Fresnel_functions.ipynb

{
 "metadata": {
  "name": "SP_Fresnel_functions"
 },
 "name": "SP_Fresnel_functions",
 "nbformat": 3,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "%load_ext sympyprt",
     "language": "python",
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "from numpy import linspace, pi, exp\nfrom sympy import *\nfrom matplotlib.pyplot import figure, plot, xlim, ylim",
     "language": "python",
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "z = Symbol(\"z\")",
     "language": "python",
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "n = Symbol(\"n\", integer=True)",
     "language": "python",
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "source": "Defining integrals"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "integrate(sin(pi*z**2/2), z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGEAAAAxBAMAAAA4ptpnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
       "prompt_number": 5,
       "text": "\n3\u22c5fresnels(z)\u22c5\u0393(3/4)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      4\u22c5\u0393(7/4)      "
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAASBAMAAADF+LEmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVIl2ZiKrMrvNEN2Z\n70TGF0JdAAAA50lEQVQYGT2Pv0rDUBjFfyFJYy+CgY5dREdBUukDXF9ACo6l0KGr4CPkEZw7BTcH\nMYPF0YKuvkAndbCO7Sg49Hw3bQ985/zO5ebPB3v5QMm+C1qD0NzcIjrtXysujaWO2YRsraiNpXYF\nSQlT3S5oFHu9ZwzHik8aZXcq68rKkdlNsYQVpK9/9tiTJr66EC5E0dm/fKQB+4FZoA/50CjzshfS\nHLqiRw1fZgsSD28i+0aUo7biYEpUqrdv4bf3k5OVHN6fvOuIuMAVD8/awVsNcvUWbLedzrfwvTtQ\ntqpQ3DhEY04rSHHFBnjmJsd78dawAAAAAElFTkSuQmCC\n",
       "prompt_number": 6,
       "text": "fresnels(z)"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "integrate(cos(pi*z**2/2), z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFYAAAAxBAMAAACyiUMmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nH0Nawv+mLiGnAAAAAElFTkSuQmCC\n",
       "prompt_number": 7,
       "text": "\nfresnelc(z)\u22c5\u0393(1/4)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     4\u22c5\u0393(5/4)     "
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACgAAAASBAMAAADbMYGVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEImrmSJ23URmu80y\n71SHC/xcAAAA5ElEQVQYGUVPvY4BURg9d2OGYSxR2EIpehKbaCQbL0Al0U0UdBuNQqKY2G4jolR6\nBBKlh+ANplJT2No5d5g9yfn5fu69ucA/PBtjTbqfNpkvmal2aiW6F6kCLpJxiNSMnlZB5IpAdg84\ndxZ2g+6ugW6PYUK2SMHfIfOnwCGuZDtYKmRvahKGTXczDIAzCjopOCdpn5yiUKf5pKOpv6bMkVdz\nQJoTZUXyeIoL8SeuwHukJxkOwEJzHIHf758I/pYvNkehehjBBBV+zeNygo9n0jcTvIVxjC97tRs2\nmPqrtl626hbxAF/aJwR9PEelAAAAAElFTkSuQmCC\n",
       "prompt_number": 8,
       "text": "fresnelc(z)"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "source": "Laplace transforms"
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "u = Symbol(\"u\")",
     "language": "python",
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "laplace_transform(fresnels(z), z, u, noconds=True)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdQAAAA1BAMAAAAKZgfMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 10,
       "text": "\n \u239b     \u239b  2\u239e                  \u239b  2\u239e        \u239b  2\u239e                  \u239b  2\u239e\u239e\n \u239c     \u239c u \u239f         \u239bu\u239e      \u239c u \u239f        \u239c u \u239f         \u239bu\u239e      \u239c u \u239f\u239f\n-\u239c2\u22c5sin\u239c\u2500\u2500\u2500\u239f\u22c5fresnels\u239c\u2500\u239f - sin\u239c\u2500\u2500\u2500\u239f + 2\u22c5cos\u239c\u2500\u2500\u2500\u239f\u22c5fresnelc\u239c\u2500\u239f - cos\u239c\u2500\u2500\u2500\u239f\u239f\n \u239d     \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0      \u239d2\u22c5\u03c0\u23a0        \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0      \u239d2\u22c5\u03c0\u23a0\u23a0\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\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                                  2\u22c5u                                   "
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_laplace_transform(_, u, z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 11,
       "text": "\n                       \u239b   \u239b  2\u239e            \u239e                          \u239b   \u239b  \n                       \u239c   \u239c u \u239f            \u239f                          \u239c   \u239c u\n                       \u239csin\u239c\u2500\u2500\u2500\u239f            \u239f                          \u239ccos\u239c\u2500\u2500\n                       \u239c   \u239d2\u22c5\u03c0\u23a0            \u239f                          \u239c   \u239d2\u22c5\nInverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f   InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\n                       \u239d   u                \u23a0                          \u239d   u  \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\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                      2                                               2       \n\n2\u239e            \u239e                                                               \n \u239f            \u239f                                                               \n\u2500\u239f            \u239f                          \u239b   \u239b  2\u239e                        \u239e   \n\u03c0\u23a0            \u239f                          \u239c   \u239c u \u239f         \u239bu\u239e            \u239f   \n\u2500\u2500, u, z, None\u239f                          \u239csin\u239c\u2500\u2500\u2500\u239f\u22c5fresnels\u239c\u2500\u239f            \u239f   \n              \u23a0                          \u239c   \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0            \u239f   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f - \n                                         \u239d         u                      \u23a0   \n\n                                                         \n                                                         \n                       \u239b   \u239b  2\u239e                        \u239e\n                       \u239c   \u239c u \u239f         \u239bu\u239e            \u239f\n                       \u239ccos\u239c\u2500\u2500\u2500\u239f\u22c5fresnelc\u239c\u2500\u239f            \u239f\n                       \u239c   \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0            \u239f\nInverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f\n                       \u239d         u                      \u23a0"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "laplace_transform(fresnelc(z), z, u, noconds=True)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeIAAAA1BAMAAABvi/WzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n39P/MjVl5V2EcsSH6lsWl3ZfBOxNIf8HjWxHaml6ERkAAAAASUVORK5CYII=\n",
       "prompt_number": 12,
       "text": "\n \u239b       \u239b  2\u239e                  \u239b  2\u239e        \u239b  2\u239e                  \u239b  2\u239e\u239e\n \u239c       \u239c u \u239f         \u239bu\u239e      \u239c u \u239f        \u239c u \u239f         \u239bu\u239e      \u239c u \u239f\u239f\n-\u239c- 2\u22c5sin\u239c\u2500\u2500\u2500\u239f\u22c5fresnelc\u239c\u2500\u239f + sin\u239c\u2500\u2500\u2500\u239f + 2\u22c5cos\u239c\u2500\u2500\u2500\u239f\u22c5fresnels\u239c\u2500\u239f - cos\u239c\u2500\u2500\u2500\u239f\u239f\n \u239d       \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0      \u239d2\u22c5\u03c0\u23a0        \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0      \u239d2\u22c5\u03c0\u23a0\u23a0\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\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                                   2\u22c5u                                    "
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_laplace_transform(_, u, z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 13,
       "text": "\n                         \u239b   \u239b  2\u239e            \u239e                          \u239b   \u239b\n                         \u239c   \u239c u \u239f            \u239f                          \u239c   \u239c\n                         \u239csin\u239c\u2500\u2500\u2500\u239f            \u239f                          \u239ccos\u239c\n                         \u239c   \u239d2\u22c5\u03c0\u23a0            \u239f                          \u239c   \u239d\n  InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f   InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\n                         \u239d   u                \u23a0                          \u239d   u\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\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                        2                                               2     \n\n  2\u239e            \u239e                                                             \n u \u239f            \u239f                                                             \n\u2500\u2500\u2500\u239f            \u239f                          \u239b   \u239b  2\u239e                        \u239e \n2\u22c5\u03c0\u23a0            \u239f                          \u239c   \u239c u \u239f         \u239bu\u239e            \u239f \n\u2500\u2500\u2500\u2500, u, z, None\u239f                          \u239csin\u239c\u2500\u2500\u2500\u239f\u22c5fresnelc\u239c\u2500\u239f            \u239f \n                \u23a0                          \u239c   \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0            \u239f \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f \n                                           \u239d         u                      \u23a0 \n\n                                                           \n                                                           \n                         \u239b   \u239b  2\u239e                        \u239e\n                         \u239c   \u239c u \u239f         \u239bu\u239e            \u239f\n                         \u239ccos\u239c\u2500\u2500\u2500\u239f\u22c5fresnels\u239c\u2500\u239f            \u239f\n                         \u239c   \u239d2\u22c5\u03c0\u23a0         \u239d\u03c0\u23a0            \u239f\n- InverseLaplaceTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, u, z, None\u239f\n                         \u239d         u                      \u23a0"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "source": "Fourier transforms"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(fourier_transform(fresnels(z), z, u))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAAqBAMAAAAnoVjxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 14,
       "text": "\n     \u239b     2\u239e        \u239b     2\u239e\n\u2148\u22c5sin\u239d2\u22c5\u03c0\u22c5u \u23a0   \u2148\u22c5cos\u239d2\u22c5\u03c0\u22c5u \u23a0\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\n    2\u22c5\u03c0\u22c5u           2\u22c5\u03c0\u22c5u    "
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(fourier_transform(fresnelc(z), z, u))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAAqBAMAAACkZWHKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
       "prompt_number": 15,
       "text": "\n       \u239b     2\u239e        \u239b     2\u239e\n  \u2148\u22c5sin\u239d2\u22c5\u03c0\u22c5u \u23a0   \u2148\u22c5cos\u239d2\u22c5\u03c0\u22c5u \u23a0\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\n      2\u22c5\u03c0\u22c5u           2\u22c5\u03c0\u22c5u    "
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "#expand(fourier_transform(fresnels(z)*fresnelc(z), z, u))\n# takes looong or does not work",
     "language": "python",
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "source": "Further integrals (all solvable in terms of sin, cos, S, C and Gamma!)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "integrate(fresnels(z**2),z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAATgAAABICAMAAABV9BktAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nnv2VcHasR0U8vBzVXpbjudT/ATTpXYTJ+1sIAAAAAElFTkSuQmCC\n",
       "prompt_number": 17,
       "text": "\n                        \u239b               \u2502   2  8\u239e\n   7                \u250c\u2500  \u239c   3/4, 7/8    \u2502 -\u03c0 \u22c5z \u239f\n\u03c0\u22c5z \u22c5\u0393(3/4)\u22c5\u0393(7/8)\u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                   2\u2575 3 \u239d3/2, 7/4, 15/8 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                64\u22c5\u0393(7/4)\u22c5\u0393(15/8)                "
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAATgAAABICAMAAABV9BktAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nnv2VcHasR0U8vBzVXpbjudT/ATTpXYTJ+1sIAAAAAElFTkSuQmCC\n",
       "prompt_number": 18,
       "text": "\n                        \u239b               \u2502   2  8\u239e\n   7                \u250c\u2500  \u239c   3/4, 7/8    \u2502 -\u03c0 \u22c5z \u239f\n\u03c0\u22c5z \u22c5\u0393(3/4)\u22c5\u0393(7/8)\u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                   2\u2575 3 \u239d3/2, 7/4, 15/8 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                64\u22c5\u0393(7/4)\u22c5\u0393(15/8)                "
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPIAAAAuCAMAAAAlSrTCAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nWdpFRqK8+2nI7q8gPt+Pfzb6B/qcL5eeQnaaAAAAAElFTkSuQmCC\n",
       "prompt_number": 19,
       "text": "\n          \u239b               \u2502   2  8\u239e\n   7  \u250c\u2500  \u239c   3/4, 7/8    \u2502 -\u03c0 \u22c5z \u239f\n\u03c0\u22c5z \u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n     2\u2575 3 \u239d3/2, 7/4, 15/8 \u2502   16  \u23a0\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\u2500\u2500\n                 42                "
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "integrate(fresnelc(z**2),z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAS0AAABICAMAAACUc1OBAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n1zj8Px5OWnopldXBAAAAAElFTkSuQmCC\n",
       "prompt_number": 20,
       "text": "\n                      \u239b               \u2502   2  8\u239e\n 3                \u250c\u2500  \u239c   1/4, 3/8    \u2502 -\u03c0 \u22c5z \u239f\nz \u22c5\u0393(1/4)\u22c5\u0393(3/8)\u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                 2\u2575 3 \u239d1/2, 5/4, 11/8 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               32\u22c5\u0393(5/4)\u22c5\u0393(11/8)               "
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAS0AAABICAMAAACUc1OBAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n1zj8Px5OWnopldXBAAAAAElFTkSuQmCC\n",
       "prompt_number": 21,
       "text": "\n                      \u239b               \u2502   2  8\u239e\n 3                \u250c\u2500  \u239c   1/4, 3/8    \u2502 -\u03c0 \u22c5z \u239f\nz \u22c5\u0393(1/4)\u22c5\u0393(3/8)\u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                 2\u2575 3 \u239d1/2, 5/4, 11/8 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               32\u22c5\u0393(5/4)\u22c5\u0393(11/8)               "
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAAuCAMAAABwK1ecAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 22,
       "text": "\n        \u239b               \u2502   2  8\u239e\n 3  \u250c\u2500  \u239c   1/4, 3/8    \u2502 -\u03c0 \u22c5z \u239f\nz \u22c5 \u251c\u2500  \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n   2\u2575 3 \u239d1/2, 5/4, 11/8 \u2502   16  \u23a0\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\n                3                "
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "integrate(fresnels(z)*fresnelc(z), z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAApBAMAAADuROvKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJlmVLuJMnar791E\nIs0RwGsuAAACfUlEQVRIDaVUO2gUURQ9s5/MbHYmLilCRDABm2AKA6aLyBYWgkJSWAiCbhUCFgnY\nWOlARCIqrkYsRGFtxCBCwMJGcRC/VWJnl02lYpFVo/iJ4rnv7o6ZyTY7c+Hdc+65n/fmzewCxnpH\nFRP7I9OJW02j3TidbkCmmq4f3X7KAWdnUg64krIfx9IO+JlygP0j5QBnI+WAfCM2IGti9WGqrajZ\n7sWwSsltA9agRk0fE+21IEyvtD7EvmuTbytAtqypgwZyU7PvSKIihRUtEj/uK3ceA8MjQFFD9JSE\nzMNeJ0RFCvslqbYnUDzOhpVlQHcGHA5DdgJYJUZEqb8hTm2NjbTMHzrZ6JZENLtOV6gCFWJEZAwe\nt2W/lCz5RLnrBtdN/5WSwrqOj4jA3GgDhXvuDEthfxMPnNBKWKx19p33gTtUvad/yWIi8n6mjtnX\nU8xw0+8G8FsBXk2I3PwTIbmTX+hj4hgyFYo+M3x2uWSa+UXwTN4iA3uE7pHIwG6umHgXxTJwSrJA\nj1webYHLY59VI3nOJY/glYFDpBER3gYGSnCZE9vWUBwm9AplnCuDo0iyhKG4CPszxnI4YK6cr74u\nBTzJINyKkPfAi3NvyrAngPwqcoSoCDzwPjru0cPXJYPxigHgwtAlw+Zg+Tsf6u6ZvsldW0Tg2d7t\nl/utTzwebTow8N/taFL9lJtBW1FzrfcfTugKlL4MFZKugI4WEVW6r7DJXzXcqm6SgLaiVFhb/xH7\nTadTigxoK0qF+zVS13ngNL+jzjubHYVa4lZtLEbvqvNpA/o1dN7Y6lhabrGEeDFhX9j2IWSJSMlK\n+RYXnJQvYf5MKdHJwyY3CGki8g9yyIss5WN3EQAAAABJRU5ErkJggg==\n",
       "prompt_number": 23,
       "text": "\n\u2320                           \n\u23ae fresnelc(z)\u22c5fresnels(z) dz\n\u2321                           "
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "source": "Differentiation"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "diff(fresnels(z), z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAsBAMAAAAX/bLtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
       "prompt_number": 24,
       "text": "\n   \u239b   2\u239e\n   \u239c\u03c0\u22c5z \u239f\nsin\u239c\u2500\u2500\u2500\u2500\u239f\n   \u239d 2  \u23a0"
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "diff(fresnelc(z), z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAsBAMAAAAa48KqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nX8kAAAAASUVORK5CYII=\n",
       "prompt_number": 25,
       "text": "\n   \u239b   2\u239e\n   \u239c\u03c0\u22c5z \u239f\ncos\u239c\u2500\u2500\u2500\u2500\u239f\n   \u239d 2  \u23a0"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "source": "Values and arithmetic"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnels(0)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 26,
       "text": "0"
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnelc(0)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 27,
       "text": "0"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "conjugate(fresnels(z))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAASBAMAAADF+LEmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVIl2ZiKrMrvNEN2Z\n70TGF0JdAAAA6UlEQVQYGT2PPUoDURSFv2EmGfMQMmBpE7QUZCJZwHMDQUgpQgrbgEuYJVinGuws\nJCkSLA1o6wZSGQtNOSkFQc99k+TAPec7jzc/F/bygZJ9FzSvQnMLi+i0N1BcGktHZrekG8WU9p9U\ntUpIChjrdk6t2Os9Q+goPqiV3qtsSitts1H+DRU0Xn7ssYkm7l8Il6Lo7Fd+owH7gXmgd/m1Uepl\nzzQyOBY9aViZLUk8vIrsG1GGWsXBmKhQb93BuvuVkRYcPpy86Yg4x+WPM+3grQa56RZst53Ot/C5\nO1A2y1DcMERtTitIcck/BPorwigkF1cAAAAASUVORK5CYII=\n",
       "prompt_number": 28,
       "text": "\n        \u239b_\u239e\nfresnels\u239dz\u23a0"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "conjugate(fresnelc(z))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACgAAAASBAMAAADbMYGVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEImrmSJ23URmu80y\n71SHC/xcAAAA5UlEQVQYGUVPvc4BQRQ9I7vLsqwoKJRf9CQkGol4Aaov+bqNgk40Coli8+lERKn0\nCCRKD8EbbKVeBS3nztp1kvMz996ZyQW+sHWMNKm2dFJdMfXTq5XodiAn4CYy9mHM6Wm4LyLMFYHs\nETAf8QTd2gL9AcOUbJMC54DMUwKbCMmOt5aQvUuRUCxau6EHXOHKTYF5Ef0lZ3DrNIc0petsKQvk\npfhHqgtlQ/K6wYFoiRAoBPIlwwn4lz7OwGqyDODs+WNz5EsNIyivytVsDieofJKsmSDlRzF6LC43\ndFD1+Ky9rNUq4g0xqCv/zyCs7QAAAABJRU5ErkJggg==\n",
       "prompt_number": 29,
       "text": "\n        \u239b_\u239e\nfresnelc\u239dz\u23a0"
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnels(I*z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAD0AAAASBAMAAAAatss5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIrt2q0RUiWYyzRDd\nme9T6PRGAAAA+0lEQVQoFWNgwAoawKIQEosCFgGw4F4MKbZiC2GgYBtEgs0AXYEHA+c3oNgBqPhq\nNHkOBQYGoBhcnwWaPIsDA0MBAwNLAFR8Frr8tw0gEX4gZnnMOgHMQFbCeP4XyEn7gdgiuJiBgQ+s\nHEkFW81fIE8OJMIIVMkjwCCkBATKLC5A4AoSvgfEMiDGDCDmmQBiwQFjAgNDDpC3D4hZgWx08zka\nGBguA4VB7ktj4IAwgGwYYFrNwKYA5HBNYGBVTnVjYJgEk4HQvNvLb4BYzAYMm7nXNDAwdEDE0Unu\nA1AR9PCFKSyFMFgLYAJoNAskXLagCcO53MCwAQJrBgYAvSgnK5qZt5EAAAAASUVORK5CYII=\n",
       "prompt_number": 30,
       "text": "-\u2148\u22c5fresnels(z)"
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnelc(I*z)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADIAAAASBAMAAADrvZC0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAq0QQiZkidt1mu80y\n71TFCCmFAAAA8klEQVQYGWNgQAOcYD6ERJUSA3OZAxCiJqIuyQ4MDJwPIELP4TLsTQwMERMYGDig\nItwGMKnVQFZ+AgMDTC07UBUYsH4DUiD1QhA+A88GKEO/AMgAOegDEMsW6EAYIMn1BiCSgYEZKMM+\nqQSo7jJEgOEHlGa7AGKkA3EbgyAIKHwECRxgYGBrANI8E4BEDxCDwEUgZgMKMIP06IFEYKZFANmm\nIIEPDAx8DxiAaoAMMOAOYGByALH2MDBo1Sk+YOBZAOKBQGF4EZguZ2AusO4E+gCoDRVYQLmI0IHJ\nsyhAWCowAQQtDGYyCyBEYCxzMIPdgAEAQS8nv7ty+8cAAAAASUVORK5CYII=\n",
       "prompt_number": 31,
       "text": "\u2148\u22c5fresnelc(z)"
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "rp, ip = fresnels(2+3*I).as_real_imag()",
     "language": "python",
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "rp",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAM4AAAAlBAMAAAD4ssu2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 33,
       "text": "\nfresnels(2 + 3\u22c5\u2148)   fresnels(2 - 3\u22c5\u2148)\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\u2500\n        2                   2        "
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "ip",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAAlBAMAAADfHEpeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nD4QdtwcGAy0GAAAAAElFTkSuQmCC\n",
       "prompt_number": 34,
       "text": "\n\u2148\u22c5(fresnels(2 - 3\u22c5\u2148) - fresnels(2 + 3\u22c5\u2148))\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                    2                    "
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(rp + I*ip)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAASBAMAAAA+r0T5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVIl2ZiKrMrvNEN2Z\n70TGF0JdAAABYElEQVQoFXVRPUvEQBB9ueSSu/XEgHY2hzaCoOEQsYxyP+DAUsQUIlio5z9IYZFG\ntD4RFnvxGrH0QAsbe7Hy4w/cqYWCeM7sJnH9erAz770ZZjZZIEeYs1/EMR23YarvXHRYW+Mzi5Tm\ngYUrn40c9dkg5cOcV+H1KLVhN7wXXdhWqRCLZ61RloATAy2aG2AwwAYURlQstHGjNewQcCOgSukO\nA1VMSzB0I5BP9Papo6eKQ6pjV8W8sUJ1jS5QPH/jK5+wkU1IJzrrkl3GLR1r8p3iMstSh+PXau9D\na+BUkWuKS8xqHCpJcpAkEVMcumuETeAMRR8YJeuYjhUIrmYTXR9bTW3QaicELkjxxzzC1r6+40qE\nPakNdFFqwYpJlZvwdupz2teNrhRPaZ8Xo3I0dsnKph/e77+ajaI2EWqt9qZUtFPC6d7givITZpjK\nyF/5wTBdaYgfVESGIfh9/oEt8Qlnyz82QxrqnAAAAABJRU5ErkJggg==\n",
       "prompt_number": 35,
       "text": "fresnels(2 + 3\u22c5\u2148)"
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "source": "Taylor expansions"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Sum(fresnels(z).taylor_term(n, z), (n,0,oo))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAAzBAMAAAAQr0tWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nb6+dqtAzdAbN/3oEY9n6GayD/wB2dddzMU6a4AAAAABJRU5ErkJggg==\n",
       "prompt_number": 36,
       "text": "\n  \u221e                               \n_____                             \n\u2572                                 \n \u2572                               n\n  \u2572    -2\u22c5n - 1  2\u22c5n + 1  3 \u239b  4\u239e \n   \u2572  2        \u22c5\u03c0       \u22c5z \u22c5\u239d-z \u23a0 \n   \u2571  \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  \u2571       (4\u22c5n + 3)\u22c5(2\u22c5n + 1)!    \n \u2571                                \n\u2571                                 \n\u203e\u203e\u203e\u203e\u203e                             \nn = 0                             "
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Sum(fresnelc(z).taylor_term(n, z), (n,0,oo))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAAAzBAMAAADvDW60AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\noW2z1Vcn7O372matKvAvDcWMl1Hc5n4AAAAASUVORK5CYII=\n",
       "prompt_number": 37,
       "text": "\n  \u221e                      \n_____                    \n\u2572                        \n \u2572                      n\n  \u2572    -2\u22c5n  2\u22c5n   \u239b  4\u239e \n   \u2572  2    \u22c5\u03c0   \u22c5z\u22c5\u239d-z \u23a0 \n   \u2571  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  \u2571     (4\u22c5n + 1)\u22c5(2\u22c5n)! \n \u2571                       \n\u2571                        \n\u203e\u203e\u203e\u203e\u203e                    \nn = 0                    "
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "source": "Series"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnels(z).series(z ,n=10)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAM8AAAAlBAMAAAAXcKCIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
       "prompt_number": 38,
       "text": "\n   3    3  7         \n\u03c0\u22c5z    \u03c0 \u22c5z     \u239b 10\u239e\n\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500 + O\u239dz  \u23a0\n 6      336          "
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnelc(z).series(z ,n=10)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAAmBAMAAAAhPqM9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 39,
       "text": "\n     2  5    4  9         \n    \u03c0 \u22c5z    \u03c0 \u22c5z     \u239b 10\u239e\nz - \u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500 + O\u239dz  \u23a0\n      40     3456         "
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "source": "Rewrites"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(fresnels(z).rewrite(erf))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAgEAAAAsBAMAAAAOZXaTAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 40,
       "text": "\n\u239b1   \u2148\u239e \u239b       \u239b  ___   \u239b1   \u2148\u239e\u239e      \u239b  ___   \u239b1   \u2148\u239e\u239e\u239e\n\u239c\u2500 + \u2500\u239f\u22c5\u239c- \u2148\u22c5erf\u239c\u2572\u2571 \u03c0 \u22c5z\u22c5\u239c\u2500 - \u2500\u239f\u239f + erf\u239c\u2572\u2571 \u03c0 \u22c5z\u22c5\u239c\u2500 + \u2500\u239f\u239f\u239f\n\u239d4   4\u23a0 \u239d       \u239d        \u239d2   2\u23a0\u23a0      \u239d        \u239d2   2\u23a0\u23a0\u23a0"
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(fresnelc(z).rewrite(erf))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAfMAAAAsBAMAAACDPkw2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 41,
       "text": "\n\u239b1   \u2148\u239e \u239b     \u239b  ___   \u239b1   \u2148\u239e\u239e      \u239b  ___   \u239b1   \u2148\u239e\u239e\u239e\n\u239c\u2500 - \u2500\u239f\u22c5\u239c\u2148\u22c5erf\u239c\u2572\u2571 \u03c0 \u22c5z\u22c5\u239c\u2500 - \u2500\u239f\u239f + erf\u239c\u2572\u2571 \u03c0 \u22c5z\u22c5\u239c\u2500 + \u2500\u239f\u239f\u239f\n\u239d4   4\u23a0 \u239d     \u239d        \u239d2   2\u23a0\u23a0      \u239d        \u239d2   2\u23a0\u23a0\u23a0"
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnels(z).rewrite(hyper)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAM8AAAAuCAMAAAC4R71KAAAANlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABHL6OuAAAAEXRSTlMAEKtEMol2\nVCK73Zlm781Aod7tH+cAAAUZSURBVGgFzVlZFqQgDARBxHWG+192IBAgEdul7ffGj1b2KghJQQvx\n80cNS6fZKJJnsPL/KmkVgbNqoVaSI4TuWcZ3SUlH/K4z3tpukmRZIZQjOa/zEfNSDSC7N+lJRicM\nRIYLGSfrcx/ROIRuw6N743IiZn31u+06031HV+yEzxNEcvJmgM+bfPoOe63eamWETtZH3EekpjLe\n/dalLfvSHLkYgi9wtX379Pt8xGgylBf5jDvHFaBLx/zzD/hol23gPT5Vp3m2BrN0fE/9gI8oU/ke\nn7G1ezKz8vELPiUovMZnZ1eFAf36BR+x4ib9yKclVyi4kjJcB/gil55Sy3/9+UuSu8QBIm3MTjr1\neWvOW+rnoHUsbcmV3fgpY7tobg/9m/QujDtQ5fGlR6FH+MinJVewB/aWRx2VOUwtntmbDrLJETEj\nly3ziVHL9qObZlKJwdzLFV4hpQecIFZezWEq+cjnGJGHLl0lBIQwouIz7YIFAwLJnVyx8+pm/4yO\nte8b28d3QeYwjvCRTwtEzpvJmIOt+XRjrvbxYydXpthwQYeSWo+4IWlvZA5j0WM+y1z3LX1cq9bH\ncBlf103fLbkik3zRzEqnpjugc/gdH+U9QpYBQizGmLXslYHaYoNNVFo8rEA7b8u26jo0XoktpO7Y\nHMbch+ujjbRL2f/Q11TSmvoKT31MwSLsuW41QmnRkCtz0LKNteCqE8Zjcwh5p/461oq/BZQFdJCb\nwAlpXDm9We5fOy17qRRMu1mU6YtmrUeYtrlzxJBjKe8ut6nmMObdWZ8aFPbYBof7AGtpKewiTHaI\nltIZUwGEmSFITBqvd9OT+iVzGPNu8OGgECwDB9nOZDniom/obTEkTdzX0K+JD4SZwS8ii9fUfBs6\naQr2AnaKeseO+Qlzl6y9fgWcNSjA7X8ouJTLA4j3fkLgQU9xkY98YPuEHli8pnwaOqm31s5gzDfW\nx49TgUrAxQ4cFOz4KD97CTYYFFkh5DPlrUPjNbU3v5hFwcNo0lNR0cXf4lOBQjp7cJEP3SBCjJ7A\nBCTUaAZFz2GJjyVurIrXfDu2dFLy6Lf4FFBIpwEu8iHz77MmP4VzIOm3htwiM+wkLpydJ7cVfUni\nNSHqffLuWkdgw1t8MihE0gIXyg71MDakb7S3KpfGa+9eyLPTSQIF3i0+pM9PCRvjqY+YpgTZ4wZ7\nPixer3ljiYNrHfQ1x3zyVeJVVBVeBXqn9zZ9QZkqH4mZeVbxGnodK30bEHOdJBYUrEd8ylXiRVQV\nGy/nQszRwQbAX5CyJwly3G7oJDGgSDri40eNIuMRKggkl8/I5wzzgfe06imfR6jgdsn1y2KYIZ3i\naVeQXN+2q/ncUz6PUAX/at3offT2DqHqwIuapaJUZaHeqUrxE+ztESpwBxqE8pWTHQ744d2j//pQ\nB4rO1ucRKhhdQtBY+AXzGaB2ub5wQLzE5xGqDcRH4pMPCW2kF3OnElHpWQLbJ4Fwtj7iAap0d96F\nIPiSvYkhG1w5S+jqNIc3V6d8HqBKMdSGf2xe8gcoZv0MlbOELio+31yd8rmPKl/M6a6f+VEHzeP2\nG66DoFV1lsjOM99cHfEpV4m3UTX/GLyNf9cgiHt88CyBWeXm6ogPtrz/hgW93+y0RfXHLJ4lPA14\nqpur9/ls7C7wFOjVCgo1Zz5LoDFXN1ev8wny9UdPEp3sLJEGS77ubT5DdVJ5ndYQ9gs/S8Ao+ebq\nZT72l3Ren587Hf4DAYAmUmqyuaUAAAAASUVORK5CYII=\n",
       "prompt_number": 42,
       "text": "\n          \u239b         \u2502   2  4\u239e\n   3  \u250c\u2500  \u239c  3/4    \u2502 -\u03c0 \u22c5z \u239f\n\u03c0\u22c5z \u22c5 \u251c\u2500  \u239c         \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n     1\u2575 2 \u239d3/2, 7/4 \u2502   16  \u23a0\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\n              6              "
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAASBAMAAADF+LEmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVIl2ZiKrMrvNEN2Z\n70TGF0JdAAAA50lEQVQYGT2Pv0rDUBjFfyFJYy+CgY5dREdBUukDXF9ACo6l0KGr4CPkEZw7BTcH\nMYPF0YKuvkAndbCO7Sg49Hw3bQ985/zO5ebPB3v5QMm+C1qD0NzcIjrtXysujaWO2YRsraiNpXYF\nSQlT3S5oFHu9ZwzHik8aZXcq68rKkdlNsYQVpK9/9tiTJr66EC5E0dm/fKQB+4FZoA/50CjzshfS\nHLqiRw1fZgsSD28i+0aUo7biYEpUqrdv4bf3k5OVHN6fvOuIuMAVD8/awVsNcvUWbLedzrfwvTtQ\ntqpQ3DhEY04rSHHFBnjmJsd78dawAAAAAElFTkSuQmCC\n",
       "prompt_number": 43,
       "text": "fresnels(z)"
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnelc(z).rewrite(hyper)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALEAAAAuCAMAAABQxwhhAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
       "prompt_number": 44,
       "text": "\n       \u239b         \u2502   2  4\u239e\n   \u250c\u2500  \u239c  1/4    \u2502 -\u03c0 \u22c5z \u239f\nz\u22c5 \u251c\u2500  \u239c         \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n  1\u2575 2 \u239d1/2, 5/4 \u2502   16  \u23a0"
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACgAAAASBAMAAADbMYGVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEImrmSJ23URmu80y\n71SHC/xcAAAA5ElEQVQYGUVPvY4BURg9d2OGYSxR2EIpehKbaCQbL0Al0U0UdBuNQqKY2G4jolR6\nBBKlh+ANplJT2No5d5g9yfn5fu69ucA/PBtjTbqfNpkvmal2aiW6F6kCLpJxiNSMnlZB5IpAdg84\ndxZ2g+6ugW6PYUK2SMHfIfOnwCGuZDtYKmRvahKGTXczDIAzCjopOCdpn5yiUKf5pKOpv6bMkVdz\nQJoTZUXyeIoL8SeuwHukJxkOwEJzHIHf758I/pYvNkehehjBBBV+zeNygo9n0jcTvIVxjC97tRs2\nmPqrtl626hbxAF/aJwR9PEelAAAAAElFTkSuQmCC\n",
       "prompt_number": 45,
       "text": "fresnelc(z)"
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnels(z).rewrite(meijerg)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAABLCAMAAABnT8qlAAAANlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABHL6OuAAAAEXRSTlMAMrsQmSKr\nRHZUzYnd72ZAoYkXTVUAAAhXSURBVHgB7VuBtoMmDFXRitq6+f8/uwRISBCsdHZ1Z/Oc9xQTQi6B\nEDBtmn/DZdp/g5ZHOg7jEfUNrV3eMJwnm7+jx/lmEs5hNsmbmuKF8Jt+rWn5Gl7zt9A3V8Jvuuka\nTBVS5pomzSMdoJfCN8+hQvMrWJfHeSntYre0sy6F34zP89pcwdm+6ib+l+E3nf0U1Whtapr3orpK\nx/1t+O1WZw5GaOam6bh08qG6tW/Db2rtQUAnmMQ7x0TE0r2rmPlOxtfhj1tJ1+P3I8LPLpwdudNh\nWRd6dsLMVhuzfR1+88piaNqNr3w/wMh/Zib/tLwIMq7wMEXiZV/x+dzTDv4ffx5U5I4/4ElJvdKQ\nqd07n2DW8UFAuRY+EPwWV5VZLtxz7dhvdvAPFj7R8Uqf1tpHOuoWfjFmnV/bKxGZAgyaPBqCv2K/\ndmJsmR2YjFj9alfjAH7seCXDwNqWrrfji+Hvexhrvx9H/brkBwjBtw6+WFinbEcrXdPCBfBbdG6b\nHISNWecI/5lZi1s07Lr0Z6Niszz6ZRkGFEXwnfVnAX+pnPrD0m3PXil+HPNTy7oTAanZ1DS1jYD/\nyCzfOKst/LWbGLxKanCM/p19OiWXF/pCUsLNfU/wXF3eyyix7wr1gx8l9srC0yDh2/3SN6DxX2i4\nx4HFJuqaLuzijBvdDv4Iff6EySGD6mfeV6B+p6+P4K/KkRmwkbD+pEcGauI8pZsUS3m+GgqYexYA\n+Ea7YTjQw5BqwT3EOQb9qWxwGrFi/AT+CHYUbmq11r7inGq1X4DWnPF9qx1Y33RhpOMEesCgQNOC\na1j9vB43Mb99LaTyEz8UJxJzvH84gB863ssQOrfWDKvTOOr+jGYZ2L0S7J6JBqE9WrOYcXQdaNfR\nLg7uOAT4XXaAZLqE23mPsshxAF/ViToPznZIZN0NjFD2qIasAt3nwjgTfWEHs6Y1zbA6R+gbGBwy\nmEEB/uY9mu1nsX+YxGgLesVuDi8+uZ2En+pMTXndqeTvcfB63xwnrA2zFUJ3dlutH9YTxFKd68KN\nSJvyMLoNKOlJNk7rLhbjKuWog4LeoeMLrcEBun9AQVJnEhx0p6K/b+ySRtyTRONPINlZEexLLnyM\ncb71A/wV4LdvBreGD3HXWFhVStEranvS+sApdPYwwS1H3ekV3CP85gnjfqFpgR6zwT/c3YXVfEIJ\n3v7j7AP6PqCgBYBNlxhYD35wo+XNJoUO0FZynYYvdCYRQnd6hfc4+BtYBNn4bbeCc0c/gIH702Ee\nOzuNj6QTZzfoRx8iCNMlBmYfQ22XD5o/ge97fbLkkFlnai6rO8L31nRsr96S8V9uHiF8jF96HAaw\nfTCz7wjHHf7ZR48nX0EM654aWLaDw/ixd49BIIuQrbjnkvVDr68LBLiOkXUmEQXdgV9Y027R7VPF\nyrvUXRlYjDInciyee0oRjnWCCMppWYIfZidKxOik4hpk2KP6okKIYI26JwZ+iZVhQoehh0NWhH85\n4trq1plj+O1rmuK6JQQePI4csyITRzwHNY5JET54N2ngTgwshFE++5IisLEZ55XbQR7DXxGKbPJY\nU0dd91ueE7XKLKT7zsDqrAt8VOpCSaSKXvGlH5LuXOYYvltKc0dwJDpz72lJz9A+eeXgw7ZgZ+D8\nudKJJnzE0GJQcgx/wClVCb/69PlQYbHjSw1spJM5FJIQXTTmo8Zj+M1cP/iLDihRoq4oFlOuKM6V\nKEplWnzYkwR8Cnoju38KvW56G/drKU+2rD1fluWTlz4g1jWXD6eZH/yuE8rW102dLn2q03EDmR0f\nTFy1xhwLkFTv+txJ6eXwZ97wyBa/8/xUY+JghU5I7lzpzcL3mcbVXx0/a8bXmuTol4ftidBAaulQ\nxoU9boN1tfVz57yJMhcWxX5BHbbrJojU8l50Wlb/Of1i+MkJuFbj+pILhbxYddiuW4qk3fpxMfya\nZBOt42cl/uilD9uVMEH6MvyhMkBWan5SoGyi5LBdihIk6Ijkutb66gNs0tJ3is6Lwf5FH7bLtgRJ\n7MQDx6Xwl39w0SOEmBbiL/LrVBb3IulK+JPYgIu2v/wYvo2pw3bd5AHpQvjDT9BrpP+XbtIDtNP6\nb95vYoT/qBoTfDU7D72O+7zcn3HCZqjwzSunUh13TsLt3g3+S/FJveq4Twr9IduK53Snrzru02J/\nyYjfpc5fddzn5f6EE/c5Z7Po4OC/ivsngOoaHSECLQb6O1F13LvqN3yxrj5l6JxqddznZH6Pa3dq\nwU0VKYoQspLVOxZx+4d85rdT24RtV4i0GYqqQlnJxEypPMx9tweVDrzuTy2ivpg/tL90Fc5KzjPv\nq//4jU4Hlqfbe8X4Z42cIws8SRVMuHKfSJi5kdx7ob99o9KB35jMhhnNObKgeqaKz0omZkg/y46a\n38Km1lU6cEygJLK6tyHWpRxZJO6rhKxkYuaMWiXqVgVMB8Yrnz0R82s9nXNkZRVm4qzkIExxu1bu\n9s+lA4NSIdMqUY/za0MyCsRxISNNVGGmmJXsD+YVdyL5JkVMB8bLZVz4R/2f8mvd74hjjqyu4phi\nVnLjf3SsuLXUm5QoHbgZvBdPknDhazcFMRTrxuOOUAWQMBOhIuYmchPpTnf03X4DZ/KnGDG/Nnxo\nohxZQMFVIhNho69SgptIN7pzOjDolHV9Ir82Qw+vBBNhyzAT6T73mA4MOonfzbCGIr+2Fdl+RPdV\nBBMRcsxEu889pgODTplZKvNrV/IBQn1XRTIRLcdMtJveTRLBJmrGODYSilVyzLHaPZ/4BwI59cbs\nV9ZClTxzTuyd3pUz1xvD33u1wtkqJWZd9XYl3K8XLls43sxWKTEXZFe9/gt36UhP31wSRQAAAABJ\nRU5ErkJggg==\n",
       "prompt_number": 46,
       "text": "\n                     \u239b            \u2502   2  4\u239e\n  ___    9/4 \u256d\u2500\u256e1, 0 \u239c       1    \u2502 -\u03c0 \u22c5z \u239f\n\u2572\u2571 2 \u22c5\u03c0\u22c5z   \u22c5\u2502\u2576\u2510     \u239c            \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n             \u2570\u2500\u256f1, 3 \u239d3/4  1/4, 0 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                           3/4             \n                   3/4 \u239b 2\u239e                \n             2\u22c5(-z)   \u22c5\u239dz \u23a0                "
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fresnelc(z).rewrite(meijerg)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAABICAMAAADh27gLAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 47,
       "text": "\n                     \u239b            \u2502   2  4\u239e\n  ___    3/4 \u256d\u2500\u256e1, 0 \u239c       1    \u2502 -\u03c0 \u22c5z \u239f\n\u2572\u2571 2 \u22c5\u03c0\u22c5z   \u22c5\u2502\u2576\u2510     \u239c            \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u239f\n             \u2570\u2500\u256f1, 3 \u239d1/4  3/4, 0 \u2502   16  \u23a0\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                          ____             \n                4 ____ 4 \u2571  2              \n              2\u22c5\u2572\u2571 -z \u22c5\u2572\u2571  z               "
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "source": "Limits"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "limit(fresnels(z), z, oo)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAlBAMAAACJ5mVtAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEKtEMol2VCK73Zlm72LS\nT58AAABdSURBVAgdY2BgVGZgYGAJew4kGRjIITkiX20GayaSeAcChNQe3VnAwMDWwPKGgYE3gUGX\ngYErgCFOAKRrLohgfAYiOTeAyFQQwZ7ACCTNGNiAfplzJhOo6927lwwAwqYc3HKvKN0AAAAASUVO\nRK5CYII=\n",
       "prompt_number": 48,
       "text": "1/2"
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "limit(fresnels(z), z, -oo)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAlBAMAAABFf1+GAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIrt2EKtEMolU3Zlm72iX\n7e4AAABxSURBVCgVY2CAAdcEGAtIV9hNQOIx8A0kT0JvNbLTkN1FVbaQEhAoM/C9A4IHVDWZgYGn\nWxPJREOGugMI7mUG1gsI3goGjicIHgMDE5IcA4OfAbKcNjKHuQGZN5nBAcFlM2BA0ld05rACQu7e\nu3cKDACvRhvL+nKZMgAAAABJRU5ErkJggg==\n",
       "prompt_number": 49,
       "text": "-1/2"
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "limit(fresnelc(z), z, oo)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAlBAMAAACJ5mVtAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEKtEMol2VCK73Zlm72LS\nT58AAABdSURBVAgdY2BgVGZgYGAJew4kGRjIITkiX20GayaSeAcChNQe3VnAwMDWwPKGgYE3gUGX\ngYErgCFOAKRrLohgfAYiOTeAyFQQwZ7ACCTNGNiAfplzJhOo6927lwwAwqYc3HKvKN0AAAAASUVO\nRK5CYII=\n",
       "prompt_number": 50,
       "text": "1/2"
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "limit(fresnelc(z), z, -oo)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAlBAMAAABFf1+GAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIrt2EKtEMolU3Zlm72iX\n7e4AAABxSURBVCgVY2CAAdcEGAtIV9hNQOIx8A0kT0JvNbLTkN1FVbaQEhAoM/C9A4IHVDWZgYGn\nWxPJREOGugMI7mUG1gsI3goGjicIHgMDE5IcA4OfAbKcNjKHuQGZN5nBAcFlM2BA0ld05rACQu7e\nu3cKDACvRhvL+nKZMgAAAABJRU5ErkJggg==\n",
       "prompt_number": 51,
       "text": "-1/2"
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "source": "Plot of the two Fresnel integrals $S(x)$ and $C(x)$"
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "t = linspace(0, 8, 8000)\nu = [ fresnels(i).evalf() for i in t ]\nv = [ fresnelc(i).evalf() for i in t ]\nu = array(u)\nv = array(v)",
     "language": "python",
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure(figsize=(10,8))\nplot(t, u, label=r\"$S(x)$\")\nplot(t, v, label=r\"$C(x)$\")\ngrid(True)\nlegend(loc=\"best\")",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 53,
       "text": "Legend"
      },
      {
       "output_type": "display_data",
       "png": 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4hkfxtHfvXhgMBgCA0WhEYWGhy/H9+/cjNzcXAPDwww8jO1v9l9pUorprYsST\nWpSYxe2k6lM19zylpbF2BTabpsOqZtQ2irMdZ5E1P0v1Y1fMXYGzHWdRUqIs6wSwrVvOnAFGRlRf\nzmdsgg3b92/HN5d/ExXfq8B/fvKfKG0tnfiJEARBECI8iier1Yro6GjH7e7ubpfjJSUl6O7uRllZ\nGZ555hn/zHCCEAQB57vPT0nPk5qyndFg1NzzFBEBREUx75W/UBKTqq4qJEQkICI0QvX4y+ctx5n2\nMzhxAvhS78sSEQEkJwPnzqm+nM8UnCtASGAInv37Z5GsT8Z/bPwP/OyTn3l8jCAA3d3+78k1FSC/\nBh+KixiKCR+Ki2942OyDIdczKDY2FtnZ2SgsLERBQQG2bdvmcnzHjh1ISUkBAOj1emRlZTleNHva\ncCrcbh1oReDFQJw6empKzMf5dnV1HhYvVnb+qG0UrQOtGBkbwZFPj2g2n/R0YN++YuTkTF48/vLu\nX7CwZyHsqHn84tjFMJeZ0fn5ATz77FbFj1+4EDh5Mg8rV07s8/3Nid/g1uBbcfjwYeTl5eE7Wd/B\nj1/6MV6f8zq2f2W76PzRUeCGG4px9Chwyy152L8fOHJk4uZLt+k23abbV+Nt+/83NDRAFYIHdu3a\nJRQWFgqCIAj79u0Tnn76aZfjTz/9tLB//35BEAThxRdfFHbt2uVyXGb4KcXH5o+FDf+7YUKudejQ\nIcXn9vcLQliYIIyOKh8/6VdJQl1PnfqJeeD++wXhxRc1HdIFJTF56MBDwlOfPOX1NRY/t0yIzDgp\n2GzKH/PrXwvC//t/Xl/SKy5aLwrRv4gWLo9cdonLA+88IPzyyC+5j/nFLwRh82ZBGBwUhPx8dns6\no+YzNJOguIihmPChuPBRqlsCPAmr7du3w2xm/pn6+nps2bIFACvnAcAdd9zhOG61WrFmjfLGhVON\n6u6p2Vn8/HnmOQpU0XrKH+0KjEbArK2VSjUVHRVYOnep14+fhxVIXH0GOp3yx6xaBZSUyJ+nJfvP\n7cfXFn8NoUGhLvffteQu7D23V3T+pUvAs88Czz8PhIUBL7wA/PKXtDcfQRCEv/AonuwG8KKiIkfJ\nDQA2b94MAEhNTYVer0dBQQF6enrwjW98w8/T9R8TtdIOGE8bKqGmhvVZUkOqQXvTuL/Fk5KYnOs8\nhyVxS7y+RrBlOcJTz6h6zIoVzPM0kWb5A+YDuCXtFgCucbk+5XpUdlaiZ6jH5fz9+4E1a4DMTHZ7\n8WLm63o0EurOAAAgAElEQVTjjYma8cSj5jM0k6C4iKGY8KG4+IZH8QQAO3fuRH5+Pnbu3Om4r8Tp\np/jOnTuxbds2/PznP/fPDCeIqbrSrraWZZ7UYNQbNW9XMNmZp4ErA+i41IFUfarXYwxdWIbhSHXu\n78hIICYGUFsO95bh0WEcuXgEN6SKW6CHBIZgfdJ6HKo/5HL/a68B3/ym67n33AO8/ro/Z0oQBDFz\nkRVPM4WJLNs5G9XkqK1lfZbU4I9Gmf4WT3IxqeysREZshk9b57SVL0YXqlU/btkyoLzc68uq4oum\nL7A4djGiw9gqV/e45Kfmo7B+vGWIxQIcOQLcdpvrOLffDhQXA/3TtL+mms/QTILiIoZiwofi4hsk\nnsB+7Tf3NfuU1fAX3mSe/OF5io0FrlwBvrS7TTgVnRVYGue932l4GGgqT0H3cCsGR9SZgSZSPB1q\nOIR8Y77k8RtSb8AnFz5x3D58mG1yPGeO63kREayf1UR1SB+4MoBPLnyCkbFJaIpFEAQxwZB4AlDb\nU4sUfQqCAxW0ndYAtZ4n1eLJD5knnY5ln+q1HdaBXEx89TtVVQGm1CCYok2o6VbXLn0ixdPx5uO4\nduG1jtvucVk+dzkarA3oG+4DAHz8MbBpE3+s/HygqMhfMx2nf7gfuXtycf/b9+PWv94Km+B/gxj5\nNfhQXMRQTPhQXHyDxBOm7kq7/n6grw9YsEDd4+bPmY++4T4MXBnQdD6T6XvyVTyVlzMRtDh2Maq6\nqlQ9dqLEkyAION58HLnx0l08gwODkTU/CyUtzHc4FcTTf37yn7hm4TWo/sdq9A/344+n/8g9b3QU\n+MMfpreRnSCImQGJJ0y8WVxprbmuDjCZgACVr1KALgAp+hQ0WBtUz80TRiObkz+Qi4mvZTu7eMqI\nyUB1tzrf0+LFLAPo721azBYzZgfPxoKIcbXMi8vahLU43nwcHR1AUxPbRobH6tWs7NvX56cJA+gb\n7sNLZS/h8esfR2BAIJ684Un86uivuM11H34YeOkl4N//HXjlFd+uS34NPhQXMRQTPhQX3yDxhIlt\nU6AGb8zidqZTr6dLVy6hfaAdRoPR6zHOnvU+8xQWBiQlsZ5b/uR483GsSZDvlbY2YS2ONR9zbDUT\nJLFPQHAwkJUFnDyp8USdeKf6HVyXeB2S9ckAgE2pmzBwZQBlba6bhJvNwJ/+BLz3Hmut8MgjwNCQ\n/+ZFEAThT0g8YeLLdkprzd74nez4w/dkMvlPPHmKSVVXFdJj0n1aaVdeDixf7p14Alj2qUr9w1Rx\nvEUsnnhxWRW/CqWtpYo2Oc7NBU6c0HCSbrxV9Ra+sXi8v1uALgBfX/x1vFP9jst5L7wAPPAAEB3N\nBF12NlBQ4P11ya/Bh+IihmLCh+LiGySewMp2i2JUdqKcALxZaWcnVX/1tSuQ4nz3eZ8ygwMDQEcH\nkJo6XrZTa2rOyPB/5qm0tRQ5C3JkzzMajOge7MYXZb2ymxyvWQMcP67RBN0YHh3GQfNB3Jbh2ifh\ntkW34d3z7zpuCwKwbx9w333j53znO8D//Z9/5sWuKaC1v1V2b06CIAhvmPHiqXuwGzbBhrjwuAm7\nptJas6/iSesu48nJQGMjM/5qjaeYnO8+j/QYL+uXcN3iJmpWFCJDI9Hc16xqjEWL/CueBEFAeUc5\nls9d7nI/Ly4BugAsnbsUJxrKZTNP/hRPJS0lSI9OR2x4rMv91yVeh/Pd52EZsgAASkuB8HCWvbNz\n442sP9WlS95dW+4ztPPdnUh5LgV/9+bfzSgBRT4WMRQTPhQX35jx4qm2pxZp0WnQqdnwbILwxfNk\nNBg19zyFhgLz5jGT8kRS01OD9GjfxFOGU+IqIyZDdelu0SKgWn1/TcW0DrQiUBeIeXPmKTrfNGcF\nrhjOIDFR5jwT683V0+P5PG/49OKn2JC8QXR/cGAw1iSswRdNXwBgPqfbboPLnoJRUayk6I/VgAfr\nDqK4oRhtP2zDmfYzLlkwOxUVrIz71a8Cly9rPweCIKY3M1481fTU+JTV8AYlteZLl9gXXkKCd9ew\ne560/tXtr9Kdp5jU9NT4VFY9f951f8C06DTUWdQtG/R32a68oxzL5i4T3S8VlzmXlsOw+KzsJsc6\nnf9aLXx68VNsSBKLJwBYn7Qen138jJ33KcB7Gps3e9/E09P75bljz+E/Nv4HDGEGPLr+UTx37DmX\n44IAfPvbwM6dzFT/s595N4epCPlYxFBM+FBcfIPEk49ZDX9RV8eEito2BXb0s/QICghC91C3pvOa\naN+TIAisbOdj5slX8TR3LmtV0K1tOB2cbT/LFU9SCG0rYItTtsnxsmVstaGW2AQbPm/8HOuT1nOP\nr09k4ml0FDh2DLjuOvE5110HfP65tvNqH2jHkcYjuGPJHQCAb2R+A6faTrmUaQ8dYt3y/+mfgGee\nAX73O2BQXdN5giBmODNePNnLdhOJklqzL34nO/5qV+CPXk9SMeke6oYgCCJfjRrcxZPJYEJtT62q\nMXQ6/2afyjvFfidAOi7W6uXoCTqrKLO4fLn2mae6njpEhUZh7uy53OOr41fjVNsplJbZkJTEVtm5\nk5sLnD7tXdlMKi4f1n6IzcbNmB0yGwAQGhSKG0034v2a9x3nvPwy8OCD413zc3KA99/nDuc1H9Z+\niNUvrsYrp17RdmAZyMcihmLCh+LiGzNePNV0T83MkybiyaC9aXyiM0813ays6q0nTRCYV8nZ85QW\nnYa6HvUK0J+mcamynRS1Z2MwKzgUrQOtsuf6I/N0qu0UsuZnSR43hBkQHRaNdz+rw7p1/HNmz2Ym\nci37UB00H8QW4xaX+76S/hW8X8vU0dgY8OGHwNe+Nn78rrt8a5vgTvdgN+576z7845p/xMMHH8b5\nbtc3zaVLrGS5bBnQ0KDddQmCmDhmvHiajMyTklpzTY33ZnE7RoPxqmlXIBUTX8uqHR3M1+Kc+TBF\nm1BnqVPtB/OXeBqzjeFc5zksnSvuoM6Ly9gYE4SL4zJQ3SXvYrdnnrS0v5W1lSF7vkRr8y/JXpCN\nz2pPYdUq6XNWr2ar8dTCi4sgCCg0F4rE08bkjThy8QgEQUBJCVv04Gy037qVbXOjVXxePf0qbjTd\niB1ZO/D93O+LPFf/9V9so+077mClQy0hH4sYigkfiotvzGjxZG9T4EtJyF9oVra7SsSTFFqbxQEg\nMjQSs4Nno22gTdVYGRn+WXF3sfciosOiERkaqej8+nrmwVoyV9lWM7GxrEt6Y6OvMx1HLvMEAFnz\nslBpLcPKldLnrFzJSndaYLaYERwYjFRDqsv9iVGJmBU0CzU9NSgsZG0SnElOZlmwc+e0mccrp17B\nAzkPAADuz74fr5W/hpExtrfP8DCwZw/w1FPAj37E/GBafZ66BrvwwwM/RHFDsTYDEgQhyYwWT/aV\ndhPdpuBq9jzFxTGzbW+vpsNKxkQLs3gGp7+mKVq978lfmSdPTUB5camoAJYuVbdP3+LF2s5diXha\nFpeFzsBTWC62cjnwVjzx4nKi5YTkpsrrktbh88bPcfQocO214uM33AAcPqx+Hu409TWhdaDVYaRP\nikpCclQyjjUfAwB88AEr1xmNrPXH9u3AX/7i+3UB4N4378XJz0/ijr13oLHXVSn/7W9ASgrw619r\nc62rCfL28KG4+MaMFk+TUbJTwtAQ0NkJ2R4+cvhjc2Cdjv0Rniivht3z5C28zBPg3Yo7e9ZN656L\n57vPq8quOcRTrLKyHaBtn6r2gXZcHr2MpKgkj+fNGchCwILTCA+XPmfFCpbx0aLxaklLCVbH87uG\nXpNwDY41HcPx48DateLja9YAJSW+z+Fg3UFsSt2EAN34n9ab0m7CB7UfAGB+q9ucGrLfeivw0Ue+\nX7e0tRQVnRX48cYf4zvZ33EpFfb3s61xdu9mJUOtRPTQCG1OSMxcZrR4mqw2BXK15ro6tpVIoPdb\nuQFg4uli70XVW5HIjpuivXiS8rD4+hpVV/PFk8lgUi2eoqKAWbOYj0pLzvdIiydeXLzJPGm5UrCi\nswLL5i6Tzdi2n0+EMMuKvuE+yXMiIoD585nHTw28uJS0lEhmnlbOX4njF08jMBBYuFB8fNUqbYzr\nhfWF2Jy62eW+G1JuwKcXPgXAmoLm548f27ABOHUK6JMOkSJeK38N317xbWzZtAUPZD+AP5/9s+Nz\nX1DAxOHdd7NVhr/7nW/XAoDnjz2P8KfC8WjRo6Jjf/mLtgZ8XyFvDx+Ki2/MbPHUXTMlM09mM8ty\n+EpYcBgMYQa09Lf4PpgTKSnMd+Nv2i+1Y1bQLBjCDF6P4SnzpLZsB/hnc2S1pcnqalaGMxqMaO5r\nxvDosOxjtCw5VnVVITMuU/a8M6cDMC9QPju2ciVwRlnLKknGbGMobS3Fqni+O33lvJU4130Wa9ba\nuI1Fly9nAm7Ix2TK0aajot5XuQm5KG0thblhFFYrXMqY4eFMuB096tt136x6E9/IZBs0Z8RmICo0\nCqfaTgFgYubv/o6dd889wP79gM2H31Pdg934afFPUfr3pXip7CWX1YQFBcBjjwH/+q9AYaH317Az\nk7bWIa4uZrR4qu2pnZTMk1ytub6eZZ60wB++J39knngx8dXvZLOxWJpM4mMmg8mrdgX+MMx7Ktvx\n4mI2s+cUHBiMpKgkRSJQa/GkZKPmc+eANP1iVHZVejwvMxOoUrdbjigu9dZ6RIdFIzqM01AKrHVC\nyFg0krP4L15oKBOkvpjXLUMWdFzqEL2W+ll6JEYlouDTclx3nbjxra/7Dzb2NsJ62Yrs+dmOuGwx\nbcHBuoO4fJk1Ir35Znbu0qXsufrS9+vV06/i9ozbkb0gG/euvBcvlb3kOPaznwEvvMBKhE895f01\nAODtqrcR9l9heOzjx1zu7+0FnnhCueAmbw8fiotvzFjx5CgJTfDWLEpoaGACRQtS9Cmar7hLTZ0Y\nz1NdTx1M0Rzlo5DWVlZq43luvM08ad0kdHh0GK39rUjRpyg632plnc5jYtjtjFhlpbvUVKC5ma32\n8pWqriosjl0se151NZC9MFN2H8HFi9WLJ3ekWj04E9a7EiFJ0uooK8u3DFhpaymy5mchMEBcb1+b\nsBZF1ce4bRt8FU9HGo9gXeI6lzJqfmo+ii8U49gxJpgiIsbPz8vzflscAHj3/Lu4c8mdAIB7lt2D\nt6veBsDEeXs7cNNNwLZtQFkZ0KZuQauDkbERfO/972Hfnfuwp3SPy3voH/6BtZb4yld86wzfcakD\nJ1s0bDJGzChmrHjqGeqBIAiICYuZ8GvL1Zo1zTwZUjU3jU+U56neWg+jwfv6pac4xobHYtQ2ip4h\ndTvmal22q7PUIVmfjODAYO5x97jU1zMBZ/+ezIjJEDVh5BEczJbkayH8lIin4WEm1tamyWeevGkB\n4R6Xc53nsCRuiec5XVyBoUhpdbR0qW/tCk62nsSqBfyyYc6CHFR0nUZOjvhYbi4TT95WqOziCRiP\ny5qENShpKUFxsYDrr3c9f+NG71cW9l7uxcmWk7gh9QYAQNb8LPQM9eCC9QLefZeZ4QMCmDfwxhu9\n79z+Xs17MBqMuC3jNty78l5Hp/amJuDAAbbZ9MqVwF//Kj8W72/LwJUBXPfSdcj/Yz7eqHzDcX9P\nD/OhffObvpU2rwbI8+QbM1Y8TVabAiVoXrbTOPNk9zz5245gtphh1PtHPOl0OtYsU2XpTuuyndqV\ndmaz63MyGUyKu8hrUbq7dOUSOgc7kRyV7PG82lr2Plk+Xz7zZBdPvnxZnes8hyWx0uLp0iXg0oVM\ndNik55KZ6T/xtGzucrTZyrmZp6Qklk1sb/fuukebjuK6RNfNA+Mj4hEcEIxDZRdEHd6vvdb7TNex\n5mPIXpCN8GCWzg3QBWBT6iYUNxTj0CHWcNROXh7bFNob3q95H9sytwEAti/djrerWXZr3z7g9tuB\nOXOA++7z3pj+5zN/xrK5y/D6Ha/jicNPOO7fvZu9b+vqgL17vRv788bPcc0frsF7599zuf+NN7Tf\nBoiYPGaueJpEs7inWrMgaFu284fnyWBg87RatRuTF5N6a72o4aEa5ERoql59Vk7rsp2ceBJ5e+pd\nFxMYDcYJFU92HxqvNOWMfUuc9Oh01FvqHU0ieURFAZGRLFOlFPe4yGWezp0DUiMyUN0tLZ6WLPFN\nPJ1pPyPZ+8owsgxjsWcxf774F4dOx7JeFRXqrzlmG0NFRwVWzFsBwDUuuQm5ON1Zgmy3RvAmE2Cx\nsCyLWo43H8faBNdeD2sS1uBEywlRDy1vM1yCIOBA3QFsNTEllj0/Gx2XOtDc14wPPmDiCQC2bGHi\nTK50x/vb8urpV7EzZye2mLbAMmRBeUc5RkeBV14BnnwSeOgh4A9/UD93m2DDd9/5LvJS8vDAuw/g\n8ijbuPHQIeD732eCr6xM/bhjtjE8feRpfFTr2teivt77v0fkefKNGSueai2TYxaXw2Jh/zV4v8DM\nhVSD9pknnW5ifE9mi9lvZTvAu9gkJADd3b6vyrJzvvs8FkWryzy5iyelLRe0EE9q/E6LFrGNeRdG\nLpQVeBkZ3vuebIJNdgVgRQWQtTADNd01kq07kpLYDwJvGsCOjI2g3lIv6aFsq4tDsC5EcuXrsmXe\niafanlosiFiAiNAI0bHFkaswpC8V9YsLCGAlr1On1F/vePNxrElY43JfbnwuPjOfQHg4EB8/fn9m\nJhNoalt7NFgbcGXsCjJj2esZGBCI65OvR5G5GEePAuu/XMyo17O4qc2i9V7uxdmOs9hs3IwAXQC+\nmvFVfFj7IY4cYW0sUlOZn+rYMdYjSw3Hmo5BBx1+nv9zLI1bineq3wEA/OpXrMfWrl3Af/+3ujEB\n4MWTL+JPZ/6Eb77xTTT1NQEALl5kKzXXrGH/r5aa7hr86fSfXFY09vV5N9ZMZMaKp8ncENhTrdn+\nha9VNTExMhGt/a0ef/l7g9a+J/eYDI4MwjJkQXxEPP8BCvBH5ikwkHmHtGrVcL77vMdFC+5xcS/b\nJeuT0dLfouj11cKvVdWtXDzZO7vb9xL0xOLF6nxPznG52HsRhjCDx+1tysuBrCURMIQZRN237QQE\nsHlUerZocTFbzFgYuRCzgmZxj1dWAnN1y1DewV/m5m3m6Uz7GUfWCXCNy6y+ZYgwnuP+LcnOVp8B\nEQQBx5uPi3pp5SzIQVVPOdZce8Xlfp2OmfDVrmAsaSlBbkKui6ViTcIaHDh7EgsXji+WAFjDUznx\n5P4Z+uziZ1iTsAahQaHseEoeihuK8fHHzOwOsEUmubnqM2cFlQW4a+ld0Ol0uGPJHXiv5j309bFx\ntm1jXqo331TfFPa3Jb/Fb2/5Le5edjdeLnsZABNhDzzA/j33nMwAblgvW/FY/WN47NBj+Gs5M44N\nD7N4Zmaq30h81DaK3574Lc51jqdux8aYAB0bUzfW1cLMFU89U7PHk5YlO4AtZ18QsQCNfRpubAb/\n93pqsDYgWZ/s0qlZLXLiyduViFr6nuosdTAZlK8odC/bhQSGYMGcBbjYK/9zUYt5K/VouYgnBW0h\nfNk38FznOUeWQoqaGnaNjJgMjx4sb0t3lV2VHkVlVRWQHukH8dRxBsvn8ve/Gbq4BKMG/qDebIvT\nNtCGUduoqLP87JDZmD2WhIQV4rRmVpb6DFdpW6nIO7ZqwSocu3gS17lau7BmDfuCVkPxhWJcnzzu\not+YvBGfXfwMXxy1uZQdvfFsHb5wGJuNrEnqptRN+Lj+Yxw+LCA3l5Wn4+NZdkuNcK3qqoJlyIJ1\nSetwz7J7UFBZAEFgZvn77gPuvZf5s9R4UP985s/YlLoJv/vK7/Dro2zPnr172a4WTz7JvF9qeP7Y\n83j2i2dx619udfyQ27WLZQl/+lN1Y7X0t+CfP/hnl9XQZ8+yrY2mEjNSPAmC4PO2H77gqdaspVnc\nztXQ60nk7bHUI1XvfSBGRtgyaU9b3HgbF61W3F0evYyuwS4sjOS0vP4S57jYbMCFC2JxrSSzA7BY\ntLay2HiL2WKWFXuCwBFPMvNLS2Mmc6U4x6W2p1b2s2wXnYtjF3ts7bBokfpu54B8ObOqCliesAjn\ne/h106VLWXZM7SKMs+1nXTJPznFpPmvCpaAm7jYqS5aoL5Pa20HwFtkEW5cgZKFYqHklnlpLkbPA\ndVlizoIcXLhShqxs15KrkjYP7n9bSltLXUqPc2fPRURoBI5W17ts3bN6tbqu85euXMK5znMO4Zce\nnQ6bYMMHR+tdRF9eHqDGblTcUIytpq0I0AVgbcJamC1mHD3dg+Bg9r5ZupRlTdWU5N+sehNLBpZg\nq2kranpq0Nrfin37mBD79rfZasbLl5WNJQgCXjj+AvbesRcLIxfivZr30N/PPGNHjwK/+Q1bsKGU\n77//fRxtOorvvvNdAKyMvmUL8K1vqcsENvc1Y8PLGxwrNQG24ODHP9ZmJeWMFE/dQ90AMCltCuTw\ni3jyg+/J354nX/1OFy8CCxawJfpSpOhTcKH3guouxlqZxi9YL2Bh5EJZ87WdlhYgOhoIC3Obj0LT\neHAw++Xri6eh3iJv4u/qYiIgLo7dViLufBGk9dZ6j6syBWG83Cm3pY1aEWdHTjxVVgLXLkpHTTdf\nmcXFsddHbV+kc53nsDSO39+qpjoYibNN3FYW9kyfmrd+ZVelZIZv6MJSDEeIU3Zqy3aCIOBky0mR\neIoJj0HAcDSiTa7vI6OR+USVLl4RBAGn205j5byVLvenz8lGWMopzJ07ft+qVUBpqfIYnWg5gRXz\nViAsmH1AdTodVsevxic1pS4ZLbWrHY80HnGspgwODMY1C6/Bnz/91GUV5YYNyrNkl0cv44umL5Ab\nn4uggCBsNm7GB+cPOHpnzZ3L3h8nTigbr6KzAjbBhpwFOY5S5d/+xrJOq1axfwcPKhurtb8VhxsO\no/DeQtR016C6qxqvvcbG2r0beP55ZeMAwOOHH0d8RDx+8NEP0D/cj9ZWtj3RW28Bf/6z8nGkmJHi\nyf5LdbLaFHjyPGldtgP8167An56neqtvmSclInR2yGxEhESgbUDdN5ZWZTslz9E5LlLb9qjZp8+X\nuQ9cGcDAlQHMmz3P43m1tUB6+rhvT0nZLjWVZdWU+iOc4yIn6Do7WVftqChgUcwij9vFpKV5J4yr\nuqokhUVXF8v2rTGlo6ZHOq2Vnq7u2mO2MVzsvejy3N3fL8vmLUFFpzgjFB3NYqJGrEmJp/5+4HLj\nErSOisVTRgZ7Tkpf187BTtgEm8jrKAjAaOsSCLGuhrSAAPkWE84xaR1ohU6nw/w5813Oib6SDcMS\n11ravHnM+6TUnlDWWiYqN2bNy8b5/jKXjJbabNznjZ+7tKK4ZuE1+NRc4iKe1q8HjhxRNt6ptlPI\niMnATVuYwWtd4jp8cPYYUlLGFyqtXw989pmy8Q7UHcDN6TdDp9Nhq2krDtQdQHHxeNuKm29WvlVP\nUX0Rbki9AZGhkbgl/RZ8VPcR3nqLbSv09a+zca5ckR/nytgV7K3Yi+dueg7rk9bj7eq38cc/Anfc\nwYz7//u/yubjiRkpnibTLC6HPzJPKfoUvzTK9GevJ3+vtLPjTVZOq7KdkiyOM+5mcTtq2hX4Ip7q\nLfVI0afI/uhwn6fRYES9td7jBtVhYcwIrKZdgeN6Mu8VZ5+YKdrk8fU2mZj4U/O+FgTBo+fJvhdh\nsj4JnZc6MTjCX1uflqauZNjc34zY8FiuSb23l5VdshIyJZuUqu3sLtUO4tw5wBTJF2lhYUyEKP2h\nZbaYubsKNDYCs/oz0TwsnrCa5qb2rJP7eziwMwtjcWJFs3Kl8q1s7BtmOxMfkI3AhFJEO+0alJHB\nsshKNoO2b/nj/N5aOW8l6gdPuwiynBzlGb5jTcewduH4g1fHr8aJ5hKX8datUy7GSlpKcE3CNQBY\nZnfgygCKS9ocqyKvvRb44gtlYxXVFyE/le2cvcW4BYV1Rfj8c9b2Ii6OldWVeNxONJ+AyWDC/Dnz\ncXPazSg0F+LgQdbEdcsWoKREXSmRx8wUT5NsFpfyPGnd48mOPzxPej1beeZNrxgevL3K/NnjyY43\nwjI1VRvhqCTz5BwXd7O4nQkTTwpfE/fYzw6ZDf0sPZr7PCsjNeVQe1wEQZCNo3PGLjkqGU19TRi1\n8Zc7GQysfNbVpWweANvAOjggGDHhfBtAVRUTKoEBgay1hEQWTm3JkCca7XGxv1fSotMkr6dWPFV2\nVnLbQVRUAFmJi2C2mHFlTJwWULMYoK6njiuEy8uBpNn8bvVLlng22zt/htxXJ9rprc1Ef6g4GGpi\nVN5RLiqhBndlQ5jnqmoCA1mLBSVip6KzAkvilrgsnFkam4X+2aeQ6fRSLF3K5qlkFd/xluNYE7/G\nEZfs+dloulKOVWvGXzs15daSlhKsjl8NgJUqV8Tm4OLISaz4Msw5OWxuSsTK542fY0PSBgAsw3a0\nsQQLF45bANauVVZOLG4odnTBzzfm41A9a3OxcSMwezabk9LMmhQzUjxN1obAcnR0sDRxhLhli0/4\nw/ME+M/3JAjCxGWevBCWc+awf97u22WnwdqgqjQplXmyl8WUeLdSU33LPCmZLy/2SkqL3mT0uga7\nEBwQjKhZUZLnOMctNCgU82bPk2xXAHgnYjztwVhby8YEgPQY6dKdFuLJcczsJJ4k4q6mt5ZlyILB\nkUEkRCSIjlVWAsszZyEhMoH7Q2TRIuXiSWpBQnk5sGwev1u9mpWKlV2VXI/YxdNGWMaaMDzquvmj\n0tYVgiBw91dsr1kIW3Af+oZd00zLlinLlvGyfaOdqQgIt2II479cZ89mq/iUmMaruqpc5jk7ZDaC\nB5MxO3k8tikpzEdm7zsohfWyFa0DrS6ZsXjdKsQuL0VQELs9axZ7D8i9RoMjg2jsbXSMlRSVhMHh\ny1h+7fgfWqUm/i+avnBsWZQWnYbuQQuSM7sR9eWfibVr1S0G4DEjxdNkZ56kPE/+KNkBbKsGy5CF\nu4renj8AACAASURBVOrGF7T0PTnHpHuoG0EBQdDP0ns9nirx5GW7Al9bNSjJ5Lh4eyQyT4YwAwID\nAh0LITzha+ZJiaDliicFW+GomZs9Lkrm5B43OQO7vXSnFLPF7FFUOl8/PTpdci/C9HTfxZM9LmYz\nex6maJPkBthqmqbaDfG8km1dHRN+Ut42NZkns5UvCGtqgNzUTFR2Vop+JGRmeh7fxQfGEbojI0B9\nbQiSopJE74vMTGUCs7GvEXNC5iA6LNrl/spzAVgQki7y2SmNSUVnhUjsVZ4LQNSVJS49lQBg+XL5\nja0FQWAbrhtMLnGxtWdiOGL8iQYEMIEnV7I83XYay+cud1n0EtabjaCFriVQJQK3vKMcGbEZjn0+\ndTodoodzELGo1HHOqlWs5CbH2Y7xVagBugAkBGQhPmfc05aV5V2nd2dmnHia7DYFnvCXeArQBSAx\nKtFvviet8TXrBPi3bAf4lsGxo7Ydg5RhHFBmygZ8E31KTfw8kZdmkM6A2DGZ1Ju1zRazrADldWX3\nVOZUaxqvt3gWcM7vxfRo+cyT0nKwksxTXHgcRsZGYBkSpxDUZPrqLHWSPzidS4Q8oaa2bMfLPNXX\nAyvSYhAcGIz2S66bACYlsSzw8LDoYSJ4MaurY1mbxXEZIpFjL9vJvSYVHRWirBPABMMizgpPpcK1\nokMsnioqgIVhi0QrN+VEJADHRujOIq+3FxA6MtEy4ppiW7FCXozVWepEfd8G6jMxNMdVcSoRT2fa\nz4hWQaJ9JWxx45PIzGSrhT21Uei93IvuwW6X1zm8LxshyeMizJsmse7MOPE0FdoUSHme/OF3suNN\nN205tMw8uXh7fOzxdOkSM2POny9/rrclTbvvyVv6h/sxNDqEubPnejzPHpehIeYvi5douK7U9xQT\nw3wRcul4HkqEyugoM8MmufZRVNSuQE3myeHtkREuAMfArpcXT6oyQFbPmSfn60sJDID5rYKClPut\nPHme7OLJsQE2J/YpKcpXOEq99s5tIKRKsxkZyjNcUoLQ/nx4PxKCgtj7TerzaI+Jva+ae+nR7knj\nNVCNjWUeJbktZqq7q0ULBgSBjb0qRSyeVGWe5orF0+I4cc+w9HT5ONszbzqdzhGXujpgXtBi0b6P\nSsQYr8lvS3k6LDC7+AqVmPpPt58W+dEstRkYmDU+iaAg9r71tLCivKNc5BMbaliOEf34BBYtYn+n\nBgY8z8kTM048Ob95phr+yjwBV1evJ18zTw0NbAuVAAXvbruBeMymbg8BX9sV1FuVrVyzI/eclL6+\nOp132SdBEBSJ2sZGtroqJMT1fpPBJCvuvMo8yQiXkRHWGNRZzMkJTbXz8CTgBgbYxrXzvuzukGrw\n/CNGjXBTknkCpAVbeDhrWdDC327PBaleWhYLe08ZDNLXse8HKdd0cWhkiNs0dnQUaGpir6Epmv8+\nUvKaNVgbkBSVJOqrZo+VVANVJUKH59Vqb2depBXx4oyWycQ+K56W3fcP96P3cq8oHufPM0HmXv5N\nT5dfrVlnERvy6+oAUyQriTqjZPUn7z1YdTYM82bPd3mfK8k8VXZWuvi7OjoAdGWgcVCcDfT0ejiX\n7Oy0lmegRzf+oMBA9eV5d2aceJJKC08kE+15AqZ+rycXb49Cb40UDQ3K4xgaFIrY8Fg096tbI+9r\n5klpds3Zw+LpOcllU1zO9UL4dQ12ISQwxKMxG5B+D6caUmXnFxfHSi9KGh46PE8ymaeLF1m2zrlZ\nqtQXsB21mSdP3rX6evY5sWvkxMhEtA20Se5FqLRdQf9wP7fnVl5eHsbG2PNOTv5yTA/ZLqXvBU8Z\nIftenFIZrsBAJnzk/lZIiZvGRpZFDg2VFr6exJPjMyST1ZIy1yv5scHzvXlqzBoSwkqFnmJvf185\nZ1Dsmb51ixdJiidPJUbn7z97XOrqmMA7333epZ2IEg9eXU+di4fMYmFZ8iVzXQVjSgoTk542VK+3\n1rt8N1dWAplz+Vk7Tz409yxgTw8w1rEI9f2u8fJ1o/SZJ544ynuq4O+yndbtCpKT2Zy17vUkZ8CV\nQ60I9SY2WmSe1LRikDKL21GTWfTGr+VtmwI7ceFxGB4dhvWytDLS6dSvuFPSpsB9PkaD0WMJce5c\nli1S0ofnytgVtA20ITGSvw+Q+/WDA4M97kWoNJtrfz14mcumJiZEZ33Z/snTSkc14on3+ju/L40G\nI+ot9dwsrpIfG3WWOu6qRecsmlHPf+2U+NSkxJP9OaTq+QJfSYx4P/icvWBmi1lkdJcrZ/Lm29XF\nhFd2EmtB4Sx2YmPZ3+JuD+tGeGW2ujog0xSBqFlRaOkfT0OmpDAR7mk7J/c5Om+D5FwCldtQfdQ2\niqa+JiTrk8fHNgOLE+dizDaGrsHxWrZcJtA9QVJXB6TFx8Em2FzGIfGkEiV7c/kbnudpbIz9wvKX\nePJHo8yoKPZBVtMTRwoXz5OPmSfV4smLkmZiIvslpaTbLQ+l5mtnD4vHzJOfez0p8RYB0rHX6XSO\nL1ct5lZcXMz9g+sOz2QfExaDMdsY10TN5qq8tHmx9yLiI+IdK4Tc4YleTxtSK81oSgmB4uJi0XP2\nlHlSIlaHR4fRcamDuwej8/syPDgcMeEx3CyuktdVLrsFeM48SWVJHJ8hmczTwsiF6BrswuVR1/qi\n3NwdJW2DOPNkNAJRs6IQHBDs8sUNyL/WUuZ2o5G1F4gOi3ZpuaHTye/N6CxQnT1PJpM4tqGhLGt7\n4QJ/rN7LvRgeG0ZceJzoOS+KEXuyPGUHG3sbMX/OfIQEjtf7zWbAZNQhI9Y1iyXXe8s9bnV1QHqa\njs3JKVtH4kklUr9uJhv7vmWzxM2CNeFq6fVk/0J037ldDWrFkzfCMiiIeTmk/rDIoeVKO4D1RGnp\nb5EsBznjTclRzUo7qdgrEXhq5tbU14R5s+e5/MHlzcc9bnYh52kuqjIyKjNfnnxPSkvhSv1OgGe/\nmZLneaGX7cEYFBAkOuYeXymhpjjzJLHSzrlDPO+5eJt5stnGM/6BAYFIjEzEBavrh1ouRu2X2jEn\nZA7mhMxxvZ7ZLSvn9vdXkXhy85nJjSnne+LZVqTEk9x49ng6Zz+ds3juP5Q8iSfea2N/runR6S7v\nKU+vNa9HoP35ZcS4ijASTyqR6mA7kfA8T/4s2QHjZRP3Zm2+opXvyR4T+xdiaFCo12N5Vbab4BV3\nSstgDm+PTNkuJDAE8+fMR2OfdPNHO97MW2kp1VOGTIl4Uipa8vLyFC0s8LSljVyvJyXzUNOmwI6n\n95vS10bKwJ2XlycST/ER8ege7Ob2eVPS1d3Tc3SPr5RQ8zXzZH8+8RHx6BnqEW1x42lvRGfPk/t7\nuLWVZdBnz/5ynpz3qFyZW0nGLNUgFhPeZJ7s/bukxvTk13M35Ofl5WF4mLV5SErivy89efB4Fhj7\na8UTdt6KJ/cf/rGxLOPf2ysep22gDRGhEYgIHe80bRdP7p42JasTPTGjxJP9zSPlT5hM/GkWB9iv\n7RR9iua+Jy1N44Cy5fByeCOevClpeut7Urpybfx8+bIdAEVlMWDcy6B0s1bAd8+TY34yIlWNsFOy\nN6BUxk4uVkq3ipHLyPFEryePXWIi+0KX22ZDTeYpMCAQyfpkbuyVihqp5+j+eksJZEWZJ4nFPM7v\n/QBdAPfvmH1vxKYm/thSuxa4vz68DH18PDNCD/K3JJR8Hzq/Djw/lbfiyXlMNQKlwdqAZH2yiyG/\noYEZ14OD+a+dJzHGs8DY55esT0Zjb6OL/82jeLJKZ9ncn6dOJx07nqCrrWXXdh8nLk5ahClhRokn\nqdUcEw3P8+Rv8QT4p3SnVaNMNX17PGGxsFS8fXdwJXgrKr3NPClduQawuHR3sz9uepmG61KGV3fC\nwpQvUbejROwNDrKVcr70olLjeeL9wXVHKmMnl230dRUawEQvN/Pk4XMYHMxWljXKJBDVeJ4A6djP\nn8/aKfT3S19LyoNoX9XnnDGXyujZ4ym1uMQm2CQFOq9DvJTvifd5LC4uRtdgF0KDQkWfOfdY8T5D\nAQGe/87xXovhYbbUfuHC8XGlyna8mNgEG9u+ScJHBfC9c54EiruwKC4udmRlAP57xFMG1lPmaVbQ\nLMSEx7gY0OUyT87P1f6enD+f/2NDUjxJlCXT0sR/53U63378zyjxNFX9ToD/y3aAf0zjWnue5Pr2\nyGH/slLTxisxKhHtl9q5m5p6wtvMk9qVdkqyToCyzI4dNcJvzDaGxr5Gj8ZsQL4XlRLxpCYrJpd5\nslrZl1hsrPq5KH1tPb2WUntVyn0O5V4bqS9WO2rEk6df8Y7xJDJPzc0sts4+TanrGAzsWlLNWVv7\nWxEZGinyDfX1saa385w6MsgJNKnnIFdas48tlaGTFE+cv1kXLrAson1/N964ej07zlsd19LfAkOY\nAeHB4S732w3jgHpfkSe/k32OPPHkSfA4j+feIsNdiHoqrbr/aHb+O877sSH1njVbXbffGRxk8U1I\n4HsNfbFezCzxNAX8TgDf8zQhmacp3OvJHhO1m+W6400cgwKCEB8RL7l8XApvP3hqSnY8D4vkfBRm\nngB1c2/ub0ZceBxmBXlezSAX+xR9Ci72XvTYkFRpVszueVJSMuMJabksrFIRJ1c+48VDbq9Juc9U\na38r9LP0oi9WAMjJycPgIGu34IynPmByKwuVeJEcY3kQpXLixpNZ3Pk1lHouUuN78sfxMk+8LLSn\nufOy5e6vvVSfM0kRwJnv5ctu2SyOGJg3j/VS4rXZcDfk5+XluYgn+/vS2U9m/3Fss0GE+/epe4sM\nd8HoqbTq/nydX5eFkQvRcanDZdNmKR+au0A0m79cDBA47pdz/tz5VTwVFBSgqKgIe/bs4R7ftWsX\nAEgen0qYrZPfpkCKCRNPU7zXU4O1ASn6FK8f720cvcnKeS2evuwurvh8GbO4HTWZJzVZM6U+NLnY\n21P5cg1J1WR95MzaUnFL0aeIPBkuc53FvgikPDQA0Dfch+FR16Xa7tfnxSNAF4CkqCTJ95s3Xhjn\na/IEo6fGoHKGaE/lNPfn56mfl6fnJdV/T03Z05NPTa7Hk2MMCfGndmx3USa1k4FUTHiCzD2blRCR\ngM7BThdRYW+zwZsrr/LiLJ4CdAFI1ie7vC9nz2YZMvcfMyNjI2jubxb1ZZLzj/FKq72Xe3F59DK3\n5QHAftwmRCS4/LhV6nlyf36JUYm40Du+mtKXyolH8VRayjbSy8/PBwCUcXbS27NnD9LT02EyTU1R\n4sxU6C4OiD1PIyNsxUOin33s/vA8RUSw0oTc3k9yOHueJkM8eSMs7R2x1RoOlS77B8Y9LEqek5Iu\n3o5z1RqzfWxTYEerdgUfHvwQ/cP9mD9HegNDT3FTIuTkRJz9vSq1xY4n8ebpsyiXefIknt5+u1jS\nIO9NRsgyZMGYbYy7Fygv82TfS09t9sa+bZaSa3gSOLzxPfnj3N8j0WHRsAk2UQ8wqffklbEraL/U\nLuqB5f7ahwaFIi48Dk19rmrcU/nJ00o7gC0EWBi50EUMANKlNvfvP3fPE6C8dHex9yIWzFkg6ssk\nl8XjCXX7jyDnz5GcEPOUsXN+jqIFAW5z8sWz61E87d27F4YvnbdGoxGFhYWic/bs2YOamhps2rTJ\nuxlMIFO1u7h9+4Fgfp89zbAb5tw73fqKVr6ny6OX0T3UjfgICcexAnwSTyqFpRK/CA8lq8RczleY\neZo3ex4GRwbRP+zB/fslqsSTBivt7GhlGm8daJXdG1Cu3CknmOXmIdcqwZN483Rt2cyTB19ga6u0\nQZ7X5VruerwvNscxidfbmxV3vJ5GAP81tK+OdX8uaj1PQ0Pjfhg7Uj3ApMa+YOX3wFIq+jyW7Tir\nz7htLxT4nsZsY2iwNrjEwGbjZ96UjMfLYvGEipI4KsncuT9P+3eO81tg4MqA6AeV+3vUvdTpt7Kd\n1WpFdHS043Y3x9nW09ODoqIiPPPMM9wxduzYgccffxyPP/44fv3rX7tkXYqLiyfstk2wwVxmRvOZ\nZq8er+Vtu7/Hftv+Avv7+qeOnoLugg7dQ92ajm//pezLeHl5edj3/j7Etsc6VkN6M15FRbHjw6Lm\n8amGVBw7ckz19SIjix1/DJRez555UnI+MP5HU+78w4cPI64jziECPT7fVKCqStv5nj1bjJ4ez+MF\nNAQ4/qBKjWf/g+bperFLYhHZGulxPidPFuPSJenj4c3heP/g+5LHdbpiHDok/fiDHx9EcGOw5PHS\n0mL09fEfn6JPwaeffMqdv9znyf5lwzve0jL+peN8PCI0AiGNIXjjgzdE49m/0HjjvfvRuw7h7H68\nrKwYvb3i+dkN3e7nDwwU4+RJfjzqLHXoq+4TXb+kRPx5jgiNQHhwON788E2X88+dK0Z/f7HD72M/\n3+556qjocDl/375ixMYWIzDQ9Xx7lsN5fqmpQG2t+P3w1kdvOYSs8/lmM9DT4/r8w5rD8EHhBy6P\n7+8vdnx5uzzeYoa12ury+MOHiyEIrtef1TTLIQbsj7eLHefxmvubMadlDo4dOeZ4fHc3EBZWjDlz\nxscTzALMVtfPp70M6D6/sKYwl/l98UUxhofHb7dXtKOqZLwVeHExO+7+95L3fjabge5up/jrU3H4\n8OHx93MEEBxcjDffHL/evvf2Ia4zziH0i4uLceKE6/vHZra5/H1saipGXV0xHn/8cezYsQM7duyA\nYgQPPPjgg0JpaakgCIJQWFgo7Nq1S/LcXbt2CYWFhS73yQw/oTT2Ngrzfzl/sqfB5Q9/EIQdOybm\nWtn/ky0cbzqu6ZgPPSQIu3f7Ps5HtR8J+a/me/14m00QZs0ShP5+9Y/97P+z997hcVzVH/d3JVmS\nJdlqVrOsakm2JBfJvVu27ADpiRNCCr+E4kD4AYGQEKdAAuRNgOQFXggEYtovgUASOwRIAklcZMfd\nsoqLZFllV8WSbLVVl9Xm/eN6Vrs7d2Zntmhn5fN5Hj+Pp925e3ZW+91zzj2n/pCwcudKzdc9/LAg\nvPSS+vNHx0aFwB8FCgPDA6rOHxkRhMBAQbhyRd34N75xo/CPyn84nscoG3dw0PGYa/+wVigyFjk8\nLzxcENrblc95rew14Z7d9yiec+CAIKxZozzOL47+Qvj6B19XPCcrSxDOnZM//v393xe+t+97ssf/\n8hdB+Nzn5K//3/f/V/jF0V/IHk9JEYSaGv6xv5/5u7DtzW3cY+J7MzTEv3bNH9YIB0wHuMc+9SlB\neO89/nUrd64UDtUfkuzv7RWE6dPZ58eenx76qfDIh49wx4uPF4TGRun+l4+/LHzl31+R7D9/XhAy\nMvhzi30xVrjYc1Gyf/58QThzRnr+ip0rhMMNhyX7FywQhLIy231XRq8IgT8KFEbGRmz2v/++IFx3\nnXTsRz58RPjJoZ9I9kdHC0Jrq+2+V06+Imz/13abfePjgjBzpiB0dNie++z+Z4Wn9z1ts6+iQhAy\nM6VziH8pXmjstjXu7bcLwptv2p733IHnhMc/tv1e/ugjQdi82fa8/cb9wvo/rrfZV1Qk/Zztrtgt\n3Py3m232vf669HPw6EePCi988oLNvpUrBeGw1VsyOjYqBP0oSBgcmfgjc+gQO8+ah957SPjV8V9Z\ntsfG2N/xvr6Jc/56+q/CZ9/+rM11y5cLwpEjE9v/Ov8v4fq/Xm9zzsKFgnBVwgiCIAh/O/M34Y63\n7rA5JyJCENraJrbV6hZFz1NERAQ6OzsBAF1dXYiOto1779y5E7t37wYAREdHo86VTqkeRi/5TgBs\n1DoAS+f1yUCvtZ6KiopczndqbWW/SMLCHJ9rj7N20VquoLm3GVHTozB92nRV57/9dhHi41kPQTWo\nzd3y92c5dmray6gJ24n1tawc1VzclfP0ycFPFPOwxsfZa1P6XKVHKCfYKy3TBpTtMjLCQmjJyfxr\nlZ43f3+2oqpBZvGnUrjw7NkiyKWfyiWNh4Wxf62tnHvJhAgHBth7zqvpJfcep6SwFAX7FYy9V3rR\ne6UXCWEJNvvF1im80KCWVXFvvf8WN7QmG3aUeS54qxJ5+YtiOQb7WnO8nETeqs7BkUF0DXZJ0hfU\nJs9zw2yclebvvy99VtTmPMmF2qzn5+/nL1kYwXt/7Bd+2Fd9B9TlT9m/F7w6a1pqRjlCUTzddddd\nFkFkNBqxdetWACycB7A8qC1btgBgIb3ly5drn8Ekodd8J2ByVtqJeGLFnbtynkzdk1+mQCQ+LB49\nV3rQP9yv6TqtHzytpRhaWrS9pvTIdIvb3RFq5j44MoiOgQ4kzkhUPE/8w+movpYa8TR7NtDZyXJS\n5GjubVb8PIu9IkOkq/ktOEqwV5MwLvdeOspjdGQHufdmYGSA+8UKsC/gy5flBaOjpHG5VV+816hU\n00vuPsHBrC7URbscfVGE2udVtbYCM2fafok6ugfvPWvpbVG9kg9QLiugJV/H/rPAm7O4fN96NZtY\nzNnPYGtc2VY/dn/Pk5PZ340rE4vwuH0Dm5shEU/ieIJVMhFv9Z69M8K6qKXSa+YVZbW3oVqRaP/M\n2ounjg62MtG6uDBvVbWz31+K4ik/Px8AsHfvXkRERCAvLw8ALIKpsLAQe/bswe7duzFr1izLcT0i\nV0fEG9jXeZL7deUJlDq6Oz1mquviqaCgwGtlCoCry3TDUzSXK9DqedJaIHPmzAJVyeIiWsSxo/o+\nAGsKmxSe5LAqv1rbx4fFo/dKL/qG+2TP8fdnXwBKz1Tv7F7NDXntcWSrmBhWW4e3mlIQBIeFKpXu\nHz09GmPjY5JVXZa5yfxBFz8j9l+sABMlsbEFss3F0yPkhbVcuQK551UpGT81IhWNPY0YHZf2mOF9\nXpTassiuVpRZ4MEbPywrTJN4UhJmEs8TZ/GH0rhqvGU8m5vNrGWPXfCHKyoCAphX2fr54SV4j44W\nSMRTeHA4ggKC0DbQZtkXG8uE2FWfCbfVjVxxYntb2i+yGRsfQ7253ubvPs9+4mIY696sErvZvRe8\n79XY0FgMjg7aLKqxno+gYTGVwzpP27dvR2FhIbZv327ZV1xcbPn/tm3bsG3bNjz66KOqb+oN9Fxd\nfFLDdk72cVMiJYWFSHiF1LTgTfEEOBe6S03V9tq1FMgE1FcXF1Hj2RFxVN8HcG+ZAkB9j0UlUSqI\nvQEVRKiawqK8onm2c5UXmJf6LyE0MFRSEVvE0QpJg8HgsFyB2uKJlmMOXrNWz9O4MC75YhNRer+D\nAoIQFxonWZYP8D1qWopwWuarwfMkV6ZA7jXI1QBT63mSGzc+LB7dV7ol3m2uCIjgCzJ7ccITFYA0\n1OaourjNfDiCx7pNS/tAOwL8AhA5fSIuqUWIWr/e5t5mRIdE2xTglSuBYT+WfesYe88T73vVYDBI\nVgFa//i/1H9J+iJkcCiepgp6qS4O2OY8DQ6yEIVcPzB344mcp9BQ5l7n5UyoxR05T66KJ2d63Imv\nvaVF3flaajwBwLFj/Lo9cohLcdX8glITttNSpkDtPF3Ne2obaIN/vT9mBs10aT68nAzJXGVEnCNR\nqbZsg1K5Ap7nyZF4CgkpUryflkKZSpXMnRVqXM8TJ6QEKL+HcuPz8nNOHDqhyfMkVwPMfu5dg10Y\nHR+V1MCSs42lqTEn/KQkApTmKldaQSKeOM6D8+f5+XGOxlOT76Q0lrVQ5733cq91buRc1HZOvChr\nu4k/qBx5sACW+2fd3sf62dfiWLhmxJOewnbWNDQwF6u/clTEbaRGpKLeXI9xwUU3kR2u1MsAYKlK\nnDAjwfHJMrjseXKyfY2a8JeI1rCdXN0eOcICwxAWGIbWPsdKVrV4cqPnCXC91pOxy+jwOXFXP0C5\nas2O3kdXa14563lKUDCLkqdNLpFX7jU6en3pkek2X3QiWj1PcveQ60fJS8Bu7pPmx3V18cNg1vN3\nlFgsVwNLyTZqakjx7K40pr2oAGzFTudgJ8aFcRuR19XFbBTDKY7PC2dbz1FNjSebsRTEIs+podaL\nNWcOcOkSCyl2DnbCz+Bn4w2TS4ext1dGxoSttPx4vibEU/dQN66MXUFsaKzjkycB65ynyQzZAUDI\ntBCEB4ejpVelq0QlzjbJFUnJS+EmSWrBW+JJTfhLRGvYrr29QPNrUutdVCP63B22A9QltTsqqLh4\n1WLF61X3A3SQNC7XVd4dnqe0iDTFHCRnxFNhYYHs/fz9/JESnsJ9Nnj3U3qN9tWu7ZF7j2U9T5yU\nCrmwEjDRsqPeXG+z3z4pXRAEtMW0yX5Byy1w4IkcMRF7ZIRtK7V8URJPSsIEkA/baVkIYO8pmhs5\n10bk1dYCWVkF3NfPe+8ceZ4cCR77BHTx9fJapskJsbmRth4j69wuXv6hkgerpqvGsp2ayhZ4jIxA\n09//a0I8iSvtlKoRe4vJXGkn4om8J1c9T67mO42OstUjckvD1cBrtKkGtZ4nsZVDUri6Pjy9vWxJ\nuHVHeVXzUZn3FB3N/mCYpW3ILDiqog2oKwtgPz9Xcp7UeMPUhhEdCWbZsJ2DObgatouLY81dBwZs\n9yu9H7W1jl+z3LORlDTxK15EzvMkCI49e2qrjI+Nj6Ghu4H72XdYIV6hx534nnUOdsJgMNh4JADH\n7w9P2E6bxtIrxBISvP5zY2PKnwVe0r69d9Mpz1OXvOeptlO5p51kjg7EWE1nDTIiM2yOy71X4cHh\nCPQPRPtA+8T4Cp6n4WH2HM6ZYz+SstdOS6hzbpSt5ykoiHlsGxpIPEnQU74TYJvz5BXx5IG8Jy2h\nKx4f7vlQUzjLnsZG9oWjth4SD2fLOKgVjg3dDZg9Y7ak3owcRiMQE1PkcPm/PWrECaCuvYyaMKPS\nknK5+anJeaqr4zecruuqw0jdiOy1AwPq8wgd2UpRPMnYpb+fCR/7Zdv28NpXiPj5TTTdFhFXOSl5\ng1pbixTvKWf7gABpbSk5gXj5MvPwhIdrv09CAhProihs7GlEbGisTcIwoO49VJNXVdNZg9jLlLmi\n0QAAIABJREFU0oiDmrAj77mw9jLz+s81N7MfJdNlyrjxPJ3Wy/fNQ2ZuHpUzoUCjkf2w4ZXpqa1l\nFbrVjmftga3prEFG1IR44tVTUhpPzOcT52Yt7OrrWbucAM6fSPtcJfF11tVJV9qJP+hSUqTjZERl\nSMbJyABqaqB6sQ1wjYgnveY7AewhmsywHeC8SFAcU0PoikdrfytSw1Odvt4dIlSuKagj1IYsnVlp\n58xCAqVwkORcBfGk1BTWGq22F709Snl3kZHsDyinIxSMZqOkoKI1SjWIeHNR+oOZkiLNoQGU30u1\n90+NSEVDd4NkVZfleKrte9Pa14rQwFDMCJohObe3l4k2+8KM9mhJGpd7jWpConMj+QU5RVEovi6l\n0FdqqnIuqNx7Z5+fM3um9EOkRjw5KlfAE7LOjGv9I0a0uXWURBCUy9nwREVoKKtv1NwMXOi4gMyo\nTJvj1dV87w4AJM1MQmtfq00+WXIyG2t4WCqeRDE9U2b9hv1rDglhc2tpkX43K9kvJTwFTT1NNiUw\nRFFX21Vrs6Ly4kVW5433gy4lPAXNvc02r08UTxc6LvBvzuGaEE9yqzm8hX3OkzfCdu72PLkathtP\nGffqSjvA8fJxOdS+dq3J4kYjsGxZgaa5AOo9T4Cyx1CueKHkPI22Dw0MRXhQuMOkdjlBXttZi9s/\nc7vsdVrKO4gJ43KrE4ODWZ2bxsaJfaPjo7jYexHJ4fwYsdr7T582HdEh0WjubeYet8+3Uvo7Jobs\nNm0qULynlnIF9pWfRdSIp1khszA8NgzzkDQmbH0f+y9iLfeQS/a3DwutXrdaco6qsJ2DQplaVp1Z\nj6vU1Jj3N+LSJSY4Zkg1MwC+qAAmQm3VndVc8XTjjQXc8ab5T8PsGbPR0D3hhpw2jXmEztX0oudK\nj82CDWcEY3o6UF5lxvDYMGaFzLLsVwonBgUEIT4s3mZeot2qOqowb9Y8y/6qKiAriz/ONP9pkny5\nzEygorofHQOcX2syXDPiSU9hO2u8IZ48USiTlzOhBW/XeBJxxis3Zw779eXotWstU6A26dkeR94U\nm3MVPIZq8p0A52yvdsWdvbAbHhtGS18LkmbK5405Sma2JnJ6JAwwoHOwU/YcexHT1NOE2NBYBAUE\ncc/XYg+l90r8NSzCy12xHKtl5ztCziME2D4LI2MjaO1r5ebnqXku5ZbQ29+Hlz+j9h5qwnZKZRCU\n3qOEGQnovtKNgRHbpDPxmRRztVIibONCjsadETQDodNCJfWExDnXdNZIPnPV1fJCAOCLCsBKPHVU\nIzNaKp4ybXfZzkcmdHf0PHsGrRf2OJofzxOeng6crKmVJLKfPw/Mn69+Xhbx1F6FrOiJSVy4AMyb\nxxvh6muJmouazokPV0YGcPpitaZakNeEeKrrqtNVgUwx50lMCI6d5EWAziZGKxEQwH6ZyPXjckRV\ncZVLOU9uE09OeJ7EfBFHfeK0hu2MRqC/v0jTXAD5Zdw8lLxmnlhpZ7mvg1Vu4tzshV1DdwMSZyTi\n8CeHZa9T+vUqNxctSeOOWuxoXXkod2+JeFLwPNXUsPPt+2baI9qd52mzFqtK+XlqRb2a0Jec50nN\ne6jU3846ubn3Qq/N8bExFgZTeg2Wmkwy/dREAW2fq1VTo2LenGdffMYudFzAvGjbb/0LF5TFCcAX\nxXPnAudqmQC0DnP39LAcqwsXiuTnyBH16elAab30/Tp/Xlmo8MpWpKcDZy7WSL6Xq6ociB67MgNz\n5wI1jT3ovtKNOTMn4pBKnieA5T3Zi6da8wUbAeaIKS+ehseG0dzbjJRwTuaYlxHznSZ7EWByeDKa\ne5u57RNcwdnQXf9wPwZHBxEXqnFZmRVu9Tx5qEGw1rCdo7o9csgt4+ahFLbjJcRyz9MQJrPc10nP\nk5rFH2pWndnPRUvSuKPq5loKhiqJSC3iSa1gDAsMw4ygGdyQqbVYVfKSuiqeJJ4nJ8N2s0JmYWR8\nRJKjGBc3kbRf21Ur6QPY0MDKGTha4CBXo8holI9mVFUpe04A5YTsqo4qiXhyJATEMXm1ns5crEZG\nVIaNd6e6mj1bSt87GVEZqO6slox3/nKNJAToyFuUE5ODirYK2/mmAxfMFciJydE01vxZ81HRPjHW\nzJnAjNQLSAnLtPGGORJhObNybMZJTwfaxi8gI4LEk4V6cz0SZyRimr9Mh04vIOY8eSNkBwCB/oGI\nC41DY3ej45M14Gytp/rueqTlOc6tUcKbYTtAnXDU4nkSV7B89rMFmucCOC7+KJKaOrHyxR7eUmwe\nToXtItSvuLNG9CLb94e0OUdD2A5wHOZUUwHaGk2epwj59yktjXkzR6/+xqntrOUKDWDC46FkF8s9\nVYS7qjuqZe+lWjzJvMeiABEEQbbGk9rQIE/giG11Kqr7YR4y447r77A57iikY5knR5CI/Q5LGisx\nf5btt7wgqBs7KzpLkpickcGuvdBxwSZ3R+18s6KzUNVRZbNv7lygpks+ZKf0rCyIXYBzl89Jxqvv\nr5KIJ0eCMSEsASPjI7jcf3livllA01AFcmNyLfsGBljqh9ICqoWxC3Hm0hmbffELqhAl2IoeR966\nhXELcfrSact2cDAQklKBmcMOlK8VU1486TnfyRsr7UQ8Ua7AWc+TUoNVNQwOsoq57mhx42w+mKPV\nhn3Dfegd7kV8mIP161dpbWUJomH81mmO56MiLAYot9ZRWhYvMjLCVs1ora+lRtzxPE9yfcpExse1\neX7UzIVbh0fGLo6WbfPuLfc+BQczL4qYrF7TKQ1ziKjNeVK6Z3Q0C2l1dQEXOvkhjKEhlt8nt1LL\nmrlR/Pwq8bPS3NuCsMAwSZudsTH1NpTzGs6dCxytqkVaRJqk8K6aMBjAvByV7ZU2+wwGJmRO1J5H\n9qxsm2MtLew9c7TiMWdWDs612QqTjAygqd2MgeEByUpSNfNdELsAZy+flYzZckWaLH7hgnK+k9x4\nc+cC7X5nsCB2gWXf6Ch79pTGMxgMyI3JtRFjCxYA5sBzyIqc8DxVV7PPmtIKy0Vxi3D60mmbsPP0\n5AoE9UyM09PDnlGlvwGiCLMJX8eXQWjJk7/IjikvnvSW7wRM5CV4y/MEwKk+bo5w1vNk7DIisNH5\nAk0mE0tYV7M03RFaesNZ46jOlclsQkp4imrvmhgKc5TDIjsfBY+GPTzRq1S80JqGBhZanKbRsasm\nbJeSAjQ1TXhegImwnZxdmpvZMmi1NacA7YUylUKH7e3sj7+jL1DLvSOVPZ1i6K57qBtDo0Pc0PaV\nK0z8Jiere17kbG+9ZL66o5ornmpr2fvCq8Oj9j7h4ez9OV7ND9nV17OwmpofDrzwEsDes7LGC8iM\nzpTYxFFIRyQ3JlcicgAgNxc4d+m8xPOketzYXEkYKyAAmLO4CnNCsmz+RohC0pEw5omd6GhgNOos\nUkMW2Ow/exZYuFD5WUkOT0b3lW6bkGhK6hgGQyuRY+UtMhqZwA+Rtj9UnF9QyDAQYUSAecJgp08z\nUaWE+OPTOuw8MLMEIw1LLNtlZWwcJREWHRKNGUEzUN/NUhsGRgYwGGRCW2W2/EV2THnxpLcyBdZ4\nUzylRaTB1G1y75jOep66TYgPVeeR4aHV06CElt5w1jjyPDnKk7FHa+hJMh+VnieAL/zEbufTp8lU\n+7uKs8/w7Bmz0THQwe2zJhIUxBZTNDVN7HO0AtCZFYqObBUTw+rbiJXYL3TIJ5aq9WqIzJ4xG11D\nXegf7uceF8WTUpcEo5EJJzWCBriaXCxTB0x8FuRe4/nzQLbK75eU8BQ09jRycytzcoAj5/niScs9\ncmKkXhyAvY7KdtuwkIja9ygnJgfnLp+T/JDKzQUaBqVhO7XiKTMqEyazCVdGbZfnzppfhYhR2wFq\natiPE7mimyJJM5PQN9xns9TeYAD8Z5/GzMFFNueePg0sWmQ/gi1+Bj+JeOwYN8L/SgzaL054CktL\ngTwVzprcmFycbZsQT1XtVQgdTUHl2YkVq6dOAUuXKo9jMBgs3ieAhX4bx06h+dSEeCotBfLzHc8p\nLz4Pp5pPAQBOXzqNlND5OF2q/kf81BdPOqsuDkzEmr0atvNQoUxnw3abN212+r7uFqHOtK9x5HnS\nWqZATABWk8PCnY+GWk9yzVrVrrRzRrj6+/kjJSLFoZ3tO6eL4knOLlpX2gHMC9vY3ShbrFLMoTEa\nWbuPkfER2T6ZjpZt2+Nn8JP1ngBMPFVXOy5TIL5mV3KexPtVVo2gobuB+3fTUUKvNUEBQbK5lTk5\nQGnjeUlyNABUVqoXT7zcHIDZo2GQJSTb20RtzlNsaCz8DH7SsgLZvRgUuiR1vtTaJiggCKkRqZK8\nJ//EMgR12fZsLCtTJwQMBoPEuzMwMoCR0HpcaZ54sQMDzFs8b57jZ8V+vNOXTiNGWICTJyfOUSN4\nAGDp7KU4eXHiwuMXj2Nu8AqUlk6cU1wMLFvmeKzlictxrOkYAOBi70X4Bwhoq0tEWxs7fvKkujmt\nT16PA/UHAACf1H+CjXNX49Qpx9eJTHnxpNfq4lpzI9yNJ3KeYmJYCKG7W9t1ruY8OVsPSQ5nbBMd\nzcJLXTLFyZ0VT87iaq0nT9Z4ElHbpkUUdu0D7QjwC5D0KbPGGY9dcEAwokOicbH3ovxcr4q46g6W\nQyIXftXqeQKA7FnZqGyr5B4TPU81nTWyf8fE1VNq4SVCi+TmAieqjZgzcw4C/aW/wrWIJ/FevPc4\nJweo7j7L9QxVVqq/R05MDs63n5cI30WLgHa/c5LVXD09LLTKa9thj8Fg4K4Um5ZQCb+uLEkulVov\njDhve49ZT0gpBo22SqmsDFis3APbwsK4hThzeSKZuqKtAnH+81ByciKmfu4cez7VhNmXJizFiYsn\nLNvHmo5hQeRK58RTwlJUdVSh50qPZayNc1fhANMuGB4GysuBJUsUBrnKptRN2G/aDwDYb9yPDSkb\nsG6tAQcPsu/VffuATZvUjbPPuA8AsMe4BzfM34KFCx1fJzKlxZP1L1U9UVRUZPmSVZsb4W48kfOk\nplcaD2OXERfPyH9xObzeA54nrbax9k7wcCZsl57ufM6TuIybV+HZHt57prasgtayANaoLVfAq+gs\nZxdn5+PoPReTxqs7pauXrHFGPM2fNR/nO85zj4mep8r2SkmCsoi1p0bN8zJ7xmx0DnZKCkACTDyd\nbZEPS2oVT5nRmZJVYAATT5eFczbJx9b3UOt5CgsMQ1xYnOQ5iksYxVh4DSJG59vYRMyrUcqHsZnn\n1dCdNS0ogdCyxKah9vi4ei8RACyJX4Li5mLLtiAIaBgpQ92RPJt+juXl6gXZitkrcLTpqGX7WNMx\nLIlfhmPHJs45ehRYuZL939Gzsj5lPQ7WH7RsH2k8guuy1+D4cbY9MsK8RStWOJ5bUEAQliYsxdHG\noxAEAQfqD+DudWtw5gwTtIcPs/c8IsLxWOuS16G4uRi9V3rx39r/Ymv6VhQWAu+9x96D6dPV/YBa\nNnsZuq9048OaD3Hi4gkUphfittscXycypcXTpf5LCA4IRniwQgdLL+GtGk8iiTMS0THYgaHRIbeO\nq1U89V7pxcDIACKCVHxqZHC758nJWk9KeU+OCiva46rnybKMW4UI5K5q61Je1SbiqFKxEmp68Nm3\nw3Ak6Jy1m33FYXssnqdOfiK1iLs9T5mZ7G9FxeVKiRdFpKKCiRG1yBWABNgXWONQJbKipHEtQdAu\nnvLi8lB+qVyyPymjB1cC2pFq95kQBG1hO4Cf2F3TWY3pI7Nx4ZxtJnNZmXoxAgD58fkobim22Xeq\npRjJAUttQjxGI0uEj1ZuA2lhddJqHGk8MnG92YiwoBAEj8VanvfxceDECXWeHYCJnU/qP7Fsf9Lw\nCW7JW4+zZ9mKZAA4eBBYv17deDkxOega6sLFnovoG+5D+aVyPLBlJc6cYT0njx5l4n7WLMdjAcBn\nMj6Df5z/B863n8fQ6BBWpizGunXA++8D//wn8JnPqBsnLDAM1829Ds8feh4fVH+A27Nvx333Ae++\nC+zYAfzP/6gbx9/PH4+teQyf/uun8eUlX8bMoJl48EF11wJTXDzp0esEsFizN0N2AHtwkmYmqSqk\nqAWtK+7qu+uRGpGKTWr8rBw8Ef50NqQp53kSBEFTgcy+Phb6TEhwPucJUF/rKSmJrdYatipIruaz\nIwiuiSethTKtk5h5dhGEiUrbWsmZlSNZlm6NWMSQ12RVZHzcufvPnzUf59v5nqfgYCAldRwVbZXI\njpEqCkFgoRhRPKl9XnJjcyWrswC2wi0o6QziDdKM4osX2aoqLd7yvPg8lLWWSfa3oQL+XfPRdtn2\nK6ihAQgMZCu41LIwbiHKW20FWnFzMZIClqGszNYmWsXT6qTVlvwakVMtp7AmbSmOTGgfFBerCzmJ\nrEhcgfJL5Zak8QOmA1ifvB5r1jAvDMDe18hI1rlBDZlRmRgeG4axizXdPlh/EIWZ67FkCQtljY4C\nBw4AGzey8x09K34GP9yQeQN2VezCB9UfYE3SGsSEh2HzZiZ2du0CbrhB/Wu+d9G9eLvibXx3z3dx\n36L7YDAY8NWvAk8/Dbz+OvCFL6gf64ebfojfl/wej6x6BLGhsYiNBX7yE/Z8PvKI+nG+seIbKP9q\nOX5c+GMA8s2NeUxp8aS2yJ838LZ4AvRR68nVfKeuLua9c2f4092FMruGWIw2MljdJMVnw9XSC2pX\n3AUEsBpZ1q111NRHu3SJrYhz1vZqktqtPU+86svWtLczMRETo30uvNwWm7la5TzJeZ6amljYQa6B\nqxxZ0Vmo7qyWTVifm9+EIMxERLDUO3v5Mnv+tbZ4yovLQ9klqagBAL/Z5ZjWKRVP5eXq829EFsUt\nwtnLZyUr7s5cPo1YYQGKbZ06KClR72kRWZW4yiZcBQAnmk9gadwKlJTYnnvqlDbxlBuTi5beFssq\ntr7hPlR3VOOmFYssIgcAioqADRvUjxsWGIbsWdkW79N+035sSt2EjRuBjz9m5+zdC2j57WQwGHDL\n/Fvw1rm3cKTxCGaFzEJ6ZDruuAN48002bno6+7Gkli/mfxH/3/H/D88dfA5fzPsiAODrXweeegp4\n4w3gy19WP1ZyeDJ+UPADAMDjax8HANxyC/CNbwC//722xVMLYheg7bE2fG/j9yz7HnwQ+Mc/tH3+\nxNV7/n4q47hWTG3xpLEdxmRRVFTk1ZV2Ip5YcafV82TsMiI1ItXp3B6xHpI7w5/J4cm42HtRc/sa\nudcuVhZXW+PJOvTkrF0A52s9dQ91o3+4X9LWwh5XvE7ARFK7Uk2t+PiJVhvn2ydq6/DsIoaUnHkW\nHImnlBSgoVHgdqgXcSZkBwChgaGIC42TXXkYNa8S4SP8OJYYshNfs9rnZXH8Yom3BmDtrAanX0B3\njTQOWFKiPqdHZEbQDMyeMRvVHbarCY9fPI5Fs1ZY8mdE1CYgW7MmaQ2ONR2zEZ8nLp7ArStW4OBB\nYP/+IgCs1ERNjTYPkb+fP1bNWWXJ/SkyFWFF4gpsXj8dx46xoqEAsH+/uiRla26bfxveOf8OhseG\n8UH1B/hUxqdw++0sd2dwEPj734Hbb9c25hfyvoBfn/w1nt73tEXs3Hsv8N//Ag89xISKiJpnpSC1\nAF/K/xKum3sd7sy9EwBQWAj88pfA7t3ahBgAfH3F1/Hvu/9t+SFgMADf+hY05RrphakvnjTkmUwm\nevA8OVtNWwnNnqduE1LDU52+nztrPImIXcq1hjTlXruaXB2b812s8WSZj4ZaT3PnTvRRE5OiHYk9\nV8VTeHA4ggOC0TbQJnuOnx8TROcqxrlNU63Rmo9jTWpEKi73X0bfcB/3eFAQEDO3EcF+obKr/c6e\nZQnXzpAdk82tVwQAAfEV8GuXz3fSkh8kIhdOq2qvQlxQKspPSQsLlZZqEx4i+fH5ONl80mbf8abj\nuC5nJU6csD1X7TJza2JCYxAbGmuxX++VXlS0VeCG/CUICZlo2H3oEEtuDtRYj/fmeTfj3ap3AQD/\nqfkPtqZvxaxZTEh++CF73/v6tHvl7l54N/5+9u/4yaGfYFHcIqRGpCI+Hti8GbjpJuZJ3bJF25ir\n5qzC15Z/DWmRaXho+UMAWE7Se+8Bzz7LhJRWntrwFF667iWb1YV33jkR/rtWmdriSWMX+8lCDzlP\ngHP1jByh1CuNhxi2cza3x5mmtGrIjMqUrb0jR2oq+0Nt/9prOqXNNJWwXjHmcs6TSs/i/PmsyB+g\nXATSGlfFE6Au7yknBzh8+iLCAsMsiz94dnFFPPn7+SMrOks29wgAEvPPYHaA/FpmNcUH5ciPz0dJ\nSwn3WPf0cvTW8u9rvzxe7fOSNDMJg6ODNv3GAKCkpQRLEhfj6FHA3iHojOcJADakbLDU0wGYuDGa\njfjsxkU4cWKigvzwMEtCXrdO+z02p23Gf2v+CwDYa9yLVXNWITQwFFu2AB0dBQCAf/8b+NSntI99\n2/zb8N6F99DY3Yg3z76Jzy34HACWmPyznwEvvAA88ID2MHt6ZDoeXvkw/lj2R/zsUz+z7P/1r9lz\n/Pbb2iv3A8COdTvwp1v+hOCAYMu+FSvYHK1/D7nyt4WY4uJJrwnjguDdApkinsh5CguT75XGw2Q2\nOWwBooQnPE8AW2JtH2pwhJhM29xsu7+mi19JWQ5XV9qJpEakwmQ2YVxwrGTnz2ernIDJF09yNYdE\ncnOB47VVkorO9rgingDHobuwuWcxvUe+f8SZM9BUJ8aapQlLZcVTdd8p9Ncs5dYQKy4Gli/Xfj+D\nwYDls5dLkqEPNx5GYdYaTJtm60VtbgZ6e51Lxt+Uugn7jfst22Loa05CIFJTmWACgOPH2fMUFaX9\nHnfk3IG3zr0FANhVsQs3Zt4IgHla/vAH5hnavRu46y7tYyfOTMTdC+5G7m9ycWPWjRYv8uc/z3Lc\namuBRx/VPi4APL3haRgfNiIvfkIBx8cDL7/snFAlJo8pK55GxkbQ0tciqQKrB959twghIdoTS92N\nJ3KeAG2hO1dznjzlwcuKytLseQL45QrEwopqsQ7buZLzFDItBJHTI9HS2+Lw3OxsJj6Aq+IpanLE\nk1x7DWtYL7Eqm27zSjlPrsxFSTyNRp3BUANfPI2NsRCao95cciydvRSnWqTljQdGBlDbVYtlSQsk\n+UEDAyzPytrbpeV5KUgtQJHJ9vzDjYexLnktVq+GzWqyoiIWpnFmEUNOTA4GRwctFbU/qPkAN2Sy\nZVo33cRWbgFM3Nx4o/bxAfZazENmvHTkJXxQ/QE+v/jzAMQk7iKsWAFs3aquOCaPX3z6F3jvnvew\n86adln0BAWzux46pq0+kN1z520JMYfHU2NOI+LB4TPN3wu/pYVpavB+yA1j7gYGRAfRe6XXruI76\nvImYh8wYGR9B9HSVxVE4uLvGk0hmdKakfYIaeOUKajrVe57GxtiqN3d5JTOiMlS9jpQUoK2N/UJX\n43kSywK4Kp4Wxi609KmSIycHaBzkt/IQGRxk3hFXnoVFcYu4eUAibYYzaCnnu5Zqa9mKNy1Lna1J\nCU/B0OiQpKdieWs5smOysW51kMVDYzlWzmwTFASn2Jiy0UY8tQ+0o7G7EYvjF2PLFpZkLLJvn7aV\nX9YYDAbcveBuvFb+GoZGh7C7YjdunX8rAOYZeu015qn+29+A++5z7h4BfgH4w81/wP+V/x9+9Zlf\nIWp61NV7A889B3zzm8Crrzo3tjj+hpQNuvw+IbzDlBVPes13AoCoqAKvh+wA9kfNE0njalfcGbuM\nmBs5FwaDwan4+9gY0Njo/K9JJZzJeQKkwrF/uB/mITMSZ6or1tLYyJbaB19NV3A1LyEnRrl+kYi/\nPxNCVVUCq2WkUEUbYMvyZ8xwXiyI2LeU4JGWBgyEnkNq6ETStL1dKirYSje1zXF5LJu9DMXNxdzV\nf8NjwzD1XUBvXTY3fFZSom0JvD1yYbRjTcewInEFVq+GRDwdPAisWWO7T8vzsjxxOeq66iyeyfcu\nvIetc7ciwC8AN98MfPABy0MaGQH+9S/mJXKWB5c+iN+d+h2+9d9vYUXiCsuPiXnzgJtvZs/eLbe4\nJsY3pm7EmYfO4N5FtlnRt99egK9+1fuefr1BOU+uMWXFk17znQB9rLQTSYt0f9K42I/LEWpqCSlx\n8SKr6Bsc7PhcraRFpqGppwnDY8OOT7bC3vNU01mD9Mh0SR8sOaqqnFvuLkfOLOVQlDXz5wPHzl5C\nUECQ5Ze7HOfOOb+yzJr0yHR0DHSge0i+IaLBIMCQUC5pmmqNlr5icsyeMRtBAUHcz8PpS6eREZWB\nvNxQSe0ggAmb1atdu//mtM3YU7fHZt8+0z5sSt2ENWtYTpBYKRoA9uzRvhrLmkD/QNyWfRv+dvZv\nAIC3K97GrfOYR2j2bJZz8+abrHZOVpZrf7Pmz5qPl7a+hMv9l/HKDa/YHPvtb9lS/1dekbmYIHTI\nlBVPei5TcPhwkX7EkwfynjIzWT6MI9T0KlPCU8niAPtimTNzjmbb2HuetITsACaerDu+u5qX4CiP\nx5rsbOBEjXL7EZFz55zP77HGz+CHnJgcbrVrkYu9FzHNPwANFfGWffZ20Vo5Wg7R+2TPsaZjWDVn\nFdauZR4fe9whnrakb8HHdR9btkfHR/FJ/ScoSC1AdDQTM3v3smN9fUxM2S8X1/q8fDn/y/jl8V/i\nYP1BFDcXY1vONsuxZ55hidAPPwz84AfOvqoJ7s+7H+/c9Q6Swm2LAwUEAMuWqe83pxXK7eFDdnGN\nqS2edFggE2DxfT2E7QDn+7gpoUU8yXWKV4OnyhSIiJWftSA2kBVxVTy5ihbxNH8+cOZShcNVbYD7\nPE8AyzVSCt2Vt5YjbfpiFBfL153S0pRViWUJy3Ci+YRk/7GmY1iVuAobN8LSCV5kcJDZQ2t9Invy\n4vNgHjJbeuztM+5DVnQWYkNZ+fDbbmOeIAB45x2WgxTuYtvOtclrcfO8m1H4WiFe/syYrJ1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NWWbYMBuPnmiXpJ1rS1scriVj8EJej1WfE2ZBc+ZBcpZBM+ZBfXUBRPALB9+3YUFhZiu9U65eLi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\n"
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "source": "The Cornu spiral defined as the parametric curve $u(t),v(t) := C(t), S(t)$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure(figsize=(8,8))\nplot(v, u, \"b\")\nplot(-v, -u, \"b\")\ngrid(True)",
     "language": "python",
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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lZej7sceA1avl4I6NG4GHHpLnd+yQ3nbW4zBtPe2Clp3FxckkPD0sT7tdw4ZA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      }
     ],
     "prompt_number": 54
    }
   ]
  }
 ]
}