{
 "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=\"#Table-of-Contents\" data-toc-modified-id=\"Table-of-Contents-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Table of Contents</a></span></li><li><span><a href=\"#1(a)-微分\" data-toc-modified-id=\"1(a)-微分-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>1(a) 微分</a></span></li><li><span><a href=\"#1(b)-パラメータ微分\" data-toc-modified-id=\"1(b)-パラメータ微分-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>1(b) パラメータ微分</a></span></li><li><span><a href=\"#2(a)\" data-toc-modified-id=\"2(a)-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>2(a)</a></span></li><li><span><a href=\"#3(a)\" data-toc-modified-id=\"3(a)-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>3(a)</a></span></li><li><span><a href=\"#3(b)\" data-toc-modified-id=\"3(b)-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>3(b)</a></span></li><li><span><a href=\"#4-センター試験原本\" data-toc-modified-id=\"4-センター試験原本-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>4 センター試験原本</a></span><ul class=\"toc-item\"><li><span><a href=\"#4(a)-a=2の時の頂点移動，セソタチツテ\" data-toc-modified-id=\"4(a)-a=2の時の頂点移動，セソタチツテ-7.1\"><span class=\"toc-item-num\">7.1&nbsp;&nbsp;</span>4(a) a=2の時の頂点移動，セソタチツテ</a></span></li><li><span><a href=\"#4(b)-ト\" data-toc-modified-id=\"4(b)-ト-7.2\"><span class=\"toc-item-num\">7.2&nbsp;&nbsp;</span>4(b) ト</a></span></li><li><span><a href=\"#4(c)-最小値　ナニヌネノ\" data-toc-modified-id=\"4(c)-最小値　ナニヌネノ-7.3\"><span class=\"toc-item-num\">7.3&nbsp;&nbsp;</span>4(c) 最小値　ナニヌネノ</a></span></li></ul></li><li><span><a href=\"#5\" data-toc-modified-id=\"5-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>5</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1(a) 微分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "\n",
    "x,y = symbols('x y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 \\sin{\\left(x \\right)}}{\\sqrt{\\frac{\\sin^{2}{\\left(x \\right)}}{\\left(4 \\cos{\\left(x \\right)} + 5\\right)^{2}}} \\left(4 \\cos{\\left(x \\right)} + 5\\right)^{2}}$"
      ],
      "text/plain": [
       "                3⋅sin(x)               \n",
       "───────────────────────────────────────\n",
       "      _________________                \n",
       "     ╱        2                        \n",
       "    ╱      sin (x)                    2\n",
       "   ╱   ─────────────── ⋅(4⋅cos(x) + 5) \n",
       "  ╱                  2                 \n",
       "╲╱     (4⋅cos(x) + 5)                  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(acos((4+5*cos(x))/(5+4*cos(x))),x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1(b) パラメータ微分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "\n",
    "x,y, t = symbols('x y t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 t}{t^{3} + 1}$"
      ],
      "text/plain": [
       " 3⋅t  \n",
       "──────\n",
       " 3    \n",
       "t  + 1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 3*t/(1+t**3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 t^{2}}{t^{3} + 1}$"
      ],
      "text/plain": [
       "    2 \n",
       " 3⋅t  \n",
       "──────\n",
       " 3    \n",
       "t  + 1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 3*t**2/(1+t**3)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{t \\left(t^{3} - 2\\right)}{2 t^{3} - 1}$"
      ],
      "text/plain": [
       "  ⎛ 3    ⎞\n",
       "t⋅⎝t  - 2⎠\n",
       "──────────\n",
       "    3     \n",
       " 2⋅t  - 1 "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(y,t)/diff(x,t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "\n",
    "x,y, t = symbols('x y t')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = (1-2*cos(x))/(5-4*cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x}{2} - \\operatorname{atan}{\\left(3 \\tan{\\left(\\frac{x}{2} \\right)} \\right)} - \\pi \\left\\lfloor{\\frac{\\frac{x}{2} - \\frac{\\pi}{2}}{\\pi}}\\right\\rfloor$"
      ],
      "text/plain": [
       "                       ⎢x   π⎥\n",
       "                       ⎢─ - ─⎥\n",
       "x       ⎛     ⎛x⎞⎞     ⎢2   2⎥\n",
       "─ - atan⎜3⋅tan⎜─⎟⎟ - π⋅⎢─────⎥\n",
       "2       ⎝     ⎝2⎠⎠     ⎣  π  ⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(f,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "複素数が出たままで気持ち悪いんですが，これも正解なようです．ここらがsympyの限界なんで．．．\n",
    "\n",
    "2(b)はパスね．"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 & 1 & 1\\\\1 & 2 & 1\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡2  1  1⎤\n",
       "⎢       ⎥\n",
       "⎢1  2  1⎥\n",
       "⎢       ⎥\n",
       "⎣0  0  1⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[2,1,1],[1,2,1],[0,0,1]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-1 & -1 & 1\\\\1 & 0 & 1\\\\0 & 1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-1  -1  1⎤\n",
       "⎢         ⎥\n",
       "⎢1   0   1⎥\n",
       "⎢         ⎥\n",
       "⎣0   1   0⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P, D = A.diagonalize()\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 3\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0  0⎤\n",
       "⎢       ⎥\n",
       "⎢0  1  0⎥\n",
       "⎢       ⎥\n",
       "⎣0  0  3⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.inv()*A*P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "a,b,c = symbols('a b c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & c & b\\\\c & 0 & a\\\\b & a & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  c  b⎤\n",
       "⎢       ⎥\n",
       "⎢c  0  a⎥\n",
       "⎢       ⎥\n",
       "⎣b  a  0⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=Matrix([[0,c,b],[c,0,a],[b,a,0]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-1 & 1 & 1\\\\1 & -1 & 1\\\\1 & 1 & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-1  1   1 ⎤\n",
       "⎢          ⎥\n",
       "⎢1   -1  1 ⎥\n",
       "⎢          ⎥\n",
       "⎣1   1   -1⎦"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B=Matrix([[-1,1,1],[1,-1,1],[1,1,-1]])\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAOCAYAAACsAAXLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACYUlEQVRIDa2V7U0cQQyGlxMFHEkH0EFCKgh0cEkHCSUgft39i5IOgArI0QF0AEcH0EEIHVyeZ3Y8MgtIq1Msef0xnndsj3d3a71ed9JisZgiTorRP7SX+K+Tb7Ra8ZZs2IcfsfdGb45Ak5Pn8/lp6CHxLeFZ2JtI9q9ewx6DNTFJqvqOWEXCSX5Dz91MS6PVD0RejY5OgSU5bFt+mPz/RaXogwq00WhEcjeAzAC7gp21oJ8op2FsIC34AcynDfZ2W969BIDDOytG1x0j7abJXlZfE/h2MUz8Af4DG2Nxv5CNsB0VYyxe+gRfvIEpnliSxdy25PSwyS45f5Kgh/iUjbC9Kgv5GGtIZ0r/DnrpEtIb+AvfwZ/1J98eesFFWqj7j9FLI5DmsRvX2uGwawLbMWfETffVj9o+NyYmUE5afXh9MW8lsbpffDluSLeJXYKXb+ir/m1XWbBbduJIG7JjApjIOfo1LKitn6KfITOZSAZ3zXm7q/u0g6Yo7zVYKx1C/aEdhH9HPTrnoc5ZIwI8zC4KFl2womdvHnGux9WgNnLPMDZwYgYLHhgW/oImFdxuvAjA53WZ5LuIQx9+szygY/1ZIrhMOJIwRPrSi86bsCh5iFdD6BxBJuWwCvYaCZAPzrNmfLk+FTB8YzNOi8UvjoUcoXue50ohe6s+WT+YVN2K/I8K0AjbWfRzEsNuku1w/M6lf4BbWMpvtx3fL97+4fz+Zk+eV/XoZgslxjF7bJ8SHB5yorNFDX78xJj8Oex1OdQXsJULps/r8tPRpVi7574VvpyYYca5V7rvRYk9w//0Dw+obN/DSATWAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle 8 a b c$"
      ],
      "text/plain": [
       "8⋅a⋅b⋅c"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "det(A*B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 センター試験原本"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "a,b,c,x = symbols('a b c x')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = a*x**2+b*x+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle a - b + c$"
      ],
      "text/plain": [
       "a - b + c"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1=f.subs({x:-1})\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 4 a + 2 b + c$"
      ],
      "text/plain": [
       "4⋅a + 2⋅b + c"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2=f.subs({x:2})\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ b : 1 - a, \\  c : 5 - 2 a\\right\\}$"
      ],
      "text/plain": [
       "{b: 1 - a, c: 5 - 2⋅a}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1=solve({eq1-4,eq2-7},{b,c})\n",
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{1 - a}{2 a}$"
      ],
      "text/plain": [
       "-(1 - a) \n",
       "─────────\n",
       "   2⋅a   "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = solve(diff(f,x),x)[0].subs(s1)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - 2 a + 5 - \\frac{\\left(1 - a\\right)^{2}}{4 a}$"
      ],
      "text/plain": [
       "                  2\n",
       "           (1 - a) \n",
       "-2⋅a + 5 - ────────\n",
       "             4⋅a   "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x:p}).subs(s1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - 9 a^{2} + 22 a - 1$"
      ],
      "text/plain": [
       "     2           \n",
       "- 9⋅a  + 22⋅a - 1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qq = simplify(f.subs({x:p}).subs(s1)*4*a)\n",
    "qq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = qq/4/a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4(a) a=2の時の頂点移動，セソタチツテ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{1}{4}$"
      ],
      "text/plain": [
       "-1/4"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-p.subs({a:2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{7}{8}$"
      ],
      "text/plain": [
       "-7/8"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-q.subs({a:2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4(b) ト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAVCAYAAABLy77vAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVQ4EWOsr68vY2BgSAdiEAhtaGg4B2HiJ4HqUPQxAg3qBGrZDZTYg18rdlmgPrB+FuzSCFGgQiMgbzUQGwPZHxAyqCysBgE1CACVzQbid0BsAsRKQIwX4DIIZHMoSCfQUFBYgFyFFzDhlSVBctQgwoE1GkbUCSNhqDFC+IzDmkVAGoBZA5RRQcAFQjGsBordA7JBJcUsqBicwmcQOK/BVRJgDOPoh4XRTGAAgkKBnDIbFJu7Ab7gLy7OjVWTAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[ 1\\right]$"
      ],
      "text/plain": [
       "[1]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(p,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVQoFXWS4Q2CQAyFwTiArOAIRjdgBF1BRjD+4y8j6Ao6AiOoq8gG+H0ndwGiLylt3732rg153/eZqOt6jatCkmUrvHkD38rlCkk8kIxCuT3cDTsQ3xcE4qgNh4HgEzrhzxJR+CLuBpO3o3nC0gjS6iKxX86rxcVP7GicQGFJ0mAV8dWD0NFAQG5winaYz3lgAWHqmIw9RZOp/wotQvzGuboivNErNQ9niFeXcZgngidiq38iDuPOWoST3cFth6o2Ck/zNhQ5jDe4oi4NQ+JaDqOCNXH6KT7nF1G9okQFwwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 3$"
      ],
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.subs({a:1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4(c) 最小値　ナニヌネノ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANsAAAA/CAYAAABpVr3UAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAIBUlEQVR4Ae2d65HURhSFB8oB4HUE4AxgyWDJgC0iWMjAlH/t/nPhDLAzMGSAHQFrQsARGDYD+3xjSdboMWqN1C/17SpNS91X3fecvlf90GPuXV9fX+x2uw/auuHzzc3N991EOzYGjIFxBuQzfyr38YDE5TetxGetfXa/dI7t0BgwBqYZuJLIWUds35k1ziaP/L0jYIfGgDEwkwH50afuKUq7I+1+N8OOjQFjwA8DTc/mp/iyS9UVjbE7Y3inIPl7ToIJClVYX0i1H1zVyxmvK8a2nDlbm43199+oyCcyqt7QYv2qopcI1tfC+jq6JokqYMNITw1TXel3JThaSViXmIv1bEvYO37uj8rmao/DPVJ0oe037e8ny6RvKDRYwVQA3pOa7mRnE6HMR95pY5g0akCucidpv/JJla6vFL9aUrTOx7keKa5XeOHqLZvSFPXCndK/7aV6TFB96OQDK1onh3eMyoqHIHY8y9mk2AMp/as27sGda8OoesFVrndi/ARIX2N+xbylPXd5qmMc77O2bqDHa8t2830d+8KKvinibXh0tU9XuabgiZ25zkYPdkmZUoRVJ65gvaA8J7neiRETKjyLNVA5XJDOFR/0jjruPjSwU9r+YqX4/eKKZxSg+pxXDI8Vq3IGsXKO8pLB28Ug3Zzs01WuW/7Y8SxnGysk93SRykWDBmBbGpin/dQp5GPnuD58o7r3F686wXccACsQksHrm8855d+fI7xh2Rcywl+W4lMZXOkvFB/0VN1j6lHakFMuVcHlfK9YK2wH+Ku0WHhdOAkiU7yzyegZUrF4sUY4WJUbK1B1Mnx8rHiN+eFYNb30GFhRIhbeHgGRE4oeRlZGwErg0MLFQdNI5rkSkK1XGA/yq4Pnynd5U4KrPFuwIL1w8BhYwRgcbzBiZ1RUes/G0vfk8FEy9H6swo46SCUz2UNWRs9Q85jTzmhCZ9HgWNEsIl5nYkIJFutsMoKXItnFOVg8wSHZGPoNrsAqD2P+WfFUYJVysiedKmROfkSsqBkc7xxuQsoW6WwyPoZUDxRPGr1kPmljlbJeYWRedhCU7+S41UkMR7lPGSRIt5hYwRgUbxBST6yk1DkbBvhUhsiN3Xag1+LJD9J5U7252ax95jv0bi8VI9N2VOSeaDsadA6rldQdcmEkClaIiISXqpMMRTqbjID5Um/OpPSvpCseu/fFnI1eDOdieLSTLFfu94pd7tGdc45CyJ4tFlZwBsdLpamG+wsU+64692yiDFe5iWKCZNPzsA0GORS9GcZL71bLMaysh5iD57US63PuWmmxdtGl1qenwwpYKbMuPwW8PYxVgqt9usqN1bOb3bOpEeqh10VV6ruqYT4oblb2XOVGNQuYIV1ZKGG4RbiodP+oeGjBg94N7Dgczner2NWYGD4iO/aEhbL8BukaCitAouMdY1M8BLfje/XXtVR5tm8JjxHqK11c8fY1zomzXeq4PX/zVW2UckvC6otgccj05GrJMNKXbjmUy7CRIRKLKJt1tKohSsLq1fbM2U6gVw7Gs38MkZrVyhOKyeKU1LBKH4b5LFJlF2bP2bJD6ElhNfgTT0UnV2xiWBlRsGUXrGfLrslM4VwZMGfLteVM7+wYMGfLrslM4VwZMGfLteVM7+wYSHaBRJNyJsF/aJszGeaeF6uEFjJnQO3Izff6wYk2mv0TS8rfPy7XztA+D42PPWrXEQ1/6OxsAvHP2uqpzNEb6cq7U31eVvx8YFmLm2OcnFJHrlil95Az7ZTOs6g8CD70dM8kRTovqB23FZrjbKOO0S4wh30RvhksU3yXhHWKC/Jj8mFzNpcWiiQjw5gzhI6kpVXryoA5mytTgeUqR/uq2PlfcAKraNXNZMCcbSZhocTlZMxZee6SN8qthwtFvMd6zNk8kru0aDkZX+ra/POXS3nK5XznBZIpQDIMlmrrwPLsVXV1rtM2FQfEy+cbeh89DUlmQKwusOjx2bwEn1gXO5uUY4jDvIJ/aNkvxyrmWx5/KeYfbjb1CorwBMNb1fW3F6tyKDQkVgd19iLSqfc5C9dzj8mFwLrGMJLvKZ5J2ea+h/a5sXyrrd3bHcOaU15IvLwN3vAagaSQWCPAO6jSO9Y1nI2bjEO9Fw7Hu0f0BFsKwfBGdjTaLBjWBAzEO9ZFztZypC8DZNXDn/OBvCyTSsJrWBsTXc2OlzpbPVEd+sJW/TWiR43ame/IAIvBa1gbY13Njhc5W6UOK2VDDsUiCWFrw8iS8BrW///wc7Edr+FsV3iUroQXxATt42h1LzA0n9vLZfpTEl7DuqIdr7H0z2e5H8px+BdNnIxul+8iso1NOpWVZxDGYvAa1nXteLGz4TI0iqKDVyKUVv+90tZ6tqLwltS2vrGuMYwc66Lo5fhufj2cHJPbSnpJeA3rCVa7uGeTMzFU5Ibgw9qxFDOZZA7n5eVPlRstlITXsK5rx2v0bKxEdu+z8R11/hyQG9tbCyXhNawr2vEq3/qXU9XzM3o0An+24eUZtv+Kj/tbEl7DutyOxeH+W/+rOFtc07fajYG0GaidbY1hZNpITTtjIBEGzNkSaQhTY/sMmLNtv40NYSIMmLMl0hCmxvYZMGfbfhsbwkQYMGdLpCFMje0zYM62/TY2hIkwYM6WSEOYGttnwJxt+21sCBNhoHkQWXe5u//u8VlpfCTUgjFgDDgyIJ/hs468FdELOBufnHvWy+k/XDwgYknGgDHQYYC32886aRze/gtyHofcTOHAWQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{11}{9} - \\frac{4 \\sqrt{7}}{9}, \\  \\frac{4 \\sqrt{7}}{9} + \\frac{11}{9}\\right]$"
      ],
      "text/plain": [
       "⎡11   4⋅√7  4⋅√7   11⎤\n",
       "⎢── - ────, ──── + ──⎥\n",
       "⎣9     9     9     9 ⎦"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(q, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 6 - 2 a$"
      ],
      "text/plain": [
       "6 - 2⋅a"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(s1).subs({x:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 3\\right]$"
      ],
      "text/plain": [
       "[3]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(f.subs(s1).subs({x:1}),a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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 0x7fbde3dd8eb0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plot(f.subs(s1).subs({a:2}),\n",
    "     f.subs(s1).subs({a:3}),\n",
    "     f.subs(s1).subs({a:4}),\n",
    "     (x,0,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.6.1 (Python 3.8.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.6.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()\n",
    "a,b,c,x = symbols('a b c x')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = a*x**2+b*x+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle a - b + c$"
      ],
      "text/plain": [
       "a - b + c"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1=f.subs({x:-1})\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 4 a + 2 b + c$"
      ],
      "text/plain": [
       "4⋅a + 2⋅b + c"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2=f.subs({x:2})\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ b : 0.833333333333333 - a, \\  c : 4.83333333333333 - 2.0 a\\right\\}$"
      ],
      "text/plain": [
       "{b: 0.833333333333333 - a, c: 4.83333333333333 - 2.0⋅a}"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1=solve({eq1-4,eq2-6.5},{b,c})\n",
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{0.833333333333333 - a}{2 a}$"
      ],
      "text/plain": [
       "-(0.833333333333333 - a) \n",
       "─────────────────────────\n",
       "           2⋅a           "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = solve(diff(f,x),x)[0].subs(s1)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - 2.0 a + 4.83333333333333 - \\frac{\\left(0.833333333333333 - a\\right)^{2}}{4 a}$"
      ],
      "text/plain": [
       "                                                   2\n",
       "                            (0.833333333333333 - a) \n",
       "-2.0⋅a + 4.83333333333333 - ────────────────────────\n",
       "                                      4⋅a           "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = f.subs({x:p}).subs(s1)\n",
    "q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -0.291666666666667$"
      ],
      "text/plain": [
       "-0.291666666666667"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-p.subs({a:2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -0.663194444444444$"
      ],
      "text/plain": [
       "-0.663194444444444"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-q.subs({a:2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 0.833333333333333\\right]$"
      ],
      "text/plain": [
       "[0.833333333333333]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa= solve(p,a)\n",
    "aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.16666666666667$"
      ],
      "text/plain": [
       "3.16666666666667"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.subs({a:aa[0]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 0.0335512192016034, \\  2.29978211413173\\right]$"
      ],
      "text/plain": [
       "[0.0335512192016034, 2.29978211413173]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(q, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 5.66666666666667 - 2.0 a$"
      ],
      "text/plain": [
       "5.66666666666667 - 2.0⋅a"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(s1).subs({x:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 2.83333333333333\\right]$"
      ],
      "text/plain": [
       "[2.83333333333333]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(f.subs(s1).subs({x:1}),a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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 0x7fbde3e05c10>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plot(f.subs(s1).subs({a:2}),\n",
    "     f.subs(s1).subs({a:2.83333333}),\n",
    "     f.subs(s1).subs({a:3}),\n",
    "     (x,0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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