{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10 符號式的數學運算 Sympy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-1 先來我們標準資料讀入"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8333333333333333"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/2 + 1/3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可不可以加出 5/6 呢?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAqBAMAAACXcryGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAzXYQMplU74mrIma7\nRN0SDTw+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAqklEQVQYGWNgEDJwTWBgYKj//wNIMkhMWgCi\nJoAIODV7UwiId5hh/QUQzcDzAEyx/mJg4BRg4PjLwMAuwMD6mYGBlYGBT4CBgSuAYfsCoJKlncFg\nheQR/0HgA3F6OzQcgAoNL7ACbWc4ysBzgIGBF+g6IOApAFP8Ik2xQIa9NAN7ApD6zMBazMDA/4CB\nG+h4oJO5fwO9UgDmsQDlQHpmMJgDVTJwhE5hYAAAsEYnsoUVooQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{5}{6}$$"
      ],
      "text/plain": [
       "5/6"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rational(1,2) + Rational(1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5/6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S(1)/2 + S(1)/3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "美化輸出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "設一個變數。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = symbols('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "設兩個變數可以用:\n",
    "\n",
    "    x, y = symbols('x y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = x**3 + 2*x**2 - 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAWBAMAAAAFoW4BAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
      "text/latex": [
       "$$x^{3} + 2 x^{2} - 5$$"
      ],
      "text/plain": [
       " 3      2    \n",
       "x  + 2⋅x  - 5"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAAWBAMAAACcWbe0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$3 x^{2} + 4 x$$"
      ],
      "text/plain": [
       "   2      \n",
       "3⋅x  + 4⋅x"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIQAAAAwBAMAAAAiMc/3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\noNgV9081AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{x^{4}}{4} + \\frac{2 x^{3}}{3} - 5 x$$"
      ],
      "text/plain": [
       " 4      3      \n",
       "x    2⋅x       \n",
       "── + ──── - 5⋅x\n",
       "4     3        "
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "順便畫個圖。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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45Ravqzl1CnwREZGj7N8PvXvDn/8Mf/+719WUDg3pi4iIHOW++yA1Fb78EiIjva6mdCjw\nRUREjjBrlnt97pQpcOGFXldTejSkLyIictDatdC3L3TtCnff7XU1pUuBLyIiAuzdC126QN26MG0a\nGON1RaVLQ/oiIiLAgAFuZv7SpVC1qtfVlD4FvoiIBL3p02HmTPfcfbNmXlfjGxrSFxGRoJaR4Xr3\n/fpBjx5eV+M7CnwREQlaOTnuvn3jxjB5stfV+JaG9EVEJChZC336wE8/wccfQ6VKXlfkWwp8EREJ\nSpMnw9tvwzvvwDnneF2N72lIX0REgs5XX8Fjj7nlbm++2etq/EOBLyIiQeWHH6BTJ2jTBh5/3Otq\n/EeBLyIiQeOXX+DGG6FKFXjxRahQweuK/Ef38EVEJCgUFrqlbr//Hr7+GmrV8roi/1Lgi4hIUHj4\nYXjvPbc1b+51Nf6nwBcRkXLvjTdg/Hh3z/6GG7yuxhu6hy8iIuXasmXQuzfcdhuMHOl1Nd5R4IuI\nSLm1daubpNeihZukV95WwCsJBb6IiJRLe/fCTTdBaKi7b1/e36T3R3QPX0REyh1r3TD+qlXw5ZcQ\nG+t1Rd5T4IuISLnz9NMwaxb861/QsqXX1QQGDemLiEi5Mm2ae2Xus8+6lfDEUeCLiEi58c47cPfd\nbn37e+7xuprAosAXEZFyYcEC6NbN9eqfeSa4Z+QfiwJfRETKvBUr3ON3l14Kr77qZuZLcQp8EREp\n077/Hq6+Gho2dEP6FSt6XVFgUuCLiEiZlZUFiYkQGQlz50LVql5XFLj0WJ6IiJRJOTlwzTXuBTvB\nuPpdSamHLxIAxo0bR0hISLGtadOmxdo89NBD1KlThypVqnDVVVeRmZlZ7PP9+/czYMAAoqOjqVq1\nKl26dOHHH3/052WI+M2vv7q36G3cCPPmQf36XlcU+BT4IgGiWbNmZGdnk5WVRVZWFl9++WXRZxMm\nTODZZ59l2rRpLF26lIiICBITE8nLyytqM2TIEObMmcPbb7/NokWL2LZtG507d/biUkR8qqAAuneH\n1FT48MPgXOr2ZGhIXyRAhIWFUes4Y5LPPPMMY8aM4brrrgPg1VdfJSYmhvfee49bbrmFPXv2MH36\ndN58800uu+wyAGbMmEGTJk1YunQpCQkJfrsOEV+y1j1j//778O67cMklXldUdqiHLxIg1q1bR926\ndTnnnHO47bbb2Lx5MwAbNmwgKyuL9u3bF7WNjIykdevWLF68GIBvvvmG/Pz8Ym0aNWrEWWedVdRG\npDx4+GF44QW38t3113tdTdmiwBcJAG3atGHmzJnMmzePqVOnsmHDBtq1a0dubi5ZWVkYY4iJiSn2\nOzExMWRlZQGQnZ1NeHg4kZGRx20jUtaNHw8ffwxPPAG9enldTdmjIX2RAJCYmFj0fbNmzUhISKBe\nvXrMnj2bxo0be1iZiPeshXHjDm8jRnhdUdmkwBcJQFFRUTRs2JDMzEwuv/xyrLVkZ2cX6+VnZ2fT\n8uAyYLGxseTl5bFnz55ivfzs7GxiT2Bd0KFDhxIVFVVsX1JSEklJSaV0RSInx1oYMwb+9jd49FF4\n4AGvKyq7FPgiAeiXX34hMzOTO+64g7i4OGJjY0lJSeG8884DYM+ePSxZsoQBAwYAEB8fT1hYGCkp\nKdx8880ArF27lk2bNtG2bds/PF9ycjKtWrXy3QWJnARrYdQoN4Q/cSLcd5/XFZVtCnyRADBixAiu\nv/566tWrx9atW3n44YepUKECXbt2Bdwjd+PHj6dBgwbUr1+fMWPGcMYZZ3DjjTcCbhJfnz59GDZs\nGNWrV6dq1aoMGjSIiy++WDP0pUyy1gX8U09BcjIMGeJ1RWWfAl8kAGzZsoVu3brx888/U6tWLS65\n5BJSU1OpWbMmACNHjmTv3r3079+f3bt3c+mll/LRRx8RHh5edIzk5GRCQ0Pp0qUL+/fv5+qrr2bK\nlCleXZLISbPWBfzkyfD3v8PAgV5XVD4Ya60/zuOXk4hIyaSnpxMfH09aWpqG9CUgFBbCvffCc8/B\n88/DXXd5XVFAKJWFftXDFxGRgFBYCHff7Z6xf/FF6NvX64rKFwW+iIh4rqAA7rwTZsyA6dOhZ0+v\nKyp/FPgiIuKp/HzXm3/tNXj1VbjtNq8rKp8U+CIi4pl9+yApCXbvhn/8w30vvqHAFxERT+zc6d6H\nv2IFzJ4NHTt6XVH5psAXERG/++EHuPpq2LEDPv8c9LoI31Pgi4iIX61cCddcAxUrwldfQcOGXlcU\nHLRanoiI+M2CBXDppRATA19/rbD3JwW+iIj4xVtvQWIitG4NCxfCCazrJKVIgS8iIj5VWOiWte3R\nA+65B/79b6ha1euqgo/u4YuIiM/k5rqX6Lz1llvedtQoMKXyolgpKQW+iIj4xObNcOON8N138O67\ncNNNXlcU3BT4IiJS6lJTXcAfmonfooXXFYnu4YuISKl67TW4/HJo0ACWLVPYBwr18EVEpFTk5cGI\nEfDll9Ctm1vetmJFr6uSQxT4IiJyyjZtgltugfR0mDwZ+vfX5LxAo8AXEZFTMmcO3H67e9Tuq6/g\nwgu9rkiORffwRUTkpOTnw+jRcN11cNFFrnevsA9c6uGLiEiJbd/ulrL98kt44gkYPhxC1IUMaAp8\nEREpkZQUNykvLMytdHfppV5XJCdCf4+JiMgJ2bcPhg1zr8i96CJYvlxhX5aohy8iIn8oLc0F/fr1\n7hW5Q4ZoCL+s0X8uERE5rgMH4K9/hTZtoHJlNzFv2DCFfVmkHr6IiBzTmjXucbv0dDcbf8wYqFDB\n66rkZOlvNBERKaaw0L08p2VLyMmBr792vXyFfdmmwBcRkSJr10LfvjB4MNx5p5uYl5DgdVVSGjSk\nLyIi/PorPPYYPP44nHWWe9zu8su9rkpKkwJfRCTIffop3HMPbNwII0fCX/7iJuhJ+aIhfRGRIJWd\nDd27w1VXQe3akJEB48cr7MsrBb6ISJApKIAXXoBGjWDePJgxAxYsgCZNvK5MfElD+iIiQeSTT+C+\n+6B6dejcGSZMgOhor6sSf1APX0QkCPz3v3DNNdChg1vG9vHH4eWXFfbBRIEvIlKObd8O/fpBixaQ\nmQlvvw1ffOHenCfBRUP6IiLlUG4uTJoEEydCxYqQnAx33QXh4V5XJl5R4IuIlCO//govvghz5rhn\n6QcPdq/FrVbN68rEaxrSFxEpB/buhaefhrPPhqFDoWFD99a8J55Q2IujHr6ISBmWmwtTp7qh+x07\n3GI3o0dDgwZeVyaBRoEvIlIG7dnjnqWfOBF27YKePeGBB1wPX+RYFPgiImXIpk3w97/D9OkQGQmd\nOrmgr1fP68ok0CnwRUTKgKVL4amn4K234LTT3Ep2gwbBGWd4XZmUFQp8EZEAlZfnZttPmuTWpD/n\nHPd4Xa9eLvRFSkKBLyISYNatg5degpkz3Vvx6taF996D666D0FCvq5OySoEvIhIA9u+Hd9+FadPc\n8/PVqrkZ9/36QbNmXlcn5YECX0TEI9bCkiXwz3/Chx+69egvvRRefRW6dNEytVK6FPgiIn62apUL\n+TfegPXroU4dGDgQbrpJS9SK7yjwRUT84NDCNW+8ARkZbsi+Sxd3r75dO92bF99T4IuI+EBBAaSm\nuqH6Dz90vfrzz4fGjWHcOLj6areojYi/KPBFRErJL7/A/PnwwQfucbodO6BWLejYER55xK1Fr8fp\nxCsKfBGRk1RQACtWuFn1330Hr7zinp3/05+gb1+4/npo3VrD9RIYFPgiIieosBD++18X8J99BosW\nwe7dbjZ99+5uZbrrr9f77CUwKfBFRI4jNxe++cbdi09Ndb34VasgPBwuusgtQ/vnP0NCgtsnEshC\n/HGSN954wx+nET/Rf8/AN2XKFOLi4qhcuTJt2rRh2bJlXpcU8Pbvh7Q0N2v+wQehVSuIioLLL4fx\n493qdL17Q0qK69V//jk89BBccklghb3+fZY/xpik0jiOAl9KTP89A9usWbMYPnw448aNY/ny5bRo\n0YLExER27NjhdWkBwVrYuhU+/dQtL9uzJ7Ro4SbTXXAB9O/vXm17/vnw3HPuEbrdu13QDx/uevSB\n/EIc/fssl0ol8DWkL1LOJCcn079/f26//XYApk6dypw5c5g+fTojR470uDr/yc11L7VZv969wS4j\nA1avdkPye/a4Nu3bu+9bt4a77oKWLeG886BKFU9LF/EJBb5IOXLgwAHS0tIYPXp00T5jDFdeeSWL\nFy/2sLLSZS3s3Ol66lu3wpYtLrhXrHAB//33kJ19uP2ll8K+fdC0Kdx4o/vatCnExWkGvQQPBb5I\nObJjxw4KCgqIiYkptj8mJoa1a9d6VNWJyctzIf7TT+759R07Dn//00/uEbhVq1y4b90Kv/56+HeN\ncc+679rllpDt0MF9Pfts9/X0010bkWDm88A3xlRp164d6enpvj6V+ElOTo7+e+J6mQUFcOCA2/Ly\nID/fPbqVn+8+Kyhw7QoL3Qbuq7VuA3fvOD8fsrKgevXDxz8UUMa4LeTgjJuQkOL7jvy6e/dPAHz1\n1Rp+/rlC0WcbNmSTk5PLp5+mFzv+unWrAViyZDU7dx6u6VCth67x0NeCguLXd+CA+/7AATfp7cjt\n11+L/xwWBj/+6Ibaf/nl8NdD3zduDCtXFv/fODTUvYK2WjU46yyoVAkuvti9zOb00yEmxn0fHe2O\nfyyHRgGChf59lktRxpgq1tq9p3IQYw/9C/cRY0wrIM2nJxERESnf4q21p/SXnD8Cv0paWlquT08i\nQa2gwA35HmsoeMcONwHrP/9xM60PDQPXr+8mch1SsaLraR/aoqJcj7FyZbdVquS+Vqni9lesCFWr\nut5uhQpuCw93venwcNd7rlDhcE/80H3io3uhxrjj7t8PP/98uId/6J/loZGAI0cHjv7+yDbWwoQJ\ndxAX14xOnUYAkJ9vGTeuI+3adaV9+9uLjmsMbNq0miefvI22bf9B165NMObwuQ+NGhyqPTS0+HVV\nqOCup0IF91nFim6rVMnt1xC6SOmIj4+PB9YEfA//IL+cRMona90ErO+/dyuObdwIP/zgvm7cCJs3\nw7nnuhnY4MImNhZq13Zb8+Zuf3R08a1aNRfsUVGB9Rz1qZo9ezY9e/Zk6tSpJCQkkJyczFtvvcWa\nNWuoVatWsbbp6enEx8fz8cdpJCa28qhiEfkDpfLnsybtScA4cMA9/7xqFaxd67Y1a9zXPXvcvduv\nvnL3bevXh3r14MILD39ft65bV7xmzcP3u4PRLbfcwo4dO3jooYfIzs7m/PPPZ968eb8J+yP9zkci\nUk6ohy+e2LkTli93z0avXOm+rlrlHpVascINbTdq5LbGjd3Xhg3dY1R6Rrr0HOrhp6Wl0aqVevgi\nAUo9fCkb9u1zIb506eEtM9P1zLOzoVkz94az3r3dS0+aNnVD7roHLCJSehT4Uup27oQvvoAFC9zj\nUO++6x7dqljRvcns2mvdYiMXXAANGujFJyIi/uCzO53GmNHGmK+MMbk1atQ4ZpvNmzfTsWNHIiIi\niI2NZeTIkRQemoIsAa9+/fqEhIQcsYVSp84TREfDTTe5oK9fHyZPdiuO7dkDixfDM8+4pUQbNVLY\ne2327NkAXHTRRVpkpwwbN27cUf8WQ2jatKnXZckJ+uKLL7jhhhuoW7cuISEhfPDBB79pY4z5qzFm\nmzFmrzHmE2NMg5Kex5c9/ArAbGAxMPzoDwsLC7n22mupU6cOqampbNu2jR49ehAeHs748eN9WJac\nqvx8WLIEdu82nHfeeDIy+gGWM8+Eyy6rypVXwmWXubCXwDVr1iySk5MBeP3115k/fz6JiYl89913\nREdHe1ydlFSzZs1ISUnh0LyssOO9iUgCTm5uLueffz59+vShU6dOv/ncGHM/MBC4HdgIjAfmGWOa\nWGvzTvhE1lqfbsAd1atXt0ebO3euDQsLsz/99FPRvqlTp9pq1arZAwcO/Ka9eOvHH6199VVru3a1\ntnp19+R3SEh9e8klz9iZM63dsMHrCqWkWrdubbt27WoBm5aWZgsLC23dunXthAkTvC5NSmjs2LG2\nZcuWXpchpcAYY99///1i+4BtwFB7OFcjgX3ALbYEeezZw0upqak0b968WE8iMTGRnJwcvv32W6/K\nkiNkZcGfQqkEAAASyElEQVSUKa63/uc/w+23u8fmBg6E1FT3qtPvv3+c4cOj6dSpFZMmTaKgoMDr\nsuUEHFpkJyEhoWhfeVxkJ5isW7eOunXrcs4553DbbbexefNmr0uSUrBhwwaAWCDl0D5r7R5gCdC2\nJMfybMwnKyvrmAt8HPqsRYsWXpQV9LKy4O23YfZsN/EuNBSuvBL69XNfY2MPtx08eDCtWrWiRo0a\nfP3114waNYqsrCwmTZrk3QXICTm0yM7R82vKwiI78ltt2rRh5syZNGrUiO3btzN27FjatWvHf//7\nXyIiIrwuT05BVlYWuEfbs4/6KBv3h8AJK1HgG2MeA+7/nSYWaGKt/a4kxxVv/fwzfPghzJgBixY9\nAEwA3GNxBQUwb57b3D7D6tWradiwIUOGDCk6RrNmzQgPD6d///489thjVKhQwYMrEQlOiYmJRd83\na9aMhIQE6tWrx+zZs+nVq5eHlUkgKWkPfxIw4w/arD+RA8XGxv5mRnD2wQWsY2NL9EeLnITCQvj0\nU5g+3c2mv+ACiIyEyZPvo3XrXlSrdvzfPfvss4+5PyEhgfz8fDZu3Mi5557ro8qlNERHRxMaGsrO\nnTuL7c/Ozta/v3IgKiqKhg0bkpmZ6XUpcooO/ns0QAzFe/kxwPKSHKtEgW+t/Rn4uSS/czxt27bl\n0UcfZceOHUX38efPn09UVJQeJ/GhjRtdT37mTNi0yb3k5rHH4Lbb3HKjUPPgVnLLly8nJCSE092B\nJIBVqFCB+Ph4li5dWrTPWktKSgqDBg3ysDIpDb/88guZmZncfvvtXpcipyguLg4gC2gPrAQwxkQC\nrYEpJTmWz+7hG2POBGoA9QoKCsjIyACgQYMGRERE0KFDB5o2bUqPHj2YMGEC27dvZ8yYMQwcOFDD\nwaUsLw/+/W94/nlISYGICEhKcm+2a9365N5ol5qaypIlS7jiiiuoWrUqX3/9NcOGDaNHjx5ERUWV\n/kVIqRs2bFhRIGzYsIEXXniBvXv30rNnT28LkxIbMWIE119/PfXq1WPr1q08/PDDVKhQgaSkJK9L\nkxOQm5tLZmZm0SOV69evJyMjgxo1anDmmWcCPA08aIzJxD2W9wiwBXi/RCcqyZT+kmy4of8CoCAk\nJMQe2hYuXFj0qMGmTZtsx44dbUREhD399NPtyJEjbUFBQWk93RD0duyw9tFHra1Tx9pLLrH20kut\nnTHD2l9+OfVjp6en2zZt2tjq1avbKlWq2D/96U92woQJNi8v79QPLn5z//33W8BWrFjRtmnTxi5b\ntszrkuQkdO3a1datW9dWqlTJnnnmmTYpKcmuX7/e67LkBC1YsMAaY+yRWRkSEmJ79ep1qAnAWNzj\neXuBeUADW8Jc1uI55dCaNfD00/Dqq+5efY8eMHiwe2e9yJG0eI5ImaDFc+Qwa91wfXIyzJ3rlpB9\n4AG46y4tfSoiIgr8Mq+wEN55B9580z0/f955blJeUpJbrEZERAR8uHiO+Ja18N57bvW5//s/qFTJ\n9fBXrICePRX2IiJSnHr4ZYy1MGcOPPQQLF8O7dvDl1/CxRd7XZmIiAQy9fDLCGvh44/dY3TXXw9V\nq7r15j/9VGEvIiJ/TIEf4Kw9HOrXXAMVKrifFyxwi9qIiIicCAV+AMvIcG/Au+oq9077jz92w/ft\n25/cy3JERCR4KfAD0E8/ucfpWrWCtDT3lrzUVEhMVNCLiMjJ0aS9AJKX59afHzfO/fzkkzBggBvG\nFxERORUK/ADx0UcwdCisWwd33gl//atemCMiIqVHQ/oeW78e+vSBa6+FOnXco3bPP6+wFxGR0qXA\n90h+Pkyc6N5vv369e0teSop7U56IiEhpU+B7IC0NLrwQRo2Cu++GDz+ETp00IU9ERGDHjh3Url2b\nxx9/vGifMeYiY8x+Y8wVJ3tcBb4f5ebC8OGQkOB+XrLETcw77TRv6xIRkcARHR3N9OnTefjhh0lP\nT8cYcxrwKjDZWvv5yR5Xk/b85LPPXG9+82Z4/HEYMkSz70VE5NiuueYa7rzzTrp16wYwFfgFGH0q\nx1QP38f27XNr0bdvD5dcAv/5D4wYobAXEZHfN3HiRPLz8wG6AN2stQdO5Xjq4fvQN99Ajx6wcSM8\n8wwMHAgh+hNLREROQGZmJtu2bQPXOY8DVp3K8RQ/PpCfD488Am3bQpUqkJ4OgwYp7EVE5MQcOHCA\nHj160LVrV4AxwMvGmOhTOaYiqJStW+eG7seOdbPwFy+GJk28rkpERMqS0aNHs2fPHv7+978DPAGs\nBWacyjE1pF+KXnkFnnsOdu50i9y0bet1RSIiUtYsXLiQyZMns2DBAiIiIrDWWmPM7cAKY0x/a+0L\nJ3NcBX4p2LfPDdm/9BLccw9MmKBH7URE5ORcdtll7N+/v9g+a+0PQPVTOa4C/xRlZsL//R+sWQMv\nvwy9e3tdkYiIyG/pHv4peOcdiI+HX35xy9cq7EVEJFAp8E/CgQPujXmdO8NVV7nH71q08LoqERGR\n49OQfglt2QK33gpLl0Jysnupjt6BLyIigU6BXwJffOF69RUrwsKFcNFFXlckIiJyYjSkf4JeeAGu\nuAJuvNG9SEdhLyIiZYkC/w/k57uFbu66yy1+8/zzUKuW11WJiIiUjIb0f0dODnTtCp98AlOmuGfs\nRUREyiIF/nGsXw/XXw9bt8JHH7nZ+CIiImWVhvSP4YsvICEB9u93z9cr7EVEpKxT4B9l1izo1Ama\nN4clS6BxY68rEhEROXUK/CMkJ7t79j16wLx5ULOm1xWJiIiUDgU+YK1bynbYMLj/fnjySQgP97oq\nERGR0hP0k/by86F/f5g+3QX9sGFeVyQiIlL6gjrw9+1zQ/hz58Krr7qhfBERkfIoaAN/92644Qa3\n8M0HH8A113hdkYiIiO8EZeBv2wZXX+0WwklJgbZtva5IRETEt4Ju0t7GjXDvvbBzp3veXmEvgaB+\n/fqEhIQUbaGhoTzxxBPF2mzevJmOHTsSERFBbGwsI0eOpLCwsFiblStX0q5dOypXrky9evWYOHGi\nPy9DRAJYUPXw1693C+CEhbmwj4vzuiIRxxjD+PHj6devH9ZaAKpWrVr0eWFhIddeey116tQhNTWV\nbdu20aNHD8LDwxk/fjwA//vf/0hMTKRDhw688MIL/Oc//6FXr15Ur16dvn37enJdIhI4gibwv//e\nhX2lSvDZZ3DGGV5XJFLcaaedRq3jrMw0b9481qxZw+eff050dDTNmzfnkUceYdSoUYwdO5awsDD+\n8Y9/cODAAV5++WXCwsJo0qQJy5cv56mnnlLgi0hwDOmvWweXXQaVK8OCBQp7CUyPP/440dHRtGrV\nikmTJlFQUFD0WWpqKs2bNyc6OrpoX2JiIjk5OXz77bdFbdq1a0dYWFixNmvXriUnJ8d/FyIiAanc\n9/DXroU//xkiI13PvnZtrysS+a3BgwfTqlUratSowddff82oUaPIyspi0qRJAGRlZRETE1Psdw79\nnJWVRYsWLcjKyuLss88+bpuoqCg/XImIBKpyHfhr1rhh/Bo13Gz82FivK5Jg8sADDzBhwoTjfm6M\nYfXq1TRs2JAhQ4YU7W/WrBnh4eH079+fxx57jAoVKvijXBEp58pt4K9e7cK+Vi0X9qef7nVFEmzu\nu+8+evXq9bttju6RH5KQkEB+fj4bN27k3HPPJTY2lmXLlhVrk52dDUDswb9kY2Nji/Ydr83xDB06\n9DcjAElJSSQlJf3u74lI2VEuAz8z061ln5AAL7/sQl/E32rWrEnNk1yBafny5YSEhHD6wb9U27Zt\ny6OPPsqOHTuK7uPPnz+fqKgomjZtWtTmwQcfpKCggNDQ0KI2jRo1+sPh/OTkZFq1anVStYpI2VDu\nJu1t2QJXXukevXvpJYW9BL7U1FSeeeYZVq5cyYYNG3j99dcZNmwYPXr0KArqDh060LRpU3r06MHK\nlSuZN28eY8aMYeDAgUVD/t26dSM8PJzevXuzatUqZs2axeTJkxk+fLiXlyciAaJc9fB//NGFvbXw\nyScaxpeyoWLFirz55puMGzeO/fv3ExcXx/Dhwxk6dGhRm5CQEP79739z9913c9FFFxEREUHPnj0Z\nN25cUZvIyEjmz5/PgAEDuOCCC4iOjmbs2LH06dPHi8sSkQBjDr3kw8d8fpLdu909+6ws91KdBg18\nfUaRsi89PZ34+HjS0tI0pC8SuExpHKRc9PBzc6FjR/jhB1i4UGEvIiJytDIf+Pv3w803w8qVbjZ+\n8+ZeVyQiIhJ4ynTg5+dD795uCP+jj9ysfBEREfmtMjtL31oYMADS0+Ff/4LLL/e6IhERkcBVZnv4\njz4K06bB9Olw3XVeVyMiIhLYymQP/5VX4MEHYdw4+IMXmYmIiAhlMPDnz4e+fd02ZozX1YiIiJQN\nZSrwV6yAzp2hQwd4/nkwpfJkooiISPlXZgL/hx/g2muhUSOYNcu9OldEREROTJkI/N27YeBAqFQJ\n5syB007zuiIREZGyJeD7yfn50LWrG85fsABiYryuSEREpOwJ+MC/7z749FP4+GNo3NjrakRERMqm\ngA78F1+EZ56BZ591q+CJiIjIyQnYe/gLF8I998Ddd7s36omIiMjJC8jAX7/ePX7Xrp3r4YuIiMip\nCbjA37MHbrgBqlVz78ivUMHrikRERMq+gLqHX1AA3bvD5s2Qmgo1anhdkYiISPkQUIH/5JMwd657\n1r5JE6+rERERKT8CJvDfegvuv9+9Mvfqq72uRkREpHwJiHv4q1e7Ve9uvRX69/e6GhERkfLH88D/\n3/+gUyc46yx46SUtiCMiIuILng7pW+t69lu3wrJleke+iIiIr3ga+E8+CW+/De+841bBExEREd/w\nbEj/88/dJL1Ro+Dmm72qQkREJDh4Evjbt7veffv28MgjXlQgIiISXPw+pH/o5TqrV7slb8MC5sFA\nERGR8svvcfu3v7l17VNStLa9iIiIv/h1SH/hQhg3Dh56CK64wp9nFhERCW5+C/yffoJu3dwKeGPG\n+OusIiIiAn4K/MJCuOMOyMuD11+H0FB/nFVEREQO8cs9/CefhI8+cludOv44o4iIiBzJLz380aPd\nM/daFEdERMQbfgn8Cy/U8/YiIiJe8kvgf/QRVKjgjzOJiIjIsfgl8KOi/HEWEREROR7Pl8cVERER\n31Pgi4iIBAEFvoiISBBQ4IuIiAQBBb6IiEgQUOCLiIgEAQW+iIhIEFDgi4iIBAEFvoiISBBQ4IuI\niAQBBb6IiEgQUOCLiIgEAQW+iIhIEFDgi4iIBAEFvoiISBBQ4IuIiAQBBb6Ijz366KNcfPHFRERE\nUKNGjWO22bx5Mx07diQiIoLY2FhGjhxJYWFhsTYrV66kXbt2VK5cmXr16jFx4sTfHGfBggXEx8dT\nqVIlGjZsyCuvvOKTaxKRskeBL+JjBw4c4JZbbuHuu+8+5ueFhYVce+215Ofnk5qayiuvvMLMmTN5\n6KGHitr873//IzExkbi4ONLT05k4cSJjx47lpZdeKmqzceNGrrvuOtq3b09GRgaDBw+mb9++fPLJ\nJz6/RhEpA6y1/thEgt7MmTNt9erVf7N/7ty5NiwszP70009F+6ZOnWqrVatmDxw4YK219rnnnrM1\na9Ys+tlaa0eNGmWbNGlS9PPIkSNt8+bNix27a9eu9pprrjluTWlpaRawaWlpJ31dIuJzpZLF6uGL\neCw1NZXmzZsTHR1dtC8xMZGcnBy+/fbbojbt2rUjLCysWJu1a9eSk5NT1ObKK68sduzExEQWL17s\nh6sQkUCnwBfxWFZWFjExMcX2Hfo5KyvrlNvs2bOH/fv3+6R2ESk7FPgiJ+GBBx4gJCTkuFtoaCjf\nffedz+uw1vr8HCJSPhj9H4ZIyRljagI1/6DZemtt/hG/cweQbK0tNlXfGDMOuN5a2+qIffWB9UBL\na22GMeYVoKq1ttMRbS4HUoAa1tocY8xCIM1aO+yINj0PnrP6ca6jFZAGLAJyjvr4DWvtG39wjSJS\nRoT9cRMROZq19mfg51I63GJgtDEm2lq74+C+DrgAXnVEm/HGmFBrbcERbdZaa3OOaHPNUcfucHD/\n8awB4oE11tq9p3gdIhLANKQv4mPGmDONMS2AekCoMabFwS3iYJP5uGB/zRhznjEmEXgEeNZae+Bg\nm38CecB0Y0xTY8ytwCDgySNONRU42xgzwRjTyBhzD9AFeOp4tVlr91pr0xX2IuWfhvRFfMwYMwO4\n/RgfXWGtXXSwzZnA88DlQC4wE3jAWlv09h1jTDNgCnAhsAOYbK2ddNS52gHJQFNgC/BXa+1rpXxJ\nIlIGKfBFRESCgIb0RUREgoACX0REJAgo8EVERIKAAl9ERCQIKPBFRESCgAJfREQkCCjwRUREgoAC\nX0REJAgo8EVERIKAAl9ERCQIKPBFRESCgAJfREQkCPw/LhnRlJqEA9MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c5ce7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x10c5ce048>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-2 微積分"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "第二種設變數的方式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.abc import a, b, c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 微分\n",
    "\n",
    "和剛剛有點不同, 我們指定變數"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = a*x**2 + b*x + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAAQBAMAAAC//t8ZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABK0lEQVQoFWNgVDJ2YMAFWC0XAKXCGNh/4FLB\nwMCdAJRLZWCYiankDlSI/wKQMYuBId8BQw1MSX8AUGp/AD4lVVDN6wMYhIpOBjDEHJM4fgAiBjNl\n2xldkADHdwaOiQz7GVgL+NZwbUBRwvo7IF4AKMKVwBD5gEGZgT2A/SsvSAAIoKbwfmXgLwBylRgY\n9AMY1jCwMnAbgOWrd+9euXv3NiCbaQNDPFAJjwIDw2QG1i9AEf4DQAIMoKZwKzD0X2BguMTAKPqd\ngfcDUMrfAaIAbhH/A5AFLAoMPKJ/GZg3XOQNOM/AEwBRBDWFv4F1HgODVHlRFsMehlcJBf0X7Bnk\noMZAlbA9YFYABt3//78Ywo475jSEnYnRe4CqhFVHDyqASUFNwZRAiAQimAwAh5RLp2SAnDUAAAAA\nSUVORK5CYII=\n",
      "text/latex": [
       "$$2 a x + b$$"
      ],
      "text/plain": [
       "2⋅a⋅x + b"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADkAAAAUBAMAAADFBIheAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJVCLvMs1Edmar\n3bti/yyrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABOUlEQVQoFWNgwADRUJGtGDJAAdYHUFGeACzS\nHDBBxgYsspvgYlZwFoJxFc4Ug7PgDNYLcCbHBAYGIWMVBkarxRMYqrxXACW4FBgYGFcdnQU0lkmB\ngTWFoSygNoDhFeMDBl6gLN8GBgZhhr0LbjAwcDcwcDQw+BdcZmCor0xk4ALK8jowMBgy2Au4MjCw\nXGCQB5rE/oWBgd/g/iuQX9iAlgkw9AFZDOwfGOYvACr6CZR9INz/CSrLwPALKgvXqyrAsB+oD2Qy\nA/t3kCznBZC9DA5JDAzzpyxg4AG6COQqR64PDAvBrmLNZmAOKCtgaGZJZOALYGBgVmDg/ML3gRWo\niMmAgUFGy5SBVdlmAqf1akuIcYynFi7aDWRyFAAJNIAIyVg0GRAXfyyALAcDrDEIj324MqhqCIWU\ncgBCYEPSNlhnwgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "cos(x)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(sin(x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAAqBAMAAAB1rqf/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWYiRInd\nuzLEnmxuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAXUlEQVQYGWNggAFGZRDLJOQzWICNGhSr03cP\nmPGk0//BgHR92HWYpczKTmBg3sBxjKeAgduA+zPjBAZmBvYLYNX8CWDq/QMgxWiQz8BmwLBe4D7D\nDGB4pJlFNDAAAN1MIGxCExJiAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{1}{x}$$"
      ],
      "text/plain": [
       "1\n",
       "─\n",
       "x"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(ln(x), x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 積分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI0AAAAvBAMAAAAspFRzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nlX8AGM22lP8FuiUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{a x^{3}}{3} + \\frac{b x^{2}}{2} + c x$$"
      ],
      "text/plain": [
       "   3      2      \n",
       "a⋅x    b⋅x       \n",
       "──── + ──── + c⋅x\n",
       " 3      2        "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(f,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "設範圍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAUBAMAAADbzbjtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\log{\\left (3 \\right )}$$"
      ],
      "text/plain": [
       "log(3)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(1/x, (x, 1, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAQBAMAAAAG6llRAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEIl2mSJE3e9UMqtmzXCQ\nkgMAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABlSURBVAgdY2AAA2Uv6wUQFrPAXvYECJOL4Q6EASKf\nwplcD7ig7DimAiYoU9pMWRHIZFQ2CYCKpAewKkCYrJ0MIgsgTO4e44MQFgPfBiiDgYFPAc7kADIN\nIDzmCwwiMMNMbA5ABAE+RA6ieYoxNgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$e^{x}$$"
      ],
      "text/plain": [
       " x\n",
       "ℯ "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(exp(x),x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "無窮大符號: oo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAVBAMAAABI7vhRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInarRM2ZVBDdiWbv\nuzJCz3LGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVQYGWNggADG/2DwAcplYHaAsSC0KCqX\nIR2VzzEBlc9WgMrvROUyrEblg7TrAx3wDSrMtIGBa12RtKIAkO8CxJwMDM8ZFjI9ADKZjgIJJSBm\nuMDcACQl9B0YGEC28xkAVQFB/wUG7gVAmm0DfwOQYmD7yMAJYvQ38DsAKQbGbwy7QLQmA88CEM1g\n3zADRN1mYF4AohneL08A0zCC9WgDjAmm2WGuhIkGwhhAGgDwdic2xV4k0wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\sqrt{\\pi}$$"
      ],
      "text/plain": [
       "√π"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(exp(-x**2), (x, -oo, oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 取極限"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(sin(x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpmJdu8QRM1mu90y\nVKvMIHo8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAARklEQVQIHWNgYFRWCWNgYCgV4PjAwMAWycC0\ngIGB6RsDtwMDA+sChvwDDAz5Bgz3GYDUBYYVvAIMHA6c+5iBKp/YyLkzAABmaAxT1tVPwQAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$a$$"
      ],
      "text/plain": [
       "a"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(sin(a*x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-3 求解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAAA/BAMAAAD+lVKYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARM1UEN0y76uZdmYi\nu4n7rLKSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADoElEQVRYCe2ZTWgTQRTHX5JN89E1iXgQTwnB\nag+CgRykpyxKQXppEAueaq+erEXxaAQ9iEiD9dAKYm5SFZq7IMGPgx9oRfAmBkSKCLXaKFRq13nT\nZHdmZ6aZxLRVyIMm/3nz/u83+7qkWwJJ207B1sYH285AMptNbC0WdmVzhLvFUIoL/Qfc5zbGUrvj\nMVl7K9d7sV3iui/M3kUtcM3U33EfsfYWuJEMa2xdT7GWFriDAK8W3xLzNbaBtjbydXt4nnhE7iFL\n0WoKzCLkygBXFQU0rbRHMnV7mLQQuMaVSUvelpw3ugzxvHy3nlXbYZCzi9c7p+DGyuA7A8OpDbkA\nKjt84ez6XPLrJYFz3jBUXDIuEo5dn3sPfcYoGLMlVKpQcaN4YGKHoZto1eL6EqQSz2t+ugEx3zga\nVSHj7iTFQfKDdqjuRqsW904KIFrCclhIPI6kqFK8SLjRCVJ7l9YvJMzMdVQ6XHPo2/p5sf6sFS+h\nURUS7pM5Mi8cF9oN+EWF8PdIYjR+Azwk1WYFdixDzkKjKiR2GJ6H3mrDHqihVed6AW5X4DgpjteQ\n22+gURUybmQVglbD7i8Qqcl9XcTzQmgegqvGcoxIZci45godF7XDcKZKzHrXG67heaG3DLmSb+kF\nkcqQcWHSwnFROyTNMtECd/pCP+b56FkboIk9M2/Ix7O471ZL7XD6YxFLqD38AKXAxaQY+/eKuRYy\n/gnLU63JzdHzerz6y8CKt1aT6694jc3XgZJbc8CV60qT67XprFmuUN/lCiNpN/Evz/nwCMY+AOeZ\n3snUc3Sj/rLkHYHRh/ZjY649lk73TaTTBVIZZ61Uk2T3vvLOsO31ZtxXxvfmx9kMLoxYTcGtcZ/d\neqfoaM68H3O2AhVHcoKxe7icXbifjQJ8TXCdnMVRiJHnu3oonjkMxm5UGsX0nbML3LAFoXGu3llc\nAjjvLIYcxQldu8AN5SH8k2vlLM4BTI41VuWG4N917QLXX1NyD1oMl8c5K2275PMqSB9wnVasOGmx\nK7nWs0u4yaq8IYBvTbXD5PXsEu4JpgkvgwV+LV3p2UVupChth8kZ5Y67oWkXubNuD4+Kqk/kVmra\nBW6gCC/dLpwawH/MmoSuXeCeArgv791ThGhTrq7dyzVHF6fzcu7Txc+X5TtuVtvu5frJg4iCe9C2\nf7gEudK2e7nydp3Pdrmdn6msY3fOsql0Ptedc+dnKuu4nXPepu8lj2zH95LZyh+ULjPJlp5tZAAA\nAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ - \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}, \\quad - \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right ]$$"
      ],
      "text/plain": [
       "⎡  1   √3⋅ⅈ    1   √3⋅ⅈ⎤\n",
       "⎢- ─ - ────, - ─ + ────⎥\n",
       "⎣  2    2      2    2  ⎦"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(x**2 + x + 1, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我們再加一個 y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = symbols('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "聯立方程組假設式子都是等於零。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAVBAMAAAByPkciAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/f+3DHwDQhtktywFkQQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ x : 1, \\quad y : 3\\right \\}$$"
      ],
      "text/plain": [
       "{x: 1, y: 3}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([x - 2*y + 5, x + y -4], [x,y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAyBAMAAABcwnH1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ x : \\frac{3}{a + 2}, \\quad y : \\frac{4 a + 5}{a + 2}\\right \\}$$"
      ],
      "text/plain": [
       "⎧     3       4⋅a + 5⎫\n",
       "⎨x: ─────, y: ───────⎬\n",
       "⎩   a + 2      a + 2 ⎭"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([a*x - 2*y + 5, x + y -4], [x,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-4 矩陣運算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = Matrix([[1,2],[3,4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B = np.matrix([[1,2],[3,4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOBAMAAAAPuiubAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIpm7MhCriUTv3c12VLge\nopIAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABOSURBVAgdY2BUMnZgYAhjYH/BwJDKwDCTgWEWA0Oe\nA8O+ABAJBOsCgATHcxCTKwFEKoEIHgUQeYmBUYCBRYGBR4BBqrwoi4Fh37t3rxgAK5QOlzv7snYA\nAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADMAAAAZBAMAAABuuAtJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAu90iVO8Qq5l2zWYy\niUQbaetyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmUlEQVQoFWMQUjJgwAIeKV1gUMAiDhJiLiBR\nyqJRBq6LJQzZVLYChvsPoAamt39DlmJPYGANgNnFiSLFqsDA/ge7FNc3nFJAw5m+YdcFlHp/AaeU\nOtzxqM5gYOBowCk1A2gmNKDQdLE0MBjjkDrBwDAZuxSz7t12BagUR+mvaqDpMMD1//9/mBRMDIUm\nOb7AuumsSwlXOiwAABrCMVhd5YweAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "[1  2]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.row(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAyBAMAAACqpzYoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhAimburRN3N\ndmbBWFV7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVQoFWOQ//+JAQT0/39kEHZxBbNDXAwZ\nRMAsEOEIZqdXtMDYrBMY9BdAxTkDGBgFoGzGDQycX6Bsnq8INlAf91eYOQwM6xUQ7J0wMxkY2AsQ\n7OtAJtRe5gKGNBjbnYHhGpTNtkmpcgOUzfP//38YG6QRCCBuHjg20KVwN+xAsHklEOy8Ewi2AoLN\nl4BgxzIg2AoINrMDgh3EgGBbzpz5cS7CXiS7GH4g7NL4Pw+hBigMdyd5bOQ0g5SWAOPkO0zUaLsN\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2\\\\4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⎤\n",
       "⎢ ⎥\n",
       "⎣4⎦"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.col(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2],\n",
       "        [4]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "reduced row echelon form 這樣做。第二項資料是 pivot 行。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALUAAAAyBAMAAADoyIf6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiUSZq1TvELvdZiIy\nds1Wk1T5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAADWElEQVRYCbWYO28TQRDHx7Gcu4vzsKBDQPwN\nYqSIklhCokCguIpElQiIoEBKEBESEiguKKCLgigQFKGJqJJ8g7iCJlJS0KRAcQEdBYiXxCPhPzN3\n7GXvzo7XZovd2Zm9383N7ozvTISWKxPNHXyGlGyjB9+TynaaBbPgOMTZrTdGEZPub03FZkcU+5rR\nwlwV0q1olhhfJzTtFWvRkql5SCls78zLBiwubL+kcO8qj8KWu6gW/XDNe47Bhe3NKsWv8Ai2d36S\nn+BfWyU6jYkLm8JNmhag+L13iP2QiG1O7KAkLj6RPoX9lWis5sgu/GLqgPQa70N+e1/A3nFkk3gc\n1DP8LiKZtvFoTjGh9Xlgt8tZbPjtzl7EE9NZQfc8JsNNcK9nsQl7OV1zjckQtnHwZyb7EUnU3OJd\nBJf53FLO4CrROVjc2BwPf4bJqeyg5vEdU9m7H+WqtG5tWbSPifrramfK+Nz7FZ1J751624CQyj5G\ndOfEydjimAgb2ijRYkW1EhMVrT6L/YHubVhLibjaKXu9TNs7juyBGco1LbZWO2UDzKeMW8d++1Uq\n/NBrYz1XDWUjIOsNtXTMHqlS37cYVUXDhn1vw5ENv/r+tGLXadSVvVmiweSrgfG7v0kTCBC3jmOy\nWWnDXqJJRXfObheTYMadjb0qtNpLsJ1j4tdpoNUZDJbc9xK5k2+GATXDob3ca6iB9zK9QkjOe/vm\nepaQH0/pbsNWU4xdJ6S9NGbbFaJwg01aT56F50kWC/v2u0tEllqqneblSIWmy7oabLtCLIxLPJVd\nCPPAsEWy1KILc74Ur1WJCjEUY+dCqMW21DE2ahVclwa/ExUizn4QQsNBfSOy1GJVG4pg0NTVYCey\nIc5e0WVRH7EttZjVhmKS/6TLwU5UiDg7gobj7gtLYaa7yyIj4aPzz2y7QrRgG1SWdBPvEGHetotJ\nFiJLX+T6a959EhWiG7/l3WRC7wy/fbtCdMP2l8AdKwsc7ESF6IYt75qBHnCwpULIjcKuGzYXluig\nMFsqhIHnL+xfxExz3qiPJuk2XpPFzE5vTmz9JpHvpY5/L9PdMNphjbQOPfY7/FIt/ubb9Zat38PA\nXuk929eQEOWrPff7Fbsr7TL6//QfB+XLvf5vhhOH/gJOBwnapPtSPgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\quad \\left [ 0, \\quad 1\\right ]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡1  0⎤, [0, 1]⎞\n",
       "⎜⎢    ⎥        ⎟\n",
       "⎝⎣0  1⎦        ⎠"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.rref()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFkAAAAyBAMAAADFFmoFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nc9m9jmZfHCnfZSJ+KUIvE/eLo6uvmQ96DW582Zh8hgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-2 & 1\\\\\\frac{3}{2} & - \\frac{1}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-2    1  ⎤\n",
       "⎢         ⎥\n",
       "⎣3/2  -1/2⎦"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-2. ,  1. ],\n",
       "        [ 1.5, -0.5]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B**(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAyBAMAAAAOzY77AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhCrmXbNZiK7\n3UTVIrvSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVQ4Ee3UMUsDMRgG4PdyTeU4qieKk9ij\ns+AJ/gMrrvcHBKc6tlNdOtTJwaGbc1d1EZcOLh3cWxx09PwFglhRQeJV+JJ85dLZwSyX5OFNLh8h\nqKpXFDShVISV+l4BQdZ3I6wWyXSuVGhhbTMxtp3a6QH8LzJ51GTWS/BNBvSYPWfy02Ww1pzNAQex\nM3fzmO9BZ+D7AWLDbVhOHblbYJQ4TKVuWweerh25S/gf+l/a1fO+VdDF406mzZo3XTqfmTG9f8Og\nc2fqMe2VWlRPeYitjGFlSFZO4UXMTrR5Y5TfbAsvtAWTGROBtjxSmdi5K2YvsWWyy+zBIgjYtpCf\nx7QdZqcGABnb5reQ32VqfqPRXOvS/dwHzkh+v96Q6hLe19pjZkvaAqUUMzF679OaLEODP3Y/572R\nc97WHzf4VWxtmHPfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 3\\\\2 & 4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  3⎤\n",
       "⎢    ⎥\n",
       "⎣2  4⎦"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAyBAMAAAAOzY77AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhCrmXbNZiK7\n3UTVIrvSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVQ4Ee3UMUsDMRgG4PdyTeU4qieKk9ij\ns+AJ/gMrrvcHBKc6tlNdOtTJwaGbc1d1EZcOLh3cWxx09PwFglhRQeJV+JJ85dLZwSyX5OFNLh8h\nqKpXFDShVISV+l4BQdZ3I6wWyXSuVGhhbTMxtp3a6QH8LzJ51GTWS/BNBvSYPWfy02Ww1pzNAQex\nM3fzmO9BZ+D7AWLDbVhOHblbYJQ4TKVuWweerh25S/gf+l/a1fO+VdDF406mzZo3XTqfmTG9f8Og\nc2fqMe2VWlRPeYitjGFlSFZO4UXMTrR5Y5TfbAsvtAWTGROBtjxSmdi5K2YvsWWyy+zBIgjYtpCf\nx7QdZqcGABnb5reQ32VqfqPRXOvS/dwHzkh+v96Q6hLe19pjZkvaAqUUMzF679OaLEODP3Y/572R\nc97WHzf4VWxtmHPfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 3\\\\2 & 4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  3⎤\n",
       "⎢    ⎥\n",
       "⎣2  4⎦"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOBAMAAAAoFKpzAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEM3dMiKZu6uJRO92VKoV\n2MsAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABeSURBVAgdY2CAAta0cgcYm4FBgoHzFYLXyMCwG8Hb\nzMDQh1CqJ4DMA6qyE0AoZeB6icRhYG5gYBAyBgEVoHAashRPAjLvGgNrAJzPksDAg+AFz5zWDJdi\n0Hv37jEDAGBWEJ9xq8kjAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$-2$$"
      ],
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASoAAAA/BAMAAACleJiAAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ \\frac{5}{2} + \\frac{\\sqrt{33}}{2} : 1, \\quad - \\frac{\\sqrt{33}}{2} + \\frac{5}{2} : 1\\right \\}$$"
      ],
      "text/plain": [
       "⎧5   √33       √33   5   ⎫\n",
       "⎨─ + ───: 1, - ─── + ─: 1⎬\n",
       "⎩2    2         2    2   ⎭"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.eigenvals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "符號也可以的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v = Matrix([[x,y]]).T\n",
    "\n",
    "# v = Matrix([[x],[y]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFEAAAAyBAMAAADWwSrxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n2n3/CfwGnjqXK79LumsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x + 2 y\\\\3 x + 4 y\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡ x + 2⋅y ⎤\n",
       "⎢         ⎥\n",
       "⎣3⋅x + 4⋅y⎦"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-5 解微分方程\n",
    "\n",
    "我們來解 $$y'' + y =0$$ 這個微分方程式。聽說解是長這樣:\n",
    "\n",
    "$$A \\sin(x) + B \\cos(x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先, 我們先來告訴 SymPy, f 是個函數。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = symbols('f', cls=Function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAArBAMAAAA6dJN0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
      "text/latex": [
       "$$\\frac{d}{d x} f{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "d       \n",
       "──(f(x))\n",
       "dx      "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x).diff(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEgAAAAvBAMAAACyMpGWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nayxWv8rUDvcPkHqVnKurwLUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{d^{2}}{d x^{2}}  f{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "  2      \n",
       " d       \n",
       "───(f(x))\n",
       "  2      \n",
       "dx       "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x).diff(x,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "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)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(f(x).diff(x,x)+f(x), f(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-6 代入"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eq = (x+1)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAbBAMAAAAzEOSeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRklEQVQoFWNgIAC2mh4goIKBW4DXgZAaNgG+\njwTVLGD8RUgNAwPHH8Jq2AoIq9kKVMKoACSwAkWQKFMAkBDGKg8S5BUAEqsZ1jEwOGJVwzGHgYHH\ngYGBz6PDBmIWQlk7hHk2FuSb7QwMnP//f2BgAxmIAFA1DOwgNSeh4mIIeRALRQ3LAohkKZA6XitV\nDQ0FFDWsID8BgRHQbRuY0tkcwDxUc5igghkMDNwHuP9wQJ2FYg5HAkTjLKA5DCwGYM4WF5dMFxdf\nEBvsZr4PcDUMDPwFEA6am2FqgHYxMLx/gFUNVwJEGOhmjgP1DOwHIFwU9zA5QASB0bq+wZ5BCMJD\n9RfrBojoMgaGs+XHgxRQ1bDe/HKJgYHlAUQUR1yAJWFxAE4fUEOA1EEEExynEK4hsigKG5Q2IAB3\nGmMWgKlhVICx0GlFqAAAVSNDOSl9DosAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left(x + 1\\right)^{2}$$"
      ],
      "text/plain": [
       "       2\n",
       "(x + 1) "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGgAAAAbBAMAAABihNf9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nOmCPi7tUbgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left(a + b + 1\\right)^{2}$$"
      ],
      "text/plain": [
       "           2\n",
       "(a + b + 1) "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq.subs(x, (a+b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAPBAMAAAD0aukfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJMkS7\nIt2ZnNffAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAcElEQVQIHWNgAAPOabOANKMyAwNzNUM4A4NJ\nyGcGBp4AhjNAUTYgc/8FsDIQ8xCYBRb9vjJ1A0QB8/cGBkUo878BQ5ABRNs/BoZ+oAqQtudAZgOE\n6YQQXQ9UC9HGwDKBGWgCq9N3DwaGqSELgKJwAADSWSGR+xZb5QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$16$$"
      ],
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq.subs(x, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAbBAMAAAAzEOSeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABPklEQVQoFWNgIAC2mh4goIKBW4DXgZAaNgG+\njwTVLGD8RUgNAwPHH8Jq2AoIq9kKVMKoACSwAiYBoDBTAJAQxioPFrwIJFczrGNgcAQyOg+AxdCJ\nIwwMfB4dNiCzeK7eh6lpR1HGXcDA+f//BwY2kKX12NXwTIBoEQNRONQweEHUlGJVU/////+vDAyh\nEDVG2NRw72sXKgQ6QgWiJgObmhcMG9kfACXaQJIMDLNABMQ9W1xcMl1cfEECDAa8B4DkexATRQ2Q\nB/M73wU2kCRUDVa7GFgV+A8A1SwDKWRgwOpmhvMH+BcAJaFuBkUrZviUMXBuAIpHgyQhxsXO91UA\nc+DuMWLgBanxg4iC4wLCBJIwN0MEGBMgNDh9QJhA8iCcBWIA4xQCDKE0FgqYNiAATxqDa2dUgCrG\noMBpFSgKAGCCRyOZiumVAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left(1 + \\pi\\right)^{2}$$"
      ],
      "text/plain": [
       "       2\n",
       "(1 + π) "
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq.subs(x,pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-7 畫圖\n",
    "\n",
    "之前我們簡單畫過一個圖, 我們再深入研究一點。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6g6ws8rStXjhqGu0WOTEfnwWfOY1ecCckxPp7jx9Pgs/n+PZn+XIqUTpkiPX3vuACKvhT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\nF8CCzzAMwzAu4P8BZQlxPw80krEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe08470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x10fd38160>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sin(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "限制範圍。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KoCCgbVsWafqbUlIUuH6BNURFAQcOcNc6co5bijSv0q3FsY43ESBdHwcPsj/a\nKjgLg1xR5iLtGDUaEeGOOOQO0dFyYma/NAFSDAxDBi2RftWrS2sXizQ5o8xFeu9eabrhVbp18Eqd\nLpWaCrRpI1P0yBoc/dJEJSlzkU5NlV85P9o6goLkpMx+aQI4P9qKoqKkpWvfPt1JyOrcUqRbteJ6\n3VbjWMebfNvBg7IzHYu0tTi6B3k3TSUpc5FOS+MJwIqio4EjR6Q7gnxXWpr8yjEj1lKrltzcsEhT\nScpUpDMzgR07WKStqEcP4OzZv0/S5JtSU4FrrwWCg3UnoX9ivzQ5o0xFmlfp1lWrlpycHWMGyDex\nP9q6oqKAXbuAjAzdScjKylSkU1OBpk2BevXcFYfcKTKSd9K+7PBh2UOaRdqaHH8vvJCm4pT5Tpon\nAOuKiJCNFQ4d0p2EdHBcoHGlMWsKDuaGOFSyUhfpY8eAjRtZpK3M0Q2xbJneHKRHairQqBHQoIHu\nJFSU0FB+P6l4pS7Sy5fLamPsj7auBg3kJM3mNN/E/mjri4yULokjR3QnIasqdZFOS5O+6CZN3BmH\n3I390r7pxAlgwwYWaatjaxeVpNRF2nGVbhjujEPuFhEhJ+uTJ3UnIU9asQLIz2eRtrqGDYGrruKF\nNBWtVEX6zBlg7Vo2ddtBZKScrFes0J2EPCk1FahbF7j6at1JqCQREeySoqKVqkivWgXk5vIq3Q6u\nuQaoU4cnAV/Dli77iIwE1q0DTp/WnYSsqFRFOjVV1upu0cLdccjdDIP90r7m7FlgzRpeRNtFRASQ\nlwf88ovuJGRFpS7SPXoAfmVe+Zs8ISICWL0aOHdOdxLyhF9+AXJyWKTtolkzWSGQrV1UGJfL7IUL\nchLgCcA+IiPl7231at1JyBMcLV0tW+pOQs4wDLmQZmsXFcblIp2eDmRns0jbSevWQNWqvFL3Famp\nctJnS5d9RETIzc/587qTkNW4/DVOTQUCA4H27c2IQ2bw95fuCV6pe7+cHGDlSl5E201kpHRHpafr\nTkJW43KRTksDunUDypUzIw6ZJSJCpmHl5upOQmbaskVO9izS9tK2LXDFFWztosu5VKTz8mRlHJ4A\n7CcyUqZ4bNigOwmZaeNGIDoaaNdOdxJyRblyQPfubO2iy7lUpDdtkuUGWaTtp0MHICCAV+rebvVq\noEIFtnTZUUSE7ImQl6c7CVmJS0U6NVVOAJ06mRWHzFKhAtClC6/Uvd2vv3IlQLuKiJCboE2bdCch\nK3GpSKcMa2wJAAAgAElEQVSlSYEOCDArDpnJMc0jP193EjLLmTMs0nbVqZNcTPNCmi7ldJFWilvf\n2V1kpGyJt22b7iRklnLl2NJlVwEB8nfHLim6lNNFescO4NAhXqXbWZcuMh2LJwHv1bIlUKmS7hRU\nWo4lfJXSnYSswukinZYmiyN061b866ZNm1bWTD5Bx8/piiuA8HB7Nad5y7+nCRMmoHHjxqhUqRK6\ndOmCNWvWFPv65ORkhIeHIyAgAKGhofjiiy+Kfb3jpM71C0pm5X9TERFAVhawc6fuJNb+OVmJ2T8n\np4t0aqqcAKpWLf51/It1jq6fk2NbPLtcqXvDv6cZM2bg8ccfx8svv4z169ejbdu26N27Nw4fPlzo\n6/fs2YN+/fohNjYWv/76Kx555BHcfffdWLx4cZHH2L9ffmWRLpmV/0116yY3Q1a4kLbyz8lKLFWk\n2dRtf5GRwIEDwN69upP4jvHjx2PUqFEYPnw4mjVrho8//hiVK1fGZ599VujrP/roIzRp0gTjxo3D\ntddeiwceeACDBg3C+PHjizzG+vXya9u2ZvwJyFOqVgVuuQXYvl13ErIKp4v03r0cNOYNuneXX61w\npe4LcnJykJ6ejtjY2IvPGYaBuLg4rFy5stD3/PLLL4iLiyvwXO/evYt8PfB3ka5SpeyZSa/gYGDm\nTN0pyCpcmoLVo4dZMchTatYE+vXjCG9POXz4MPLy8hAcHFzg+eDgYGRmZhb6nszMzEJff/LkSZwv\nYgcGR5Em+4uIAP74Q1q8iJxal8gwjMqNGqVj//6/+76KcuLECaxbt84d2byazp9TQADw9dfAwIFa\nDu8Su/97+uuvvwAA27ZtQ/ny5S8+n5WVhTNnzhT6Zzt//jwOHjxY4Pd27doFAFi/fj0qVKjwj2MA\nBw5sBQBs3brV7X8Gb2P1f1PVqsmvU6cC112nL4fVf05W4czP6dQpIDo6PAzANqXUWVc+31BOjCAy\nDCMMAPdnISIiKr1wpZRLVz7OFunK6enpZ0odiywlKwvo0wcYNw64pKuUTHLHHXegVatWePLJJwEA\nSin07dsXt956K4YPH37Z69977z2sWLEC06dPv/jcs88+i9OnT+O999677PVvvgkkJ2/FoUO346uv\nvkLz5s3N+8OQR/znP9KFwb5p+zt6FIiPB2QCrOt30k41d7v6oWR9jRtLn1dYmO4k3u+FF17AiBEj\nkJCQgE6dOmH8+PHIycnBc889h9q1a2Ps2LHIyMi4OBf6pZdeQuvWrTFjxgzceeedSExMRFJSEubP\nn4+wQv7Ctm2ThWp+/BFo3rx5oa8hexkwAJg9G7jqKqBWLd1pqCxmz5ZfXb2DdnB5P2nyDo6Vjch8\ngwcPxv/93//hxRdfRPv27bFx40YsWrQItWvXBiADxfZfMtijUaNGmDdvHpYsWYJ27dph/PjxmDx5\n8mUjvgHg2DHZkIHzo72LY7rrsmV6c1DZpaUBjRqV/v1ONXf/j02WvyBnTJ4M3HuvNMU4BqqQ/cyd\nC1x/PfDDD+vQv3840tPTeSftJRo1kjvqt9/WnYTKIjxcluudOhVGad7PO2kfFREhu2GtWKE7CZVF\nWhoQEgLUr687CbkbW7vs7+RJYMOGsq0xwiLto665RhZN4EnA3tLS5ILLKNU1OllZRASwbp1M3yF7\nWrFCbobKslqn6UV63rx56NKlCypXroygoCAMGDDA7EPa1oULF9CuXTv4+flh48aNph7LMP5ex9sO\n9u7di7vvvhtNmjRB5cqVcc011+Cll15CTk6O7mjanD0LrF0LKDUB119/PQAZSV7S5h2+5vXXX0en\nTp1QtWpVBAcH46abbsKOHTt0xypRZKSc4ItZaM5Ub7zxBvz8/PDYY4/pCWBhGRkZGDZsGGrVqoXK\nlSujbdu2hc6VTksD6tQBQkNLfyxTi/SsWbMwfPhw3HXXXdi0aRNWrFiB2267zcxD2tpTTz2F+vXr\nw/DQbVFkJLBmDZCd7ZHDlcm2bduglMKkSZOwZcsWjB8/Hh9//DGee+453dG0WbUKyMmZgTlzHseo\nUaMAAKGhocVu3uGL0tLS8NBDD2HVqlVYsmQJcnJy0KtXL2Rb/B9+aKic4HVcSK9ZswYTJ05EWy4G\nf5njx4+je/fuqFixIhYtWoStW7fiv//9L2rUqHHZax17XpTplK6UcvbhktzcXFW/fn01ZcoUV9/q\nk+bPn69atGihtm7dqgzDUL/++qvpx1y/XilAqeRk0w9lirfeeks1bdpUdwxtXn5ZKX//zuqhhx5W\n6enpCoBau3atuvLKK9Wbb76pO55l/fXXX8owDJWWlqY7SokGDlQqIsKzxzx16pQKDQ1ViYmJKjo6\nWo0ZM8azASzu6aefVpGRkSW+LjtbqQoVlHr33YtPuVJvLz5Mu5Net24dMjIyAABhYWGoV68e+vTp\ng82bN5t1SNvKysrCvffei6+++gqVKlXy2HFbt5Zdd+zaL338+HEEBQXpjqFNSkoO8vPTERfn/OYd\nJP9uDMOwxb+dyEhg9Wrg3DnPHfOBBx7A9ddfj549e3ruoDby008/oUOHDhg8eDCCg4MRFhaGTz/9\n9LLXrV4NXLhQ9o2pTCvSu3fvhlIKL7/8Ml588UXMmzcPNWrUQHR0NI4fP27WYW1p5MiRGD16NNp7\neLKrv79smmLHIr1r1y588MEHuO+++3RH0SI3F1i58jAA1zbv8HVKKTz66KPo0aMHWrRooTtOiSIi\ngPPnpVvKE6ZPn44NGzbg9ddf98wBbWj37t346KOPcO211+Lnn3/G/fffj4cffhhffvllgdelpclN\nUOvWZTuey0V67Nix8PPzK/Lh7++PHTt2ID8/HwDw/PPPo3///mjfvj2mTJkCwzDw3XfflS21DTj7\nc3rvvfdw+vRpPP300wDkJOJJEREyAjE316OHvcjZn9OlDh48iISEBNxyyy2488479QTXbP16e4wl\nsJrRo0djy5YtBZZctbI2beRE74l+6QMHDuDRRx/F119/XWAzGCooPz8f4eHh+Pe//422bdvinnvu\nwT333IOPP/64wOtSU+UmyN+/bMdzalnQSz3xxBMYOXJksa9p0qTJxabuS9cRrlChApo0aYJ9+/a5\neljbcebn1LhxYyxduhQrV65ExYoVC/xehw4dMHToUEyZMsXMmIiMBMaOlbl8HTqYeqhCOfvvySEj\nIwM9e/ZEjx498Mknn5gdz7JSU4GAgFrIzfVHVlYW6l8yUTorKwt169bVmM6aHnzwQcyfPx9paWkI\nCQnRHccp/v6yB7wnWrvS09Px119/ISws7OLNQl5eHlJTU/HBBx/g/PnzHhvUamUhISGXrY/fvHlz\nzHas/wm56VmxAnDHuFaXi3TNmjVRs2bNEl8XHh6OihUrYvv27ejWrRsAICcnB3v27EHDhg1dT2oz\nzv6c3n//ffznP/+5+P8ZGRno3bs3vv32W3Tq1MnMiACkMAcEyElfR5F29ucEyB10z5490bFjR3z2\n2WcmJ7O2tDSgS5fyyM4OR2JiIu644w4A0hKTmJiIhx9+WHNCa3nwwQcxZ84cpKSk4KqrrtIdxyWR\nkbLhRm4uUM7lM7bz4uLisGnTpgLPjRgxAs2bN8czzzzDAv0/3bt3x/bt2ws8t3379gJ1bcMG4PTp\nsvdHA6Uo0s6qUqUK7rvvPvzrX/9C/fr10bBhQ4wbNw6GYeDmm28267C2U/8fS0UFBgZCKYUmTZqg\nXr16ph+/QgXZnCEtDbDydMiMjAxER0ejcePGGDduHA4dOnTx9/7ZJ+vt8vNlgYt+/YAGDR7DiBEj\nLl7ovPbaazh79ixGjBihN6SFjB49GtOmTcOPP/6IwMBAZGVlAQCqVauGgIAAzelK5qnWrsDAwMv6\n6QMDA1GzZk3urHaJMWPGoHv37nj99dcxePBgrFq1Cp9++ikmTZp08TVpaXLz45a/LxeGgrssNzdX\nPfnkk6pu3bqqWrVqqlevXmrLli2l+SifsWfPHuXn5+eRKVgOL7ygVM2aSuXne+yQLvv888+Vn59f\ngYdhGMrPz093NI/77TeZOrdkifz/hAkTVEhIiAKgWrdurdasWaM3oMU4/p388/HFF1/ojuaU8+eV\nCghQ6u23PX/smJgYTsEqxLx581Tr1q1VpUqVVIsWLdTkyZML/H7//kpFR1/2tlJNweIGG4TFi4Fe\nvYDNmwEbDHj1eR9+CDzyCHD8OBAYKM+tW7cO4eHcYMNbxcQA1asD33+vOwmVRCmgdm1g9GjglVcK\n/BY32KDS6dpVBqjYcSqWL3KMH3AUaPJ+js02/jdphixs61bgyBH39EcDLNIE4IorgLAw+6zj7cuU\nkr+nqCjdSciTIiLkxL9tm+4kVJK0NBng17Wrez6PRZoAyFVfaqoUAbKuXbuAP/9031U62UPXrnLi\n54W09aWmyk2Pu1q6WKQJgFypHzgA7N2rOwkVJzUV8POTubPkOwID2dplB46WLndeRLNIEwBZGQdg\nv7TVpaYC7doB1arpTkKextYu69u7V252yrJ/9D+xSBMAoGZNoGVLFmmrS0lhU7eviowEDh4E9uzR\nnYSK4jh/Om563IFFmi6KiGBzmpXt3SsPFmnf5Oji4HfUulJTgVatAHdusMYiTRdFRgLbtwOXLOZF\nFuK4SndnUxrZR1CQ7KjE1i7rSktz/0U0izRd1KOHXK3/8ovuJFSYlBTpkqhVS3cS0sXRL03Wk5Ul\nNznuvohmkaaLGjSQ6T2JibqTUGHcPWqU7CciAti5E+B24dZjVksXizQVEBUFJCfrTkH/9OefwI4d\nXMTE1zkKAJu8rSctDWjaFLjySvd+Los0FRAdDWzaBBw9qjsJXYr90QQA9epJIWCTt/Wkpprz/WSR\npgKiov6ekE/WkZoKXH21nKTJtznW8SbrOHEC+PXXgt1Rhw8fRkhICN54442LzxmG0c0wjPOGYcQ4\n+9ks0lRAw4ZAo0Zs8raalBQ2dZOIjAQ2bgSOHdOdhByWL5cV4S69k65VqxY+++wz/Otf/8K6detg\nGMYVAKYCeE8ptdTZz2aRpstERUlRIGs4cgT47TcOGiMRESGtXcuX605CDkuXymC+pk0LPp+QkIB7\n770Xt912GwB8DOA0gGdd+WwWabpMdLQ03fBK3RqWLZNfWaQJAJo0kW4PNnlbR0qKnDeNQnaMfuut\nt5CbmwsAgwDcppTKceWzWaTpMo5+aZ4ErCElBbjqKumGIDIMrg5oJSdPAunpUqQLs2vXLmRkZABS\nbxu7+vks0nSZRo2kKLBf2ho4P5r+KTISWLsWOHNGdxJatgzIzy98zEhOTg6GDRuGW2+9FQBeADDZ\nMAyXliNikabLGAb7pa3i5Elg/XoWaSooOlqavVeu1J2EkpOl++Hqqy//vWeffRYnT57E+++/DwDj\nAGwHMMWVz2eRpkJFR0txOH5cdxLftnx50Vfp5LuaN5fv5lKnxwiTWZKTC++PTklJwXvvvYevvvoK\ngYGBUEopAMMB9DAMY5Szn1/OnWHJezj6pZctA/r1053Gd6WmAsHBwDXX6E5CVmIYUhhYpPU6eRJY\ntw64557Lfy8qKgrnz58v8JxSai+AGq4cg3fSVKgmTYD69dkvrVtqqlwwFTZqlHxbTAywZg1w6pTu\nJL5r+XIgL8/cli4WaSoU+6X1O3tWTsLsj6bCxMQAubl/T9Ejz0tOBkJCzG3pYpGmIkVHS1POiRO6\nk/imX34BcnJYpKlwoaEyYIlN3voU1R/tTizSVKSoKBm0xJWN9EhNBYKCZA9pon8yDLmbZpHW49Sp\n4udHuwuLNBXJsaED+6X12L8fuPFGwI/fUipCTIy0dnEWhuc5+qNZpEkb9kvrk50NfP010Lat7iRk\nZTEx0trF1cc8LzkZqFvX/JkXLNJUrOhoadLhCFLPWrkSOH8e6NlTdxKyssaNZec6Nnl7nif6owEW\naSpBVJQ06bBf2rOSkoDatdkfTcVjv7Qep07JsqxmN3UDLNJUgtBQadJhv7RnJSXJyZf90VSSmBjZ\nte7wYd1JfMeKFZ7pjwZYpKkE7Jf2vFOngNWr2dRNzomJkV/5HfUcR390aKj5x2KRphJFR8uiGqdP\n607iG5Ytk6t0x8mXqDgNGgBNm7LJ25OSkz23EiCLNJXI0S+9YoXuJL4hKQm48kqu103O69mTRdpT\nTp+WmxZPNHUDLNLkhGbNgDp12C/tKUlJctLlet3krJgYYMsWIDNTdxLv56n50Q4s0lQi9kt7ztGj\nskUo+6PJFY6CwQtp86WkyM50117rmeOxSJNToqNlMNOZM7qTeLeUFNkilP3R5IqQEGnxYpO3+TzZ\nHw2wSJOToqJkx52VK3Un8W5JSTIIqGFD3UnIbtgvbT5P90cDLNLkpBYtgC5dZJ1gMo+jP5rIVTEx\nwM6dwIEDupN4r+XL5WaFRZosxzDk7m7WLN1JvFdmpgz+YZGm0nAUDt5NmycpCejYUboWPIVFmpwW\nHy9L4R07pjuJd3KcXNkfTaVRqxbQujWLtJkSE2UBE0/OvGCRJqfFxcmOO0lJupN4p6QkWas7OFh3\nErIrruNtniNHpLsvLs6zx2WRJqc1bCgLbCxZojuJd2J/NJVVz57Anj3AH3/oTuJ9li6VmRcs0mRp\n8fHA4sW6U3ifvXuB3btZpKlsIiOlKZZ30+63ZIn0Rdev79njskiTS+Ljgd9/55W6uy1d+veiMUSl\nVaMG0L49i7QZFi/2/F00wCJNLoqOlu0TeTftXklJcnKtUUN3ErI7R7+0UrqTeI/du+XBIk2WV706\n0KkT+6XdSSn2R5P79OwJHDwoc6bJPRITAX9/z86PdmCRJpfFx8s/2rw83Um8w86dclJlkSZ3iIiQ\ngsImb/dZskRuTqpV8/yxWaTJZfHxf28EQWWXlASUKwf06KE7CXmDKlWADh1YpN0lP19uSnQ0dQMs\n0lQKnTsDgYFs8naXpCS5Sq9SRXcS8hbsl3afX3+VOdIs0mQbFSpI3wwHj5Vdfr6cTNnUTe4UEwMc\nOiTLzFLZLF4MVK4sexfowCJNpRIfDyxbBpw9qzuJvf32G3D4MIs0uVf37kD58mzydoclS2RqZIUK\neo7PIk2lEh8PXLgApKXpTmJvSUlAxYpA1666k5A3CQwE+vUDtm/XncTezp2Tc5yupm6ARZpKqXlz\noF499kuX1ebNchcdEKA7CXmb9u2BqVOBnBzdSexrxQop1PHx+jKwSFOpGIZcXbJfuvTOnwemTZMp\nM0TulpAAnDwphYZKZ8kSoE4doFUrfRlYpKnU4uNl5GNWlu4k1nXs2DEMHToU1apVQ40aNXD33Xfj\nzJkzAKQZ7cwZoE+fgu8ZOXIk/Pz8Cjz6/PNFRCUIC5MCs2CB7iT2tWSJ3Ix4cmvKf2KRplJz9NMk\nJurNYWW33XYbtm7disTERMybNw+pqakYNWoUADl51qsHtGlz+fsSEhKQlZWFzMxMZGZmYtq0aR5O\nTnbn5wdcdx0wf77uJPZ09Ciwdq3e/miARZrKoG5d2WSe/dKF27ZtGxYtWoTJkyejQ4cO6NatG95/\n/31Mnz4dmZmZmD9fmiQLu0qvWLEiateujTp16qBOnTqopmOpI7K9hARg0ybgwAHdSexH19aU/8Qi\nTWXi6JfmogmXW7lyJWrUqIH27dtffC4uLg6GYeDHH1dh2zY5iRYmOTkZwcHBaNasGUaPHo2jR496\nKDV5k1695I564ULdSexnyRLg2muBBg305mCRpjKJj5erdE71uFxmZibq1KlT4Dl/f38EBQUhOTkT\n5coVfpWekJCAqVOnIikpCePGjUNKSgr69OkDxSshclFQkCzCwSZv1zn6o3VjkaYyiYyUSf6+1OQ9\nduzYywZ2Xfrw9/fHjh07iv2M336TBScKa8UePHgw+vXrh5YtW+KGG27A3LlzsXr1aiQnJ5vzByKv\nlpAg388LF3QnsY89e4Bdu6xRpMvpDkD2FhgIdOsmTd4PPqg7jWc88cQTGDlyZLGvadKkCerWrYtD\nhw4VeD4vLw9Hjx7F8eN18corzh2vcePGqFWrFnbt2oWYmJhiXztmzJjL+q+HDBmCIUOGOHcw8jp9\n+gAvvCBTsXRstWhHS5ZIN4EVfl4s0lRmcXHAm2/Kognly+tOY76aNWuiZs2aJb6ua9euOH78ONav\nX3+xXzoxMRH5+Qq5uZ0vm3pVlAMHDuDIkSMICQkp8bXjx49HWFiYcx9MPqFdOyA4WJq8rVB07GDJ\nEqBjR6B6dd1J2NxNbhAfD5w6BaxerTuJtTRr1gy9e/fGPffcgzVr1mD58uV46KGHEBo6BFdeWffi\nAgnNmjXDnDlzAABnzpzBU089hVWrVmHv3r1ITExE//79ERoait69e2v805BdOaZicb60c3JzZV+C\ngQN1JxEs0lRm4eFAjRq+1S/trG+++QbNmjVDXFwc+vXrh8jISOTlfVJg6tXOnTtx4sQJADKwbOPG\njbjxxhtx7bXX4p577kHHjh2RmpqK8r7QTEGm6NNHxkHs3687ifX98gtw8KB1VgI0XBgxyqGlVKRB\ng4DMTLkCpaLt3g00bQrMng3cdJP7PnfdunUIDw9Heno6m7vpMseOAbVqAR99BNx7r+401jZ2LPDp\np3I+8/d360eXat0y3kmTW8TFyRXoyZO6k1jbggVAuXJAbKzuJORLatSQAZ5s8i7ZvHkyIt7NBbrU\nWKTJLeLjgR49AM4SKt6CBfJzqlpVdxLyNZyKVbJ9+2SFtr59dSf5G4s0uUXTptI89OOPupNY17lz\nsn8098ogHRISgNOn2SVVnPnz5Q7aSmM0WaTJbfr1k6ai/HzdSawpJQXIzi56KVAiM7VrB4SEsMm7\nOPPmSUuXFaZeObBIk9tcf73cTa9bpzuJNS1YANSvD7RsqTsJ+SLD4K5YxcnOlh39rNTUDbBIkxt1\n6yZXoHPn6k5iTQsWSFO3zr1pybclJABbtkjfKxWUnCyFmkWavFb58nKl/tNPupNYz++/Azt2sKmb\n9IqPlz5XNnlfbt48oFEjoHlz3UkKYpEmt+rXT5q7Dx7UncRaFiyQixhOvSKdqleXFi82eReklBTp\nvn2t19LFIk1ulZAgyxDyJFDQggWyglGVKrqTkK9LSJC+1/PndSexjq1bZecrqzV1AyzS5GZBQbIF\nI/ul/5adLVOv2NRNVtCnD3DmDJCWpjuJdcybB1SqZM0NSFikye369ZOtK7OzdSexhpQUmSPNIk1W\n0KYNUK8e+6UvNW+edEVVqqQ7yeVYpMnt+vWTAr10qe4k1rBgAXDVVUCLFrqTEEmfa0ICi7TD8eOy\nwIsVm7oBFmkyQfPmQOPGbPJ2mD8fBXa9ItItIeHvflhf9/PPQF6edVcCZJEmtzMMWdhk7lwZNenL\ndu2SB5u6yUri4mSjF95NS1N369bS2mVFLNJkin79ZO/aTZt0J9GLU6/IiqpVkwGevl6k8/LkZ2DV\npm6ARZpMEhkJXHEFFzbZtAno319+FkRW4piKde6c7iT6rF0LHD3KIk0+qGJFoFcv3+6XPnYMmDJF\nLliIrCYhAWjQwLd3xfr+exk/06WL7iRFY5Em09xyi1ylZ2ToTqLHDz9Ic9rAgbqTEF2udWtZ0GTm\nTN1J9FAKmDVL5kaXK6c7TdFYpMk0cXHAb7/J1aov+u47WWUsJER3EqLLGQYwaJB8P/PydKfxvN9+\nk0GdVr+IZpEm0wQFyYApX7xSP3pUFnQZPFh3EqKiDRwIHDrkm03es2bJALqePXUnKR6LNJnq5puB\n1FQgK0t3Es+aM4dN3WR9nTrJHuezZulO4nmzZslU0QoVdCcpHos0merGG6VZzdeavL/9VgaM1a2r\nOwlR0fz8gAEDpGDl5+tO4zk7dkhztx0uolmkyVS1agExMb7V5H30KLBkibQiEFndoEEyuHPVKt1J\nPGf2bKByZZmBYnUs0mS6QYOA5GTgr790J/EMjuomO+nWDQgO9q0L6VmzZBnQypV1JykZizSZ7qab\nZLrDnDm6k3jGd9+xqZvsw9//7yZvX1jGd+9eWcTELhfRLNJkujp1gKgo37hSdzR1c1Q32cnAgVK8\n0tN1JzHf99/LYDGrbqjxTyzS5BGDBskShEeP6k5iLkdT94ABupMQOS8qCqhZ0zcupNetA+64A6ha\nVXcS57BIk0cMGCDFy9ubvL/9Vk54bOomOylXTtaYnzPHu5u8//gD+PJL+Y7aBYs0eUTdurL6ljdf\nqR85Iq0FHNVNdjR0KHDwoHc3eX/zjQwWu/FG3UmcxyJNHnPrrcDp097b5P3DDzLXlE3dZEcREUBg\nIPDVV7qTmEMp4OuvZSCrnXalY5EmjxkwAFi+XEY/eyOO6iY7K1cOGDIEmDYNyM3Vncb9NmwAtm6V\nFgM7YZEmjwkOBnr3BqZO1Z3E/Y4c4ahusr9hw2Qt78WLdSdxv6+/BmrXBuLjdSdxDYs0edTw4cCK\nFbL7jDf54QdpTmNTN9lZu3ZAixbe1+SdlyctBLfcYu1tKQvDIk0edcMNMvXhyy91J3Gv+fOlqTs4\nWHcSotIzDOD222Uu8alTutO4T0qKLH1qt6ZugEWaPKxSJWkSnjrVexb0P3hQ7qTvvFN3EqKyGzoU\nyM72rk1xvvoKaNoU6NxZdxLXsUiTxw0fDuzZI4PIvMHUqUDFivaa1kFUlKuuknnE3tLade6cLHk6\ndKi0FNgNizR5XPfuQOPG3jGATCngs89kbrRdVjAiKsntt8uc/4wM3UnKbu5c4ORJezZ1AyzSpIGf\nn5wEvv1WmtXsLC1NBsGxqZu8yaBB0jrkDYsPTZ4sF9GhobqTlA6LNGkxbJhc3f74o+4kZTN5MnD1\n1TJojMhbVK8uF9IffmjvZUL37AEWLQKuu053ktJjkSYtrrkGGDlSpkXY1cmTsoDJyJH27OsiKs7t\ntwPbt8te8HY1ebKsLnbLLbqTlB6LNGkTHS0L+u/cqTtJ6cyYAZw/LwPhiLxNZCTQvDnw8ce6k5RO\nburtJaAAAAjZSURBVK4U6dtvl+VO7YpFmrQZPBgICrLvSWDyZFlBrX593UmI3M8wgPvuA2bPBjIz\ndadx3bx5wJ9/AvfeqztJ2bBIkzYBAcBddwFTpgBnz+pO45pff5WBNXY/ARAVZ9gwoHx5mcFgN598\nAnTsKKuo2RmLNGk1ahRw7Jg0HdvJ++8Dv/8O9O2rOwmReWrUkN3rJk6UpTXtYu9eYOFC77iIZpEm\nrZo2lZGXH32kO4nz/vpLVjB64AG5yyDyZvffL0Vv0SLdSZz3+efSD33rrbqTlB2LNGk3ejSwZg2w\ndq3uJM6ZOFH667zhKp2oJB06AGFh9rmQPncOmDABePRRe+0bXRQWadKuTx9ZivDDD3UnKVlOjuS8\n/XagZk3daYjM5xhAtmEDsHu37jQl+/JL4PBh4I47dCdxDxZp0s7fH3jmGelD+vNP3WmKN3OmLJX4\nyCO6kxB5zm23yQXq+PG6kxQvPx94+22gf39ZZMgbsEiTJQwZApw5Y/2TwLvvArGxQKtWupMQeU5g\noIzB+PRTICtLd5qizZ8PbNsGPPGE7iTuwyJNllC9upwEPvpIRntb0cqVwKpVvIsm3/Tgg0C5cnKh\nalX/939A165At266k7gPizRZxqOPyipBH3ygO0nhXn8duOEGTrsi31Sjhoz0njABOH5cd5rLrV0L\npKQAjz+uO4l7sUiTZdSpA9x9N/DOO8Dp07rTFLR+PfDTT8DAgbKLF5EvGjNGlsK14iDPzz+Xfuj+\n/XUncS+ebshSnnhCNq6YNEl3koL+/W+Z033bbbqTEOkTEiLbsr7zjrVWCdywQe7wn39eBqJ6ExZp\nspSGDWVz9v/+V67YrWDjRuD774HnnpM+OSJf9uSTwNGjsna9VYwdK/tFDx2qO4n7sUiT5TzzDNCk\niXXWC371VaBxY5kbTeTrGjeW2Rjz5wPZ2brTyFaaCxfK99QbL6JZpMlymjWT/aaff17/SO/Vq4HU\nVBk0xiVAicTLLwOJicBbb+nNoZTcRYeHA4MG6c1iFhZpsqRXXwUuXABeeUVfBqVkpGidOt57AiAq\njSZNgMcek4vXvXv15ZgzB/jlF+CNN2RlNG/EIk2WFBICPPusTMfavl1Phu+/B5Ytk7mX3jYYhais\nnntOpmXpWjgkL0/OEbGxQFycngyewCJNljVmDFC/vp6TwLlzwMcfyw5dvXp5/vhEVlelijR3z5wp\nTd+e9uWXwMGDcjfvzVikybICAuQkMHcu8PPPnj32v/8tCyNYeXUlIt1uuw3o3l1W4cvJ8dxxDxyQ\nY95+O9Cxo+eOqwOLNFnawIFyJ/vRR56bl/nrr8C4cdKcFxrqmWMS2ZFhAO+/D2zZ4rmtLJUC7rlH\ntqF89VXPHFMnFmmyNMOQu9lFi6T522y5ucBdd8kI82eeMf94RHbXvr3srf7uu3KHa7bPPpMpV5Mm\nSZ+4t2ORJstr1gx47z1g4kTp/zLThx8CmzfLbj8VKph7LCJv8dprQKVKMn/azGbvfftkVPmIEbIP\nvS9gkSZbuOsu4OabpZnLrCkfKSlyAnjhBaBzZ3OOQeSNgoLkIvqXX8xrgcrPl7X9q1Sx/pa27sQi\nTbZgGHISqFZNlv7LzXXv5//5J3DLLUBEBPDUU+79bCJf0K2bLOf79tvmtHg9/7zsOT95smxt6ytY\npMk2qlcHvvkG2LEDePFFGUDiDmfOyHrE5csD06d759KCRJ7w0ENysTtypHvXN3j/fZlqNWAA0Lu3\n+z7XDlikyVa6dQPefFO+sO5YjSw7W/aInjNHtqIMDi77Z17qtddeQ/fu3REYGIigoCCn3/fiiy+i\nXr16qFy5MuLj47Fr1y73BiMygWHIeI4OHWS3rJ07y/6Z334r060ef9z79op2Bos02c7IkVKkX3pJ\n+qZKe0d95oxM8Vq5Epg3D2jXzq0xAQA5OTkYPHgw7r//fqff8+abb+KDDz7AxIkTsXr1agQGBqJ3\n7964cOGC+wMSudkVVwBTp8pOWd27A2vXlv6zFiwAhg2TLq5x49yX0VaUUs4+iCxl/HilypVT6q67\nlDp3zrX37t2rVMeOSsXFKbV4sTn5LvX555+rGjVqOPXakJAQ9fbbb1/8/xMnTqiAgAA1Y8aMIt+T\nnp6uAKj09PQyZyVyh8OHlercWanAQKV+/tm19+bnKzVhglKVKik1erRSFy6Yk9HDXKm3Fx+8kybb\nevRRaVqbPl36qtasKfk9+fnSrx0WBhw6JHfkVlr3948//kBmZiZiY2MvPle1alV07twZK1eu1JiM\nyDU1a8pyoZGRMubjqaec29Xuzz+BUaOAhx+W2RzvvOPbO9CxSJOt3XGHNFcfPAh06iRf6qVLZfH9\nS508CcyYIVvaDR0qTWjp6dJ3ZiWZmZkwDAPB/+gcDw4ORmZmpqZURKUTGCjjPUaMkDUImjSROdVZ\nWZe/dtMmmQIZFSWb28yeLQuk+HKBBlikyQu0bi39Xl9/LXOd4+NlF634eCAmBrjxRpnH+fTT8mtK\nivRl16xZuuONHTsWfn5+RT78/f2xY8cO9/4hiWyqfHlp9dq1S9b6XrIEqFsX6NdPdrCKj5f/j4iQ\nTTPuu09Ght9wg+7k1mAod81jIfIRhmHUBFBSid+tlLo4m9swjDsAjFdKFTvE2zCMxgB+B9BOKbXx\nkueTAaxXShW6OKphGGEA0gGkAjjxj9+eppSaVkJeIrIgzgglcpFS6giAIyZ99h+GYWQCiAWwEQAM\nw6gKoDOACcW8dRuAcADblFIe2oqEiMzG5m4iExmG0cAwjLYAGgLwNwyj7f8egZe8ZpthGDde8rZ3\nADxvGMb1hmG0BjAVwAEAc4o6jlLqrFJqHQs0kXfhnTSRuV4BMPyS/1/3v19jIE3TAHANgGqOFyil\nxhmGURnAJwCqA0gDkKCU4kRpIh/DPmkiIiKLYnM3ERGRRbFIExERWRSLNBERkUWxSBMREVkUizQR\nEZFFsUgTERFZFIs0ERGRRbFIExERWRSLNBERkUWxSBMREVkUizQREZFFsUgTERFZ1P8DKN2YtnpP\n/SEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110007dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x110012550>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sin(x), (x, -2*pi, 2*pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "多個函數一起來。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+npS0FbqPyVIs47F8efndt0Rh5UraJbqrpAcOpKEGok+L6tQJCA4Wf8NgNkQb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\nBSJzWFWUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11091ab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1104f42e8>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sin(x), cos(x), (x,-2*pi,2*pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 參數式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy.plotting import plot_parametric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.abc import t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = 1 + 0.3*sin(10*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ClyzJfcZFzuTNyzP/Ro2A//2PqyzCwpgM7NzJZOvLL7kCw8uLCVfhwkDVquwB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\nHSWF0hGQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114af198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x111489be0>"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_parametric(r*cos(t), r*sin(t), (t,0,2*pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 隱函數"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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99ZXtOAAsoKQBR02cOFHNmjWT53m2owCwhJIGHPTBBx8oOztbs2bNku/7tuMA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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c5cef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1105e20b8>"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_implicit(Eq(x**2+y**2,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "也可以畫不等式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114af0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1115585f8>"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_implicit(y>x**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-8 [練習] 自動出題系統"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def quiz():\n",
    "    c1 = np.random.randint(1,6)\n",
    "    c2 = np.random.randint(1,6)\n",
    "    c3 = np.random.randint(1,6)\n",
    "    f = c1*x**2 + c2*x + c3\n",
    "    display(f)\n",
    "    w = input(\"按 enter 告訴你答案...\")\n",
    "    g = integrate(f,x)\n",
    "    display(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAAAWBAMAAAABVL48AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMpndu3bvImbNiRBU\nq0Qb3U6NAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABwUlEQVQ4EZVSv0vDQBh9JdbWJNriP6CIg7Po\n4GRwdWgR6mCRLiI4KMFFcZCCg3UTdCk4hKKLDh5Il4JQJwcVXESXYh10cLHib6rW3F0uuQSXfMPd\ne+977+6+EECq0hiRWBiomp2bYfySVzEjHxINA5V67DeM3+fVmz4ahijpMG7b2+36Sy7iILa/Ww1I\nDo30MjDkUMQ5FxRYhP7pMRkpBmXRGaE94o5D3Xl4rooX0aS70IFJg/LlbbraFdk5H+dIWB7q2hdX\n/DpiGwZVLBFtb7UaAUvgweJIqB00GjftaHl6dUr6uq4FRxa0zPX9XuDIdRYtYxuaFR9WNnmbrm50\nZZCggrX0iD+qpVnUsqMqUZu6+U8U6gIOcEhO/VEVNKon6a0MOlG1WNyaKxYvOZ0lxDbQkvQT5q+A\ndRLSpN6Dl4BUFXhjUXtxBtEsFr2o1d6vgJ6kaNNdzNoiNBp5Fj1H12u123l21wx0kkOUCIMXtX+W\nUfMs2kCW98SRQLvBlFc8VVNY9pLurQXob13fbY1Ynje9aMKgym7r5jhTHshT7JSwdPX117Wr7EQh\noENN/eSF2b+LqF/1BgnqEtdMiUjQp/8BBIxxZZOLCAEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$4 x^{2} + 3 x + 4$$"
      ],
      "text/plain": [
       "   2          \n",
       "4⋅x  + 3⋅x + 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "按 enter 告訴你答案...\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAvBAMAAADHk+9wAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n8oKaJSiV29aSyAuuKzs2qPMPdlDXt7q8V+IAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{4 x^{3}}{3} + \\frac{3 x^{2}}{2} + 4 x$$"
      ],
      "text/plain": [
       "   3      2      \n",
       "4⋅x    3⋅x       \n",
       "──── + ──── + 4⋅x\n",
       " 3      2        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quiz()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f = coef[0]*x**2 + coef[1]*x + coef[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-9 [練習] $\\pi$ 的密碼\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s = str(pi.n(100000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADEAAAAPBAMAAAC/wjryAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJIrsy\nRN36OqqCAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVQYGWNggAPmyCkLgByeAAau0N0HgCxG\nZShh1MClBWTybWAwYeD8y8BgEvIZSjgxMLgCZZI2MDgzMCgBWWxAGTDxnYFhPgMDV/sGBj0GBv8D\nCBnm3wwM+QcYONk3MNQboMgwqAP1XGDoAsoAwXsDhB6QUfUNzAlgGd6fQFm4PewJjPMFOBnAMnwO\nyDIMbTnzD8hAZEKBEgg9QLa/8QSwDFsAukwJo4uLv0oCgygD1wIkPU0LeH4BlTJtAAUQG7JMuoF5\nA1CGfwPDuplT/RgYWJ2+e0AIztBYoATn/i8N9f///wMycQEAvJFLpV5vX70AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$11942$$"
      ],
      "text/plain": [
       "11942"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.find('1215')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1712158552'"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[11940:11950]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAPBAMAAADqo9msAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWYiibvd\nRDIcHY1cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAqUlEQVQIHWNgAAHOVasFGNiT+QKBbEZlBoap\nDIw/GJj+/1/AwGAS8pmBIV+A4Q8D+5JMkFo2IP/SBebvDCwgHoQP1PUDlW+zgIGlI/UBTH7WUQMG\nbgPOvzA+A5cukMmwB85nUDIAsuMnQMybycCwX8CdgWH9BQj/vwGQrw6UByoC2a/NwHB+QgADw3Go\n/g4Gxm9AR3NoMjCwOn33YOANjb7AwBnlClSOBgDBrC5PmVJyfgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$135$$"
      ],
      "text/plain": [
       "135"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cutepi = str(pi.n(200))\n",
    "cutepi.find('822')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-10 希臘符號\n",
    "\n",
    "數學很喜歡的希臘字母當符號..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "delta = symbols('delta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAAbBAMAAAA35TSjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIky\nqxACMlz2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRklEQVQoFYWSPUgDQRCF3wY9TC7GA8H6ChE7\no2DrTyeiYGMlQiqxPASxtBPtrEVQEGwUBCHYXmF/WqTOFunVVsU4sxP2speQfXCzM2++u11uBxit\n5rIeDSCMJtc8SBBVv3zIrfr2IMDEnxcJEi/SJELFQOUoxYBKEVmlHQrT9Mzf/Q4QwDt5D3gE1il5\ngy4gF2R0gOrG+Yp86bkA1FptQsIE5W73EwHv+MTB0akGapdizfAy1pAij4xgU+pjWtTJjxR5NMiu\n1Eu0vOrVvCmZQWYlP6Q9r7GQFhiDnIl5BYzXkTHSOWBtGd8gmUXKMTItlY39CG30kWLO9nqJQe6l\noONOpeBDOzJI77h0k2FSqTt9KgyyJy5/7IV/jqP9m+0YkJPLBThtW6iGpGYgrOskdI2iRcfuL2gY\nRDxSw2VfVvFwAGYwqfcP8IlGJ6KDgbYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left(\\delta - 1\\right)^{2}$$"
      ],
      "text/plain": [
       "       2\n",
       "(δ - 1) "
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(delta - 1)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "比較特別是 lambda, 因為 lambda 是 Python 保留字, 我們只好假裝不會拼 lambda。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lamda = symbols('lamda')p = M.charpoly(lamda)v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = Matrix([[0,1,0],[2,0,1],[0,-1,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p = M.charpoly(lamda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJAAAAAUBAMAAACQSalFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\lambda \\left(\\lambda - 1\\right) \\left(\\lambda + 1\\right)$$"
      ],
      "text/plain": [
       "λ⋅(λ - 1)⋅(λ + 1)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(p)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
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 "nbformat_minor": 1
}