{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ed98689b",
   "metadata": {},
   "outputs": [],
   "source": [
    "%display latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "15fb3be7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import fp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a3e7c085",
   "metadata": {},
   "outputs": [],
   "source": [
    "S=fp.Square(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d09d9e64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 76 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6d136a42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}10087.054885133812\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}10087.054885133812$$"
      ],
      "text/plain": [
       "10087.054885133812"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.fp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cef0fd6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "P=fp.Polygon(\"u5rd4r3u3rd4l5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1e8a664d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 83 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "42a2caa5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}13876.536297311974\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}13876.536297311974$$"
      ],
      "text/plain": [
       "13876.536297311974"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.fp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fd821da8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.36 s, sys: 13.2 ms, total: 1.37 s\n",
      "Wall time: 1.37 s\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.0947213943672983 \\times 10^{87}\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.0947213943672983 \\times 10^{87}$$"
      ],
      "text/plain": [
       "1.0947213943672983e+87"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time fp.Square(100).fp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "71e82461",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}54\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}54$$"
      ],
      "text/plain": [
       "54"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.graph_size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "068a1266",
   "metadata": {},
   "outputs": [],
   "source": [
    "P=fp.Square(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "6d53f417",
   "metadata": {},
   "outputs": [],
   "source": [
    "M=P.matrix_M()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "b2f6a196",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(21, 22\\right)\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(21, 22\\right)$$"
      ],
      "text/plain": [
       "(21, 22)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.dimensions()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "72073f21",
   "metadata": {},
   "outputs": [],
   "source": [
    "N=M.submatrix(0,0,21,21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "6d80c898",
   "metadata": {},
   "outputs": [],
   "source": []
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   "execution_count": 55,
   "id": "b3f6f70d",
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   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "type sage.matrix.matrix_generic_dense.Matrix_generic_dense doesn't define __round__ method",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "File \u001b[1;32m/usr/lib/python3.10/site-packages/sage/misc/functional.py:1723\u001b[0m, in \u001b[0;36mround\u001b[1;34m(x, ndigits)\u001b[0m\n\u001b[0;32m   1722\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m-> 1723\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mx\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mround\u001b[49m()\n\u001b[0;32m   1724\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mAttributeError\u001b[39;00m:\n",
      "File \u001b[1;32m/usr/lib/python3.10/site-packages/sage/structure/element.pyx:494\u001b[0m, in \u001b[0;36msage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4827)\u001b[1;34m()\u001b[0m\n\u001b[0;32m    493\u001b[0m \"\"\"\n\u001b[1;32m--> 494\u001b[0m return self.getattr_from_category(name)\n\u001b[0;32m    495\u001b[0m \n",
      "File \u001b[1;32m/usr/lib/python3.10/site-packages/sage/structure/element.pyx:507\u001b[0m, in \u001b[0;36msage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4939)\u001b[1;34m()\u001b[0m\n\u001b[0;32m    506\u001b[0m     cls = P._abstract_element_class\n\u001b[1;32m--> 507\u001b[0m return getattr_from_other_class(self, cls, name)\n\u001b[0;32m    508\u001b[0m \n",
      "File \u001b[1;32m/usr/lib/python3.10/site-packages/sage/cpython/getattr.pyx:361\u001b[0m, in \u001b[0;36msage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2702)\u001b[1;34m()\u001b[0m\n\u001b[0;32m    360\u001b[0m     dummy_error_message.name = name\n\u001b[1;32m--> 361\u001b[0m     raise AttributeError(dummy_error_message)\n\u001b[0;32m    362\u001b[0m attribute = <object>attr\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'sage.matrix.matrix_generic_dense.Matrix_generic_dense' object has no attribute 'round'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [55]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;43mround\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mN\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32m/usr/lib/python3.10/site-packages/sage/misc/functional.py:1725\u001b[0m, in \u001b[0;36mround\u001b[1;34m(x, ndigits)\u001b[0m\n\u001b[0;32m   1723\u001b[0m             \u001b[38;5;28;01mreturn\u001b[39;00m x\u001b[38;5;241m.\u001b[39mround()\n\u001b[0;32m   1724\u001b[0m         \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mAttributeError\u001b[39;00m:\n\u001b[1;32m-> 1725\u001b[0m             \u001b[38;5;28;01mreturn\u001b[39;00m RealDoubleElement(\u001b[43mbuiltins\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mround\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m)\n\u001b[0;32m   1726\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mArithmeticError\u001b[39;00m:\n\u001b[0;32m   1727\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(x, RealDoubleElement):\n",
      "\u001b[1;31mTypeError\u001b[0m: type sage.matrix.matrix_generic_dense.Matrix_generic_dense doesn't define __round__ method"
     ]
    }
   ],
   "source": [
    "N.r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "e1d4b05d",
   "metadata": {},
   "outputs": [],
   "source": [
    "L=[fp.Square(l).fp() for l in range(1,201)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "3219bc97",
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     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "L"
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  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "62e12849",
   "metadata": {},
   "outputs": [
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       " 402.2295751089063]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(log,L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "79762beb",
   "metadata": {},
   "outputs": [],
   "source": [
    "L2=[log(L[i])/(4*i+4)-log(4*sqrt(2.0)-4) for i in range(len(L))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "a14e534f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_plot(L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "24ddaf63",
   "metadata": {},
   "outputs": [
    {
     "data": {
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