n",
-    "            'names::string':   ['john', 'eric', 'judith', 'mila', 'hector', 'maria'],\n",
-    "            'unique':          True }\n",
+    "tab_data = {\n",
+    "    \"index\": [100, 200, 300, 400, 500, 600],\n",
+    "    \"dates::date\": [\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "        \"1964-01-01\",\n",
+    "        \"1985-02-05\",\n",
+    "        \"2022-01-21\",\n",
+    "    ],\n",
+    "    \"value\": [10, 10, 20, 20, {\"valid?\": 30}, 30],\n",
+    "    \"value32::int32\": [12, 12, 22, 22, 32, 32],\n",
+    "    \"res\": {\"res1\": 10, \"res2\": 20, \"res3\": 30, \"res4\": 10, \"res5\": 20, \"res6\": 30},\n",
+    "    \"coord::point\": [\n",
+    "        [1, 2],\n",
+    "        [3, 4],\n",
+    "        [5, 6],\n",
+    "        [7, 8],\n",
+    "        {\"same as 2nd point\": [3, 4]},\n",
+    "        [5, 6],\n",
+    "    ],\n",
+    "    \"names::string\": [\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"],\n",
+    "    \"unique\": True,\n",
+    "}\n",
     "\n",
-    "df2 = npd.read_json({':tab': tab_data}, annotated=True)\n",
-    "print('is DataFrame identical ? ', df.equals(df2))"
+    "df2 = npd.read_json({\":tab\": tab_data}, annotated=True)\n",
+    "print(\"is DataFrame identical ? \", df.equals(df2))"
    ]
   },
   {
@@ -870,10 +924,10 @@
    "source": [
     "df = pd.DataFrame({\"A\": list(\"abca\"), \"B\": list(\"bccd\")}, dtype=\"category\")\n",
     "\n",
-    "print('pandas dtype :\\n' + str(df.dtypes))\n",
-    "print('\\npandas object :\\n' + str(df))\n",
-    "print('\\nJson representation : \\n    ', df.npd.to_json())\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json())))"
+    "print(\"pandas dtype :\\n\" + str(df.dtypes))\n",
+    "print(\"\\npandas object :\\n\" + str(df))\n",
+    "print(\"\\nJson representation : \\n    \", df.npd.to_json())\n",
+    "print(\"\\nis Json translation reversible ? \", df.equals(npd.read_json(df.npd.to_json())))"
    ]
   },
   {
@@ -920,21 +974,33 @@
     }
    ],
    "source": [
-    "tab_data = {'index':           [100, 200, 300, 400, 500, 600],\n",
-    "            'dates':           [{'::date': ['1964-01-01', '1985-02-05', '2022-01-21']}, [0, 1, 2, 0, 1, 2]],\n",
-    "            'value':           [[10, 20, {'valid?': 30}], [0, 0, 1, 1, 2, 2]],\n",
-    "            'value32::int32':  [12, 12, 22, 22, 32, 32],\n",
-    "            'res':             {'res1': 10, 'res2': 20, 'res3': 30, 'res4': 10, 'res5': 20, 'res6': 30},\n",
-    "            'coord::point':    [[1,2], [3,4], [5,6], [7,8], {'same as 2nd point': [3,4]}, [5,6]],\n",
-    "            'names::string':   ['john', 'eric', 'judith', 'mila', 'hector', 'maria'],\n",
-    "            'unique:boolean':  True }\n",
+    "tab_data = {\n",
+    "    \"index\": [100, 200, 300, 400, 500, 600],\n",
+    "    \"dates\": [\n",
+    "        {\"::date\": [\"1964-01-01\", \"1985-02-05\", \"2022-01-21\"]},\n",
+    "        [0, 1, 2, 0, 1, 2],\n",
+    "    ],\n",
+    "    \"value\": [[10, 20, {\"valid?\": 30}], [0, 0, 1, 1, 2, 2]],\n",
+    "    \"value32::int32\": [12, 12, 22, 22, 32, 32],\n",
+    "    \"res\": {\"res1\": 10, \"res2\": 20, \"res3\": 30, \"res4\": 10, \"res5\": 20, \"res6\": 30},\n",
+    "    \"coord::point\": [\n",
+    "        [1, 2],\n",
+    "        [3, 4],\n",
+    "        [5, 6],\n",
+    "        [7, 8],\n",
+    "        {\"same as 2nd point\": [3, 4]},\n",
+    "        [5, 6],\n",
+    "    ],\n",
+    "    \"names::string\": [\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"],\n",
+    "    \"unique:boolean\": True,\n",
+    "}\n",
     "\n",
-    "df = npd.read_json({':tab': tab_data}, annotated=True)\n",
-    "print('pandas dtype :\\n' + str(df.dtypes))\n",
-    "print('\\npandas object :\\n' + str(df))\n",
-    "print('\\nJson representation :')\n",
+    "df = npd.read_json({\":tab\": tab_data}, annotated=True)\n",
+    "print(\"pandas dtype :\\n\" + str(df.dtypes))\n",
+    "print(\"\\npandas object :\\n\" + str(df))\n",
+    "print(\"\\nJson representation :\")\n",
     "pprint(df.npd.to_json(), width=140)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json())))"
+    "print(\"\\nis Json translation reversible ? \", df.equals(npd.read_json(df.npd.to_json())))"
    ]
   },
   {
@@ -979,22 +1045,43 @@
     }
    ],
    "source": [
-    "index   = pd.Series([100, 200, 300, 400, 500, 600])\n",
-    "dates   = pd.Series(name='dates::date',  data=[date(1964, 1, 1), date(1985, 2, 5), date(2022, 1, 21), date(1964, 1, 1),\n",
-    "                                               date(1985, 2, 5), date(2022, 1, 21)], dtype='object').astype('category')\n",
-    "value   = pd.Series(name='value',        data=[10,10,20,20,30,30], dtype='Int64').astype('category') #alias mandatory \n",
-    "value32 = pd.Series(name='value32',      data=[12, 12, 22, 22, 32, 32], dtype='int32')\n",
-    "coord   = pd.Series(name='coord::point', data=[Point(1,2), Point(3,4), Point(5,6), Point(7,8), Point(3,4), Point(5,6)])\n",
-    "names   = pd.Series(name='names',        data=['john', 'eric', 'judith', 'mila', 'hector', 'maria'], dtype='string')\n",
-    "unique  = pd.Series(name='unique',       data=[True, True, True, True, True, True])\n",
+    "index = pd.Series([100, 200, 300, 400, 500, 600])\n",
+    "dates = pd.Series(\n",
+    "    name=\"dates::date\",\n",
+    "    data=[\n",
+    "        date(1964, 1, 1),\n",
+    "        date(1985, 2, 5),\n",
+    "        date(2022, 1, 21),\n",
+    "        date(1964, 1, 1),\n",
+    "        date(1985, 2, 5),\n",
+    "        date(2022, 1, 21),\n",
+    "    ],\n",
+    "    dtype=\"object\",\n",
+    ").astype(\"category\")\n",
+    "value = pd.Series(name=\"value\", data=[10, 10, 20, 20, 30, 30], dtype=\"Int64\").astype(\n",
+    "    \"category\"\n",
+    ")  # alias mandatory\n",
+    "value32 = pd.Series(name=\"value32\", data=[12, 12, 22, 22, 32, 32], dtype=\"int32\")\n",
+    "coord = pd.Series(\n",
+    "    name=\"coord::point\",\n",
+    "    data=[Point(1, 2), Point(3, 4), Point(5, 6), Point(7, 8), Point(3, 4), Point(5, 6)],\n",
+    ")\n",
+    "names = pd.Series(\n",
+    "    name=\"names\",\n",
+    "    data=[\"john\", \"eric\", \"judith\", \"mila\", \"hector\", \"maria\"],\n",
+    "    dtype=\"string\",\n",
+    ")\n",
+    "unique = pd.Series(name=\"unique\", data=[True, True, True, True, True, True])\n",
     "\n",
-    "df = pd.DataFrame({ser.name: ser for ser in [index, dates, value, value32, coord, names, unique]}).set_index(None)\n",
+    "df = pd.DataFrame(\n",
+    "    {ser.name: ser for ser in [index, dates, value, value32, coord, names, unique]}\n",
+    ").set_index(None)\n",
     "\n",
-    "print('pandas dtype :\\n' + str(df.dtypes))\n",
-    "print('\\npandas object :\\n' + str(df))\n",
-    "print('\\nJson representation :')\n",
+    "print(\"pandas dtype :\\n\" + str(df.dtypes))\n",
+    "print(\"\\npandas object :\\n\" + str(df))\n",
+    "print(\"\\nJson representation :\")\n",
     "pprint(df.npd.to_json(), width=140)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json())))"
+    "print(\"\\nis Json translation reversible ? \", df.equals(npd.read_json(df.npd.to_json())))"
    ]
   },
   {
@@ -1119,13 +1206,33 @@
     }
    ],
    "source": [
-    "data = {\"quantity\": [\"1 kg\", \"1 kg\", \"1 kg\", \"1 kg\", \"10 kg\", \"10 kg\", \"10 kg\", \"10 kg\"],\n",
-    "        \"product\": [\"banana\", \"orange\", \"apple\", \"peppers\", \"banana\", \"orange\", \"apple\", \"peppers\"], \n",
-    "        \"plants\": [\"fruit\", \"fruit\", \"fruit\", \"vegetable\", \"fruit\", \"fruit\", \"fruit\", \"vegetable\"], \n",
-    "        \"price\": [0.5, 2, 1, 1.5, 5, 20, 10, 15]}\n",
+    "data = {\n",
+    "    \"quantity\": [\"1 kg\", \"1 kg\", \"1 kg\", \"1 kg\", \"10 kg\", \"10 kg\", \"10 kg\", \"10 kg\"],\n",
+    "    \"product\": [\n",
+    "        \"banana\",\n",
+    "        \"orange\",\n",
+    "        \"apple\",\n",
+    "        \"peppers\",\n",
+    "        \"banana\",\n",
+    "        \"orange\",\n",
+    "        \"apple\",\n",
+    "        \"peppers\",\n",
+    "    ],\n",
+    "    \"plants\": [\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"vegetable\",\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"fruit\",\n",
+    "        \"vegetable\",\n",
+    "    ],\n",
+    "    \"price\": [0.5, 2, 1, 1.5, 5, 20, 10, 15],\n",
+    "}\n",
     "\n",
-    "df  = pd.DataFrame(data)\n",
-    "df2 = pd.DataFrame(data, dtype='category').sort_values(by=['quantity', 'product'])\n",
+    "df = pd.DataFrame(data)\n",
+    "df2 = pd.DataFrame(data, dtype=\"category\").sort_values(by=[\"quantity\", \"product\"])\n",
     "df2"
    ]
   },
@@ -1551,20 +1658,24 @@
     }
    ],
    "source": [
-    "json_df = Ntv.obj(df).to_obj()[':tab']\n",
+    "json_df = Ntv.obj(df).to_obj()[\":tab\"]\n",
     "print('json_df is the JSON-TAB format with \"full\" mode\\n')\n",
     "pprint(json_df, width=200)\n",
     "\n",
-    "json_xar = Ntv.obj(df2).to_obj()[':tab']\n",
+    "json_xar = Ntv.obj(df2).to_obj()[\":tab\"]\n",
     "print('\\njson_xa is the JSON-TAB format with \"optimize\" mode\\n')\n",
     "pprint(json_xar, width=200)\n",
     "\n",
-    "df_from_xar = Ntv.obj({':tab': json_xar}).to_obj(format='obj').sort_index()\n",
-    "print('\\nDataFrame from the two JSON-TAB format are identical ? ', df.astype('object').equals(df_from_xar.astype('object')))\n",
+    "df_from_xar = Ntv.obj({\":tab\": json_xar}).to_obj(format=\"obj\").sort_index()\n",
+    "print(\n",
+    "    \"\\nDataFrame from the two JSON-TAB format are identical ? \",\n",
+    "    df.astype(\"object\").equals(df_from_xar.astype(\"object\")),\n",
+    ")\n",
     "\n",
     "print('\\nThe \"optimize\" JSON-TAB format is the image of the DataArray Xarray')\n",
     "from tab_dataset import Sdataset\n",
-    "Sdataset.ntv(json_df).setcanonorder().to_xarray(varname='price')"
+    "\n",
+    "Sdataset.ntv(json_df).setcanonorder().to_xarray(varname=\"price\")"
    ]
   },
   {
@@ -1622,57 +1733,59 @@
    "source": [
     "# json interface ok\n",
     "srs = [\n",
-    "       # without ntv_type, without dtype\n",
-    "       pd.Series([{'a': 2, 'e':4}, {'a': 3, 'e':5}, {'a': 4, 'e':6}]),  \n",
-    "       pd.Series([[1,2], [3,4], [5,6]]),  \n",
-    "       pd.Series([[1,2], [3,4], {'a': 3, 'e':5}]),  \n",
-    "       pd.Series([True, False, True]),\n",
-    "       pd.Series(['az', 'er', 'cd']),\n",
-    "       pd.Series(['az', 'az', 'az']),\n",
-    "       pd.Series([1,2,3]),\n",
-    "       pd.Series([1.1,2,3]),\n",
-    "       \n",
-    "       # without ntv_type, with dtype\n",
-    "       pd.Series([10,20,30], dtype='Int64'),\n",
-    "       pd.Series([True, False, True], dtype='boolean'),\n",
-    "       pd.Series([1.1, 2, 3], dtype='float64'), \n",
-    "\n",
-    "       # with ntv_type only in json data (not numbers)\n",
-    "       pd.Series([pd.NaT, pd.NaT, pd.NaT]),\n",
-    "       pd.Series([datetime(2022, 1, 1), datetime(2022, 1, 2)], dtype='datetime64[ns]'),\n",
-    "       pd.Series(pd.to_timedelta(['1D', '2D'])),\n",
-    "       pd.Series(['az', 'er', 'cd'], dtype='string'), \n",
-    "\n",
-    "       # with ntv_type only in json data (numbers)\n",
-    "       pd.Series([1,2,3], dtype='Int32'), \n",
-    "       pd.Series([1,2,3], dtype='UInt64'),\n",
-    "       pd.Series([1,2,3], dtype='float32'),\n",
-    "\n",
-    "       # with ntv_type in Series name and in json data (numbers)\n",
-    "       pd.Series([1,2,3], name='::int64'),\n",
-    "       pd.Series([1,2,3], dtype='Float64', name='::float64'), # force dtype dans la conversion json\n",
-    "\n",
-    "       # with ntv_type in Series name and in json data (not numbers)\n",
-    "       pd.Series([[1,2], [3,4], [5,6]], name='::array'),  \n",
-    "       pd.Series([{'a': 2, 'e':4}, {'a': 3, 'e':5}, {'a': 4, 'e':6}], name='::object'),  \n",
-    "       pd.Series([None, None, None], name='::null'), \n",
-    "       pd.Series([\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\"], name='::uri', dtype='string'),\n",
-    "       pd.Series([\"///path/to/file\", \"//host.example.com/path/to/file\"], name='::file', dtype='string'),\n",
-    "\n",
-    "       # with ntv_type converted in object dtype (not in datetime)\n",
-    "       pd.Series([date(2022, 1, 1), date(2022, 1, 2)], name='::date'),\n",
-    "       pd.Series([time(10, 21, 1),  time(8, 1, 2)],    name='::time'),\n",
-    "\n",
-    "       # with ntv_type unknown in pandas and with pandas conversion               \n",
-    "       pd.Series([1,2,3], dtype='int64', name='::day'),\n",
-    "       pd.Series([2001,2002,2003], dtype='int64', name='::year'),\n",
-    "       pd.Series([21,10,55], name='::minute'),\n",
-    "\n",
-    "       # with ntv_type unknown in pandas and NTV conversion\n",
-    "       pd.Series([Point(1, 0), Point(1, 1), Point(1, 2)], name='::point'),\n",
+    "    # without ntv_type, without dtype\n",
+    "    pd.Series([{\"a\": 2, \"e\": 4}, {\"a\": 3, \"e\": 5}, {\"a\": 4, \"e\": 6}]),\n",
+    "    pd.Series([[1, 2], [3, 4], [5, 6]]),\n",
+    "    pd.Series([[1, 2], [3, 4], {\"a\": 3, \"e\": 5}]),\n",
+    "    pd.Series([True, False, True]),\n",
+    "    pd.Series([\"az\", \"er\", \"cd\"]),\n",
+    "    pd.Series([\"az\", \"az\", \"az\"]),\n",
+    "    pd.Series([1, 2, 3]),\n",
+    "    pd.Series([1.1, 2, 3]),\n",
+    "    # without ntv_type, with dtype\n",
+    "    pd.Series([10, 20, 30], dtype=\"Int64\"),\n",
+    "    pd.Series([True, False, True], dtype=\"boolean\"),\n",
+    "    pd.Series([1.1, 2, 3], dtype=\"float64\"),\n",
+    "    # with ntv_type only in json data (not numbers)\n",
+    "    pd.Series([pd.NaT, pd.NaT, pd.NaT]),\n",
+    "    pd.Series([datetime(2022, 1, 1), datetime(2022, 1, 2)], dtype=\"datetime64[ns]\"),\n",
+    "    pd.Series(pd.to_timedelta([\"1D\", \"2D\"])),\n",
+    "    pd.Series([\"az\", \"er\", \"cd\"], dtype=\"string\"),\n",
+    "    # with ntv_type only in json data (numbers)\n",
+    "    pd.Series([1, 2, 3], dtype=\"Int32\"),\n",
+    "    pd.Series([1, 2, 3], dtype=\"UInt64\"),\n",
+    "    pd.Series([1, 2, 3], dtype=\"float32\"),\n",
+    "    # with ntv_type in Series name and in json data (numbers)\n",
+    "    pd.Series([1, 2, 3], name=\"::int64\"),\n",
+    "    pd.Series(\n",
+    "        [1, 2, 3], dtype=\"Float64\", name=\"::float64\"\n",
+    "    ),  # force dtype dans la conversion json\n",
+    "    # with ntv_type in Series name and in json data (not numbers)\n",
+    "    pd.Series([[1, 2], [3, 4], [5, 6]], name=\"::array\"),\n",
+    "    pd.Series([{\"a\": 2, \"e\": 4}, {\"a\": 3, \"e\": 5}, {\"a\": 4, \"e\": 6}], name=\"::object\"),\n",
+    "    pd.Series([None, None, None], name=\"::null\"),\n",
+    "    pd.Series(\n",
+    "        [\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\"],\n",
+    "        name=\"::uri\",\n",
+    "        dtype=\"string\",\n",
+    "    ),\n",
+    "    pd.Series(\n",
+    "        [\"///path/to/file\", \"//host.example.com/path/to/file\"],\n",
+    "        name=\"::file\",\n",
+    "        dtype=\"string\",\n",
+    "    ),\n",
+    "    # with ntv_type converted in object dtype (not in datetime)\n",
+    "    pd.Series([date(2022, 1, 1), date(2022, 1, 2)], name=\"::date\"),\n",
+    "    pd.Series([time(10, 21, 1), time(8, 1, 2)], name=\"::time\"),\n",
+    "    # with ntv_type unknown in pandas and with pandas conversion\n",
+    "    pd.Series([1, 2, 3], dtype=\"int64\", name=\"::day\"),\n",
+    "    pd.Series([2001, 2002, 2003], dtype=\"int64\", name=\"::year\"),\n",
+    "    pd.Series([21, 10, 55], name=\"::minute\"),\n",
+    "    # with ntv_type unknown in pandas and NTV conversion\n",
+    "    pd.Series([Point(1, 0), Point(1, 1), Point(1, 2)], name=\"::point\"),\n",
     "]\n",
     "for sr in srs:\n",
-    "    print(sr.npd.equals(npd.read_json(sr.npd.to_json())), sr.npd.to_json())  "
+    "    print(sr.npd.equals(npd.read_json(sr.npd.to_json())), sr.npd.to_json())"
    ]
   },
   {
@@ -1706,24 +1819,25 @@
    ],
    "source": [
     "# json interface ok\n",
-    "for a in [{'test::int32': [1,2,3]},\n",
-    "          {'test': [1,2,3]},\n",
-    "          [1.0, 2.1, 3.0],\n",
-    "          ['er', 'et', 'ez'],\n",
-    "          [True, False, True],\n",
-    "          {'::boolean': [True, False, True]},\n",
-    "          {'::string': ['er', 'et', 'ez']},\n",
-    "          {'test::float32': [1.0, 2.5, 3.0]},\n",
-    "          {'::int64': [1,2,3]},\n",
-    "          {'::datetime': [\"2021-12-31T23:00:00.000\",\"2022-01-01T23:00:00.000\"] },\n",
-    "          {'::date': [\"2021-12-31\", \"2022-01-01\"] },\n",
-    "          {'::time': [\"23:00:00\", \"23:01:00\"] },\n",
-    "          {'::object': [{'a': 3, 'e':5}, {'a': 4, 'e':6}]},\n",
-    "          {'::array': [[1,2], [3,4], [5,6]]},\n",
-    "          True,\n",
-    "          {':boolean': True}\n",
-    "         ]:\n",
-    "    field = {':field': a}\n",
+    "for a in [\n",
+    "    {\"test::int32\": [1, 2, 3]},\n",
+    "    {\"test\": [1, 2, 3]},\n",
+    "    [1.0, 2.1, 3.0],\n",
+    "    [\"er\", \"et\", \"ez\"],\n",
+    "    [True, False, True],\n",
+    "    {\"::boolean\": [True, False, True]},\n",
+    "    {\"::string\": [\"er\", \"et\", \"ez\"]},\n",
+    "    {\"test::float32\": [1.0, 2.5, 3.0]},\n",
+    "    {\"::int64\": [1, 2, 3]},\n",
+    "    {\"::datetime\": [\"2021-12-31T23:00:00.000\", \"2022-01-01T23:00:00.000\"]},\n",
+    "    {\"::date\": [\"2021-12-31\", \"2022-01-01\"]},\n",
+    "    {\"::time\": [\"23:00:00\", \"23:01:00\"]},\n",
+    "    {\"::object\": [{\"a\": 3, \"e\": 5}, {\"a\": 4, \"e\": 6}]},\n",
+    "    {\"::array\": [[1, 2], [3, 4], [5, 6]]},\n",
+    "    True,\n",
+    "    {\":boolean\": True},\n",
+    "]:\n",
+    "    field = {\":field\": a}\n",
     "    print(npd.read_json(field).npd.to_json() == field, field)"
    ]
   },
@@ -1757,22 +1871,32 @@
    ],
    "source": [
     "# json interface ok (categorical data)\n",
-    "for a in [{'test': [{'::int32': [1, 2, 3]}, [0,1,2,0,1]]},\n",
-    "          {'test': [[1, 2, 3], [0,1,2,0,1]]},\n",
-    "          [[1.0, 2.1, 3.0], [0,1,2,0,1]],\n",
-    "          [['er', 'et', 'ez'], [0,1,2,0,1]],\n",
-    "          [[True, False], [0,1,0,1,0]],\n",
-    "          [{'::string': ['er', 'et', 'ez']}, [0,1,2,0,1]],\n",
-    "          {'test':[{'::float32': [1.0, 2.5, 3.0]}, [0,1,2,0,1]]},\n",
-    "          [{'::int64': [1, 2, 3]}, [0,1,2,0,1]],\n",
-    "          [{'::datetime': [\"2021-12-31T23:00:00.000\", \"2022-01-01T23:00:00.000\"] }, [0,1,0,1,0]],\n",
-    "          [{'::date': [\"2021-12-31\", \"2022-01-01\"] }, [0,1,0,1,0]],\n",
-    "          [{'::time': [\"23:00:00\", \"23:01:00\"] }, [0,1,0,1,0]],\n",
-    "          {'test_date': [{'::datetime': [\"2021-12-31T23:00:00.000\", \"2022-01-01T23:00:00.000\"] }, [0,1,0,1,0]]},\n",
-    "          [{'::boolean': [True, False]}, [0,1,0,1,0]],\n",
-    "          [[True], [2]], # periodic Series\n",
-    "          {'quantity': [['1 kg', '10 kg'], [4]]}]:  # periodic Series\n",
-    "    field = {':field': a}\n",
+    "for a in [\n",
+    "    {\"test\": [{\"::int32\": [1, 2, 3]}, [0, 1, 2, 0, 1]]},\n",
+    "    {\"test\": [[1, 2, 3], [0, 1, 2, 0, 1]]},\n",
+    "    [[1.0, 2.1, 3.0], [0, 1, 2, 0, 1]],\n",
+    "    [[\"er\", \"et\", \"ez\"], [0, 1, 2, 0, 1]],\n",
+    "    [[True, False], [0, 1, 0, 1, 0]],\n",
+    "    [{\"::string\": [\"er\", \"et\", \"ez\"]}, [0, 1, 2, 0, 1]],\n",
+    "    {\"test\": [{\"::float32\": [1.0, 2.5, 3.0]}, [0, 1, 2, 0, 1]]},\n",
+    "    [{\"::int64\": [1, 2, 3]}, [0, 1, 2, 0, 1]],\n",
+    "    [\n",
+    "        {\"::datetime\": [\"2021-12-31T23:00:00.000\", \"2022-01-01T23:00:00.000\"]},\n",
+    "        [0, 1, 0, 1, 0],\n",
+    "    ],\n",
+    "    [{\"::date\": [\"2021-12-31\", \"2022-01-01\"]}, [0, 1, 0, 1, 0]],\n",
+    "    [{\"::time\": [\"23:00:00\", \"23:01:00\"]}, [0, 1, 0, 1, 0]],\n",
+    "    {\n",
+    "        \"test_date\": [\n",
+    "            {\"::datetime\": [\"2021-12-31T23:00:00.000\", \"2022-01-01T23:00:00.000\"]},\n",
+    "            [0, 1, 0, 1, 0],\n",
+    "        ]\n",
+    "    },\n",
+    "    [{\"::boolean\": [True, False]}, [0, 1, 0, 1, 0]],\n",
+    "    [[True], [2]],  # periodic Series\n",
+    "    {\"quantity\": [[\"1 kg\", \"10 kg\"], [4]]},\n",
+    "]:  # periodic Series\n",
+    "    field = {\":field\": a}\n",
     "    print(npd.read_json(field).npd.to_json() == field, field)"
    ]
   },
@@ -1795,22 +1919,26 @@
    ],
    "source": [
     "# json interface ko\n",
-    "srs = [# without ntv_type\n",
-    "       pd.Series([math.nan, math.nan]), # bug pandas conversion json : datetime NaT\n",
-    "       \n",
-    "       # without ntv_type, with dtype\n",
-    "       pd.Series([math.nan, math.nan], dtype='float64'), # bug pandas conversion json : datetime NaT\n",
-    "    \n",
-    "       # with ntv_type in Series name and in json data\n",
-    "       pd.Series([1,2,3], dtype='UInt64', name='::uint64'),   # name inutile\n",
-    "       \n",
-    "       # with ntv_type unknown in pandas\n",
-    "       pd.Series([datetime(2022, 1, 1), datetime(2022, 1, 2), datetime(2022, 1, 3)], dtype='datetime64[ns, UTC]'), #à traiter\n",
+    "srs = [  # without ntv_type\n",
+    "    pd.Series([math.nan, math.nan]),  # bug pandas conversion json : datetime NaT\n",
+    "    # without ntv_type, with dtype\n",
+    "    pd.Series(\n",
+    "        [math.nan, math.nan], dtype=\"float64\"\n",
+    "    ),  # bug pandas conversion json : datetime NaT\n",
+    "    # with ntv_type in Series name and in json data\n",
+    "    pd.Series([1, 2, 3], dtype=\"UInt64\", name=\"::uint64\"),  # name inutile\n",
+    "    # with ntv_type unknown in pandas\n",
+    "    pd.Series(\n",
+    "        [datetime(2022, 1, 1), datetime(2022, 1, 2), datetime(2022, 1, 3)],\n",
+    "        dtype=\"datetime64[ns, UTC]\",\n",
+    "    ),  # à traiter\n",
     "]\n",
     "for sr in srs:\n",
-    "    print(sr.npd.equals(npd.read_json(sr.npd.to_json())),  \n",
-    "          npd.read_json(sr.npd.to_json()).name == sr.name, \n",
-    "          sr.npd.to_json(text=True))  "
+    "    print(\n",
+    "        sr.npd.equals(npd.read_json(sr.npd.to_json())),\n",
+    "        npd.read_json(sr.npd.to_json()).name == sr.name,\n",
+    "        sr.npd.to_json(text=True),\n",
+    "    )"
    ]
   },
   {
@@ -1829,8 +1957,10 @@
    ],
    "source": [
     "# json interface ko (categorical data)\n",
-    "for a in [{'test_array': [{'::array': [[1,2], [3,4], [5,6], [7,8]]}, [0, 1, 0, 2, 3]]}]: # list -> tuple to be hashable\n",
-    "    field = {':field': a}\n",
+    "for a in [\n",
+    "    {\"test_array\": [{\"::array\": [[1, 2], [3, 4], [5, 6], [7, 8]]}, [0, 1, 0, 2, 3]]}\n",
+    "]:  # list -> tuple to be hashable\n",
+    "    field = {\":field\": a}\n",
     "    print(npd.read_json(field).npd.to_json() == field, field)"
    ]
   }
diff --git a/example/example_size.ipynb b/example/example_size.ipynb
index a5cd777..a363438 100644
--- a/example/example_size.ipynb
+++ b/example/example_size.ipynb
@@ -76,7 +76,6 @@
     "import pandas as pd\n",
     "import numpy as np\n",
     "from ntv_numpy import Xdataset\n",
-    "import ntv_pandas as npd\n",
     "import cbor2\n",
     "import matplotlib.pyplot as plt"
    ]
@@ -130,10 +129,14 @@
    "outputs": [],
    "source": [
     "def coords_int(val, leng):\n",
-    "    return np.arange(val, val+leng)\n",
+    "    return np.arange(val, val + leng)\n",
+    "\n",
     "\n",
     "def coords_str(leng):\n",
-    "    return np.array([''.join(random.choices(string.ascii_letters, k=12)) for _ in range(leng)])\n",
+    "    return np.array(\n",
+    "        [\"\".join(random.choices(string.ascii_letters, k=12)) for _ in range(leng)]\n",
+    "    )\n",
+    "\n",
     "\n",
     "def variable(nb, dim):\n",
     "    return np.arange(nb**dim).reshape([nb] * dim)"
@@ -251,12 +254,14 @@
     }
    ],
    "source": [
-    "dimensions = 3   \n",
+    "dimensions = 3\n",
     "nb1 = 2\n",
     "\n",
-    "fields = ['dim_' + str(i) for i in range(dimensions)]\n",
-    "xds = xr.Dataset({\"var\": (fields, variable(nb1, dimensions))}, \n",
-    "                   coords={field: coords_int(val*nb1, nb1) for val, field in enumerate(fields)})\n",
+    "fields = [\"dim_\" + str(i) for i in range(dimensions)]\n",
+    "xds = xr.Dataset(\n",
+    "    {\"var\": (fields, variable(nb1, dimensions))},\n",
+    "    coords={field: coords_int(val * nb1, nb1) for val, field in enumerate(fields)},\n",
+    ")\n",
     "\n",
     "df = Xdataset.from_xarray(xds).to_dataframe(ntv_type=False, info=False).reset_index()\n",
     "df"
@@ -280,7 +285,7 @@
     }
    ],
    "source": [
-    "df.to_json(orient='values')"
+    "df.to_json(orient=\"values\")"
    ]
   },
   {
@@ -306,8 +311,8 @@
     }
    ],
    "source": [
-    "Xdataset.from_xarray(xds).to_json(notype='all', header=False, encoded=False)\n",
-    "Xdataset.from_dataframe(df).to_json(notype='all', header=False, encoded=False)"
+    "Xdataset.from_xarray(xds).to_json(notype=\"all\", header=False, encoded=False)\n",
+    "Xdataset.from_dataframe(df).to_json(notype=\"all\", header=False, encoded=False)"
    ]
   },
   {
@@ -503,19 +508,29 @@
     }
    ],
    "source": [
-    "dimensions = 5    \n",
-    "fields = ['dim_' + str(i) for i in range(dimensions)]\n",
+    "dimensions = 5\n",
+    "fields = [\"dim_\" + str(i) for i in range(dimensions)]\n",
     "\n",
     "nb1 = 4\n",
     "nb2 = 10\n",
-    "xdss = [xr.Dataset({\"var\": (fields, variable(nb1, dimensions))}, \n",
-    "                   coords={field: coords_int(val*nb1, nb1) for val, field in enumerate(fields)}),\n",
-    "        xr.Dataset({\"var\": (fields, variable(nb1, dimensions))}, \n",
-    "                   coords={field: coords_str(nb1) for val, field in enumerate(fields)}),\n",
-    "        xr.Dataset({\"var\": (fields, variable(nb2, dimensions))}, \n",
-    "                   coords={field: coords_int(val*nb2, nb2) for val, field in enumerate(fields)}),\n",
-    "        xr.Dataset({\"var\": (fields, variable(nb2, dimensions))}, \n",
-    "                   coords={field: coords_str(nb2) for val, field in enumerate(fields)})] #,\n",
+    "xdss = [\n",
+    "    xr.Dataset(\n",
+    "        {\"var\": (fields, variable(nb1, dimensions))},\n",
+    "        coords={field: coords_int(val * nb1, nb1) for val, field in enumerate(fields)},\n",
+    "    ),\n",
+    "    xr.Dataset(\n",
+    "        {\"var\": (fields, variable(nb1, dimensions))},\n",
+    "        coords={field: coords_str(nb1) for val, field in enumerate(fields)},\n",
+    "    ),\n",
+    "    xr.Dataset(\n",
+    "        {\"var\": (fields, variable(nb2, dimensions))},\n",
+    "        coords={field: coords_int(val * nb2, nb2) for val, field in enumerate(fields)},\n",
+    "    ),\n",
+    "    xr.Dataset(\n",
+    "        {\"var\": (fields, variable(nb2, dimensions))},\n",
+    "        coords={field: coords_str(nb2) for val, field in enumerate(fields)},\n",
+    "    ),\n",
+    "]  # ,\n",
     "\n",
     "Xdataset.from_xarray(xdss[2]).to_dataframe(ntv_type=False, info=False).reset_index()"
    ]
@@ -528,27 +543,38 @@
    "outputs": [],
    "source": [
     "def file_sizes(xnd, forma={}):\n",
-    "    '''calculate the size of each format'''\n",
+    "    \"\"\"calculate the size of each format\"\"\"\n",
     "    df = xnd.to_dataframe(json_name=False, info=False).reset_index().sample(frac=1)\n",
-    "    jsn = xnd.to_json(notype='all', header=False, encoded=False, format=forma)\n",
-    "    return {'JSON-pandas': len(df.to_json(orient='values')),\n",
-    "            'CSV': len(df.to_csv()),\n",
-    "            'PARQUET-pandas': len(df.to_parquet(engine='pyarrow')),\n",
-    "            'JSON-NTV': len(json.dumps(jsn)),\n",
-    "            'CBOR-NTV': len(cbor2.dumps(jsn))}\n",
+    "    jsn = xnd.to_json(notype=\"all\", header=False, encoded=False, format=forma)\n",
+    "    return {\n",
+    "        \"JSON-pandas\": len(df.to_json(orient=\"values\")),\n",
+    "        \"CSV\": len(df.to_csv()),\n",
+    "        \"PARQUET-pandas\": len(df.to_parquet(engine=\"pyarrow\")),\n",
+    "        \"JSON-NTV\": len(json.dumps(jsn)),\n",
+    "        \"CBOR-NTV\": len(cbor2.dumps(jsn)),\n",
+    "    }\n",
+    "\n",
     "\n",
     "def sizes_plot(sizes, titles, fig_title):\n",
-    "    '''plot the size of some format''' \n",
+    "    \"\"\"plot the size of some format\"\"\"\n",
     "    fig, axs = plt.subplots(2, 2, figsize=(11, 6), sharex=\"col\")\n",
     "    fig.suptitle(fig_title)\n",
     "    for idx, (size, title) in enumerate(zip(sizes, titles)):\n",
-    "        bar_colors = ['tab:red' if val == min(size.values()) else 'tab:blue' for val in size.values()]\n",
-    "        percent = [str(round(val / list(size.values())[1] * 100, 1)) + ' %' for val in size.values()]\n",
-    "        bar_plt = axs[idx//2][idx%2].bar(size.keys(), size.values(), color=bar_colors)\n",
-    "        axs[idx//2][idx%2].set_title(title)\n",
-    "        axs[idx//2][idx%2].bar_label(bar_plt, percent, label_type='center')\n",
-    "        if idx//2:\n",
-    "            axs[idx//2][idx%2].tick_params(axis='x', rotation=70)\n",
+    "        bar_colors = [\n",
+    "            \"tab:red\" if val == min(size.values()) else \"tab:blue\"\n",
+    "            for val in size.values()\n",
+    "        ]\n",
+    "        percent = [\n",
+    "            str(round(val / list(size.values())[1] * 100, 1)) + \" %\"\n",
+    "            for val in size.values()\n",
+    "        ]\n",
+    "        bar_plt = axs[idx // 2][idx % 2].bar(\n",
+    "            size.keys(), size.values(), color=bar_colors\n",
+    "        )\n",
+    "        axs[idx // 2][idx % 2].set_title(title)\n",
+    "        axs[idx // 2][idx % 2].bar_label(bar_plt, percent, label_type=\"center\")\n",
+    "        if idx // 2:\n",
+    "            axs[idx // 2][idx % 2].tick_params(axis=\"x\", rotation=70)\n",
     "    plt.show()"
    ]
   },
@@ -572,8 +598,13 @@
    "source": [
     "xnds = [Xdataset.from_xarray(xds) for xds in xdss]\n",
     "sizes = [file_sizes(xnd) for xnd in xnds]\n",
-    "titles = ['integer (6 100 values)', 'string (6 100 values)', 'integer (600 000 values)', 'string (600 000 values)']\n",
-    "sizes_plot(sizes, titles, 'multidimensional DataFrame size (bytes)')"
+    "titles = [\n",
+    "    \"integer (6 100 values)\",\n",
+    "    \"string (6 100 values)\",\n",
+    "    \"integer (600 000 values)\",\n",
+    "    \"string (600 000 values)\",\n",
+    "]\n",
+    "sizes_plot(sizes, titles, \"multidimensional DataFrame size (bytes)\")"
    ]
   },
   {
@@ -611,8 +642,8 @@
     "        arr = arr // 2\n",
     "        data_int.append(arr)\n",
     "        data_str.append(np.frompyfunc(str, 1, 1)(arr))\n",
-    "    field_names = ['idx_' + str(i) for i in range(len(data_int))]\n",
-    "    return [data_int, data_str, field_names]   "
+    "    field_names = [\"idx_\" + str(i) for i in range(len(data_int))]\n",
+    "    return [data_int, data_str, field_names]"
    ]
   },
   {
@@ -810,7 +841,9 @@
    "source": [
     "size1 = 4\n",
     "\n",
-    "df = pd.DataFrame({field: data for field, data in zip (data_int_str(size1)[2], data_int_str(size1)[0])})\n",
+    "df = pd.DataFrame(\n",
+    "    {field: data for field, data in zip(data_int_str(size1)[2], data_int_str(size1)[0])}\n",
+    ")\n",
     "df"
    ]
   },
@@ -832,7 +865,7 @@
     }
    ],
    "source": [
-    "df.to_json(orient='values')"
+    "df.to_json(orient=\"values\")"
    ]
   },
   {
@@ -861,8 +894,10 @@
     }
    ],
    "source": [
-    "forma = {name:'complete' for name in df.columns[1:]}\n",
-    "Xdataset.from_dataframe(df).to_json(notype='all', header=False, encoded=False, format=forma)\n"
+    "forma = {name: \"complete\" for name in df.columns[1:]}\n",
+    "Xdataset.from_dataframe(df).to_json(\n",
+    "    notype=\"all\", header=False, encoded=False, format=forma\n",
+    ")"
    ]
   },
   {
@@ -911,7 +946,7 @@
     "size1 = 9\n",
     "size2 = 14\n",
     "data_set = data_int_str(size1)[:2] + data_int_str(size2)[:2]\n",
-    "names_set= [data_int_str(size1)[2]] * 2 + [data_int_str(size2)[2]] * 2"
+    "names_set = [data_int_str(size1)[2]] * 2 + [data_int_str(size2)[2]] * 2"
    ]
   },
   {
@@ -1127,7 +1162,10 @@
     }
    ],
    "source": [
-    "df_list = [pd.DataFrame({field: data for field, data in zip (field_names, data_list)}) for field_names, data_list in zip(names_set, data_set)]\n",
+    "df_list = [\n",
+    "    pd.DataFrame({field: data for field, data in zip(field_names, data_list)})\n",
+    "    for field_names, data_list in zip(names_set, data_set)\n",
+    "]\n",
     "\n",
     "df_list[0]"
    ]
@@ -1160,10 +1198,15 @@
     }
    ],
    "source": [
-    "forma = [{name:'complete' for name in xnd.names[1:]} for xnd in xnds]\n",
+    "forma = [{name: \"complete\" for name in xnd.names[1:]} for xnd in xnds]\n",
     "sizes = [file_sizes(xnd, form) for xnd, form in zip(xnds, forma)]\n",
-    "titles = ['integer (5 100 values)', 'string (5 100 values)', 'integer (524 300 values)', 'string (524 300 values)']\n",
-    "sizes_plot(sizes, titles, 'tree DataFrame size (bytes)')"
+    "titles = [\n",
+    "    \"integer (5 100 values)\",\n",
+    "    \"string (5 100 values)\",\n",
+    "    \"integer (524 300 values)\",\n",
+    "    \"string (524 300 values)\",\n",
+    "]\n",
+    "sizes_plot(sizes, titles, \"tree DataFrame size (bytes)\")"
    ]
   }
  ],
diff --git a/example/example_table_pandas.ipynb b/example/example_table_pandas.ipynb
index 352f7f0..fd17f94 100644
--- a/example/example_table_pandas.ipynb
+++ b/example/example_table_pandas.ipynb
@@ -41,15 +41,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import math\n",
-    "import json\n",
     "from pprint import pprint\n",
     "\n",
     "import pandas as pd\n",
     "import ntv_pandas as npd\n",
     "from shapely.geometry import Point, Polygon, LineString\n",
-    "from json_ntv import Ntv\n",
-    "from datetime import date, datetime, time"
+    "from datetime import date, time"
    ]
   },
   {
@@ -136,12 +133,22 @@
     }
    ],
    "source": [
-    "df = pd.DataFrame({\n",
-    "            'end february::date': [date(2023,2,28), date(2024,2,29), date(2025,2,28)],\n",
-    "            'coordinates::point': [Point([2.3, 48.9]), Point([5.4, 43.3]), Point([4.9, 45.8])],\n",
-    "            'contact::email':     ['john.doe@table.com', 'lisa.minelli@schema.com', 'walter.white@breaking.com']\n",
-    "            }).astype({'contact::email': 'string'})\n",
-    "df\n"
+    "df = pd.DataFrame(\n",
+    "    {\n",
+    "        \"end february::date\": [date(2023, 2, 28), date(2024, 2, 29), date(2025, 2, 28)],\n",
+    "        \"coordinates::point\": [\n",
+    "            Point([2.3, 48.9]),\n",
+    "            Point([5.4, 43.3]),\n",
+    "            Point([4.9, 45.8]),\n",
+    "        ],\n",
+    "        \"contact::email\": [\n",
+    "            \"john.doe@table.com\",\n",
+    "            \"lisa.minelli@schema.com\",\n",
+    "            \"walter.white@breaking.com\",\n",
+    "        ],\n",
+    "    }\n",
+    ").astype({\"contact::email\": \"string\"})\n",
+    "df"
    ]
   },
   {
@@ -264,7 +271,7 @@
    ],
    "source": [
     "df_from_table = npd.read_json(df_to_table)\n",
-    "print('df created from TableSchema is equal to initial df ? ', df_from_table.equals(df))\n",
+    "print(\"df created from TableSchema is equal to initial df ? \", df_from_table.equals(df))\n",
     "df_from_table"
    ]
   },
@@ -315,14 +322,14 @@
     }
    ],
    "source": [
-    "sr = pd.Series([1, 2, 3], name='value')\n",
-    "print('pandas object :\\n' + str(sr))\n",
+    "sr = pd.Series([1, 2, 3], name=\"value\")\n",
+    "print(\"pandas object :\\n\" + str(sr))\n",
     "\n",
     "json_table = sr.npd.to_json(table=True)\n",
-    "print('\\nJson Table representation :    ')\n",
+    "print(\"\\nJson Table representation :    \")\n",
     "pprint(json_table, width=100, sort_dicts=False)\n",
     "\n",
-    "print('\\nIs Json Table translation reversible ? ', sr.equals(npd.read_json(json_table)))"
+    "print(\"\\nIs Json Table translation reversible ? \", sr.equals(npd.read_json(json_table)))"
    ]
   },
   {
@@ -346,18 +353,25 @@
     }
    ],
    "source": [
-    "list_sr = [pd.Series([1, 2, 3],   name='value'),\n",
-    "           pd.Series([1.1, 2, 3], name='value'),\n",
-    "           pd.Series([True, False, True], name='value'),\n",
-    "           # additional types\n",
-    "           pd.Series([1, 2, 3],   name='value', dtype='int32'),\n",
-    "           pd.Series([1, 2, 3],   name='value', dtype='uint64'),\n",
-    "           pd.Series([1.6, 2, 3], name='value', dtype='float32')]\n",
+    "list_sr = [\n",
+    "    pd.Series([1, 2, 3], name=\"value\"),\n",
+    "    pd.Series([1.1, 2, 3], name=\"value\"),\n",
+    "    pd.Series([True, False, True], name=\"value\"),\n",
+    "    # additional types\n",
+    "    pd.Series([1, 2, 3], name=\"value\", dtype=\"int32\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value\", dtype=\"uint64\"),\n",
+    "    pd.Series([1.6, 2, 3], name=\"value\", dtype=\"float32\"),\n",
+    "]\n",
     "\n",
-    "print('reversibility, schema field : ')\n",
+    "print(\"reversibility, schema field : \")\n",
     "for sr in list_sr:\n",
     "    json_table = sr.npd.to_json(table=True)\n",
-    "    print('    ', sr.equals(npd.read_json(json_table)), ', ', json_table['schema']['fields'][1])"
+    "    print(\n",
+    "        \"    \",\n",
+    "        sr.equals(npd.read_json(json_table)),\n",
+    "        \", \",\n",
+    "        json_table[\"schema\"][\"fields\"][1],\n",
+    "    )"
    ]
   },
   {
@@ -395,20 +409,41 @@
     }
    ],
    "source": [
-    "list_sr = [pd.Series([[1, 2], ['val1', 'val2']],   name='value::array'),\n",
-    "           pd.Series([[1, 2], 3, 'test', {'val1': 5, 'val2': 6}],   name='value'),\n",
-    "           pd.Series(['az', 'er', 'cd'], name='value', dtype='string'),\n",
-    "           pd.Series([\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\"], name='value::uri', dtype='string'),\n",
-    "           pd.Series([\"philippe@loco-labs.io\", \"John.Doe@example.com\"], name='value::email', dtype='string'),\n",
-    "           # additional types\n",
-    "           pd.Series([{'val1': 5, 'val2': 6}, {'val1': 5.1, 'val2': 6.1}],   name='value::object'),\n",
-    "           pd.Series([\"///path/to/file\", \"//host.example.com/path/to/file\"], name='value::file', dtype='string'),\n",
-    "           pd.Series([None, None, None], name='value::null')]\n",
+    "list_sr = [\n",
+    "    pd.Series([[1, 2], [\"val1\", \"val2\"]], name=\"value::array\"),\n",
+    "    pd.Series([[1, 2], 3, \"test\", {\"val1\": 5, \"val2\": 6}], name=\"value\"),\n",
+    "    pd.Series([\"az\", \"er\", \"cd\"], name=\"value\", dtype=\"string\"),\n",
+    "    pd.Series(\n",
+    "        [\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\"],\n",
+    "        name=\"value::uri\",\n",
+    "        dtype=\"string\",\n",
+    "    ),\n",
+    "    pd.Series(\n",
+    "        [\"philippe@loco-labs.io\", \"John.Doe@example.com\"],\n",
+    "        name=\"value::email\",\n",
+    "        dtype=\"string\",\n",
+    "    ),\n",
+    "    # additional types\n",
+    "    pd.Series(\n",
+    "        [{\"val1\": 5, \"val2\": 6}, {\"val1\": 5.1, \"val2\": 6.1}], name=\"value::object\"\n",
+    "    ),\n",
+    "    pd.Series(\n",
+    "        [\"///path/to/file\", \"//host.example.com/path/to/file\"],\n",
+    "        name=\"value::file\",\n",
+    "        dtype=\"string\",\n",
+    "    ),\n",
+    "    pd.Series([None, None, None], name=\"value::null\"),\n",
+    "]\n",
     "\n",
-    "print('reversibility, schema field : ')\n",
+    "print(\"reversibility, schema field : \")\n",
     "for sr in list_sr:\n",
     "    json_table = sr.npd.to_json(table=True)\n",
-    "    print('    ', sr.equals(npd.read_json(json_table)), ', ', json_table['schema']['fields'][1])"
+    "    print(\n",
+    "        \"    \",\n",
+    "        sr.equals(npd.read_json(json_table)),\n",
+    "        \", \",\n",
+    "        json_table[\"schema\"][\"fields\"][1],\n",
+    "    )"
    ]
   },
   {
@@ -450,25 +485,33 @@
     }
    ],
    "source": [
-    "list_sr = [pd.Series(['2022-01-01', '2021-01-01'], dtype='datetime64[ns]', name='value'),\n",
-    "           pd.Series([date(2022,1,1), date(2021,1,1), date(2023,1,1)],   name='value::date'),\n",
-    "           pd.Series([time(10,20,50), time(9,20,50), time(8,20,50)],   name='value::time'),\n",
-    "           pd.Series([1, 2, 3], name='value::month'),\n",
-    "           pd.Series([2021, 2022, 2023], name='value::year'),\n",
-    "           # additional types\n",
-    "           pd.Series([1, 2, 3],   name='value::day'),\n",
-    "           pd.Series([1, 2, 3],   name='value::wday'),\n",
-    "           pd.Series([1, 2, 3],   name='value::yday'),\n",
-    "           pd.Series([1, 2, 3],   name='value::week'),\n",
-    "           pd.Series([1, 2, 3],   name='value::hour'),\n",
-    "           pd.Series([1, 2, 3],   name='value::minute'),\n",
-    "           pd.Series([1, 2, 3],   name='value::second')\n",
-    "          ]\n",
+    "list_sr = [\n",
+    "    pd.Series([\"2022-01-01\", \"2021-01-01\"], dtype=\"datetime64[ns]\", name=\"value\"),\n",
+    "    pd.Series(\n",
+    "        [date(2022, 1, 1), date(2021, 1, 1), date(2023, 1, 1)], name=\"value::date\"\n",
+    "    ),\n",
+    "    pd.Series([time(10, 20, 50), time(9, 20, 50), time(8, 20, 50)], name=\"value::time\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::month\"),\n",
+    "    pd.Series([2021, 2022, 2023], name=\"value::year\"),\n",
+    "    # additional types\n",
+    "    pd.Series([1, 2, 3], name=\"value::day\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::wday\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::yday\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::week\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::hour\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::minute\"),\n",
+    "    pd.Series([1, 2, 3], name=\"value::second\"),\n",
+    "]\n",
     "\n",
-    "print('reversibility, schema field : ')\n",
+    "print(\"reversibility, schema field : \")\n",
     "for sr in list_sr:\n",
     "    json_table = sr.npd.to_json(table=True)\n",
-    "    print('    ', sr.equals(npd.read_json(json_table)), ', ', json_table['schema']['fields'][1])"
+    "    print(\n",
+    "        \"    \",\n",
+    "        sr.equals(npd.read_json(json_table)),\n",
+    "        \", \",\n",
+    "        json_table[\"schema\"][\"fields\"][1],\n",
+    "    )"
    ]
   },
   {
@@ -501,18 +544,36 @@
     }
    ],
    "source": [
-    "list_sr = [pd.Series(pd.Series([Point(1, 0), Point(1, 1), Point(1, 2)], name='value::point')),\n",
-    "           pd.Series([Point(1, 0), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])], name='value::geojson'),\n",
-    "           # additional types\n",
-    "           pd.Series([Point(1, 0), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])], name='value::geometry'),\n",
-    "           pd.Series([Polygon([[1, 2], [1, 3], [2, 4]]), Polygon([[1, 2], [1, 3], [2, 5]])], name='value::polygon'),\n",
-    "           pd.Series([LineString([[1, 2], [1, 3], [2, 4]]), LineString([[1, 2], [1, 3], [2, 5]])], name='value::line')\n",
-    "          ]\n",
+    "list_sr = [\n",
+    "    pd.Series(pd.Series([Point(1, 0), Point(1, 1), Point(1, 2)], name=\"value::point\")),\n",
+    "    pd.Series(\n",
+    "        [Point(1, 0), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])],\n",
+    "        name=\"value::geojson\",\n",
+    "    ),\n",
+    "    # additional types\n",
+    "    pd.Series(\n",
+    "        [Point(1, 0), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])],\n",
+    "        name=\"value::geometry\",\n",
+    "    ),\n",
+    "    pd.Series(\n",
+    "        [Polygon([[1, 2], [1, 3], [2, 4]]), Polygon([[1, 2], [1, 3], [2, 5]])],\n",
+    "        name=\"value::polygon\",\n",
+    "    ),\n",
+    "    pd.Series(\n",
+    "        [LineString([[1, 2], [1, 3], [2, 4]]), LineString([[1, 2], [1, 3], [2, 5]])],\n",
+    "        name=\"value::line\",\n",
+    "    ),\n",
+    "]\n",
     "\n",
-    "print('reversibility, schema field : ')\n",
+    "print(\"reversibility, schema field : \")\n",
     "for sr in list_sr:\n",
     "    json_table = sr.npd.to_json(table=True)\n",
-    "    print('    ', sr.equals(npd.read_json(json_table)), ', ', json_table['schema']['fields'][1])"
+    "    print(\n",
+    "        \"    \",\n",
+    "        sr.equals(npd.read_json(json_table)),\n",
+    "        \", \",\n",
+    "        json_table[\"schema\"][\"fields\"][1],\n",
+    "    )"
    ]
   },
   {
@@ -625,35 +686,62 @@
     }
    ],
    "source": [
-    "df = pd.DataFrame({\n",
+    "df = pd.DataFrame(\n",
+    "    {\n",
     "        # numerical\n",
-    "        'float':       [1.1, 2, 3],\n",
-    "        'boolean':     [True, False, False],\n",
-    "        'int32':       pd.Series([1, 2, 3],   dtype='int32'),\n",
+    "        \"float\": [1.1, 2, 3],\n",
+    "        \"boolean\": [True, False, False],\n",
+    "        \"int32\": pd.Series([1, 2, 3], dtype=\"int32\"),\n",
     "        # json\n",
-    "        'ex1::array':  [[1, 2], ['val1', 'val2'], [1, {'val3': 3}]],\n",
-    "        'json':        [[1, 2], 'test', {'val1': 5, 'val2': 6}],\n",
-    "        'string':      pd.Series(['az', 'er', 'cd'], dtype='string'),\n",
-    "        'ex2::uri':    pd.Series([\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\", \"\"], dtype='string'),\n",
-    "        'ex3::email':  pd.Series([\"philippe@loco-labs.io\", \"John.Doe@example.com\", \"\"], dtype='string'),\n",
-    "        'ex4::object': [{'val1': 5, 'val2': 6}, {'val1': 5.1, 'val2': 6.1}, {}],\n",
+    "        \"ex1::array\": [[1, 2], [\"val1\", \"val2\"], [1, {\"val3\": 3}]],\n",
+    "        \"json\": [[1, 2], \"test\", {\"val1\": 5, \"val2\": 6}],\n",
+    "        \"string\": pd.Series([\"az\", \"er\", \"cd\"], dtype=\"string\"),\n",
+    "        \"ex2::uri\": pd.Series(\n",
+    "            [\"geo:13.412 ,103.866\", \"mailto:John.Doe@example.com\", \"\"], dtype=\"string\"\n",
+    "        ),\n",
+    "        \"ex3::email\": pd.Series(\n",
+    "            [\"philippe@loco-labs.io\", \"John.Doe@example.com\", \"\"], dtype=\"string\"\n",
+    "        ),\n",
+    "        \"ex4::object\": [{\"val1\": 5, \"val2\": 6}, {\"val1\": 5.1, \"val2\": 6.1}, {}],\n",
     "        # datation\n",
-    "        'datetime':    pd.Series(['2022-01-01', '2021-01-01', '2023-01-01'], dtype='datetime64[ns]'),\n",
-    "        'ex5::date':   [date(2022,1,1), date(2021,1,1), date(2023,1,1)],\n",
-    "        'ex6::time':   [time(10,20,50), time(9,20,50), time(8,20,50)],\n",
-    "        'ex7::month':  [1, 2, 3],\n",
-    "        'ex8::hour':   [1, 2, 3],\n",
+    "        \"datetime\": pd.Series(\n",
+    "            [\"2022-01-01\", \"2021-01-01\", \"2023-01-01\"], dtype=\"datetime64[ns]\"\n",
+    "        ),\n",
+    "        \"ex5::date\": [date(2022, 1, 1), date(2021, 1, 1), date(2023, 1, 1)],\n",
+    "        \"ex6::time\": [time(10, 20, 50), time(9, 20, 50), time(8, 20, 50)],\n",
+    "        \"ex7::month\": [1, 2, 3],\n",
+    "        \"ex8::hour\": [1, 2, 3],\n",
     "        # location\n",
-    "        'ex9::point':  [Point(1, 0), Point(1, 1), Point(1, 2)],\n",
-    "        'ex10::geojson': [Point(1, 0), LineString([[1, 2], [1, 3]]), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])],\n",
+    "        \"ex9::point\": [Point(1, 0), Point(1, 1), Point(1, 2)],\n",
+    "        \"ex10::geojson\": [\n",
+    "            Point(1, 0),\n",
+    "            LineString([[1, 2], [1, 3]]),\n",
+    "            Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]]),\n",
+    "        ],\n",
     "        # additional types\n",
-    "        'ex11::geometry': [Point(1, 0), LineString([[1, 2], [1, 3]]), Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]])],\n",
-    "        'ex12::polygon':  [Polygon([[1,2], [1,3], [2,4]]), Polygon([[1,2], [1,3], [2,5]]), Polygon([[1,2], [1,3], [2,6]])],\n",
-    "        'ex13::line':     [LineString([[1, 2], [2, 4]]), LineString([[1, 2], [2, 5]]), LineString([[1, 2], [2, 6]])]           \n",
-    "})\n",
-    "print('\\nJson Table representation :    ')\n",
+    "        \"ex11::geometry\": [\n",
+    "            Point(1, 0),\n",
+    "            LineString([[1, 2], [1, 3]]),\n",
+    "            Polygon([[1.0, 2.0], [1.0, 3.0], [2.0, 4.0]]),\n",
+    "        ],\n",
+    "        \"ex12::polygon\": [\n",
+    "            Polygon([[1, 2], [1, 3], [2, 4]]),\n",
+    "            Polygon([[1, 2], [1, 3], [2, 5]]),\n",
+    "            Polygon([[1, 2], [1, 3], [2, 6]]),\n",
+    "        ],\n",
+    "        \"ex13::line\": [\n",
+    "            LineString([[1, 2], [2, 4]]),\n",
+    "            LineString([[1, 2], [2, 5]]),\n",
+    "            LineString([[1, 2], [2, 6]]),\n",
+    "        ],\n",
+    "    }\n",
+    ")\n",
+    "print(\"\\nJson Table representation :    \")\n",
     "pprint(df.npd.to_json(table=True), width=100, sort_dicts=False)\n",
-    "print('\\nis Json translation reversible ? ', df.equals(npd.read_json(df.npd.to_json(table=True))))"
+    "print(\n",
+    "    \"\\nis Json translation reversible ? \",\n",
+    "    df.equals(npd.read_json(df.npd.to_json(table=True))),\n",
+    ")"
    ]
   },
   {
@@ -762,15 +850,23 @@
     }
    ],
    "source": [
-    "data = {'index':           [100, 200, 300, 400, 500],\n",
-    "                'dates::date':     [date(1964,1,1), date(1985,2,5), date(2022,1,21), date(1964,1,1), date(1985,2,5)],\n",
-    "                'value':           [10, 10, 20, 20, 30],\n",
-    "                'value32':         pd.Series([12, 12, 22, 22, 32], dtype='int32'),\n",
-    "                'res':             [10, 20, 30, 10, 20],\n",
-    "                'coord::point':    [Point(1,2), Point(3,4), Point(5,6), Point(7,8), Point(3,4)],\n",
-    "                'names':           pd.Series(['john', 'eric', 'judith', 'mila', 'hector'], dtype='string'),\n",
-    "                'unique':          True }\n",
-    "df = pd.DataFrame(data).set_index('index')\n",
+    "data = {\n",
+    "    \"index\": [100, 200, 300, 400, 500],\n",
+    "    \"dates::date\": [\n",
+    "        date(1964, 1, 1),\n",
+    "        date(1985, 2, 5),\n",
+    "        date(2022, 1, 21),\n",
+    "        date(1964, 1, 1),\n",
+    "        date(1985, 2, 5),\n",
+    "    ],\n",
+    "    \"value\": [10, 10, 20, 20, 30],\n",
+    "    \"value32\": pd.Series([12, 12, 22, 22, 32], dtype=\"int32\"),\n",
+    "    \"res\": [10, 20, 30, 10, 20],\n",
+    "    \"coord::point\": [Point(1, 2), Point(3, 4), Point(5, 6), Point(7, 8), Point(3, 4)],\n",
+    "    \"names\": pd.Series([\"john\", \"eric\", \"judith\", \"mila\", \"hector\"], dtype=\"string\"),\n",
+    "    \"unique\": True,\n",
+    "}\n",
+    "df = pd.DataFrame(data).set_index(\"index\")\n",
     "df.index.name = None\n",
     "df"
    ]
@@ -837,8 +933,8 @@
    ],
    "source": [
     "df_to_table = df.npd.to_json(table=True)\n",
-    "pprint(df_to_table['data'][0], sort_dicts=False)\n",
-    "pprint(df_to_table['schema'], sort_dicts=False)\n",
+    "pprint(df_to_table[\"data\"][0], sort_dicts=False)\n",
+    "pprint(df_to_table[\"schema\"], sort_dicts=False)\n",
     "print(npd.read_json(df_to_table).equals(df))"
    ]
   }
diff --git a/example/example_xarray.ipynb b/example/example_xarray.ipynb
index 805fa27..9fd1eee 100644
--- a/example/example_xarray.ipynb
+++ b/example/example_xarray.ipynb
@@ -62,33 +62,68 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import os\n",
     "from random import random\n",
     "\n",
-    "columns = ['camp', 'date', 'hour', 'city', 'coord', 'prop', 'unit', 'value']\n",
+    "columns = [\"camp\", \"date\", \"hour\", \"city\", \"coord\", \"prop\", \"unit\", \"value\"]\n",
     "\n",
-    "camp = 'air quality sensor measurement'\n",
-    "dates = ['2024/05/24', '2024/05/25', '2024/05/26', '2024/05/27', '2024/05/28', \n",
-    "         '2024/05/29', '2024/05/30', '2024/05/31', '2024/06/01', '2024/06/02',\n",
-    "         '2024/06/03', '2024/06/04', '2024/06/05', '2024/06/06', '2024/06/07',\n",
-    "         '2024/06/08', '2024/06/09', '2024/06/10', '2024/06/11', '2024/06/12']\n",
-    "cities = ['lille', 'toulouse', 'marseille', 'strasbourg', 'brest']\n",
-    "coordinates = ['[3.06, 50.63]', '[1.44, 43.6]', '[5.37, 43.3]', '[7.75, 48.57]', '[4.49, 48.39]']\n",
-    "properties = ['PM10', 'PM2.5', 'NO2', 'O3', 'CO']\n",
-    "units = ['µg/m3', 'µg/m3', 'µg/m3', 'µg/m3', 'mg/m3']\n",
+    "camp = \"air quality sensor measurement\"\n",
+    "dates = [\n",
+    "    \"2024/05/24\",\n",
+    "    \"2024/05/25\",\n",
+    "    \"2024/05/26\",\n",
+    "    \"2024/05/27\",\n",
+    "    \"2024/05/28\",\n",
+    "    \"2024/05/29\",\n",
+    "    \"2024/05/30\",\n",
+    "    \"2024/05/31\",\n",
+    "    \"2024/06/01\",\n",
+    "    \"2024/06/02\",\n",
+    "    \"2024/06/03\",\n",
+    "    \"2024/06/04\",\n",
+    "    \"2024/06/05\",\n",
+    "    \"2024/06/06\",\n",
+    "    \"2024/06/07\",\n",
+    "    \"2024/06/08\",\n",
+    "    \"2024/06/09\",\n",
+    "    \"2024/06/10\",\n",
+    "    \"2024/06/11\",\n",
+    "    \"2024/06/12\",\n",
+    "]\n",
+    "cities = [\"lille\", \"toulouse\", \"marseille\", \"strasbourg\", \"brest\"]\n",
+    "coordinates = [\n",
+    "    \"[3.06, 50.63]\",\n",
+    "    \"[1.44, 43.6]\",\n",
+    "    \"[5.37, 43.3]\",\n",
+    "    \"[7.75, 48.57]\",\n",
+    "    \"[4.49, 48.39]\",\n",
+    "]\n",
+    "properties = [\"PM10\", \"PM2.5\", \"NO2\", \"O3\", \"CO\"]\n",
+    "units = [\"µg/m3\", \"µg/m3\", \"µg/m3\", \"µg/m3\", \"mg/m3\"]\n",
     "hours = list(range(24))\n",
     "\n",
+    "\n",
     "def data_acquisition(n_dates, n_round=None, n_hours=24):\n",
-    "    '''return a list of records for a set of dates defined by the n_dates parameter.\n",
-    "    The n_round parameter defines the type of the measurement value: \n",
+    "    \"\"\"return a list of records for a set of dates defined by the n_dates parameter.\n",
+    "    The n_round parameter defines the type of the measurement value:\n",
     "        n_round : None -> integer\n",
     "        n_round : 0    -> float\n",
-    "        n_round : n    -> round(float, n)'''\n",
-    "    return [(camp, date, hour, city, coord, prop, unit, random()*10 if n_round == 0 else round(random()*10, n_round))\n",
-    "             for city, coord in zip(cities, coordinates)\n",
-    "                 for date in dates[:n_dates]\n",
-    "                     for hour in hours[:n_hours]\n",
-    "                         for prop, unit in zip(properties, units) ]"
+    "        n_round : n    -> round(float, n)\"\"\"\n",
+    "    return [\n",
+    "        (\n",
+    "            camp,\n",
+    "            date,\n",
+    "            hour,\n",
+    "            city,\n",
+    "            coord,\n",
+    "            prop,\n",
+    "            unit,\n",
+    "            random() * 10 if n_round == 0 else round(random() * 10, n_round),\n",
+    "        )\n",
+    "        for city, coord in zip(cities, coordinates)\n",
+    "        for date in dates[:n_dates]\n",
+    "        for hour in hours[:n_hours]\n",
+    "        for prop, unit in zip(properties, units)\n",
+    "    ]"
    ]
   },
   {
@@ -293,7 +328,11 @@
    "source": [
     "import pandas as pd\n",
     "\n",
-    "meas_df_10 = pd.DataFrame(data_acquisition(10), columns=columns).sample(frac=1).reset_index(drop=True)\n",
+    "meas_df_10 = (\n",
+    "    pd.DataFrame(data_acquisition(10), columns=columns)\n",
+    "    .sample(frac=1)\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "meas_df_10"
    ]
   },
@@ -761,9 +800,6 @@
     }
    ],
    "source": [
-    "import xarray as xr\n",
-    "import ntv_pandas\n",
-    "\n",
     "meas_xr_10 = meas_df_10.npd.to_xarray()\n",
     "meas_xr_10"
    ]
@@ -797,7 +833,7 @@
     }
    ],
    "source": [
-    "meas_xr_10.sel(city='lille', prop='NO2', hour=0, date='2024/05/24').values"
+    "meas_xr_10.sel(city=\"lille\", prop=\"NO2\", hour=0, date=\"2024/05/24\").values"
    ]
   },
   {
@@ -847,8 +883,12 @@
    "source": [
     "from pprint import pprint\n",
     "\n",
-    "notype = [True]*len(meas_df_10.columns)\n",
-    "meas_df_1 = pd.DataFrame(data_acquisition(1, n_round=2, n_hours=4), columns=columns).sample(frac=1).reset_index(drop=True)\n",
+    "notype = [True] * len(meas_df_10.columns)\n",
+    "meas_df_1 = (\n",
+    "    pd.DataFrame(data_acquisition(1, n_round=2, n_hours=4), columns=columns)\n",
+    "    .sample(frac=1)\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "meas_xr_1 = meas_df_1.npd.to_xarray()\n",
     "meas_json = meas_xr_1.nxr.to_json(notype=notype, header=False, encoded=False)\n",
     "pprint(meas_json, compact=True)"
@@ -872,30 +912,47 @@
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "import ntv_numpy\n",
     "import cbor2\n",
     "\n",
-    "notype = [True]*len(meas_df_10.columns)\n",
+    "notype = [True] * len(meas_df_10.columns)\n",
+    "\n",
     "\n",
     "def file_sizes(df):\n",
-    "    '''calculate the size of each format'''\n",
-    "    return {'pd.to_json(values)': len(df.to_json(orient='values')),\n",
-    "            'pd.to_csv': len(df.to_csv()),\n",
-    "            'pd.to_parquet': len(df.to_parquet(engine='pyarrow')),\n",
-    "            'nxr.to_json': len(df.npd.to_xarray().nxr.to_json(notype=notype, header=False, encoded=True)),\n",
-    "            'nxr.to_json(cbor)': len(cbor2.dumps(df.npd.to_xarray().nxr.to_json(notype=notype, header=False, encoded=False)))}\n",
+    "    \"\"\"calculate the size of each format\"\"\"\n",
+    "    return {\n",
+    "        \"pd.to_json(values)\": len(df.to_json(orient=\"values\")),\n",
+    "        \"pd.to_csv\": len(df.to_csv()),\n",
+    "        \"pd.to_parquet\": len(df.to_parquet(engine=\"pyarrow\")),\n",
+    "        \"nxr.to_json\": len(\n",
+    "            df.npd.to_xarray().nxr.to_json(notype=notype, header=False, encoded=True)\n",
+    "        ),\n",
+    "        \"nxr.to_json(cbor)\": len(\n",
+    "            cbor2.dumps(\n",
+    "                df.npd.to_xarray().nxr.to_json(\n",
+    "                    notype=notype, header=False, encoded=False\n",
+    "                )\n",
+    "            )\n",
+    "        ),\n",
+    "    }\n",
+    "\n",
     "\n",
     "def sizes_plot(sizes, titles, fig_title):\n",
-    "    '''plot the size of some format''' \n",
+    "    \"\"\"plot the size of some format\"\"\"\n",
     "    fig, axs = plt.subplots(1, 4, figsize=(24, 6))\n",
     "    fig.suptitle(fig_title)\n",
     "    for idx, (size, title) in enumerate(zip(sizes, titles)):\n",
-    "        bar_colors = ['tab:red' if val == min(size.values()) else 'tab:blue' for val in size.values()]\n",
-    "        percent = [str(round(val / list(size.values())[1] * 100, 1)) + ' %' for val in size.values()]\n",
+    "        bar_colors = [\n",
+    "            \"tab:red\" if val == min(size.values()) else \"tab:blue\"\n",
+    "            for val in size.values()\n",
+    "        ]\n",
+    "        percent = [\n",
+    "            str(round(val / list(size.values())[1] * 100, 1)) + \" %\"\n",
+    "            for val in size.values()\n",
+    "        ]\n",
     "        bar_plt = axs[idx].bar(size.keys(), size.values(), color=bar_colors)\n",
     "        axs[idx].set_title(title)\n",
-    "        axs[idx].bar_label(bar_plt, percent, label_type='center')\n",
-    "        axs[idx].tick_params(axis='x', rotation=55)\n",
+    "        axs[idx].bar_label(bar_plt, percent, label_type=\"center\")\n",
+    "        axs[idx].tick_params(axis=\"x\", rotation=55)\n",
     "    plt.show()"
    ]
   },
@@ -919,9 +976,16 @@
    "source": [
     "# plot measurement of one date\n",
     "options = [(None, \"integer\"), (0, \"float\"), (4, \"round(4)\"), (6, \"round(6)\")]\n",
-    "sizes = [file_sizes(pd.DataFrame(data_acquisition(1, opt[0]), columns=columns).sample(frac=1).reset_index(drop=True)) for opt in options]\n",
+    "sizes = [\n",
+    "    file_sizes(\n",
+    "        pd.DataFrame(data_acquisition(1, opt[0]), columns=columns)\n",
+    "        .sample(frac=1)\n",
+    "        .reset_index(drop=True)\n",
+    "    )\n",
+    "    for opt in options\n",
+    "]\n",
     "titles = [opt[1] for opt in options]\n",
-    "sizes_plot(sizes, titles, 'one date')"
+    "sizes_plot(sizes, titles, \"one date\")"
    ]
   },
   {
@@ -943,9 +1007,16 @@
    ],
    "source": [
     "# plot measurement of twenty dates\n",
-    "sizes = [file_sizes(pd.DataFrame(data_acquisition(20, opt[0]), columns=columns).sample(frac=1).reset_index(drop=True)) for opt in options]\n",
+    "sizes = [\n",
+    "    file_sizes(\n",
+    "        pd.DataFrame(data_acquisition(20, opt[0]), columns=columns)\n",
+    "        .sample(frac=1)\n",
+    "        .reset_index(drop=True)\n",
+    "    )\n",
+    "    for opt in options\n",
+    "]\n",
     "titles = [opt[1] for opt in options]\n",
-    "sizes_plot(sizes, titles, 'twenty dates')"
+    "sizes_plot(sizes, titles, \"twenty dates\")"
    ]
   }
  ],
diff --git a/example/other examples/example_communes.ipynb b/example/other examples/example_communes.ipynb
index 20ca134..5bc662f 100644
--- a/example/other examples/example_communes.ipynb	
+++ b/example/other examples/example_communes.ipynb	
@@ -246,8 +246,8 @@
    "source": [
     "import pandas as pd\n",
     "\n",
-    "comm = pd.read_csv('donnees_communes.csv', sep=';')\n",
-    "comm_min = comm[['REG', 'DEP', 'Région', 'COM']]\n",
+    "comm = pd.read_csv(\"donnees_communes.csv\", sep=\";\")\n",
+    "comm_min = comm[[\"REG\", \"DEP\", \"Région\", \"COM\"]]\n",
     "comm"
    ]
   },
@@ -277,8 +277,6 @@
     }
    ],
    "source": [
-    "import ntv_pandas\n",
-    "\n",
     "analys = comm.npd.analysis()\n",
     "print(analys.tree())"
    ]
@@ -305,9 +303,9 @@
     "from tab_dataset.dataset import Sdataset\n",
     "\n",
     "comm_sd = Sdataset(comm_min)\n",
-    "jsn = comm_sd.to_ntv(modecodec='optimize').to_obj(encoded=False)\n",
+    "jsn = comm_sd.to_ntv(modecodec=\"optimize\").to_obj(encoded=False)\n",
     "len(json.dumps(jsn))\n",
-    "#jsn"
+    "# jsn"
    ]
   },
   {
@@ -329,6 +327,7 @@
    ],
    "source": [
     "import cbor2\n",
+    "\n",
     "len(cbor2.dumps(jsn))"
    ]
   },
@@ -601,7 +600,7 @@
     }
    ],
    "source": [
-    "comm = pd.read_csv('v_commune_2024.csv', sep=',')\n",
+    "comm = pd.read_csv(\"v_commune_2024.csv\", sep=\",\")\n",
     "comm"
    ]
   }
diff --git a/example/other examples/example_hierarchical.ipynb b/example/other examples/example_hierarchical.ipynb
index 42351e2..404870e 100644
--- a/example/other examples/example_hierarchical.ipynb	
+++ b/example/other examples/example_hierarchical.ipynb	
@@ -52,14 +52,25 @@
     "from datetime import date, timedelta\n",
     "from random import random\n",
     "\n",
-    "columns = ['study', 'n_event', 'date', 'year', 'yearmonth', 'month', 'weekday', 'yearday', 'day']\n",
+    "columns = [\n",
+    "    \"study\",\n",
+    "    \"n_event\",\n",
+    "    \"date\",\n",
+    "    \"year\",\n",
+    "    \"yearmonth\",\n",
+    "    \"month\",\n",
+    "    \"weekday\",\n",
+    "    \"yearday\",\n",
+    "    \"day\",\n",
+    "]\n",
     "\n",
-    "study = 'event analysis'\n",
-    "t0 = date.fromisoformat('2000-01-01')\n",
+    "study = \"event analysis\"\n",
+    "t0 = date.fromisoformat(\"2000-01-01\")\n",
     "event0 = 100\n",
     "\n",
+    "\n",
     "def data_acquisition(n_dates):\n",
-    "    '''return a list of records '''\n",
+    "    \"\"\"return a list of records\"\"\"\n",
     "    data = []\n",
     "    for dt in range(n_dates):\n",
     "        dat = t0 + timedelta(dt)\n",
@@ -68,10 +79,16 @@
     "        yearmonth = dat_iso[:7]\n",
     "        month = dat.month\n",
     "        weekday = dat.isoweekday()\n",
-    "        yearday = (dat - date.fromisoformat(str(dat.isoformat()[:4] + '-01-01'))).days\n",
+    "        yearday = (dat - date.fromisoformat(str(dat.isoformat()[:4] + \"-01-01\"))).days\n",
     "        day = dat.day\n",
-    "        n_event = round(event0 + (month-6) * random() + (weekday - 3.5) * random() + 0.1 * yearday * random() + random() * 10) \n",
-    "        #data.append((study, n_event, dat_iso, year, yearmonth, month, weekday, yearday, day))\n",
+    "        n_event = round(\n",
+    "            event0\n",
+    "            + (month - 6) * random()\n",
+    "            + (weekday - 3.5) * random()\n",
+    "            + 0.1 * yearday * random()\n",
+    "            + random() * 10\n",
+    "        )\n",
+    "        # data.append((study, n_event, dat_iso, year, yearmonth, month, weekday, yearday, day))\n",
     "        data.append((study, n_event, dat_iso, year, yearmonth, month))\n",
     "    return data"
    ]
@@ -241,7 +258,11 @@
    "source": [
     "import pandas as pd\n",
     "\n",
-    "time_sr = pd.DataFrame(data_acquisition(10000), columns=columns[:6]).sample(frac=1).reset_index(drop=True)\n",
+    "time_sr = (\n",
+    "    pd.DataFrame(data_acquisition(10000), columns=columns[:6])\n",
+    "    .sample(frac=1)\n",
+    "    .reset_index(drop=True)\n",
+    ")\n",
     "time_sr"
    ]
   },
@@ -266,8 +287,6 @@
     }
    ],
    "source": [
-    "import ntv_pandas\n",
-    "\n",
     "analys = time_sr.npd.analysis()\n",
     "print(analys.tree())"
    ]
@@ -290,13 +309,13 @@
     }
    ],
    "source": [
-    "from tab_dataset.dataset import Sdataset, Ndataset\n",
+    "from tab_dataset.dataset import Sdataset\n",
     "\n",
     "time_sd = Sdataset(time_sr)\n",
-    "jsn = time_sd.to_ntv(modecodec='optimize').to_obj(encoded=True)\n",
-    "jsn2 = time_sd.to_ntv(modecodec='optimize').to_obj(encoded=False)\n",
+    "jsn = time_sd.to_ntv(modecodec=\"optimize\").to_obj(encoded=True)\n",
+    "jsn2 = time_sd.to_ntv(modecodec=\"optimize\").to_obj(encoded=False)\n",
     "len(jsn)\n",
-    "#jsn"
+    "# jsn"
    ]
   },
   {
@@ -318,6 +337,7 @@
    ],
    "source": [
     "import cbor2\n",
+    "\n",
     "len(cbor2.dumps(jsn2))"
    ]
   },
diff --git a/example/xarray_pandas_converter.ipynb b/example/xarray_pandas_converter.ipynb
index e49466a..9b4a3bc 100644
--- a/example/xarray_pandas_converter.ipynb
+++ b/example/xarray_pandas_converter.ipynb
@@ -429,11 +429,8 @@
    ],
    "source": [
     "import numpy as np\n",
-    "import pandas as pd\n",
     "import xarray as xr\n",
     "\n",
-    "import ntv_pandas # activate pandas npd accessor\n",
-    "import ntv_numpy  # activate xarray nxr accessor\n",
     "\n",
     "ds = xr.Dataset(\n",
     "    {\"foo\": ((\"x\", \"y\"), np.random.randn(2, 3))},\n",
@@ -443,7 +440,7 @@
     "        \"along_x\": (\"x\", np.random.randn(2)),\n",
     "        \"scalar\": 123,\n",
     "    },\n",
-    "    attrs={\"example\": \"Xarray user-guide\"}\n",
+    "    attrs={\"example\": \"Xarray user-guide\"},\n",
     ")\n",
     "ds"
    ]
@@ -1102,7 +1099,9 @@
     }
    ],
    "source": [
-    "df_min = ds.nxr.to_dataframe(ntv_type=False, info=False, index=False)  # without additional data\n",
+    "df_min = ds.nxr.to_dataframe(\n",
+    "    ntv_type=False, info=False, index=False\n",
+    ")  # without additional data\n",
     "df_min"
    ]
   },