{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A simple SymPy example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we import SymPy and initialize printing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import init_printing\n",
    "from sympy import *\n",
    " init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a few symbols:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x,y,z = symbols('x y z')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a basic expression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
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       "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\n",
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       "iDIu0NS2v90KGShJYi7T7tgvkrQ2vIT2XtRISWNra6lzGc8/PW3ji4PL7Vmge095YIX0iB71NCaZ\n",
       "5N3XyM0VCuNIyFNIyY3AMG/KDUvjn90DGmwq9wpIl5AyU5WsTYy0aJf6JFGB5An3Der5jExKHjNR\n",
       "4JKPge/EXqDBoOXpkxkmkJHFfAFRVhDIveWA0S57N2Me6yw+DSX1n1uCq3sIfCF2IcjNkjeWyKli\n",
       "ginHubboOB4vSNAjyaiXE26ygrkyTfod55Lj3CTE+n2P73ImJpnk6wJJKjYJSwt3OQbNJu4icM5s\n",
       "KGGbzMuD70N6JSbJD44x7pLDyJrbkfiLpOEhYVMJSVEj83x5YFLyNrAzJsmvJ+uhLrieXvcJDshy\n",
       "HtQuD54c2IWWEnSXfUTDZJJfAjcpOW5imp9aHvw4ZZ4NDV4FGjw0tzadKgbFwinJUd//AT0P1tdW\n",
       "BtuRU39oKdk9ONQ163fM+nvu/s4D/FX30otdQIZGlSnJKpq6KUxKVqV1WxGHFIhishjhEO1Gi3r4\n",
       "kZCMg+hH1henV8EjmFoly1PTMs/Uadaox+FceY2STpmvt9co/Pe0Jvt1GvgDK/Osw/4jQ4wAAAAA\n",
       "SUVORK5CYII=\n"
      ],
      "text/latex": [
       "$$x^{2} + 2.0 y + \\sin{\\left (z \\right )}$$"
      ],
      "text/plain": [
       " 2                 \n",
       "x  + 2.0\u22c5y + sin(z)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e = x**2 + 2.0*y + sin(z); e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAABQAAAAOBAMAAADd6iHDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\n",
       "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\n",
       "VGZoascqAAAAgElEQVQIHWNgVDJ2YICAMAb2H1BmKgPDTChzFgNDvgOEvT8AzgQKrA9gPZPYUwNk\n",
       "cXxnCGd4dWA1kMllwFDKUB9wEchUZmAIYNgMZDDwJIDIPyDiEgOjAAPLFwZWBhYFBh6BqzwfGI4y\n",
       "SJUXZXH8Zf7A+IBh////v1hzjh5/xwAAW80hUDE8HYkAAAAASUVORK5CYII=\n"
      ],
      "text/latex": [
       "$$2 x$$"
      ],
      "text/plain": [
       "2\u22c5x"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(e, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAALsAAAAZBAMAAACbakK8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\n",
       "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\n",
       "me8Q6PJIAAADAklEQVRIDbVVS2gTURQ90/wmk0k6tCJCsR1SKShIsxE3CgNWBKUxq9qFmqFqShfF\n",
       "UKQrkaDiF0pcCKYgBBcuBLV+wIWKARe6kQ4UhNKKWdiF4KIptmA/xPvmzZuMxdYUzIPcd+655568\n",
       "vLlJAL6G32oOasQWNHz5Rvg6nrKh/mygfSzlX2ygPaBUGmov6//NXs1yq4sex2EPrsHemTd2snNg\n",
       "tkb+Cx1zBL6SqwxZLvQAKYHzKZaPY4fh4TeHd0S5Nox9OClItm/jiU9DrEwwVEawpiVis9VkimqX\n",
       "AOr4o2cCs/0BT2I5+FYJRhJbePQxgzcD7QLEqtV5gdnu2Icr3L45gcCyt74Z7neL4SLQ0nm4S+dM\n",
       "YCz1gSPHnhKZDWyHhcCCNKwjqaF/TkwGl0L6nClie/wc1D1xdoNsSLhT0IJkhi7Lzr22xb8keE/N\n",
       "Pm0Sc9yEuhRUyuiG9HzvFNeImCyq39SriOhtQI7IV/TiTqE8glqwohjE0NJwiANxOZTdZoxtfzSa\n",
       "x2tI8DtHcKQoQFmV6f1XT2swibxFL+6k5EgenhBCqKLTPX3ULnaYdDlaTMcCSd8zuXTvBq2bJUJr\n",
       "lE4WgSV5ZRdBzLFgO6nzhJp1ltvrlB2HCoWxQuG+jTvt2GxBWUZaU2mMApZNuSHA3vJpCliRhqqs\n",
       "ZtvbTrb9ZIk+i70Ut1OcnpgeKskTCFUwjaYy8Jhr3eiefq0HIfa7yC6HOwVyULRuNDn21JngbcL+\n",
       "E8A+MNnSxb+w59+Cj2tELJBbjEZr8SGwn0j2aLkTPdp08R2OcKV6fXB3ikPH3n8tM5WTfrETtZcw\n",
       "g3QWH0dH7nKNiMkszqo/EDafaHhJ5Bm6ee4UtdAabxnMcmUUl0SnYx+uVqs5XAGN9QGgdeCrASv0\n",
       "3TmCsJcOdhnozexD38goK9HXynEKr1OKDs9guhQD039kGySyIQpJAdbvJ9YTlPvyUl3/aLUf34G/\n",
       "uGxIyXpE37DoLbAHwJaU53t9MRCfrU8o/k4iRn36Lar8Wd5wAfgN4R6xelyy/ssAAAAASUVORK5C\n",
       "YII=\n"
      ],
      "text/latex": [
       "$$x^{2} z + 2.0 y z - \\cos{\\left (z \\right )}$$"
      ],
      "text/plain": [
       " 2                     \n",
       "x \u22c5z + 2.0\u22c5y\u22c5z - cos(z)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(e, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 0
}