{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# この notebook を読み進める前に\n",
    "TeX 出力のためには次のコードを読み込ませること。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from IPython.display import display\n",
    "init_printing(use_unicode=True)\n",
    "\n",
    "# シンボル定義\n",
    "x = Symbol('x')\n",
    "y = Symbol('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 参考サイト\n",
    "何と言ってもまずは公式。\n",
    "\n",
    "- <http://docs.sympy.org>\n",
    "\n",
    "次のサイトは sympy の結果をランダムで色々教えてくれる。\n",
    "適当に眺めるのにすごくいい。\n",
    "\n",
    "- <http://www.sympygamma.com/>\n",
    "\n",
    "次のサイトにアクセスすれば sympy をインストールしなくてもオンラインで使える。\n",
    "\n",
    "- <http://live.sympy.org/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## サンプル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "display で出力すると mathjax 連携してくれて素敵."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$2 x - 3 y$$"
      ],
      "text/plain": [
       "2⋅x - 3⋅y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(x + y + x - 4 * y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\int e^{x} \\cos{\\left (x \\right )}\\, dx = \\frac{e^{x}}{2} \\sin{\\left (x \\right )} + \\frac{e^{x}}{2} \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "⌠                 x           x       \n",
       "⎮  x             ℯ ⋅sin(x)   ℯ ⋅cos(x)\n",
       "⎮ ℯ ⋅cos(x) dx = ───────── + ─────────\n",
       "⌡                    2           2    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = Integral(cos(x)*exp(x), x)\n",
    "display(Eq(a, a.doit()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 単純なサンプルその 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABsAAAAVBAMAAABF8IgWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInarRM2ZVBDdiWbvuzJCz3LGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVQYGWNggADG/yDwAcpjYHaAscC0KAqPIR2FyzEBhctWgMLtZGCQWnUdLrSagTGBoX4DlA/UyvSdgR9mANMGBpYjDP0BQFkXIOYEqwIpZjoKZCqBuByzgISEvgMDA0gT48oMIMnQf4GBewGIwbDGAUiwfWTgbADSDAw8J4AE4zeGXSBKgIH3O0jQvmEGkOT/AeW+X54A5PJcYOD8CKQZWI82AEnuDQz1CkCagf0biGRwS7sCphkCIRSIBACw+SqCprwr6QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\sqrt{3}$$"
      ],
      "text/plain": [
       "√3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy\n",
    "display(sympy.sqrt(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "勝手に計算やってくれるので素敵."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$2 \\sqrt{2}$$"
      ],
      "text/plain": [
       "2⋅√2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sympy.sqrt(8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 2 y$$"
      ],
      "text/plain": [
       "x + 2⋅y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "x, y = symbols('x y')\n",
    "expr = x + 2*y\n",
    "display(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 2 y + 1$$"
      ],
      "text/plain": [
       "x + 2⋅y + 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(expr + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAASBAMAAACp/uMjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12VGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmklEQVQIHWNgVDJ2YICAMAb2H1BmKgPDTChzFgNDvgOEvT8AzgQKrA+I0WFgnApkcXxnKLjJwPMByORKYLygzcBsAGQqMbAyzGHgP8DAwKMAVPOVwd+BgeESA6MA0waGkwwMLAoMPALMCQxmDAxS5UVZDEwGHP8YGPb///+LgTX90EcGGACqhoBshvgGKHMdgw2UxdBzyIGBAQCs7SBbH+RNaAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$2 y$$"
      ],
      "text/plain": [
       "2⋅y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(expr - x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAAAUBAMAAAD7IecQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsyme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABqUlEQVQoFX2TT0sCURTFz9Nx1Jm0R0HQbrRoJ0b0AWZRBEERrdpZLtqF7spFMFQE7dwESS0KWrQUaldQXyASgkIMctsugzYR2L0z88YppAu+e865P2X+XIGg5gLVV8TtUKzVQyaQC60bpaeVoJ60Q0ZJMYnSkm9GVUh9O6QBw3JtVCLd9ge6F7luz8+85sNpB9FvfyDaAaE5gWThw8lOD8YhMDQ2O2EBkQYgstPLRe87Pkwm0RE5C4sS2IBYje8kqoBZBkawZR38hQurutFGnuIKdKl3DJt+4BRYQ0me/4V3MZ+q4priCwgk6zxPLwESxy6q12pHb7XaJJtUAzJt4YPkA30GLTpcGG7GTt0gkCNTkAP8SBh+uKPDvQy4GbsANhqYQRORNmUrMGQeEend4FnkHRlGe/A9MI5LmHxJFRROb8ErpDcQ+zLftTKjAaztrz86aKHA8ROGs0PPrGIOxFQmt8kklXop3W7XwXDx1abshAde9X3datgkoTl0+PV7kYStciBaFZ/kwotkhsY9kFWibFrUwivaf/kZjmVfuF3xoYqfyT9Ff6sfIrBR8JmXC9wAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x \\left(x + 2 y\\right)$$"
      ],
      "text/plain": [
       "x⋅(x + 2⋅y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(x*expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x^{2} + 2 x y$$"
      ],
      "text/plain": [
       " 2        \n",
       "x  + 2⋅x⋅y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import expand, factor\n",
    "expanded_expr = expand(x*expr)\n",
    "display(expanded_expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x \\left(x + 2 y\\right)$$"
      ],
      "text/plain": [
       "x⋅(x + 2⋅y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(factor(expanded_expr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "x, t, z, nu = symbols('x t z nu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算: diff(sin(x)*exp(x), x)\n",
    "\n",
    "導関数の計算."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALsAAAAVBAMAAADsqILHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEIl2mSJE3e9UMqtm\nzbsXyEShAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACkElEQVQ4EZWVQWgTQRSG/924SbtpkqVEEAq6\nNehFi1sbBWmFoHjQ03ryIrroQT01CIIXlWIvQg8VETyIBgpaLGJFvIhCtYoXweBVo4EiCKIEtcWq\nGN9kZjezmV2I7zD88977fmbfsLtAKwoHRitc/cfaNZSwnqS8COPDIvciooY4CApl4p1vYF70FWDU\nhU677WSgJCjIMRFFLfsd5jdfARnfVau2k5IKICkXSZkNM9TCN8+DXEGoK0GGRDQElTqql3UZFPpM\nkFsnlGwfA0GlBnYWBoWBcSfwNMqBzHhcyvYSFPSR6KC0QtEfsblrsXrkN+5Ozow61JgoAdrIw+M0\nGZ0kC99egpDfuB9aYbuHmeu7qaWDOuEaNiMp1gNlvAXOOwa7tewC0I+XzjmgT9ytby9BxiXMurdd\nLGl1pBSKqvkKZVmctODgM/AJ+EPb1DQwiG3WVaC33GrwTy9DmSpuVk4D925NIKFQ6amRpxwlv787\nwOy/AN8p1+MBFt6zqtmgZahWO1ur0dNBhjaUqLwK5OwLSy7VwlRunlIitKFmidl/bdtzxe2pSwxH\nhsYdergVsq/3f/hBLcy+TeVstuNxEH0rkj0bDsxfrJYs8w7f3uZbtgan32fhtcdH2qZ6bNDAeRD8\nWLJnV3s50cCwcrUyRLPH9CQwfspBmogwlagi7wr7axY+ssmI4eglJFezDYOYNTZvEaeXIWMKujtb\nwZveCWTJSQ9TxbEFjgLHFp95c837c81HN37OtyaiPRguvqJypsJ7hD0kCAN7N8HYs8VLbh3bTF00\nx06Ks8rafr0PiZpvr7RKCZWSirJUP05r5XKMVqmYRjbKVsR8kKOxrqngxxAQ0YbhbPeU8lsLG8Xs\nJOof0wC6kqC5+2UAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$e^{x} \\sin{\\left (x \\right )} + e^{x} \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       " x           x       \n",
       "ℯ ⋅sin(x) + ℯ ⋅cos(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(sin(x)*exp(x), x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算: integrate(exp(x)*sin(x) + exp(x)*cos(x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE8AAAAVBAMAAAD1D64kAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEIl2mSJE3e9UMqtm\nzbsXyEShAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABhUlEQVQoFX2TPUjDQBiG3yTG1vTHIB0EQVIy\niymtgtShs1OdXESDDjpmcdRFF8FBEcFJCm4WQREXUVCruDhkV8RFEEQJiuIf1rvm7hJq8Bt6T7/3\nCd8duQCNMoeKFZ/+/1X0o5gdoYyy3jnPNFwLnOcEqLeME2XRfOWkPXMCUjyXXN7UPI1jaD0TbDIa\nlx1ZNAOYEdjJqKvfzDJUt0SqOgJTNiCZBb4VbaDmjn1he2GzaBFHKZE0vz9J5soEp8qqAb+6AQdX\nwJyl0sOlj4EOXFizQNKFuohMxfcwrcPCA3APfJNWbBnIoldfA9ocJJbyJ8xD7KcPVHwEXkgvbgM6\nbmiqeWjfoeCX1FMvUfEpEH1qiAbXgGEk30IiHQ3tk+atDuIGyMb8WgUOQyI9zIriIdc4jOIiU2bi\nuo47OpeNlkto/Uh7KvFbDKAwSMCvidqpXa3vVusHG+9k62SetJcrXJIwVWFK9BK8wpFogXf/Xgqe\nNK1pvvngmjUZ7K+4uOKJaA8IfQq/cxxdrNiwbSAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$e^{x} \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       " x       \n",
       "ℯ ⋅sin(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(exp(x)*sin(x) + exp(x)*cos(x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADoAAAAvBAMAAABAjsQzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{\\sqrt{2} \\sqrt{\\pi}}{2}$$"
      ],
      "text/plain": [
       "√2⋅√π\n",
       "─────\n",
       "  2  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 計算: integrate(sin(x**2), (x, -oo, oo))\n",
    "display(integrate(sin(x**2), (x, -oo, oo)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算: limit(sin(x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(limit(sin(x)/x, x, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算: solve(x**2 - 2, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAmBAMAAAAB22msAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nlGFRenAfBAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ - \\sqrt{2}, \\quad \\sqrt{2}\\right ]$$"
      ],
      "text/plain": [
       "[-√2, √2]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**2 - 2, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 微分方程式の解: y\" - y = e ** t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAyBAMAAACuW3N5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
      "text/latex": [
       "$$f{\\left (t \\right )} = C_{2} e^{- t} + \\left(C_{1} + \\frac{t}{2}\\right) e^{t}$$"
      ],
      "text/plain": [
       "           -t   ⎛     t⎞  t\n",
       "f(t) = C₂⋅ℯ   + ⎜C₁ + ─⎟⋅ℯ \n",
       "                ⎝     2⎠   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = Function('f')\n",
    "display(dsolve(Eq(f(t).diff(t, t) - f(t), exp(t)), f(t)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算, 行列の固有値: Matrix([[1, 2], [2, 2]]).eigenvals()')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASoAAAA/BAMAAACleJiAAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nN8pz5H1D+8R75cir+wqmuON/XXDIZa78azsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ \\frac{3}{2} + \\frac{\\sqrt{17}}{2} : 1, \\quad - \\frac{\\sqrt{17}}{2} + \\frac{3}{2} : 1\\right \\}$$"
      ],
      "text/plain": [
       "⎧3   √17       √17   3   ⎫\n",
       "⎨─ + ───: 1, - ─── + ─: 1⎬\n",
       "⎩2    2         2    2   ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Matrix([[1, 2], [2, 2]]).eigenvals())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベッセル関数を球ベッセル関数で書く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "besselj(nu, z).rewrite(jn)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAAA0BAMAAAC0vv2mAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{\\sqrt{2} \\sqrt{z}}{\\sqrt{\\pi}} j_{\\nu - \\frac{1}{2}}\\left(z\\right)$$"
      ],
      "text/plain": [
       "√2⋅√z⋅jn(ν - 1/2, z)\n",
       "────────────────────\n",
       "         √π         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('besselj(nu, z).rewrite(jn)')\n",
    "display(besselj(nu, z).rewrite(jn))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LaTeX コードにする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "latex(Integral(cos(x)**2, (x, 0, pi)))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\\\int_{0}^{\\\\pi} \\\\cos^{2}{\\\\left (x \\\\right )}\\\\, dx'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('latex(Integral(cos(x)**2, (x, 0, pi)))')\n",
    "display(latex(Integral(cos(x)**2, (x, 0, pi))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数値の計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAUBAMAAAB/pwA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdpmJMlQiZrurEN1E782PMUhmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAeUlEQVQIHWNggACjpgVQFnMC5wMokzuB5RuMeYDtD5TJwMD6C87kFoAzjeAsdgU48zDDESib5WloF5TJ+///BwYG+f///38CizCbBKaLJYCZrgxmjA5gFpBo4FwAZbJM4IYJMhXww0TXL+A/ABWWZuA1gDLbGTghTAAGIxneC3jWjAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\pi^{2}$$"
      ],
      "text/plain": [
       " 2\n",
       "π "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(pi**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3.14159265358979$$"
      ],
      "text/plain": [
       "3.14159265358979"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(pi.evalf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$5.85987448204884$$"
      ],
      "text/plain": [
       "5.85987448204884"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display((pi + exp(1)).evalf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sqrt(2) を 100 桁まで評価"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABBEAAAAPBAMAAABARkqgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEOHFtxD/wVv4B0GHNAr/Fsj7r/cTkP4LgFvf5ByZYwUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573$$"
      ],
      "text/plain": [
       "1.4142135623730950488016887242096980785696718753769480731766797379907324784621\n",
       "07038850387534327641573"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sqrt(2).evalf(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 無限大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAALBAMAAABv+6sJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKvvZom7mXYyzVQi\n3UQ6SGZXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAaklEQVQIHWNgYBBgAAIQwaj82YGBIayogYGB\nbQLHLwapDQxTGRg8GRj2J6xkYGA5wACUYP0LJBgcQEyGfBDRAGYm/wNqd2BwZGDgiDE+wMBxgIGd\ngSGcYb4dgytQolxtAwNjvXEAUDncNgBJUBUwaYAbUgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\infty$$"
      ],
      "text/plain": [
       "∞"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(oo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 無限大に 1 を足しても 無限大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAALBAMAAABv+6sJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKvvZom7mXYyzVQi\n3UQ6SGZXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAaklEQVQIHWNgYBBgAAIQwaj82YGBIayogYGB\nbQLHLwapDQxTGRg8GRj2J6xkYGA5wACUYP0LJBgcQEyGfBDRAGYm/wNqd2BwZGDgiDE+wMBxgIGd\ngSGcYb4dgytQolxtAwNjvXEAUDncNgBJUBUwaYAbUgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\infty$$"
      ],
      "text/plain": [
       "∞"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(oo + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 無限大は有限の数よりも大きい"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACoAAAAPBAMAAABgjEDtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA782r3SJ2ZjIQmUS7\nVIlAnjihAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVQYGWNg/GQs72z0hQEV8Acw5BcwNKIK\nMsxiAIkyo4mGg0XZJqAKR4BFOUCi0Q2c3QFwWaAJ3Iq5j0LXH+A9n8DAuvwxWAooysC4dn4B0wEG\n/gSGLRO4JUEaQKJMDgwMPGBROQYGMaAgRNQAKsrxq7zcHC66ACrK/hckBARgExbA1H4DiyFEmQ8w\nxCcwODEwTIOpZQGqZRdguHiSob+AYSUDA/caeZkV3Of/XGBgeJc2RWQCp1XeBKghaBQAM0c287zN\nvm0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\mathrm{True}$$"
      ],
      "text/plain": [
       "True"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(oo > 99999)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 展開"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOQAAAAUBAMAAABv64ynAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\Re{\\left(x\\right)} + \\Re{\\left(y\\right)} + i \\Im{x} + i \\Im{y}$$"
      ],
      "text/plain": [
       "re(x) + re(y) + ⅈ⋅im(x) + ⅈ⋅im(y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(expand(x + y, complex=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOQAAAAUBAMAAABv64ynAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\Re{\\left(x\\right)} + \\Re{\\left(y\\right)} + i \\Im{x} + i \\Im{y}$$"
      ],
      "text/plain": [
       "re(x) + re(y) + ⅈ⋅im(x) + ⅈ⋅im(y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(I*im(x) + I*im(y) + re(x) + re(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARcAAAAUBAMAAABVHmT9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nr387/wILkC24gEKoSQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\sin{\\left (x \\right )} \\sin{\\left (y \\right )} + \\cos{\\left (x \\right )} \\cos{\\left (y \\right )}$$"
      ],
      "text/plain": [
       "-sin(x)⋅sin(y) + cos(x)⋅cos(y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(expand(cos(x + y), trig=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARcAAAAUBAMAAABVHmT9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nr387/wILkC24gEKoSQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\sin{\\left (x \\right )} \\sin{\\left (y \\right )} + \\cos{\\left (x \\right )} \\cos{\\left (y \\right )}$$"
      ],
      "text/plain": [
       "-sin(x)⋅sin(y) + cos(x)⋅cos(y)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(cos(x)*cos(y) - sin(x)*sin(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 多項式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAbBAMAAAAzEOSeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ns5YkAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left(x + y\\right)^{5}$$"
      ],
      "text/plain": [
       "       5\n",
       "(x + y) "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = (x + y)**5\n",
    "display(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多項式を展開してくれる: (x + y)**5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAAYBAMAAAACMPt7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wfJiGchSxm0tQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}$$"
      ],
      "text/plain": [
       " 5      4         3  2       2  3        4    5\n",
       "x  + 5⋅x ⋅y + 10⋅x ⋅y  + 10⋅x ⋅y  + 5⋅x⋅y  + y "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(expand(expr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\cos^2 y + \\sin^2 y = 1$ を自動で計算してくれる."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAALVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEHarIkSJZt3NVLsymT3iYlMAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABASURBVAgdY2AQUnZVU2BgTGBv4pjAwCbA9pDLgYGRgXMDAwjwKYCpcweAFJeAHgOTAEPcgn0M7gwMwkpC1wsYAB0ECeuXDPmiAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$x$$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = (x + x**2)/(x*sin(y)**2 + x*cos(y)**2)\n",
    "display(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 式を単純化: (x + x**2)/(x*sin(y)**2 + x*cos(y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAAQBAMAAACb51DZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAhklEQVQYGWNgIAFwPURRzKUA4Qpf/ohVnIEJ\nn7iQsqsaxACYOWD1jAnsTRwTwOahiLMJsH3kcsAUZ2Tg3AASZZs5c8bLmTMNQGyIvfwKIDYQoJjD\nwHD+AFgUTZxLQJ+BSQAsg6I+fsF+BneIBhRxYSWh6wWo4rx2P82hRqOagywIZDM6IAQA3T8eD35X\nQnsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x + 1$$"
      ],
      "text/plain": [
       "x + 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(simplify(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多項式の割り算: div(x**2 - 4 + x, x-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGMAAAAUBAMAAABrMp7fAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left ( x + 3, \\quad 2\\right )$$"
      ],
      "text/plain": [
       "(x + 3, 2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(div(x**2 - 4 + x, x-2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最大公約数: gcd(2*x**2 + 6*x, 12*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAOBAMAAADd6iHDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAf0lEQVQIHWNgVDJ2YICAMAb2H1BmKgPDTChz\nFgNDvgOEvT8AzgQKrA9gPZPYUwNkcXxnCGd4dWA1kMmVwFDKUB9wEchUYmAIYNgMZDDwKIDIPyDi\nEgOjAAPLFyCLRYGBR+AqzweGowxS5UVZHH+ZPzA+YNj///8v1pyjh94xAABbhSE1xl33oAAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$2 x$$"
      ],
      "text/plain": [
       "2⋅x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(gcd(2*x**2 + 6*x, 12*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最小公倍数: lcm(2*x**2 + 6*x, 12*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGEAAAAWBAMAAAAiD+/pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$12 x^{2} + 36 x$$"
      ],
      "text/plain": [
       "    2       \n",
       "12⋅x  + 36⋅x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(lcm(2*x**2 + 6*x, 12*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 因数分解: factor(x**4/2 + 5*x**3/12 - x**2/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAwBAMAAABDKe21AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nF60EfZ8CBwe9UJf3DwSuwkBl/BqjAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{x^{2}}{12} \\left(2 x - 1\\right) \\left(3 x + 4\\right)$$"
      ],
      "text/plain": [
       " 2                    \n",
       "x ⋅(2⋅x - 1)⋅(3⋅x + 4)\n",
       "──────────────────────\n",
       "          12          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(factor(x**4/2 + 5*x**3/12 - x**2/3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多変数の因数分解: factor(x**2 + 4*x*y + 4*y**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAbBAMAAAAZoBUxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABqklEQVQ4EY2TsUvDQBTGv2ttEptag0IHpw7+\nAVURF8UKQcTBFrE4uIiLbnYpIiJ2UXRzEEVx6KSDoF06uWQQOhUriIuC+Q9aHRy0UF/ukpNiCnlD\n3r3v++Xl7nIHBInKuBUEg270pQOBihH/CAaW2HcgENBaAUElHxCsEMeS9OgeIYO8UJYeg34Qy43Z\nrv5E+Qa3wIwfWIPurfMBiM8dToquktXcSb8B566o59HbbjehOHOQ4YGnwLst1NixyAkJOQMPzFgS\nxLwgCpSqu0M74pseSOKmVV0GuwScraEYBWLl0LqS5tUfGP1B+QhqExjmDjYA3dJbmpjqH6jUWXEJ\n4RRwIMAL6ogequkF05w9Mc06N3Ikn6E/DzQkCF7zUnZUs0C0hYYtQfo0janmIcF9MCOSxjapV8Ki\nxWjWHlSrA4xnoRrhOqZIdRdDi78rTmNAvOZ1TNxXXhBJRT9JXhEWNa5tVReTnWCm3f5C7LXg3IAF\nYfn/QuGBZgm2Kgp+1FyddsqQQ+AZjyXaNNohHiNu/p/WMEEiHTMRvgeXW9cFm7JsxJJUdQ9+Fcj+\nBc2OWoUFf0vwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left(x + 2 y\\right)^{2}$$"
      ],
      "text/plain": [
       "         2\n",
       "(x + 2⋅y) "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(factor(x**2 + 4*x*y + 4*y**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 根を求める: solve(x**2 + 4*x*y + 4*y**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF8AAAAVBAMAAADSoS/MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left [ \\left \\{ x : - 2 y\\right \\}\\right ]$$"
      ],
      "text/plain": [
       "[{x: -2⋅y}]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**2 + 4*x*y + 4*y**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 根を求める: solve(x**2 + 4*x*y + 4*y**2, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAAmBAMAAACi8w9qAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEO+Zu3ZEIs3dMquJ\nZlR1/quKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVQoFWMQUlJmQAPMSkoCDELIgoyh21OP\nAgWY0MRlGG4GzMAifpDhvMBzLOICDC1gY9HNYWD4il2c6xdW8YesHxgCMc1n+8fygf0Cpjjj1sDg\nuyCDMO0FiQ41ccbOmUAwYwED/38Q+DCI3F9s4oUtPBk3MJxPwBLO3AIMTApYxJkmMHCDYh49vjg+\nYhcHKuX8iEU9UCj/AHbx2UBhDPMZGJgNsIsHg4Qx1fMZMJRjE1/MwBAOEZd3cQXphAD2OWesJzCw\nuvgLMLClpcNEGRg4gNE4gYE9LY0BAEFKNHHUJivtAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ - \\frac{x}{2}\\right ]$$"
      ],
      "text/plain": [
       "⎡-x ⎤\n",
       "⎢───⎥\n",
       "⎣ 2 ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**2 + 4*x*y + 4*y**2, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 複雑な根を求める: solve(x**2 + 4*x + 181, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSP9RhUnswAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ -2 - \\sqrt{177} i, \\quad -2 + \\sqrt{177} i\\right ]$$"
      ],
      "text/plain": [
       "[-2 - √177⋅ⅈ, -2 + √177⋅ⅈ]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**2 + 4*x + 181, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 無理数解: solve(x**3 + 4*x + 181, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HQ478L729SZe1OPtxCQMHJQ/vqEeFyEbxxkyogftp4MdqEKxACrjwheDAhFD/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\n",
      "text/latex": [
       "$$\\left [ \\frac{4}{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}} - \\frac{1}{3} \\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}, \\quad - \\frac{1}{3} \\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}} + \\frac{4}{\\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}}, \\quad - \\frac{1}{3} \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}} + \\frac{4}{\\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}}\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                        ___________________  \n",
       "⎢                                       ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409   \n",
       "⎢                                       ⎜- ─ - ────⎟⋅3 ╱  ──── + ──────────   \n",
       "⎢                 4                     ⎝  2    2  ⎠ ╲╱    2         2        \n",
       "⎢──────────────────────────────────── - ────────────────────────────────────, \n",
       "⎢                 ___________________                    3                    \n",
       "⎢⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409                                          \n",
       "⎢⎜- ─ - ────⎟⋅3 ╱  ──── + ──────────                                          \n",
       "⎣⎝  2    2  ⎠ ╲╱    2         2                                               \n",
       "\n",
       "                   ___________________                                        \n",
       "  ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409                                         \n",
       "  ⎜- ─ + ────⎟⋅3 ╱  ──── + ──────────                                         \n",
       "  ⎝  2    2  ⎠ ╲╱    2         2                          4                   \n",
       "- ──────────────────────────────────── + ────────────────────────────────────,\n",
       "                   3                                      ___________________ \n",
       "                                         ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409  \n",
       "                                         ⎜- ─ + ────⎟⋅3 ╱  ──── + ──────────  \n",
       "                                         ⎝  2    2  ⎠ ╲╱    2         2       \n",
       "\n",
       "       ___________________                          ⎤\n",
       "      ╱ 4887   3⋅√2654409                           ⎥\n",
       "   3 ╱  ──── + ──────────                           ⎥\n",
       "   ╲╱    2         2                    4           ⎥\n",
       " - ─────────────────────── + ───────────────────────⎥\n",
       "              3                  ___________________⎥\n",
       "                                ╱ 4887   3⋅√2654409 ⎥\n",
       "                             3 ╱  ──── + ────────── ⎥\n",
       "                             ╲╱    2         2      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**3 + 4*x + 181, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多変数多項式を解く: solve_poly_system([y**2 - x**3 + 1, y*x], x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAroAAAA/BAMAAAD9MXZoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nMp8/WRX8K5v3/w8edwc/TibF1QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ \\left ( 0, \\quad - i\\right ), \\quad \\left ( 0, \\quad i\\right ), \\quad \\left ( 1, \\quad 0\\right ), \\quad \\left ( - \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}, \\quad 0\\right ), \\quad \\left ( - \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}, \\quad 0\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡                         ⎛  1   √3⋅ⅈ   ⎞  ⎛  1   √3⋅ⅈ   ⎞⎤\n",
       "⎢(0, -ⅈ), (0, ⅈ), (1, 0), ⎜- ─ - ────, 0⎟, ⎜- ─ + ────, 0⎟⎥\n",
       "⎣                         ⎝  2    2     ⎠  ⎝  2    2     ⎠⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve_poly_system([y**2 - x**3 + 1, y*x], x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 関数の評価"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x^{2} + 3 x + 2$$"
      ],
      "text/plain": [
       " 2          \n",
       "x  + 3⋅x + 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = x**2 + 3*x + 2 \n",
    "display(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この多項式に $x=1$ を代入する."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiXYyEM1Embsi72ZU3au6f2Q3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVUlEQVQIHWNgYBBUNGBgcE1gD2BgaGfgaGBg+8kABBwLQCR/sFAZA4N/NAPXAQb/LwzsSxj4LzBwf2PgDWDg/s3AtwDEZgaKAxU/ZPA6wMDAWP6YAQCADRI3fgJiQgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$6$$"
      ],
      "text/plain": [
       "6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1 = f.subs([(x, 1)])\n",
    "display(f1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 方程式をある変数で解く"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 式の表示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\log{\\left (y \\right )} \\cos{\\left (x \\right )} + \\frac{2}{y}$$"
      ],
      "text/plain": [
       "                2\n",
       "log(y)⋅cos(x) + ─\n",
       "                y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = cos(x) * ln(y) + 2/y\n",
    "display(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $x$ に関して解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbgAAAAyCAMAAAAZSD6LAAAAM1BMVEX///8AAAAAAAAAAAAAAAAA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\n8fQQ3x8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ - \\operatorname{acos}{\\left (- \\frac{2}{y \\log{\\left (y \\right )}} \\right )} + 2 \\pi, \\quad \\operatorname{acos}{\\left (- \\frac{2}{y \\log{\\left (y \\right )}} \\right )}\\right ]$$"
      ],
      "text/plain": [
       "⎡      ⎛  -2    ⎞            ⎛  -2    ⎞⎤\n",
       "⎢- acos⎜────────⎟ + 2⋅π, acos⎜────────⎟⎥\n",
       "⎣      ⎝y⋅log(y)⎠            ⎝y⋅log(y)⎠⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(expr, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $x^4 - 1$ を解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKUAAAAUBAMAAAAek+A5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEEFTvq5lm\nIrvActx7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABHElEQVQ4EWMQMmGgKuAxSmAIo8BErgcYmtcx\nsKKa2VmAoYaBYzqmGEyE6wCMBafXoJrJvno9pplVu77D1RPHQHOnPKaZDIxD38zCjeihwS4tgBqe\nDAwk+j0gE91MVrYJlJnJ27AZ3cwb3AYQM9mNlIBA2YFodxaD1CuZsDN8RDezgJ9Sv3NgJon+Asr8\nzsC8ACPtWbFTaGZ9QwCa59l/sGIxk/0zmjJQmq83QBOEcPN5D6ApZ/twB83MXfOtDjAoofqHe+Xn\nNQxM6ljN5DrDgK58zQE0M8EaOS5g0d+LRQwihKkcLb+DlLFi044ebgg1mMqxmFmIUA9nsQvAmegM\nTOVYzDyArgvI58EiBhU6gCEFNFNIBUOUIgFGpQQA/QdISsoM2NsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ -1, \\quad 1, \\quad - i, \\quad i\\right ]$$"
      ],
      "text/plain": [
       "[-1, 1, -ⅈ, ⅈ]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(x**4 - 1, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAVBAMAAABicsu7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ x : -3, \\quad y : 1\\right \\}$$"
      ],
      "text/plain": [
       "{x: -3, y: 1}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve([x + 5*y - 2, -3*x + 6*y - 15], [x, y]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x^4 - 3 x^2 + 1 = 0$ を解く."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAcBAMAAACKU66wAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left(x^{2} - x - 1\\right) \\left(x^{2} + x - 1\\right)$$"
      ],
      "text/plain": [
       "⎛ 2        ⎞ ⎛ 2        ⎞\n",
       "⎝x  - x - 1⎠⋅⎝x  + x - 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJIAAAAbBAMAAABl6sutAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
      "text/latex": [
       "$$\\left(x - 2\\right)^{2} \\left(x + 2\\right)^{2}$$"
      ],
      "text/plain": [
       "       2        2\n",
       "(x - 2) ⋅(x + 2) "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = x**4 - 3*x**2 + 1\n",
    "display(factor(f))\n",
    "display(factor(f, modulus=5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 超越方程式も一部サポート"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABwAAAAUBAMAAABscEDKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEq7tmEJnv\nIlQ+/2OHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAlElEQVQYGWMQMmGAg8lqDGFATgVMIAzMrUTl\nwnhAOZBiOMDC5ZIWYGD8DwQbwIpZ2Q4whPrJTrzLAObe4zZgecB6QQRoAkjvAn4BBgYOhiool+H9\nAgYGdwYFGNeci4FhJ8MvKJfrHysD1y+Gb1Au24ebDIwKDEehXIbKCQwcExhKYVwgDQVYHAmTAtIY\nskIqCFkhNQAatiY1Sgd5FgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ i \\pi\\right ]$$"
      ],
      "text/plain": [
       "[ⅈ⋅π]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(solve(exp(x) + 1, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 論理式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{y: True, x: True}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(satisfiable(x & y))\n",
    "display(satisfiable(x & ~x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 連立方程式を解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x y z + 234$$"
      ],
      "text/plain": [
       "x⋅y⋅z + 234"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, z = symbols('x y z')\n",
    "eq1 = x * y * z + 234\n",
    "display(eq1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + y + z - 20$$"
      ],
      "text/plain": [
       "x + y + z - 20"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eq2 = x + y + z - 20\n",
    "display(eq2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$5 x - y + 2 z - 85$$"
      ],
      "text/plain": [
       "5⋅x - y + 2⋅z - 85"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eq3 = 5 * x - y + 2 * z - 85\n",
    "display(eq3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ \\left ( 13, \\quad -2, \\quad 9\\right ), \\quad \\left ( - \\frac{9 \\sqrt{17}}{4} + \\frac{39}{4}, \\quad - \\frac{9 \\sqrt{17}}{4} - \\frac{21}{4}, \\quad \\frac{31}{2} + \\frac{9 \\sqrt{17}}{2}\\right ), \\quad \\left ( \\frac{9 \\sqrt{17}}{4} + \\frac{39}{4}, \\quad - \\frac{21}{4} + \\frac{9 \\sqrt{17}}{4}, \\quad - \\frac{9 \\sqrt{17}}{2} + \\frac{31}{2}\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡             ⎛  9⋅√17   39    9⋅√17   21  31   9⋅√17⎞  ⎛9⋅√17   39    21   9⋅\n",
       "⎢(13, -2, 9), ⎜- ───── + ──, - ───── - ──, ── + ─────⎟, ⎜───── + ──, - ── + ──\n",
       "⎣             ⎝    4     4       4     4   2      2  ⎠  ⎝  4     4     4      \n",
       "\n",
       "√17    9⋅√17   31⎞⎤\n",
       "───, - ───── + ──⎟⎥\n",
       "4        2     2 ⎠⎦"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([eq1,eq2,eq3], [x,y,z])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 線型代数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  1⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "display(Matrix([[1,0], [0,1]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Numpy` と違ってシンボルを含む行列が書ける"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAyBAMAAAAKOF7GAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhCrmXbNZiJE\n3btGuGCyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVQ4EWOQ//+JARtg+v9fgEHYxRWbHAOr\ni7MAgwhWKZAgCzGShgFY9EN0sqbn45ZkYOinlmRE256mBrhrUY1lVeC6wTsBhyRTANNX5g04JFkZ\nOB8gBQKqsQwM/A14JP0dcEoyB/QzcATgsPO8wXuGXfCAL5OftgBoDgyEdURULYBLwkRRaaKiDFUL\nlDeqExgQuAIBnMixS0ITOXZJaCInQpK1vYFhI0qGACc4iE4mZgGGfpRYQ5LczD6B4R0uyQDGBoYf\nuCQZzgewfMEpWcnAIYBT8hkDXwJOyTqG8wtwSoZp1G9AloQkcngIVSLLQdkQSbYJrH9wSvIu4GvA\nKcnTUYJFDmdkg9XCHYRDJ94iFV9hDACNkktQo2Jb7QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & x\\\\y & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  x⎤\n",
       "⎢    ⎥\n",
       "⎣y  1⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJYAAAAyBAMAAABMoj8pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\niZYV5W++CH+L/gaxXs1X3ePmxQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x y + 1 & 2 x\\\\2 y & x y + 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡x⋅y + 1    2⋅x  ⎤\n",
       "⎢                ⎥\n",
       "⎣  2⋅y    x⋅y + 1⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "A = Matrix([[1,x], [y,1]])\n",
    "display(A)\n",
    "display(A**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 微分積分"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 極限"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\lim_{x \\to \\frac{\\pi}{2}} \\tan x\n",
    " =\n",
    " - \\infty.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAALBAMAAAAHCCkxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMqvvZom7mXZUIkRJD0iWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfklEQVQIHWNggAMBEAtMQIUYw74VMDB0Lt0AV8LA6cD9iUHoAIMHQqiEgeH8BBUGBvYLDELGIKDCANTA8RmkC6gdCkC8+SAChCEAxJr2j4GBsQAmwlDIwMDdm3aBgfsCXIiLgaGLwT+PoQIuwsC4KvIAA+P6tAaEENThAgwMAMSLGqu/gFQwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$-\\infty$$"
      ],
      "text/plain": [
       "-∞"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(limit(tan(x), x, pi/2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\lim_{x \\nearrow \\pi/2} \\tan x\n",
    " =\n",
    " \\infty.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAALBAMAAABv+6sJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKvvZom7mXYyzVQi3UQ6SGZXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAaklEQVQIHWNgYBBgAAIQwaj82YGBIayogYGBbQLHLwapDQxTGRg8GRj2J6xkYGA5wACUYP0LJBgcQEyGfBDRAGYm/wNqd2BwZGDgiDE+wMBxgIGdgSGcYb4dgytQolxtAwNjvXEAUDncNgBJUBUwaYAbUgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\infty$$"
      ],
      "text/plain": [
       "∞"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(limit(tan(x), x, pi/2, dir=\"-\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\lim_{x \\to 0} \\frac{\\sin x}{x}\n",
    " =\n",
    " 0.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(limit(sin(x)/x, x, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\lim_{x \\to \\infty} \\frac{\\sin x}{x}\n",
    " =\n",
    " 0.\n",
    "\\end{align}\n",
    "\n",
    "コードとして無限大は `oo` で書く."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77urRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVElEQVQIHWNgEDIxZWBgSGeQmMDAsoCBOYGB+wAD+0cG/gMMvN8Z5BUYeP8xzDdgYP3MMF8BREJEgLLs3xm4NzCwfATpYkpgYGhnkApgYBB+d5QBAPogE3QldevOAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(limit(sin(x)/x, x, oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 微分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAzgAAAA3BAMAAAAyHPL5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{x^{2} \\cos{\\left (x \\right )}}{\\tan{\\left (\\cot{\\left (x \\right )} \\right )} + 1} - \\frac{x^{2} \\sin{\\left (x \\right )}}{\\left(\\tan{\\left (\\cot{\\left (x \\right )} \\right )} + 1\\right)^{2}} \\left(\\tan^{2}{\\left (\\cot{\\left (x \\right )} \\right )} + 1\\right) \\left(- \\cot^{2}{\\left (x \\right )} - 1\\right) + \\frac{2 x \\sin{\\left (x \\right )}}{\\tan{\\left (\\cot{\\left (x \\right )} \\right )} + 1}$$"
      ],
      "text/plain": [
       "    2              2 ⎛   2            ⎞ ⎛     2       ⎞                       \n",
       "   x ⋅cos(x)      x ⋅⎝tan (cot(x)) + 1⎠⋅⎝- cot (x) - 1⎠⋅sin(x)      2⋅x⋅sin(x)\n",
       "─────────────── - ──────────────────────────────────────────── + ─────────────\n",
       "tan(cot(x)) + 1                                 2                tan(cot(x)) +\n",
       "                               (tan(cot(x)) + 1)                              \n",
       "\n",
       "  \n",
       "  \n",
       "──\n",
       " 1\n",
       "  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff((sin(x) * x**2) / (1 + tan(cot(x)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAAAcBAMAAAAZ99lXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nVZRso/iwmfjYpBtjHzaW9r+sf+xqnQ0hbAhKAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$x \\left(- \\cot^{2}{\\left (x y \\right )} - 1\\right)$$"
      ],
      "text/plain": [
       "  ⎛     2         ⎞\n",
       "x⋅⎝- cot (x⋅y) - 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(cot(x*y), y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANMAAAArBAMAAAAQ6KCeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADwElEQVRYCb2XTWgTQRTH/5tkmzRJk0VBpIca\ni9KDH0REQSwaPKkIXTy0SAuJBxG0aBS1IqK5KkpFKKhorRcFP+MH1IPQEPxE0Sh40INWb36gVSyK\nqPXN7s7uJu3sqgw+yMybeb/9z+7s7LwM4G2hRSlvQGI0WZEo5i3Vq3vHJUZ3SdTykbriE5cVVlpu\n/pSl5aOzTwuO+iCSwmo/AkVJWj4ygVFE8z6MpHB9GtmCJC0fmWweL30QWeFsBYsbNFlqnjqxUuJ0\n2JP456AybF6asJ5E7d425a5brRZwxyb2m6zuV1QrzfMznJrMnbXcqanFwA19WaUGZk0lbXXW0d23\nI/yNM5e508mdmloMnBz7WsMazZg1P1CLwDrgqAUlUpwOl7hXVXsAg91ctOqK13ZrN3AM2JwxO6I2\nrR6yEbfjAeTcnOOfst01wJBuD9Vo9+O647o8DyDnwhxXGbD9WIG5l/Su2VD6UCa/6/bUOyVgK+t3\nmS+w6f0Mhq/umQN1950CVr24T814ClAfrD1AsxcmF5GvyD9DfARLqD+fOB+lN/iO+t3mCyzAtAIt\nuBNYoa3U0KqmEaXrg8NAB96WzgEJUkU0p1RmIZjGBRpbD4+y/eE59bvMFyA2OADEiniZOQO0Le9D\nnPqiFWA79uqPgQYKoxkqjiNZwhF6KsTS1IU2VjgmADrPMrtmcoFPQDYFhCiZJvOXWumGUV8AdFxl\nQGjEnM/IKNoybCiiSqykocYcG8FEAOO41RWNz7O3RLdPn2ky3TH0mWJsKOAHK9hQT6BolADvgU0g\nDZJh5X5WuMwPqC+CkpvzVNN1fCyYE4jQFyYUGUAohbgWzGEh2LJo0B8hro9fFn5AgGSLxrtC5TDQ\ne7CEumFzWTylBXfLWBaNPVs3IJCO/DJWeG9lKZroHlro5zY/QEnhjUYrsB9hbUUGgw19CFKbVnjk\nZ3CE7dKBPIbGxr5DXV+ml0qz1v6gay71w3rV5JnmC0zaMZOR7bO3QGnZUYjsebiTmjRravet8gdy\nYxkqDGN/V5x9x/WV/zHAwara2Zj4TrPR+A8xbjd1zgYCoEp2okbVdmsAF9HK6nmc5knEPhuIAH6B\nqGYvzDCWRAw7UM6w2s58fEz7bCAC2FVeZqdGe0yLZiuFGU/42GW27XIcYEdEDlvOzF6Zlbj8r2cD\nKwWI70ZKxDgbWClAiqBQxDwbWClASEkJmGcDKwVIURSK8LOBkQKElJSAdTYwU4AURaGIeTawUoCQ\nkhIwzgY8BUhRFIoYZwOeAoTUXwR+A3LPDqrJkrJaAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2 y{\\left (x \\right )} \\frac{d}{d x} y{\\left (x \\right )} - 5 \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "       d                  \n",
       "2⋅y(x)⋅──(y(x)) - 5⋅cos(x)\n",
       "       dx                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(y(x)**2 - 5* sin(x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADwAAAAuBAMAAACGzGfRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRUlEQVQ4EbXTP0vDQBgG8Ccp6b80Wp2cpCC4\nKJJBnASLX8C4OAXs5uCSzcHBfgAhLm4OmSqCSCeXLDWDIhTsKjj4ERTMarxcEzvkngyC7/j+7t47\n7uGAxZVN8DJ6OOtzrjpoXHBuBKh+cTbjUhYbmzHcx6WnEZnhe4Y3d9scEh6g5tRiq61mvQMDpq1G\nIEphfkTY6mAB2OsS3gUeLOcFLUe1QLs+WQ38yQ6WVQozSZLgYOxuvCuZN/8W5dt0IIsyYxZlxizK\njMURIspizdj3iooZDwDxKnl9iLWnYXgThvdyl4hSUb+7ZZSFBTlPo6ScRllA5FeTUXKWUXJWiGzt\nM/iPvrsO7ZIP9l7RSt9bXdpkDRVbbaJr4Ir/IeH1mP8hwfoQz3Q2UOlhq4R1u/5dwsZR9FnC8nTu\nxzjsc8UdtksU51GX8Q+VHlugdewoMwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{2 x}{y} + 2$$"
      ],
      "text/plain": [
       "2⋅x    \n",
       "─── + 2\n",
       " y     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = x**2 / y + 2 * x - ln(y)\n",
    "display(diff(f,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 高階微分\n",
    "\n",
    "微分の階数は第 3 引数で指定する."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAUBAMAAADo9qfkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrB/UuBb+nWYVdOamRfUr/AFco2eWtO0dyAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$2 \\cos{\\left (2 x \\right )}$$"
      ],
      "text/plain": [
       "2⋅cos(2⋅x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(sin(2*x), x, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF4AAAAUBAMAAAD2P5dXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\na7nPLUqD0HtR0DpaEZrpz/f4DbsBYYE9hr4hAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- 4 \\sin{\\left (2 x \\right )}$$"
      ],
      "text/plain": [
       "-4⋅sin(2⋅x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(sin(2*x), x, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAAUBAMAAACABSXcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\njwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- 8 \\cos{\\left (2 x \\right )}$$"
      ],
      "text/plain": [
       "-8⋅cos(2⋅x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(diff(sin(2*x), x, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 微分方程式"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 未定義の関数を定義"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, g = symbols('f g', cls=Function)\n",
    "display(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$f{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "f(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} + \\frac{d^{2}}{d x^{2}}  f{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "         2      \n",
       "        d       \n",
       "f(x) + ───(f(x))\n",
       "         2      \n",
       "       dx       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f(x).diff(x, x) + f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHsAAAAVBAMAAACUF4xmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = C_{1} e^{- x}$$"
      ],
      "text/plain": [
       "           -x\n",
       "f(x) = C₁⋅ℯ  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffeq = f(x).diff(x) + f(x)\n",
    "display(dsolve(diffeq, f(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQYAAAAUBAMAAACdco4rAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = C_{1} \\sin{\\left (x \\right )} + C_{2} \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "f(x) = C₁⋅sin(x) + C₂⋅cos(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffeq = f(x).diff(x, x) + f(x)\n",
    "display(dsolve(diffeq, f(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$f{\\left (x \\right )} = C_{3} e^{- x} + \\left(C_{1} \\sin{\\left (\\frac{\\sqrt{3} x}{2} \\right )} + C_{2} \\cos{\\left (\\frac{\\sqrt{3} x}{2} \\right )}\\right) \\sqrt{e^{x}}$$"
      ],
      "text/plain": [
       "                                                 ____\n",
       "           -x   ⎛      ⎛√3⋅x⎞         ⎛√3⋅x⎞⎞   ╱  x \n",
       "f(x) = C₃⋅ℯ   + ⎜C₁⋅sin⎜────⎟ + C₂⋅cos⎜────⎟⎟⋅╲╱  ℯ  \n",
       "                ⎝      ⎝ 2  ⎠         ⎝ 2  ⎠⎠        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffeq = f(x).diff(x, x, x) + f(x)\n",
    "display(dsolve(diffeq, f(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### キーワード引数を使ってヒントを出すこともできる。\n",
    "\n",
    "方程式が可分離であることを知っているならキーワードとして hint='separable'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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urNbTy0mfe+czE06zQvPTHr1Ev3pSCyFyvbyl6zVkMGciZ4XmmJGjVoA68GVQTB0uZH0I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\n",
      "text/latex": [
       "$$\\left [ f{\\left (x \\right )} = - \\operatorname{asin}{\\left (\\sqrt{\\frac{C_{1}}{\\sin^{2}{\\left (x \\right )} - 1} + 1} \\right )} + \\pi, \\quad f{\\left (x \\right )} = \\operatorname{asin}{\\left (\\sqrt{\\frac{C_{1}}{\\sin^{2}{\\left (x \\right )} - 1} + 1} \\right )} + \\pi, \\quad f{\\left (x \\right )} = - \\operatorname{asin}{\\left (\\sqrt{\\frac{C_{1}}{\\sin^{2}{\\left (x \\right )} - 1} + 1} \\right )}, \\quad f{\\left (x \\right )} = \\operatorname{asin}{\\left (\\sqrt{\\frac{C_{1}}{\\sin^{2}{\\left (x \\right )} - 1} + 1} \\right )}\\right ]$$"
      ],
      "text/plain": [
       "⎡             ⎛     _________________⎞                 ⎛     _________________\n",
       "⎢             ⎜    ╱      C₁         ⎟                 ⎜    ╱      C₁         \n",
       "⎢f(x) = - asin⎜   ╱  ─────────── + 1 ⎟ + π, f(x) = asin⎜   ╱  ─────────── + 1 \n",
       "⎢             ⎜  ╱      2            ⎟                 ⎜  ╱      2            \n",
       "⎣             ⎝╲╱    sin (x) - 1     ⎠                 ⎝╲╱    sin (x) - 1     \n",
       "\n",
       "⎞                  ⎛     _________________⎞             ⎛     ________________\n",
       "⎟                  ⎜    ╱      C₁         ⎟             ⎜    ╱      C₁        \n",
       "⎟ + π, f(x) = -asin⎜   ╱  ─────────── + 1 ⎟, f(x) = asin⎜   ╱  ─────────── + 1\n",
       "⎟                  ⎜  ╱      2            ⎟             ⎜  ╱      2           \n",
       "⎠                  ⎝╲╱    sin (x) - 1     ⎠             ⎝╲╱    sin (x) - 1    \n",
       "\n",
       "_⎞⎤\n",
       " ⎟⎥\n",
       " ⎟⎥\n",
       " ⎟⎥\n",
       " ⎠⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(dsolve(sin(x)*cos(f(x)) + cos(x)*sin(f(x))*f(x).diff(x), f(x), hint='separable'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = - \\frac{C_{1}}{- C_{1} + x}$$"
      ],
      "text/plain": [
       "         -C₁  \n",
       "f(x) = ───────\n",
       "       -C₁ + x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(dsolve(x * f(x).diff(x) + f(x) - f(x) ** 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = \\frac{1}{x \\left(C_{1} + \\frac{1}{x}\\right)}$$"
      ],
      "text/plain": [
       "           1     \n",
       "f(x) = ──────────\n",
       "         ⎛     1⎞\n",
       "       x⋅⎜C₁ + ─⎟\n",
       "         ⎝     x⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(dsolve(x * f(x).diff(x) + f(x) - f(x) ** 2, hint='Bernoulli'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## テイラー展開"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x - \\frac{x^{3}}{6} + \\frac{x^{5}}{120} + \\mathcal{O}\\left(x^{6}\\right)$$"
      ],
      "text/plain": [
       "     3     5        \n",
       "    x     x     ⎛ 6⎞\n",
       "x - ── + ─── + O⎝x ⎠\n",
       "    6    120        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sin(x).series(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$1 - \\frac{1}{2} \\left(x - \\frac{\\pi}{2}\\right)^{2} + \\frac{1}{24} \\left(x - \\frac{\\pi}{2}\\right)^{4} + \\mathcal{O}\\left(\\left(x - \\frac{\\pi}{2}\\right)^{6}; x\\rightarrow \\frac{\\pi}{2}\\right)$$"
      ],
      "text/plain": [
       "           2          4                     \n",
       "    ⎛    π⎞    ⎛    π⎞                      \n",
       "    ⎜x - ─⎟    ⎜x - ─⎟     ⎛       6       ⎞\n",
       "    ⎝    2⎠    ⎝    2⎠     ⎜⎛    π⎞       π⎟\n",
       "1 - ──────── + ──────── + O⎜⎜x - ─⎟ ; x → ─⎟\n",
       "       2          24       ⎝⎝    2⎠       2⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(series(sin(x), x, pi/2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 積分"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不定積分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAUBAMAAAB/pwA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAg0lEQVQIHWNggAC2pAIoi2EqywMok8mAUQHK\n5FsAZTAw8C/SFYBy/C+wNkCZ8gsYvkKZ/AEM36FMzgK4KOsGrglQUYbaXKAJQsquagpgEcYE9iYO\niCSbANtHLgeIKAPnBjADRPArwJnnD0CZXAL6DExAg4AgfsF+BneIsLCS0PUCMBMAVQYWpfImCywA\nAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x^{6}$$"
      ],
      "text/plain": [
       " 6\n",
       "x "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(6*x**5, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAUBAMAAADVZMaCAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$- \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "-cos(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(sin(x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG4AAAAUBAMAAACezBVvAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nnuE8YhjVGwijOTb/T/wAtM1kFi/cfW4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x \\log{\\left (x \\right )} - x$$"
      ],
      "text/plain": [
       "x⋅log(x) - x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(log(x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAAAZBAMAAADwAgzpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$x^{2} + \\cosh{\\left (x \\right )}$$"
      ],
      "text/plain": [
       " 2          \n",
       "x  + cosh(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(2*x + sinh(x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAAAuBAMAAABQRX/xAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12VGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADQklEQVRIDa2VT2gTQRTGv2Sz+Z82th5UqAZa9FDQlkpP1QaRgqBkBWlRe0hvIkJDLy1YNCcPXpKDFS9CvChC1QiilRy6VrAHgy14E9GIRwVFm1pBiG+6Mzths63CzoNl37zvzY+Z3Z1vgY7uw1AcehZX84qZQQORomJmpITgmmJmrK6eSUuM1jH+ateyqXK1hZyea5uPllUy7yJkhOqJpEKmPwUdsT6FRGCJ0dpNlcxECjuATFol8xjwImGsIG4oo/ruTe8vFVaHsVcZErFGo1EarY4frP2L6eMdn1wbhdq23ecz8swxt5OPg/asE6ZsESomZK0l0286So/5WC8LIZMTGSBUnJc1mb3n6aAssawtJcazImm6SzVkNpVFugUzam/5rOhsuktVLzaVRboFc4/QEcvzdGfarkkVC3ZRJk3MseoMcG3q60tS6bjpSyZ2GwilaHjyw2vfcDbwvKd6iU1lh5Gb2xQbO0IyA3egmeE6Hsap5SgQShSxQk+WXpLehyhiWUSHsI89FFKFuX1x8NhQMqM5BNaCJVxk5QdAl7+MASBRAsJziEPLQiuivYZNVZjbO9AnL+I7aZcrlfuVylPKMIjMKvDLX7SYtwAjYuIPEGCNj4aS0IhZtuyHVGFuGVKdIdf5MQ/89K3pt1kLzULBCNC/a5M5tvgDGjH7bKYwt+2ZbJ0/fMvLacKxvaMX8SLtuwT4DHzLa5LJVG5u11nqCLnOSArhjUTe0ukt0OPQstY7SpgI1mgg1kmqMLft3tEAAjcQy4UXjidBwT6RbhRqgD9HgDloSQIKJqnC3A6wbkfwdY40JtAxfQFYbPxOUQvb0ujsIeLH0rT/K29mApPrZybXTw0zYyBVmNsTGjpD7J3XtVW9a55y6/T1UtZ0Zuy58mz6SnZRJqdlyrK3dH2mqy2FYFnfoGyWLmeQysPVQ4TI7+fSwBGW9yNa00z6Dsts5Ix+UXD1OiHyuz5dnUqzvBPhag/dNXqkrWF7sg1v7WmtiL/Df/07uN20UjxUuN14ILRO5XbTKniocLvxQHCZatmNi+ChZNmNB4DLVMtuXAQPJctuPABcplp24yJ4KjG7URrcbpQyLbtRiuR2o475F2lI1UocedrwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{2 x}{y} + \\log{\\left (y \\right )} \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "2⋅x                \n",
       "─── + log(y)⋅sin(x)\n",
       " y                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = cos(x) * ln(y) + 2/y\n",
    "display(integrate(expr, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- \\frac{1}{2} \\log{\\left (\\sin^{2}{\\left (x \\right )} - 1 \\right )}$$"
      ],
      "text/plain": [
       "    ⎛   2       ⎞ \n",
       "-log⎝sin (x) - 1⎠ \n",
       "──────────────────\n",
       "        2         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(tan(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$2 x y + \\frac{y^{2}}{2}$$"
      ],
      "text/plain": [
       "         2\n",
       "        y \n",
       "2⋅x⋅y + ──\n",
       "        2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(2*x + y, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$2 y + 8$$"
      ],
      "text/plain": [
       "2⋅y + 8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(2*x + y, (x, 1, 3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAOBAMAAAA/Njq6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12VGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAlklEQVQIHWNgVDJ2YGA9U9TAwBDGwP6DgYmBIZeBIZWBYSbDPQYGaQaGWQwM+Q7FDAxRDAz7A4DMflOGOgYQWB/A9v/5AxCL4zsDQ/3vABCTK4GBN2P9DBBTiYHhGQPPT6AwjwIDw0QGBv8LDAyXGBhFPzAwsD1gYFFg4BEAijILMEiVF2UxdAcwvAFa8f//LwaWJKBzAAjgJANbXSzUAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$28$$"
      ],
      "text/plain": [
       "28"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(2*x + y, (x, 1, 3), (y, 2, 4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 特殊関数もいける"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAuBAMAAAAsD6FtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{\\sqrt{\\pi}}{4} \\operatorname{erf}^{2}{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "      2   \n",
       "√π⋅erf (x)\n",
       "──────────\n",
       "    4     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(exp(-x**2)*erf(x), x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定積分\n",
    "\\begin{align}\n",
    " \\int_{-1}^1 x^3 dx\n",
    " =\n",
    " 0.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77urRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVElEQVQIHWNgEDIxZWBgSGeQmMDAsoCBOYGB+wAD+0cG/gMMvN8Z5BUYeP8xzDdgYP3MMF8BREJEgLLs3xm4NzCwfATpYkpgYGhnkApgYBB+d5QBAPogE3QldevOAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(x**3, (x, -1, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\int_0^{\\pi / 2} \\sin x dx\n",
    " =\n",
    " 1.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(sin(x), (x, 0, pi/2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\int_{- \\pi/2}^{\\pi/2} \\cos x dx\n",
    " =\n",
    " 2.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOBAMAAAAPuiubAAAALVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIpm7MhCriUTv3c12VLgeopIAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABOSURBVAgdY2BUMnZgYAhjYH/BwJDKwDCTgWEWA0OeA8O+ABAJBOsCgATHcxCTKwFEKoEIHgUQeYmBUYCBRYGBR4BBqrwoi4Fh37t3rxgAK5QOlzv7snYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(cos(x), (x, -pi/2, pi/2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 広義積分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(exp(-x), (x, 0, oo)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAVBAMAAABI7vhRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInarRM2ZVBDdiWbv\nuzJCz3LGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVQYGWNggADG/2DwAcplYHaAsSC0KCqX\nIR2VzzEBlc9WgMrvROUyrEblg7TrAx3wDSrMtIGBa12RtKIAkO8CxJwMDM8ZFjI9ADKZjgIJJSBm\nuMDcACQl9B0YGEC28xkAVQFB/wUG7gVAmm0DfwOQYmD7yMAJYvQ38DsAKQbGbwy7QLQmA88CEM1g\n3zADRN1mYF4AohneL08A0zCC9WgDjAmm2WGuhIkGwhhAGgDwdic2xV4k0wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\sqrt{\\pi}$$"
      ],
      "text/plain": [
       "√π"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(exp(-x**2), (x, -oo, oo)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAAqBAMAAAD4w+CrAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAUAiAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\infty + \\frac{i \\pi}{2}$$"
      ],
      "text/plain": [
       "    ⅈ⋅π\n",
       "∞ + ───\n",
       "     2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(tan(x), (x, 0, pi/2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 積分の厳密解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAAlBAMAAABrOn4UAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdpmJMlQiZrurEN1E\n782PMUhmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAlElEQVQYGWNgkP////8nBgZmk8B0sQQGBlcG\nM0YHBhBo4FwAolgmcIMoBqYC/gUgev0C/gMgWpqB1wBEtzNwgmkQmwIAdAUQfCDBhCSNFpBqrgkM\n9geANNC1vBeANO8GBs4vQJrvF4QGMrl/AQkgOA916E4Il0kBQgtBKFYFhjQQy4mBQQxIsW021twA\npPmAztrAAADNgiR54A4W0wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{\\pi}{2}$$"
      ],
      "text/plain": [
       "π\n",
       "─\n",
       "2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(1/(x**2 + 1), (x, 0, oo)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWMAAAAcCAMAAACDHy5zAAAANlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABHL6OuAAAAEXRSTlMAMrvvq1SJ\nIkSZZs123RDz5Zs1HLQAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAZBSURBVGgF7VrZmqQqDAZFEEXO\n4f1fdkIWWVzKmqnp+WbxQihNQvInJMFupX7RZf3g4y9a+y9Z1jqlzPqXGPuTzdTz+QIbYKwT3P7o\nK3yFdXq4WGUD7F26cMAFz+/3eDZfoPN6l3KndPf2C7T71BI2eB2MPhFnl5OHn33kbzfLdvv2UhP3\nk/T+brkh5tKSd+bCyU9GpbYcRnoYUxqMGU790BsaPVyT8v3z89+uClR94LGHJ+dSuqeO04+5SkMt\nPZNps9r2Rf+L5Drvh4Ej8uEKCshX9rthkGVUgYzUCbPGlO6UoMwZt7z8vD1sCGoUtx6S5QHE03jM\nJquY8SycDZPF8UVuRLkxE1muE8Lae+Pkt1TvyMjICDUHqR1hrIabEhQJEE/D8hDjcdrVCWOH8Qwe\nndsUNrW5Ixpvqo3Aop64Zl+1ngz3GJNcgz4dx5pR5p168jiPGpAkWyzbIKPa0MeCsU3XkcWWrUzR\n4VUvV811Qcgta8uj12mahjZKj0aEIkHk5qbv7gpX719gTHLHLcs2qXU+rXdUj55DqFpgoywQ2T0y\nKo92C8ZDKmFH3Pt9YvgH3rvZNy5HYdTzlU1QAUo4WNVhDEUArn0BnByNOGLsEISWr/k1XQXKPcYs\nd0WnvodxNGG2wXK8rNyPyhgQBMZ4YRyjDcFy+uXpYtJmDHhgTiO/Us4n8NA0JNgceh2heQkmqDmE\ngRdRyu8pBeosYzxv46z0eSp9gjHXkBiqlqXdIbUTajLCuFg3G+sXUJc8xHLpxwZI16z09KBeluX7\nEJMaJOOMXnNpBdrREDYaN82Q00o13Tg6lhx97CJCLWMMLUpmcCmAjBK9gxgf4SVRxwGWou1Ditf3\ngxHqGMcDucequWySGtXs9iKzJkOMi0loOyRLVF8plousc67+NSsJ7NWbM1KubxSkVsmoMe9QHLuN\nMsWGTPimnsoOjIvfUkJDCULCeECLc2RXJ+RVqkwWyRjDTJov0ry690aoE4xJSwft475JVIuxCnua\nb8gQ42KSyVx4Qw3YepqD3g0r6dip53JFj77P3BNrIyMdZjlXBARcc1IGV1ZTJXGMq+kRE2mDMVqM\n3R85LhMK05T14FwBPtghQGF4s2u+thEH8Qy8OcYxZBq4IPeRb5H7v/+35krSIDVkGePKJJ+jomBM\nclEcNk8N66l6ZoRMs3AWRka85RYjXzI6BJQxnjEfT6wfhGQ1Fbg4j85I1GCMGxTtLhhzHEfcGYLx\nzRG+CxRQ9ApjyAhVx4FnKTQMb3M+cfFVkWWMK5MchFQszWXBWDJzxUrCOvW445WVZBRsZWziWKcc\ni7unfT1FjCFzSarDkH+K8WTylUYoiWBlFaWiloydEfD4iLHsafDfHkJtrtD1N5KKrIljr1yAXqBs\ndJGrsC9xkGkrVlKwU+/iyDazNjLSx0WOY0et1IiZFyO1muaQhBccIeQjPGpCncsaVHiXOG7OonQG\noc7qAufOiFOMuTZF2IF7tWkxlnNgVqsmw3xcTJpKsGdKqXl05Icmu2bNBBAeXB7plxpp/fYhlHyu\nEzJKX0HhuUJ0BqVHzJ5ZQDX1YEfGGFuKSKdzbCCmEdPrKcbUGrJKVA+3xS6h2sv8kobOCHjIcRxx\niyERt0RzUuUTTtMJzlKdM3lNhioWk+Z11ro0XizXbdZan9N0zYor9xiHDGY89G6eXS8jobSmhJTR\nDwHUdd5a7uOqqTH4lws1gQbSAVvoD+M2blGblIyGXhm+CdgtUfHOau7b2Q5AsWQ3LaN056R5de8x\n9mZMK3402PaUK1vQLA2yRUpb6HcyVDH3Wrt1YHZKFNfAzXLxYUp5Z+ysIrtXD1r0EyVWzj8yXjWq\nIvVHx1JIHknqjaiYpj3iXp2lK6bb6ZA7Lzft31dfy71Rr6wk51AZ1donk0L7kZnsl4fC4g7kgWHP\nveq7vwm1MuWkskgZfy33Rr0iW74FyRjLXi5En5zpchb7MbH5oCjXcO0JIXkw0ldaqHV08gKOj8iV\nb5oyquWivj9Q8SFJ/sbxiavOvZfHxPcWirma2Cp7f0SuOEpGhR/c39PsTerdnW/y3ZKXhuKW7O2X\nH5Arf2OSUS0lyb2tz1OGyy+NTwX83nQf2RsvIeha/Zf0fxbBv/+E+ip/fgP2dzDUZvvZOQAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$\\operatorname{RootSum} {\\left(4 z^{2} + 1, \\left( i \\mapsto i \\log{\\left (2 i + e^{x} \\right )} \\right)\\right)}$$"
      ],
      "text/plain": [
       "       ⎛   2               ⎛       x⎞⎞\n",
       "RootSum⎝4⋅z  + 1, i ↦ i⋅log⎝2⋅i + ℯ ⎠⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate(exp(x) / (1 + exp(2 * x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnwAAAAVBAMAAAAupy7eAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nBPHEsY/rEgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$16 x^{8} + 192 x^{7} + 1008 x^{6} + 3024 x^{5} + 5670 x^{4} + 6804 x^{3} + 5103 x^{2} + 2187 x$$"
      ],
      "text/plain": [
       "    8        7         6         5         4         3         2         \n",
       "16⋅x  + 192⋅x  + 1008⋅x  + 3024⋅x  + 5670⋅x  + 6804⋅x  + 5103⋅x  + 2187⋅x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(integrate((2 * x+3)**7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# プロット"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 放物線"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+8BtGk8oXU/vz8OBYmUWzjeTqFHHW769OuRSD0cQ7q3KYteYg0e19mDUulR4d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\n/wEp2f+H6wi9TQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1978395c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x19781d84160>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from sympy import init_printing\n",
    "from sympy.plotting import plot\n",
    "from sympy.core import Function\n",
    "from sympy import symbols\n",
    "\n",
    "f = symbols('f', cls=Function)\n",
    "x = symbols('x')\n",
    "\n",
    "f = 2 * x ** 2 - 3 * x + 1\n",
    "\n",
    "# 関数の定義\n",
    "# xが[-1, 2]の範囲を図示する\n",
    "plot(f, (x, -1, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 楕円"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sVqvDfaakpOCPf/wjqqursXDhwtq1OPVSXS0/rM6ckRcnhZAfZpGRQJ8+upZG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19784178208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x197841781d0>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from sympy import init_printing\n",
    "from sympy.plotting import plot\n",
    "from sympy.core import Function\n",
    "from sympy import symbols\n",
    "from sympy.plotting import plot_implicit\n",
    "\n",
    "# 描画領域の修正：円がきちんと表示できるように\n",
    "plt.rcParams['figure.figsize'] = (1, 1)\n",
    "\n",
    "x, y = symbols(\"x y\")\n",
    "\n",
    "# f(x, y)は半径1の円を表す\n",
    "f = x ** 2 + y ** 2 - 1\n",
    "\n",
    "# f(x, y)を図示する\n",
    "plot_implicit(f, (x, -2, 2), (y, -2, 2))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}