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 },
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "import numpy as np\n",
      "import numpy.linalg as la\n",
      "import matplotlib.pyplot as pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Mini-Introduction to `sympy`**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as sym\n",
      "\n",
      "# Enable \"pretty-printing\" in IPython\n",
      "sym.init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = sym.Symbol(\"x\")\n",
      "\n",
      "myexpr = (x**2-3)**2\n",
      "myexpr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left(x^{2} - 3\\right)^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFEAAAAgBAMAAACY34lhAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nnG3nL5w3YTG1ne00AAAAAElFTkSuQmCC\n",
       "prompt_number": 9,
       "text": [
        "        2\n",
        "\u239b 2    \u239e \n",
        "\u239dx  - 3\u23a0 "
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myexpr.expand()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$x^{4} - 6 x^{2} + 9$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAWBAMAAAAFoW4BAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAASUVORK5CYII=\n",
       "prompt_number": 11,
       "text": [
        " 4      2    \n",
        "x  - 6\u22c5x  + 9"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sym.integrate(myexpr, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{x^{5}}{5} - 2 x^{3} + 9 x$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAvBAMAAAA4HQjXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
       "prompt_number": 10,
       "text": [
        " 5             \n",
        "x       3      \n",
        "\u2500\u2500 - 2\u22c5x  + 9\u22c5x\n",
        "5              "
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sym.integrate(myexpr, (x, -1, 1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{72}{5}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAqBAMAAACuFQ3dAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt2rmYlmIkR2uxDN\nVO+L8+I6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVQYGWNgVHYNDWUo8VrIwMDA9v///8/c\nBgzxDQwMLAUMDAbMGxj4HjAwsAKRAJ8CA/NHoCIGhk4Gnt8w9gKQANNvEMmaACL7A0DkfhDBoAUm\n54BIlgVgNlhkMpjJ/RlI8TowlAMpxi9AQoSBYTpICMhmVw11VgCy2d8yMPAAHQVi0xgAbYGCDxTb\ndHKDSAPMkPf/f8KYDEctgYEKBQYwBpBGZptlOsJlVjPUN8A5DFwKCDbLdyib+QAD6w8om+8AAws4\nJoB8FmCsHICKszsw5MEtLgn2BgkDAKR2OJTFXAjvAAAAAElFTkSuQmCC\n",
       "prompt_number": 16,
       "text": [
        "72/5"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Orthogonal polynomials**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def inner_product(f1, f2):\n",
      "    return sym.integrate(f1*f2, (x, -1, 1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "inner_product(1, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$2$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOBAMAAAAPuiubAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIpm7MhCriUTv3c12VLge\nopIAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABOSURBVAgdY2BUMnZgYAhjYH/BwJDKwDCTgWEWA0Oe\nA8O+ABAJBOsCgATHcxCTywBEKoMIngQQeYmBUYCBRYGBR4BBqrwoi4Fh37t3rxgAK1UOqPfNIGYA\nAAAASUVORK5CYII=\n",
       "prompt_number": 23,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "inner_product(1, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$0$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJdjLNVN0iZu+7\nq0QgoRR7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVklEQVQIHWNgEDJRZWBgSGeQmMDAtYGBOYGB\n5wID+0cG/gsMfN8Z5BUY+L4wzDdgYP0MJeUNQCL8Cgzs3xk4DjBwfWRg2cDAlMDA0M4gHcDAIOxy\nlQEA9FISlFfRJtkAAAAASUVORK5CYII=\n",
       "prompt_number": 24,
       "text": [
        "0"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#basis = [1, x, x**2, x**3]\n",
      "basis = [1, x, x**2, x**3, x**4, x**5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Now for plain old Gram-Schmidt\n",
      "orth_basis = []\n",
      "\n",
      "for q in basis:\n",
      "    for prev_q in orth_basis:\n",
      "        q = q - inner_product(prev_q, q)*prev_q\n",
      "    q = q / sym.sqrt(inner_product(q, q))\n",
      "    \n",
      "    orth_basis.append(q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "orth_basis"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{bmatrix}\\frac{\\sqrt{2}}{2}, & \\frac{\\sqrt{6} x}{2}, & \\frac{3 \\sqrt{10}}{4} \\left(x^{2} - \\frac{1}{3}\\right), & \\frac{5 \\sqrt{14}}{4} \\left(x^{3} - \\frac{3 x}{5}\\right), & \\frac{105 \\sqrt{2}}{16} \\left(x^{4} - \\frac{6 x^{2}}{7} + \\frac{3}{35}\\right), & \\frac{63 \\sqrt{22}}{16} \\left(x^{5} - \\frac{10 x^{3}}{9} + \\frac{5 x}{21}\\right)\\end{bmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA4AAAAAmBAMAAABnt+gKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nmoHUhwRlTIN8957GfwGPr1gpVSgIUgAAAABJRU5ErkJggg==\n",
       "prompt_number": 65,
       "text": [
        "\u23a1                                                                  \u239b        2 \n",
        "\u23a2                    ____ \u239b 2   1\u239e      ____ \u239b 3   3\u22c5x\u239e        ___ \u239c 4   6\u22c5x  \n",
        "\u23a2  ___    ___    3\u22c5\u2572\u2571 10 \u22c5\u239cx  - \u2500\u239f  5\u22c5\u2572\u2571 14 \u22c5\u239cx  - \u2500\u2500\u2500\u239f  105\u22c5\u2572\u2571 2 \u22c5\u239cx  - \u2500\u2500\u2500\u2500 \n",
        "\u23a2\u2572\u2571 2   \u2572\u2571 6 \u22c5x           \u239d     3\u23a0           \u239d      5 \u23a0            \u239d      7   \n",
        "\u23a2\u2500\u2500\u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a3  2       2             4                   4                       16       \n",
        "\n",
        "    \u239e            \u239b         3      \u239e\u23a4\n",
        "  3 \u239f       ____ \u239c 5   10\u22c5x    5\u22c5x\u239f\u23a5\n",
        "+ \u2500\u2500\u239f  63\u22c5\u2572\u2571 22 \u22c5\u239cx  - \u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u239f\u23a5\n",
        "  35\u23a0            \u239d       9      21\u23a0\u23a5\n",
        "\u2500\u2500\u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "                    16             \u23a6"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(Note: normalization different than in the book.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mesh = np.linspace(-1, 1, 100)\n",
      "\n",
      "pt.figure(figsize=(8,8))\n",
      "for f in orth_basis:\n",
      "    f = sym.lambdify(x, f)\n",
      "    pt.plot(mesh, [f(xi) for xi in mesh])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rK0kLCOC6Pn1YNHhwq1VrHM1bq2VMUBBjgoKYFxeHRSky9XqWV1Vx1969lJhM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VlxcUoMwobhn7k+U8nBEm04skF3j75bP7rnRyocX6hwCy5SDgC3o7Awh2JjJ4a6jKAoLS1VaWlp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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x566fdd0>"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}