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   "source": [
    "import os \n",
    "import sys\n",
    "sys.path.insert(0, os.path.abspath('../..'))\n",
    "\n",
    "import sympy as sp\n",
    "import numpy as np\n",
    "import itertools as it\n",
    "import pysymmpol as sy\n",
    "import pysymmpol.utils as ut\n",
    "from IPython.display import display, Latex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9742113f-57ab-4b9f-bba5-dbaf26587859",
   "metadata": {},
   "source": [
    "# Characters (utils)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64980944-f3eb-47a3-9151-e92354be2788",
   "metadata": {},
   "source": [
    "One useful function defined in the utils module is the character(young: YoungDiagram , conjugacy: ConjugacyClass), that as the name suggests, gives the character $$\\chi_{\\lambda}(\\vec{k})$$ of the symmetric group $\\mathfrak{S}_N$ in the representation $\\lambda$ and conjugacy class $C(\\vec{k})$. The nice point about the State class is that we can build the character table for any given integer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "894b472b-f52d-457d-91ee-c3a8d737ee1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's define the function character_table:\n",
    "def character_table(n):\n",
    "    '''\n",
    "    Gives the table of characters for the level n.\n",
    "    '''\n",
    "    chi = sp.Symbol(f'chi')\n",
    "\n",
    "    states = sy.State(n)\n",
    "    partitions = states.partition_states()\n",
    "    conjugacy = states.conjugacy_states()\n",
    "    \n",
    "    for a in partitions:\n",
    "        yg = sy.YoungDiagram(a)\n",
    "        display(Latex(r'$\\chi$'), yg.partition)\n",
    "        for b in conjugacy:\n",
    "            cj = sy.ConjugacyClass(b)\n",
    "            if ut.character(yg, cj) >= 0:\n",
    "                print(f\"{4*' '}{b}: {' '}{ut.character(yg, cj)}\")\n",
    "            else:\n",
    "                print(f\"{4*' '}{b}: {ut.character(yg, cj)}\")"
   ]
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   "cell_type": "code",
   "execution_count": 6,
   "id": "7a17c71f-aa93-43e6-b30d-37c64bd03f39",
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    {
     "data": {
      "text/latex": [
       "$\\chi$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/plain": [
       "(1, 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    {1: 2, 2: 0}:  1\n",
      "    {1: 0, 2: 1}: -1\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\chi$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(2, 0)"
      ]
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    {1: 2, 2: 0}:  1\n",
      "    {1: 0, 2: 1}:  1\n"
     ]
    }
   ],
   "source": [
    "n = 2\n",
    "character_table(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0e7afbf-16cb-47fd-b97a-ceec8c5cbe51",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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