chezou/sympy-example.ipynb

## sympy-example.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sympy examples\n",
    "\n",
    "Original codes are in the following article.   \n",
    "http://myenigma.hatenablog.com/entry/2015/11/21/222755    \n",
    "Jupyter notebook is able to write equasion in markdown\n",
    "$$r=\\frac{1}{f}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from sympy import *\n",
    "# to print with mathjax on jupyter notebook\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = Symbol('y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD8AAAAbCAYAAADLYlf/AAAABHNCSVQICAgIfAhkiAAAAwBJREFU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\nHhfl7lW8hwPJfJfIAfkwGGaYYYap4R+VAYk4c49NPwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left(x + y\\right)^{5}$$"
      ],
      "text/plain": [
       "       5\n",
       "(x + y) "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = (x + y)**5\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV4AAAAbCAYAAAA0yedxAAAABHNCSVQICAgIfAhkiAAABvNJREFU\neJztnXuIFVUYwH8+0nR9JVKWhramaSamlq9cMUoKS8iwqIiiFxn0YFN6WOFGRCmURJCQkmNbSRAR\nWVAIZkYq9M4oMhS3TLKs6KGZodsf3xnu3Ovc3TMz59w5s/f8YLh7Zu795vu+M9835zWzkI6pwDCg\nGzAUmJ5Sjsfj8XRFrOTIAGgHjgLbgDEmhDrCcqApbyUcowm4FrgFaAUuzChvGtAMtAAbgdkZ5RUJ\n07abrpsi4mLMBljIkS1IFh9qQphDNAH7gTk56+EaB4Ab1d9XAQeBfill9QOeiJSvBg4hrYOujg3b\nTdZNEXE1ZlvoIEd2zyD4J7V1FQYAE4Fv8lbEQeYAr0XKvZAuVBoagfuBUar8DtAHuCCtcgXChu1z\nMFc3RcP1mK2aI9Mm3gaka3MdsBYYn1KOS9wGrM5bCUf5CmlJAVwJPAb8lVLWDmAGsFuVT1ef36XW\nrjjYsN1k3RQNl2PWSo6cQemuOhf4lmyt56Q8qXQ4CeiLGPUgMDylvPnAOervzbjXbamkL/BlB8fP\nAl4HVgJPAy8Cp2Q851TgYeAFdX5TtAJPGZSXhDz8GMWU7bbqRgfTsaiL6zFrJUf2jPw9EhlEnphB\n3gkJv99esR0FHkl57tOAGyLlzdSuEpPaDXA+8BFidxwDgb3A9ZF9S5GWUa8U56tkEfAJZsYRbwZW\nkL1rXEQ/mrI9iom6yTMWdbERs2muoY4wnSOZDvwNnKjKE5TQszPIXE2yCYY24HngDaTFkMWgm5A7\n9ANq26dkX5ZBpi5J7B4HvI3Mlm6nesJ4HPiZ8oofDPwH3JFCx+nI5MUZqjxWnXthCllR5iHJB+Ra\nGplBVhH8GMWU7TbqJs9Y1MVGzCa1uyNs5EiGA8si5UXAh1kEIkEwMsH3N2c8X0fsoXYt3oB0QRdQ\nPWHsBDbE7N8BbEpxrvPU73qr8jzgCDA6hayQ2cj4VzjrewXSNUtLgPt+DDFpu426CXAnFnXZQ/aY\nDch284/SaY7sSXL2Ap8CS4AeyPq0BSkVdInhwN1IMCxGumtv5apRcvojQbcx5tg+0i3i/hgZO7wT\nOAbMAi4n/YRQI+LX/hX7B6aUZwMbfgTztpuum6Lhasx2miMrE+8UZEyrHcn+twK3A4OQZvgyYBfS\nEohrDdSKXkhXYwhywY1Cuhw7K76naw+Is+5TW0c0Avci3buXgVcixxYjY4fXJDfJCCPU558xxw4i\ny296A/+qfbr+eSkiZ2UnOuj4Z4COMTliy4+70bdd9zpLUjc2MB2LSeJLN2ZNo6ujVo4cDTxLabA/\nQJw3E1lneEwJtUFAsmb+LkpLcUAqdD/li5Vt2bMKudju4fgZ8S+AVxPICjDbRZ6p9j8ac6xVHQtn\n5YvgH10CvB9NEZBvLBbB7sw6Rpc3NCN3qvBCbAB+B7YC3yPLaQJNxWwzBvghUl6PdN+WRvbZsGcW\n8AEyjnYp5Xf1QcjylvcTyjTJUfUZl0zCWdse6rMe/aOL96M+JmOxCHYb13FERflHZGbXJOuAz2O2\n34Cvqxyboim7TW0hNuwZinQxhyHBGR23mY9cWHELpU3bHRCfFBrV/paYYxvUsXB80SX/6OL9aMaP\n4GYsFsFuqzqOUwIuTisgIQH6zfwtyB2nkr3A4Sq/MW1PM/AHpdlkkDWZv5BsXWaA2S5yA9Jteybm\n2CaklRGHq/7RJcD70RQB+cei63ZDRh2rPUlxEdKU3hrZ15hAKZtM4vhZYZDB/baY/WDenkuA9yhN\nroAsE9pC9eVJteAg8BnlY24hZyJ37zjqxT+6eD/qYSsWXbcbMuoYJt4+SLaeoMpzkUHjQ5HvLTGg\nrAne5fi75STkzhPO8Nq2ZwTyCGBIAzCZ/MefQB4OmEb5XXcUkkTCl6nUs3908X7sHFux6LrdkFHH\nMPHOQ4wfjzz90kh5Jn8Imc11geXIspmwid8NafZvQyoY7NvThjzFFLICmXSp1YURPhET91z+KuQi\niD7qehcyfhW+UKSr+0cX78ds2IpF1+2GjDqGd/Mh6oe/qnIL8BwyTnMEeJP4xeSmCNQ592h+vwlZ\nOP0Psi5yBzJYH44r2bZnLLAG6XIeRlpG4ymtZdQlQN/uk5ELdBilwfsDyLsD1iDrCUPORfyxE+kK\nDkaWvoSzz0Xxjy4B3o+mCMg/Fotgdx46GifA3ON6taY78s7NtSl+G1Bcu3XJ4h9dArwfTRHgli+L\nYHetdDTOZMy/HcgW6ylfNL0AueOleT6+SHbrYtI/ung/miNvXxbB7rx0rGsOIE/hgLyebjf5PSLs\nIt4/ZqhXPxbB7sw61su/CDHJQuTF092BU5EK2J6rRm7h/WOGevVjEewugo4ej8fj8Xg8Ho/H4/F4\nPB6Px+OxxP/Vvu26dpHvyQAAAABJRU5ErkJggg==\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 "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# expand above expression\n",
    "expand(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAZCAYAAADnnhbzAAAABHNCSVQICAgIfAhkiAAABi9JREFU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\nQmCC\n",
      "text/latex": [
       "$$\\log{\\left (y \\right )} \\cos{\\left (x \\right )} + \\frac{2}{y}$$"
      ],
      "text/plain": [
       "                2\n",
       "log(y)⋅cos(x) + ─\n",
       "                y"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = cos(x) * ln(y) + 2/y\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU4AAAAlCAYAAAAtFwBEAAAABHNCSVQICAgIfAhkiAAACbVJREFU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\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)⎠⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve above expression for x\n",
    "solve(expr, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAcCAYAAACzpld9AAAABHNCSVQICAgIfAhkiAAABfpJREFU\naIHt2musXFUZBuCn7WlqUSSFloJWQVrQeq1KqQ0qB3qKiBhUvFCkUitGY6ykivpDIhqDigI/lBhv\njeKPQmOMiKB4AQ+mUdCieKGmmEaxais9AlZRrtYf75rM7nSmnTlnxoOy32Rn1l573fbe336/9/vW\nUKPGBDGMHbitHC+Z1NXUmCys1bSBf+yr4TA+NPj11JggpmIN3leOQWK0OmmNweJZWDyAcV+Bq/EJ\nLMELu+z3Apw+3klrgxksjsIb8dMBjD0fK0p5K57SZb+f4QjxJH3BsNol9QsbMGtAY8/AgaX8bTyp\nh76Pw/W6J4zRRqFmmMFhiYjFewY0/gP4O47HTfhzD33vx6/w8l4n7bfBzMaFeAjX4gOY2+c5WvEm\nbNefaO4YLK2cz8Y67JavbLE8s4/IPV6j+dCPwfeF8l+DV5fzQeKJOBEfH0ffjTitH4sYNjGXdIQ8\n4Hn9WEwXeDzGML0PY63DW1vq5sj9rKrUTRP2OKOl7TtwQCn/BEf3YU37wtvkvqdjpMe+R+GXXbYd\nbRQG4ZKWYwv+OICx22EYP5QvfqIYwXdb6u7Gv1vqVuNvYkwNHIdN+Gc5n4e7+rCmTngDPinsepfk\nznrB3Tis10mHeu3QBUbsm4qH8EFsw0ycjPPE15+DE3AxFgrlHolvys09HbtwSWW8k/GIPMAT8Rn5\ncqZK8unBMvZcrMfr8Vp5wJvxLpyNU0qfFULXG8v4j+DeynwLxSi2ahrMdAlXP1tpN9t+El4TxIZy\njBf34aB+LGTY+F3SFOwU/90JXxQDIS/xX6Laz5UH/1ucVa4fIOKuoSueKS+5is0iMIlPvqaUv4D3\nl/JMXISXiTu5TcLdqXhaaXOuPV94FVvEJU2TvMcUfA2fKtfPEeOuYqxN3aMJc3UvlEcbhX4zzCIJ\nI3/QUr8Qv8FzcaZkKJXzjaLaN+BQCRfXl+vPkxzGj8v5sbi9Mu48uYdbyvlh8tU/Q1jj7WIYM4S1\nduEQyVlcKa7md6XvS3Fdh/vaWX7X4EuiaXaWueaX8q6WPttxcEv9mtK+E24p6/pvYI5xyIZ+G8wI\nbrUnhZOo4aJyfaOwCizD98TI7intbmwZ74bK+VnCUI32x2q6DqKfrhdDux1XtFnjMglDW3XJi3G+\nsM4s/LVybUyMcJcYPtEN83EqPt1mnh/hOfh9pa5du3bY3WW78WKKuPcb99ewFf0Wve30y1qJ+Ykh\nbS/lA8VAbhIWIC+zk8HMwotEz6wudfdpGufRwliX4g5hrQam4M3ld7k9jZCwzoNiBCvFhVUxhlfi\nskrdTtEtV2uPa4W1xoMZ+KjorUvkWb0Hryq/Q+KmTy1tVoq7nCX3uL+DaL9Oa++IfjHMEnn5J0j0\ncIGEu8djAZ5a2l0pX/IKeSnrZeGbyvUFmrpjitDmzeX8/lJeqek6bhCxukqilGUiNH8uGuM8iQZm\nlj67yxwfa1n/vaXPaqHpVqr+k4jjqhHuEK23rcMzuQ7vlJf/QIc2nfAWYaavips+Xwxwk7Ds2cIQ\no/iGaLtFIsRPw7PL+kYk1F8g+aEGDhIjvFkfMKyz6F2Ez4seuAxf0UxP19gbw2JoveJzYvwNfEui\nRWIEl+NwyRv9Wpj3pEqbCyTJ2IiCniw6soELJdHYLUYbhV5c0irRBB8WFnh3WexJPYzxWMMo7tT7\nbvUvNF/ofInSGpuL8yRtsFyYaKnsXA8Jmw4J294qoT1h/YNL+fniiu7ocU2I32vFkeUYrdQtxdfx\nOs0o5TgJJy8XLVGjPbbobZ+HuI8z5IXPFcY5U5hijuSaTi/XFoqrulPyW3MkTfGQuOI/yF8sNotO\n24G/9LieVfgyTQFUxbC93dJ3xDKvKH2mSbRwlb3DyRqPPhxqYlnnUeXvEN2I3uniT9fhvROYtMbk\noW9bFN1omEOEUbb2a9Ia/7voxmDGxO20Y6PDZV+mxmME3RjMwyK6TrGn5lks+yqtSbAa/8foJHqv\n0twuXyN7OReLSt8myagtYkgPD3yVNSYDayUKJom/J0ziWmrUqFGjRo1W/Ae1uDOSwnuLmwAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ e^{\\operatorname{LambertW}{\\left (- \\frac{2}{\\cos{\\left (x \\right )}} \\right )}}\\right ]$$"
      ],
      "text/plain": [
       "⎡         ⎛ -2   ⎞⎤\n",
       "⎢ LambertW⎜──────⎟⎥\n",
       "⎢         ⎝cos(x)⎠⎥\n",
       "⎣ℯ                ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve above expression for y\n",
    "solve(expr, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAAYCAYAAAAF6fiUAAAABHNCSVQICAgIfAhkiAAAAyNJREFU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\nM2grpp2F+AGZAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$x^{2} + 3 x + 2$$"
      ],
      "text/plain": [
       " 2          \n",
       "x  + 3⋅x + 2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = x**2 + 3*x + 2 \n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAOhJREFU\nKJHN0jFKg0EQhuHnD4lBtJCgaJnKQm8gIlYeQbC18gCWFskFPIhNmnT2KjY2opUIYhdQQVCjhRb/\nBJdlIdg5zbAz8347M7v80apCbBU9vGMcvofXksAaHrAR5xXcBwAaSXETAxzjLGItzOO5pL6PTyxM\nm2Nip7iZVtQMX2ETl9jCTrTSRR9XObiIb9ziIIlvq7ezngPLAXxgNss9YpgDrQCuC21fqN+jze9a\nvzDCUwEYYwadFJgoLRWAdkCjPLGHt2yGCi84KQhp4ByHSWw3lLupQmod9deYU89V4Qh3pRv+if0A\nqXkrEnyBnzoAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$6$$"
      ],
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# substitute 1 for x\n",
    "f1 = f.subs([(x, 1)])\n",
    "f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJEAAAAcCAYAAABh9l0lAAAABHNCSVQICAgIfAhkiAAABa1JREFU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\n3tKd6dfzkNq7mYqKioqKioqKiophyf8A65dOZP1qBRQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{x^{2}}{y} + 2 x - \\log{\\left (y \\right )}$$"
      ],
      "text/plain": [
       " 2               \n",
       "x                \n",
       "── + 2⋅x - log(y)\n",
       "y                "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y = symbols('x y')\n",
    "f = x**2 / y + 2 * x - ln(y)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEkAAAAZCAYAAAB9/QMrAAAABHNCSVQICAgIfAhkiAAAAwxJREFU\nWIXt2F+oVFUUx/GPZpbcIikp61LaRUGpHlKSKBFKJQp6MHsQEZ+MoJfsz1tgUmpgkYhhhFQTWhZJ\nBBFRPVT+w16kfwQKFQaBpBaShJWmD+sMnnvac+acuTPd+zBfOMzstfdZs35r9t5n7UOfMc0Dox3A\nWGcW3h/tIKoyvtCeh/fwEb7Fqxjswe8ux84e+O2EWprn4BNMztqXYTd+xfQuB3YQk7rss8nFNcbW\n1vwhZhRst+Ic3q4TZRvmYXsX/RXZpvrsr635FH7G1QX77zhePca2bMa9XfRXpKH6zK+kOb8n/YRr\nMFC44S/dWxoX4S582iV/I6WS5gm5jttxOY7mbNdlTj4vOJmLFWJaTscqPCzW9iCexg+JoO7GHpwp\n2IfwOG7Em3gr1/cEbsOyhL+RUkdzSzbgLO7I2WZiC8Zl7QYOZ2PuxL9CWIrXszFFXsZEPIpvCn1f\n452qAau33FKkNLdkCH9gXcG+1fDp+S6+zL5fjxdwVcLfpfjKheQ2mS9KAuIxvCvXNzkL+JEqAWc0\ndJ6kVpqTXIIDeDHRN63Q/gXrK/hciucS9qnZ7w2KhCzJ9d0vlvRNifveEEkvXr/h+xZ9c0viK9Oc\nZDueqTButhCxqMLYXbi5pP8xnBTBNtmIY/47+8po6GwmtdRcrLhhrdhj1uRsK1s4Xoi/sT9nG0qM\nuwI34LuSIO/BZ+LJ0mSBKO7OldzXDdYq0VxM0orM9mzBPj/7nCT+3Vuy9mKx0f6Z8/dkIoilovQv\nYxoO5doDoiL+os19I6Wd5mElwAJswsfYkbNPcOGfvE8k4SD+EbPmZG7sU9LV9DI81CbYI7gy194o\njhi9TFIVzcM4kXWkrmaWp+A1PJ9dA2IDfUWUBYsTfqeqJnQW9uIl8YTcIzbh1JZQRkP1PamK5v+F\n1eo9wonEHBV1VV0aun8g7zn7xAwsY6fhReQSnBaFa13mqPcmYNSZIU7a7TgulitxLPhRb44hHVGn\n/uiENULwjjbjHhSvUMbjWpGwA70NbezwgXiR1adPnz5VOA+8hq2if70xVAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{2 x}{y} + 2$$"
      ],
      "text/plain": [
       "2⋅x    \n",
       "─── + 2\n",
       " y     "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# differentiate f for x\n",
    "diff(f,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAZCAYAAADnnhbzAAAABHNCSVQICAgIfAhkiAAABi9JREFU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\nQmCC\n",
      "text/latex": [
       "$$\\log{\\left (y \\right )} \\cos{\\left (x \\right )} + \\frac{2}{y}$$"
      ],
      "text/plain": [
       "                2\n",
       "log(y)⋅cos(x) + ─\n",
       "                y"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = cos(x) * ln(y) + 2/y\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJcAAAAZCAYAAAA8JbzRAAAABHNCSVQICAgIfAhkiAAABm9JREFU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\nAABJRU5ErkJggg==\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                 "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# integrate expr for x\n",
    "integrate(expr, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAcCAYAAAB4fbODAAAABHNCSVQICAgIfAhkiAAAB9RJREFU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\n9Niq+D+Fktp6Fvfs/wAAAABJRU5ErkJggg==\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        "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(x).series(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAF5JREFU\nKJFjYKAC4GJgYLhEjEJTBgaG0wwMDP/RJViQ2JoMDAw9DAwMrxkYGP6S4owF2ExmIsWEUcVUV8wB\npblwaRRjYGDYycDAcIUBEnv/GSBRv5+BgSGaFBfQGAAA/84M5lOscPUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(sin(x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAANtJREFU\nKJHN0r0uhEEUxvGf9VWItTYahSgQPYV2SxfBBbiAbfSidSE60e4trASNjghZGiHbEFnFzpscb84W\nOqd5cp6Z/5nJzMMfa6rWb+MU9xhhBV0MMngJjzgI3jFuMJcBJ3jBTPDa+MJRBtzhIvGv0auaRtFF\nbOEhAZ6wWwfWi74nwBBNzEegWfRzAgCtCHwXHSXAbNHpCLwmG6taKPoRgUGZvjwBeKsDQ/SxlgCb\nuKqaRli4xJ7fcdkoQ86zu66Wow+Dd4ZbIRoxBs/oGEdkx/gz29iXP/d/qR8UhCWn2ReXCwAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(sin(x)/x, x, oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mic/.pyenv/versions/anaconda3-2.1.0/envs/analysis/lib/python3.5/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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0woRNutu6FejdG7jtNqsjsQcOPJJemLBJdykpQJMmVkdhH9HRcohDYaHVkZDTMWGT7li/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\nBBM2EZFDMGETETkEEzYRkUP8P9a7Wyu/Vp0iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1071872e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1073cdfd0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.plotting import plot\n",
    "plot(sin(x)/x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}