sym.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import poppy\n",
    "import jax\n",
    "import functools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "THE SYMMETRIC GROUP S4\n",
      "\n",
      "[[0 1 2 3]\n",
      " [0 1 3 2]\n",
      " [0 2 1 3]\n",
      " [0 2 3 1]\n",
      " [0 3 1 2]\n",
      " [0 3 2 1]\n",
      " [1 0 2 3]\n",
      " [1 0 3 2]\n",
      " [1 2 0 3]\n",
      " [1 2 3 0]\n",
      " [1 3 0 2]\n",
      " [1 3 2 0]\n",
      " [2 0 1 3]\n",
      " [2 0 3 1]\n",
      " [2 1 0 3]\n",
      " [2 1 3 0]\n",
      " [2 3 0 1]\n",
      " [2 3 1 0]\n",
      " [3 0 1 2]\n",
      " [3 0 2 1]\n",
      " [3 1 0 2]\n",
      " [3 1 2 0]\n",
      " [3 2 0 1]\n",
      " [3 2 1 0]]\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "N = poppy.factorial(n)\n",
    "sym = poppy.sym(n,N)\n",
    "\n",
    "print(f'\\nTHE SYMMETRIC GROUP S{n}\\n\\n{sym}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3072x3072 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 5\n",
    "N = poppy.factorial(n)\n",
    "TABLE = poppy.symtbl(n,N)\n",
    "TITLE = f'S{n} MULTIPLICATION TABLE'\n",
    "size = 12\n",
    "\n",
    "poppy.plot(TABLE, title = TITLE, size = size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "28 PARTITIONS\n",
      "\n",
      "[[2], [1, 1], [3], [2, 1], [1, 1, 1], [4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1], [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1], [6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]\n"
     ]
    }
   ],
   "source": [
    "prts = [[2],[1,1],[3],[2,1],[1,1,1],[4],[3,1],[2,2],[2,1,1],[1,1,1,1],[5],[4,1],[3,2],[3,1,1],[2,2,1],[2,1,1,1],[1,1,1,1,1],[6],[5,1],[4,2],[4,1,1],[3,3],[3,2,1],[3,1,1,1],[2,2,2],[2,2,1,1],[2,1,1,1,1],[1,1,1,1,1,1]]\n",
    "\n",
    "print(f'\\n{len(prts)} PARTITIONS\\n\\n{prts}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "THE 2 1 1 REPRESENTATION OF S4\n",
      "\n",
      "[[[1 0 0]\n",
      "  [0 1 0]\n",
      "  [0 0 1]]\n",
      "\n",
      " [[1 2 1]\n",
      "  [0 2 0]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [2 1 2]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [0 2 0]\n",
      "  [1 2 1]]\n",
      "\n",
      " [[1 2 1]\n",
      "  [0 2 0]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[1 0 0]\n",
      "  [0 1 0]\n",
      "  [0 0 1]]\n",
      "\n",
      " [[0 1 0]\n",
      "  [1 0 0]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[0 0 2]\n",
      "  [0 2 0]\n",
      "  [2 0 0]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [2 1 2]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[0 1 0]\n",
      "  [1 0 0]\n",
      "  [0 0 2]]\n",
      "\n",
      " [[1 0 0]\n",
      "  [0 1 0]\n",
      "  [0 0 1]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [0 0 1]\n",
      "  [0 1 0]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [0 2 0]\n",
      "  [1 2 1]]\n",
      "\n",
      " [[0 0 2]\n",
      "  [0 2 0]\n",
      "  [2 0 0]]\n",
      "\n",
      " [[2 0 0]\n",
      "  [0 0 1]\n",
      "  [0 1 0]]\n",
      "\n",
      " [[1 0 0]\n",
      "  [0 1 0]\n",
      "  [0 0 1]]]\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "k = 8\n",
    "f = poppy.field(3,2)\n",
    "\n",
    "for prt in prts[k:k+1]:\n",
    "  p = jax.numpy.array(prt, dtype = jax.numpy.int8)\n",
    "  n = poppy.prt2int(p)\n",
    "  rep = poppy.symrep(p,f)\n",
    "  print(f'\\nTHE {jax.numpy.array_str(p)[1:-1]} REPRESENTATION OF S{n}\\n\\n{rep.proj().squeeze()}\\n\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SHAPE 14400 5 5 OVER FIELD 11"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = poppy.field(11,1)\n",
    "prt = jax.numpy.array([2,2,1], dtype = jax.numpy.int8)\n",
    "dim = poppy.prt2dim(prt)\n",
    "n = poppy.prt2int(prt)\n",
    "N = poppy.factorial(n)\n",
    "\n",
    "rep = poppy.symrep(prt,f)\n",
    "reptbl = poppy.symreptbl(rep,n)\n",
    "reptbl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2048x2048 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TABLE = reptbl.trace().reshape((1,N,N))\n",
    "TITLE = f'{dim}D REP {jax.numpy.array_str(prt)[1:-1]} TRACE OVER FIELD {f.q}'\n",
    "size = 8\n",
    "cmap = 'gist_stern'\n",
    "\n",
    "TABLE.plot(title = TITLE, size = size, cmap = cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4096x4096 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TABLE = reptbl.proj().reshape(N,N,dim,dim).swapaxes(0,2).reshape((N*dim,N*dim))\n",
    "TITLE = f'{dim}D REP {jax.numpy.array_str(prt)[1:-1]} OVER FIELD {f.q}'\n",
    "size = 16\n",
    "cmap = 'gist_stern'\n",
    "\n",
    "poppy.plot(TABLE, title = TITLE, size = size, cmap = cmap)"
   ]
  }
 ],
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