{
 "metadata": {
  "name": "",
  "signature": "sha256:8a05e10281b79f81e236915c05d87b5794bbca3d00edf4cf2ee6462a83e0f4e4"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pylab.figure(figsize=(16,12))\n",
      "pylab.xlim(-4,4)\n",
      "pylab.ylim(-2,4)\n",
      "circle1 = plt.Circle((0,1), 2, color='r', fill=False, linewidth=3)\n",
      "fig = plt.gcf()\n",
      "ax = fig.gca()\n",
      "l = plt.Line2D([-4,4],[-1,-1], linewidth=3)\n",
      "ax.add_artist(circle1)\n",
      "ax.add_artist(l)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<matplotlib.lines.Line2D at 0x7fb2c7fec390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VOtdbLzn44FrLAaADDBuWHHNMNT/55OSee+qrB+gIgiewdGbOTP7zP6v5F75Q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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb2c7fe3d10>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "var('x', real=True)\n",
      "var('a', real=True)\n",
      "# a = Symbol('x', real=True, positive=True)\n",
      "def phi(n):\n",
      "    return sqrt(2/a)*sin(n*pi*x/a)\n",
      "formula = integrate(phi(1)*phi(1),(x,0,a))*a/2\n",
      "formula"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "Piecewise((0, pi/a == 0), (a/2, True))"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "refine(formula, Q.is_true(a>0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 77,
       "text": [
        "Piecewise((0, pi/a == 0), (a/2, True))"
       ]
      }
     ],
     "prompt_number": 77
    }
   ],
   "metadata": {}
  }
 ]
}