Fourier_x.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = Symbol ('n', integer=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAABGBAMAAABPkFAwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWYiRN2J\nuzLrRHL3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGHUlEQVRoBe1YXWgcVRQ+m9m/2d+gKBSpyUuF\nitoh1vRBhYViMKJmxYp5ULuYtCQYzaJVUVG3D0ZLCy60UauGLEV8sZAViyG20gWxeWggoQjah5hV\nYkTBZtMEtSHteu787Nw7d2ZndzM285DzkD3nOz/32zszd74NgIV9WC6XixY5V8DPLNxztyuIWJAQ\noN9nkXILPDPsFibmPMSZz8wTbkF9mV/dQsWcRzgblswzm6hbdyDYvbDPrdxkXsGxTFPWzQyPPgfx\num5731Rd5fV9dzHD1AfJ1nXACQa0C3rbEnYl9eeHn/5ZbhoxtHZifBc8ETPAengDt1vCajil5x3y\nhARM58is16iBZO1dAGIJvrmVgmlXeKCLI+gv0RUO+V4JmlpxVjBZGaisHUlBKAEDmQpsdAY5guEZ\nY40DcVMevNdwTjhLDSNrC60UYObyBEdTZnXrxALLCsFP6Dny2q/TiInPExzMmZQ5AIWXcQhzIstr\nf28zmic4x110mxE1pscKWPgTXSyv/S6NmPg8wcsmVU5Ap8iQL+lJ8tq30IiJzxGMrZhUOQD5kmTI\n7fhYvHEabbwIIK+9aDObI+j/26ajwbRy9yFB3RojGF3VJzjoeZJwHMfxl/gLm0W4HYyTh815+w2g\nH6fW8JCM4u9eNI0CR3Axr6Wc/BTPTO0hg5lDRV77KeMyDzHAnh0HMgwA7yfY2Bh9xACHmMg6COCe\nEIL0BVXWfsvQJKYNgDHsShkRiN2mQ+KM7qPnzarhX9sY3CpgXnWkSCS0afM105GJfzbHgbE1HQpo\njBRISGupJc2p+kmJBaUOxQJr97IhFwllicNo4B06QP+cGodqfLYuGvpRbrH2GBtykcfmRTJh6GhT\n40jekLAIjYLVSFiwmxO5yk8WL1Uw7pYJ5JRcIFmpqeqYSX66IZKhIxM/oN1vwv7Oz/H6xfqG0iMr\n8Pu2hd4UlvuRx8nOD9BX8xGZ2PC5xWZo7/14gNSsy/AW9JNj0PL7xrWb/T44nBoHuB8gDwcAvk2J\nV3DlaAYgOZsSroCaD6YRDW2HOUkoBL8Ok2jyVWIvo9eA9QFM/dI/dNyydZTQIPYdTEtbAE5IkIIf\nAC4A/ItouBlizeMgXtPynjyibRl4EiJSZNmTJa0NWiiHjXmcH8m+gB7ZR8q0oS0l1ZPgTeKFr+Ib\nCgn+CEBURFMOBGEVgiVQ8zFSv1eCMyBAYIZ00LaLCJfTeBZTK1m4AM+m8fKmsD0Ku+khrD+NVarJ\nskaYxNsBCc5WCIKnBF5SJedlgncCkgaIp9TOhj7EdpwRJq3zuI+WNpfUUjHyIweOQnCVIoiXGHxp\niGckUPIhnCWsEdIAi0XSAeflbTsl+/X8EfAAOUIauqHKoboDGch2o78EPQA3AzxIESQPSVMBWqSC\nmicPibAE0fQWjzQIfkntbuhjbxa+wkZhGWjJN6rcE+rEyosktBQtkTMLf1xfJNdXvcTkVBnNwWTw\nTzXvK2DnK3A4URhrngNWSagza/4YTQbJNH8e7qB6WHUT0l4kQkfPvvew7OTQkdx8efd8+dGtlxN4\noORlRXLsoJYPFLFo58AfHbmd+9u7Mxg0bt7lMLkCeJUe1ocY1I1/RU+ZehMGlPmha8jVG8bWbuJb\nfM0M5iWHXTWzEgvVemrOvfgSX2pQN2H50eXLKkg0W3GJo8stBm4waEnyjQZ1Ey/xJQwizjChgS+T\nqz8wiE0ywKhuFtn1TdZgH9RDJhWOQqhuGPEwWHB0vMUwRQ9ZJFkYb0FGPHTl2Pz/Eyl6qKbZfRXx\noJSfralrnUWqHrKboqobVjz8Y9flRF7VQ3ajKuqGEg/07ze7/nXkNT1UdYSubijxELQ7BquOrDmp\n6iGbek3d0OLB22rT5Exa0UO2s1R1Q4uHeMG2y4kCWQ8VbSep6oYWD2P2XbZjayjA/9AcO2hfp6ob\nvfA8PKIHLvA4dXMhtt0FtCgKRnXz6fNFKusC10zduICWTsFE3ejJTW9zBzZ3wHQHxLfL5esjGEyX\ntwd9l3oel+zLNq5C8meTG7d61ZW3zqJJEBXdSlBlPxJKVP0eG57sjrVuOIeqBCbkf9FVLbk+yf8A\nw5vApn+5oU8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x \\sin{\\left (n x \\right )}\\, dx = - \\frac{2 \\left(-1\\right)^{n}}{n} \\sqrt{\\pi}$$"
      ],
      "text/plain": [
       "π                              \n",
       "⌠                              \n",
       "⎮  x⋅sin(n⋅x) dx               \n",
       "⌡                         n    \n",
       "-π                 -2⋅(-1) ⋅√π \n",
       "──────────────── = ────────────\n",
       "       √π               n      "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a= Integral(x*sin(n*x),(x,-pi,pi))/sqrt(pi)\n",
    "Eq(a,simplify(a.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANUAAABGBAMAAACpnMxdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ntEOCxgOdd+9Ptdr/AqxzMj2/CqlhAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x \\cos{\\left (n x \\right )}\\, dx = 0$$"
      ],
      "text/plain": [
       "π                   \n",
       "⌠                   \n",
       "⎮  x⋅cos(n⋅x) dx    \n",
       "⌡                   \n",
       "-π                  \n",
       "──────────────── = 0\n",
       "       √π           "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b= Integral(x*cos(n*x),(x,-pi,pi))/sqrt(pi)\n",
    "Eq(b,simplify(b.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJQAAABGBAMAAADY5KDDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2 \\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x\\, dx = 0$$"
      ],
      "text/plain": [
       "   π          \n",
       "   ⌠          \n",
       "√2⋅⎮  x dx    \n",
       "   ⌡          \n",
       "   -π         \n",
       "────────── = 0\n",
       "   2⋅√π       "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=Integral(x,(x,-pi,pi))/sqrt(2*pi)\n",
    "Eq(g,g.doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAuBAMAAAArYb09AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrfbp0eQ4/aUJub/GpMOVbgIB6QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\frac{2 \\left(-1\\right)^{n}}{n} \\sin{\\left (n x \\right )}$$"
      ],
      "text/plain": [
       "       n          \n",
       "-2⋅(-1) ⋅sin(n⋅x) \n",
       "──────────────────\n",
       "        n         "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=simplify(a.doit())/sqrt(pi)*sin(n*x)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAADicAAAA9BAMAAACOtkb9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\njkEFkstJgaRAUiApkBRQCvw/8ZhjkH2q1/sAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\sum_{n=1}^{30} - \\frac{2 \\left(-1\\right)^{n}}{n} \\sin{\\left (n x \\right )} = 2 \\sin{\\left (x \\right )} - \\sin{\\left (2 x \\right )} + \\frac{2}{3} \\sin{\\left (3 x \\right )} - \\frac{1}{2} \\sin{\\left (4 x \\right )} + \\frac{2}{5} \\sin{\\left (5 x \\right )} - \\frac{1}{3} \\sin{\\left (6 x \\right )} + \\frac{2}{7} \\sin{\\left (7 x \\right )} - \\frac{1}{4} \\sin{\\left (8 x \\right )} + \\frac{2}{9} \\sin{\\left (9 x \\right )} - \\frac{1}{5} \\sin{\\left (10 x \\right )} + \\frac{2}{11} \\sin{\\left (11 x \\right )} - \\frac{1}{6} \\sin{\\left (12 x \\right )} + \\frac{2}{13} \\sin{\\left (13 x \\right )} - \\frac{1}{7} \\sin{\\left (14 x \\right )} + \\frac{2}{15} \\sin{\\left (15 x \\right )} - \\frac{1}{8} \\sin{\\left (16 x \\right )} + \\frac{2}{17} \\sin{\\left (17 x \\right )} - \\frac{1}{9} \\sin{\\left (18 x \\right )} + \\frac{2}{19} \\sin{\\left (19 x \\right )} - \\frac{1}{10} \\sin{\\left (20 x \\right )} + \\frac{2}{21} \\sin{\\left (21 x \\right )} - \\frac{1}{11} \\sin{\\left (22 x \\right )} + \\frac{2}{23} \\sin{\\left (23 x \\right )} - \\frac{1}{12} \\sin{\\left (24 x \\right )} + \\frac{2}{25} \\sin{\\left (25 x \\right )} - \\frac{1}{13} \\sin{\\left (26 x \\right )} + \\frac{2}{27} \\sin{\\left (27 x \\right )} - \\frac{1}{14} \\sin{\\left (28 x \\right )} + \\frac{2}{29} \\sin{\\left (29 x \\right )} - \\frac{1}{15} \\sin{\\left (30 x \\right )}$$"
      ],
      "text/plain": [
       "  30                                                                          \n",
       " ____                                                                         \n",
       " ╲                                                                            \n",
       "  ╲          n                                                                \n",
       "   ╲  -2⋅(-1) ⋅sin(n⋅x)                          2⋅sin(3⋅x)   sin(4⋅x)   2⋅sin\n",
       "   ╱  ────────────────── = 2⋅sin(x) - sin(2⋅x) + ────────── - ──────── + ─────\n",
       "  ╱           n                                      3           2           5\n",
       " ╱                                                                            \n",
       " ‾‾‾‾                                                                         \n",
       "n = 1                                                                         \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(5⋅x)   sin(6⋅x)   2⋅sin(7⋅x)   sin(8⋅x)   2⋅sin(9⋅x)   sin(10⋅x)   2⋅sin(11⋅x\n",
       "───── - ──────── + ────────── - ──────── + ────────── - ───────── + ──────────\n",
       "           3           7           4           9            5            11   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")   sin(12⋅x)   2⋅sin(13⋅x)   sin(14⋅x)   2⋅sin(15⋅x)   sin(16⋅x)   2⋅sin(17⋅x\n",
       "─ - ───────── + ─────────── - ───────── + ─────────── - ───────── + ──────────\n",
       "        6            13           7            15           8            17   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")   sin(18⋅x)   2⋅sin(19⋅x)   sin(20⋅x)   2⋅sin(21⋅x)   sin(22⋅x)   2⋅sin(23⋅x\n",
       "─ - ───────── + ─────────── - ───────── + ─────────── - ───────── + ──────────\n",
       "        9            19           10           21           11           23   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")   sin(24⋅x)   2⋅sin(25⋅x)   sin(26⋅x)   2⋅sin(27⋅x)   sin(28⋅x)   2⋅sin(29⋅x\n",
       "─ - ───────── + ─────────── - ───────── + ─────────── - ───────── + ──────────\n",
       "        12           25           13           27           14           29   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "             \n",
       "             \n",
       "             \n",
       "             \n",
       ")   sin(30⋅x)\n",
       "─ - ─────────\n",
       "        15   \n",
       "             \n",
       "             \n",
       "             "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=Sum(c,(n,1,30))\n",
    "Eq(d,d.doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f=d.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAD7CAYAAABUt054AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11969fd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11944ce48>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(f, (x, -2*pi, 2*pi))"
   ]
  },
  {
   "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}