jupyter test

ガウス＝ルジャンドルのアルゴリズム.ipynb

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   "source": [
    "$$\n",
    "p_n := \\frac{(a_{n} + b_{n})^2}{1 - 2\\sum_{j=1}^{n}2^jc_j}\n",
    "$$"
   ]
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     "text": [
      "3.14159265358979\n",
      "3.14159265358979\n",
      "3.14159265358979\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "init_printing()\n",
    "\n",
    "def A(k):\n",
    "    if k == 0:\n",
    "        return sympify(1)\n",
    "    else:\n",
    "        return (A(k-1) + B(k-1)) / 2\n",
    "\n",
    "def B(k):\n",
    "    if k == 0:\n",
    "        return 1 / sqrt(2)\n",
    "    else:\n",
    "        return sqrt(A(k-1) * B(k-1))\n",
    "\n",
    "def C(k):\n",
    "    return (A(k)**2) - (B(k)**2)\n",
    "\n",
    "def P(n):\n",
    "    return (A(n) + B(n))**2 / (1 - 2 * sum([2**j * C(j) for j in range(1, n + 1)]))\n",
    "\n",
    "print(P(3).evalf())\n",
    "print(P(5).evalf())\n",
    "print(P(10).evalf())\n"
   ]
  }
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