{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#微積分\" data-toc-modified-id=\"微積分-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>微積分</a></span><ul class=\"toc-item\"><li><span><a href=\"#ソフトマックス関数の概形(15点)\" data-toc-modified-id=\"ソフトマックス関数の概形(15点)-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>ソフトマックス関数の概形(15点)</a></span></li><li><span><a href=\"#3D関数のプロット(15点)\" data-toc-modified-id=\"3D関数のプロット(15点)-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>3D関数のプロット(15点)</a></span></li></ul></li><li><span><a href=\"#線形代数\" data-toc-modified-id=\"線形代数-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>線形代数</a></span><ul class=\"toc-item\"><li><span><a href=\"#線形結合の確認(p.173,-5-39)(15点)\" data-toc-modified-id=\"線形結合の確認(p.173,-5-39)(15点)-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>線形結合の確認(p.173, 5-39)(15点)</a></span></li><li><span><a href=\"#解析解の確認(p.177,-5-60)(15点)\" data-toc-modified-id=\"解析解の確認(p.177,-5-60)(15点)-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>解析解の確認(p.177, 5-60)(15点)</a></span></li></ul></li><li><span><a href=\"#センター試験原題(10点)\" data-toc-modified-id=\"センター試験原題(10点)-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>センター試験原題(10点)</a></span></li><li><span><a href=\"#数値改変(30点)\" data-toc-modified-id=\"数値改変(30点)-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>数値改変(30点)</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"text-align: center;\">\n",
    "   <font size=\"5\"> 2020年度　数式処理演習　pair試験問題 </font>\n",
    "</div>\n",
    "   <div style=\"text-align: right;\">\n",
    "   <font size=\"3\"> cc by Shigeto R. Nishitani, 2020/11/26 実施 </font>\n",
    "</div>\n",
    "\n",
    "* file: ~/symboic_math/exams/20_pre_ans.ipynb\n",
    "\n",
    "以下の問題をpythonで解き，LUNAへ提出せよ．LUNAへはipynbとpdf形式の２種類を提出すること．"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 微積分\n",
    "## ソフトマックス関数の概形(15点)\n",
    "ソフトマックス関数\n",
    "    \\begin{equation*}\n",
    "      f(x) = \\frac{1}{1+e^{-x}}\n",
    "    \\end{equation*}\n",
    "    の増減，極値，凹凸を調べ，曲線$y=f(x)$の概形を描け．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{1 + e^{- x}}$"
      ],
      "text/plain": [
       "1/(1 + exp(-x))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.abc import x, y\n",
    "\n",
    "x, y  = symbols('x y')\n",
    "\n",
    "f = 1/(1+exp(-x))\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{e^{- x}}{\\left(1 + e^{- x}\\right)^{2}}$"
      ],
      "text/plain": [
       "exp(-x)/(1 + exp(-x))**2"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = f.diff(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(-1 + \\frac{2 e^{- x}}{1 + e^{- x}}\\right) e^{- x}}{\\left(1 + e^{- x}\\right)^{2}}$"
      ],
      "text/plain": [
       "(-1 + 2*exp(-x)/(1 + exp(-x)))*exp(-x)/(1 + exp(-x))**2"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = f.diff(x,x)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fdde801b100>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(f,df,df2,(x,-5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\emptyset$"
      ],
      "text/plain": [
       "EmptySet"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import solveset\n",
    "solveset(df,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(df,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(df2,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|  x | $-\\infty$ | $\\cdots$   |  0  |   $\\cdots$   | $\\infty$ |\n",
    "| ---- | ----  | ---- | ---- | ---- | ---- |\n",
    "|  f(x) | 0 | $\\nearrow$  |    0.5  |   $\\nearrow$  | 0 |\n",
    "|  f'(x) | 0 |  +  |    +  |  +  |   0 |\n",
    "|  f''(x) | 0 |  +  |  0  |  -  |  0  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D関数のプロット(15点)\n",
    "\n",
    "３変数のシグモイド関数で，１変数を固定すると次のような関数となる．\n",
    "``` python\n",
    "import numpy as np\n",
    "\n",
    "def softmax(x,y):\n",
    "    return np.exp(-x)/(np.exp(-x)+np.exp(-y)+np.exp(-1))\n",
    "```\n",
    "\n",
    "この関数を\n",
    "``` python\n",
    "x = np.arange(-4, 4, 0.5)\n",
    "y = np.arange(-4, 4, 0.5)\n",
    "```\n",
    "で３次元プロットせよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def softmax(x,y):\n",
    "    return np.exp(-x)/(np.exp(-x)+np.exp(-y)+np.exp(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-9-714deff1833d>:10: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.\n",
      "  plot3d = Axes3D(fig)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "x = np.arange(-3, 3, 0.25)\n",
    "y = np.arange(-3, 3, 0.25)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z1 = softmax(X,Y)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "plot3d = Axes3D(fig)\n",
    "plot3d.plot_surface(X,Y,Z1) \n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 線形代数\n",
    "## 線形結合の確認(p.173, 5-39)(15点)\n",
    "\n",
    "sympyを使って，$w^T x$で線形結合が得られることを確認せよ．\n",
    "1. $ w=\\left(\\begin{array}c w_0\\\\w_1\\\\w_2\\end{array}\\right)$, $ x=\\left(\\begin{array}c x_0\\\\x_1\\\\x_2\\end{array}\\right)$を作る．\n",
    "1. wを転置する\n",
    "1. `ww.T*xx`で線形結合となることを確認する．\n",
    "1. `ww*xx.T`では3x3の行列が得られることも確認せよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}w_{0}\\\\w_{1}\\\\w_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[w0],\n",
       "[w1],\n",
       "[w2]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "w0,w1,w2  = symbols('w0,w1,w2')\n",
    "x0,x1,x2  = symbols('x0,x1,x2')\n",
    "\n",
    "ww = Matrix([w0,w1,w2])\n",
    "xx = Matrix([x0,x1,x2])\n",
    "ww"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}w_{0} x_{0} + w_{1} x_{1} + w_{2} x_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[w0*x0 + w1*x1 + w2*x2]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ww.T*xx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}w_{0} x_{0} & w_{0} x_{1} & w_{0} x_{2}\\\\w_{1} x_{0} & w_{1} x_{1} & w_{1} x_{2}\\\\w_{2} x_{0} & w_{2} x_{1} & w_{2} x_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[w0*x0, w0*x1, w0*x2],\n",
       "[w1*x0, w1*x1, w1*x2],\n",
       "[w2*x0, w2*x1, w2*x2]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ww*xx.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 解析解の確認(p.177, 5-60)(15点)\n",
    "\n",
    "``` python\n",
    "xdata=np.array([1,2,3,4])\n",
    "ydata=np.array([0,5,15,24])\n",
    "```\n",
    "を対象データとして，(5-53)にしたがって，N=4, n=3で\n",
    "$$\n",
    "y=a_0 + a_1\\,x +a_2\\, x^2\n",
    "$$\n",
    "に対するfittingを行う．得られたデザイン行列$X$は\n",
    "$$X=\\left(\n",
    "\\begin{array}{@{\\,}ccc@{\\,}}\n",
    "1 & 1 & 1\\\\\n",
    "1 & 2 & 4\\\\\n",
    "1 & 3 & 9\\\\\n",
    "1 & 4 & 16\\\\\\end{array}\n",
    "\\right)$$\n",
    "となる．(5-59)式の左辺の$X^TX$が3x3行列になることを確認せよ．\n",
    "\n",
    "ヒント：https://nbviewer.jupyter.org/github/daddygongon/jupyter_num_calc/blob/master/numerical_calc/least_square_fit.ipynb\n",
    "の「正規方程式(Normal Equations)による解」の「python codeによる具体例」を参照せよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from pprint import pprint\n",
    "import scipy.linalg as linalg\n",
    "\n",
    "X = Matrix([[ 1.,  1.,  1.],\n",
    "       [ 1.,  2.,  4.],\n",
    "       [ 1.,  3.,  9.],\n",
    "       [ 1.,  4., 16.]])\n",
    "\n",
    "np.dot(X.T,X).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# センター試験原題(10点)\n",
    "(2018大学入試センター試験　追試験 数学II・B 第2問)\n",
    "\n",
    "$a$ を正の実数とし，\n",
    "放物線$y=3x^2$ を$C_1$,\n",
    "放物線$y=2x^2+a^2$ を$C_2$ とする．\n",
    "$C_1$ と$C_2$ の二つの共有点を $x$ 座標の小さい順にA,Bとする．\n",
    "また，$C_1$ と$C_2$ の両方に第1象限で接する直線を$l$ とする．\n",
    "\n",
    "(1) Bの座標を$a$ を用いて表すと\n",
    "$(\\fbox{ ア }\\,, \\fbox{ イ }\\,a^{ \\fbox{ ウ }})$\n",
    "である\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "a, s, t, x = symbols('a, s, t, x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 x^{2}$"
      ],
      "text/plain": [
       "3*x**2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC1 = 3*x**2\n",
    "yC1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + 2 x^{2}$"
      ],
      "text/plain": [
       "a**2 + 2*x**2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC2 = 2*x**2+a**2\n",
    "yC2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq = yC1 - yC2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a$"
      ],
      "text/plain": [
       "a"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xB = solve(eq,x)[1]\n",
    "xB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 a^{2}$"
      ],
      "text/plain": [
       "3*a**2"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC2.subs({x:xB})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "直線$l$ と二つの放物線$C_1, C_2$ の接点の$x$ 座標をそれぞれ$s,t$ とおく．\n",
    "$l$ は$x=s$ で$C_1$ と接するので，$l$ の方程式は\n",
    "\\begin{equation*}\n",
    "  y = \\fbox{ エ }\\,sx - \\fbox{ オ }\\,s^{ \\fbox{ カ }}\n",
    "\\end{equation*}\n",
    "と表せる．\n",
    "同様に，$l$ は$x=t$ で$C_2$ と接するので，$l$ の方程式は\n",
    "\\begin{equation*}\n",
    "  y = \\fbox{ キ }\\,tx - \\fbox{ ク }\\,t^{ \\fbox{ カ }} + a^2\n",
    "\\end{equation*}\n",
    "とも表せる．これらにより，$s,t$ は\n",
    "\\begin{equation*}\n",
    "  s = \\frac{\\sqrt{\\fbox{ ケ }}}{\\fbox{ コ }}a , \\,\\,\\,\\, \n",
    "t= \\frac{\\sqrt{\\fbox{ ケ }}}{\\fbox{ サ }}a \n",
    "\\end{equation*}\n",
    "である．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1 = diff(yC1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#y - y0 = m*(x-x0)\n",
    "yl1 = m1.subs({x:s})*(x-s)+yC1.subs({x:s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 3 s^{2} + 6 s x$"
      ],
      "text/plain": [
       "-3*s**2 + 6*s*x"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yl1.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "m2 = diff(yC2,x)\n",
    "yl2 = m2.subs({x:t})*(x-t)+yC2.subs({x:t})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} - 2 t^{2} + 4 t x$"
      ],
      "text/plain": [
       "a**2 - 2*t**2 + 4*t*x"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yl2.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 s}{2}$"
      ],
      "text/plain": [
       "3*s/2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0=solve(m1.subs({x:s})-m2.subs({x:t}),t)[0]\n",
    "t0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{6} a}{3}$"
      ],
      "text/plain": [
       "sqrt(6)*a/3"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s0=solve((yl1-yl2).subs({x:0}).subs({t:t0}),s)[1]\n",
    "s0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{6} a}{2}$"
      ],
      "text/plain": [
       "sqrt(6)*a/2"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0.subs({s:s0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "放物線$C_1$ の$s \\leqq x \\leqq {\\fbox{ ア }}$ の部分\n",
    "放物線$C_2$ の${\\fbox{ ア }} \\leqq x \\leqq t$ の部分,\n",
    "$x$ 軸，\n",
    "および2直線$x=s, x=t$で囲まれた図形の面積は\n",
    "\\begin{equation*}\n",
    "  \\frac{\\fbox{ シ }\\sqrt{\\fbox{ ス }}-\\fbox{ セ }}{\\fbox{ ソ }}a^{\\fbox{ タ }}\n",
    "\\end{equation*}\n",
    "である．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "SS=integrate(yC1,(x,s,a))+integrate(yC2,(x,a,t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a^{3} \\left(-6 + 7 \\sqrt{6}\\right)}{9}$"
      ],
      "text/plain": [
       "a**3*(-6 + 7*sqrt(6))/9"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "together(SS.subs({t:t0}).subs({s:s0}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数値改変(30点)\n",
    "\n",
    "問3.において，放物線$C_1$ が\n",
    "$$\n",
    "y = 2.9 x^2\n",
    "$$\n",
    "である場合について解きなさい．\n",
    "ただし，係数が浮動小数点数に変わったので，$\\fbox{ ア }\\,, \\fbox{ イ }$などには浮動小数点数が入る．最後の図形の面積は，$1.284186\\ldots a^3$ となる．(30点)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "a, s, t, x = symbols('a, s, t, x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.9 x^{2}$"
      ],
      "text/plain": [
       "2.9*x**2"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC1 = 2.9*x**2\n",
    "yC1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + 2 x^{2}$"
      ],
      "text/plain": [
       "a**2 + 2*x**2"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC2 = 2*x**2+a**2\n",
    "yC2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq = yC1 - yC2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.05409255338946 a$"
      ],
      "text/plain": [
       "1.05409255338946*a"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xB = solve(eq,x)[1]\n",
    "xB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.22222222222222 a^{2}$"
      ],
      "text/plain": [
       "3.22222222222222*a**2"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yC2.subs({x:xB})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1 = diff(yC1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#y - y0 = m*(x-x0)\n",
    "yl1 = m1.subs({x:s})*(x-s)+yC1.subs({x:s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 2.9 s^{2} + 5.8 s x$"
      ],
      "text/plain": [
       "-2.9*s**2 + 5.8*s*x"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yl1.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "m2 = diff(yC2,x)\n",
    "yl2 = m2.subs({x:t})*(x-t)+yC2.subs({x:t})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} - 2 t^{2} + 4 t x$"
      ],
      "text/plain": [
       "a**2 - 2*t**2 + 4*t*x"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yl2.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.45 s$"
      ],
      "text/plain": [
       "1.45*s"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0=solve(m1.subs({x:s})-m2.subs({x:t}),t)[0]\n",
    "t0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.875376219064817 a$"
      ],
      "text/plain": [
       "0.875376219064817*a"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s0=solve((yl1-yl2).subs({x:0}).subs({t:t0}),s)[1]\n",
    "s0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.26929551764398 a$"
      ],
      "text/plain": [
       "1.26929551764398*a"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0.subs({s:s0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "SS=integrate(yC1,(x,s,a))+integrate(yC2,(x,a,t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.28418609654692 a^{3}$"
      ],
      "text/plain": [
       "1.28418609654692*a**3"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "together(SS.subs({t:t0}).subs({s:s0}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.23849202216469$"
      ],
      "text/plain": [
       "1.23849202216469"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(-6+7*sqrt(6.0))/9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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