{
 "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": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{1 + e^{- x}}$"
      ],
      "text/plain": [
       "1/(1 + exp(-x))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "x, y  = symbols('x y')\n",
    "\n",
    "f = 1/(1+exp(-x))\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = f.diff(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = f.diff(x,x)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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 0x7fd634e6db50>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(f,df,df2,(x,-5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(df,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0]"
      ]
     },
     "execution_count": 6,
     "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": [
    {
     "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": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {
    "height": "12.666666984558105px",
    "width": "252.6666717529297px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": true,
   "toc_position": {
    "height": "538.3287963867188px",
    "left": "0px",
    "right": "1189.3333740234375px",
    "top": "60.801631927490234px",
    "width": "295.28533935546875px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}