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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=top></a>\n",
      "<center>\n",
      "<h1>Problem Generator Notebook</h1>\n",
      "</center>\n",
      "<p>\n",
      "This notebook doesn't go with any particular section of the notes.\n",
      "It is intended to generate \"random\" problems of various types."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b><font color=brown>This setup cell below must be run first</font></b>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%autosave 0\n",
      "%matplotlib inline\n",
      "import sglib\n",
      "reload(sglib)\n",
      "from sglib import *\n",
      "# The next import makes expressions like 1/2 work.\n",
      "# So you no longer have to say frac(1/2)\n",
      "from __future__ import division"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "javascript": [
        "IPython.notebook.set_autosave_interval(0)"
       ],
       "metadata": {},
       "output_type": "display_data"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Autosave disabled\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2>Contents</h2>\n",
      "<ul class=ult>\n",
      "    <li> <a href=\"#vector\">Vector Problems</a></li>\n",
      "    <li> <a href=\"#matrix\">Matrix Problems</a></li>\n",
      "    <li> <a href=\"#basis\">Basis Problems</a></li>\n",
      "    <li> <a href=\"#projections\">Draw Projections</a></li>\n",
      "    <li> <a href=\"#electron1\">Electron Spin</a></li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "   \n",
      "<h2>Status</h2>\n",
      "<ul class=ult>\n",
      "    <li>To run locally: <code>ipython notebook</code>\n",
      "        <br>(the \"pylab inline\" thing should no longer be necessary)</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=vector></a>\n",
      "<h2><a href=\"#top\">^</a> Vector Problems</h2>\n",
      "<ul class=sp>\n",
      "    <li>This will now generate <i>complex</i> vector problems.</li>\n",
      "    <li>If you want <i>real only</i> problems set: complex=False</li>\n",
      "    <li>Note: \"True\" and \"Fase\" must have the \"T\" or \"F\" capitalized.</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob = vector_problem(max_dim=3, max_int=5, complex=True)\n",
      "prob.new()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>Normalize: $\\left[\\begin{matrix}2 i\\\\2 + 4 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb926fcc>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "answer = sqrt(33)\n",
      "prob.check(answer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The correct answer is:\n"
       ]
      },
      {
       "html": [
        "<font size=4>$\\frac{1}{\\sqrt{6}}\\left[\\begin{matrix}i\\\\1 + 2 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb5e5c2c>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=matrix></a>\n",
      "<h2><a href=\"#top\">^</a> Matrix Problems</h2>\n",
      "<ul class=sp>\n",
      "<li> The answer must be entered in \"matrix format.\" Hopefully we've covered that\n",
      "        in the Sunday meeting. Basically, every <i>row</i> of the matrix is entered\n",
      "        as a list, in parentheses. The the whole thing looks like:\n",
      "        &nbsp;<code>Matrix([ (row2), (row2), ... ])</code>. \n",
      "        <br>Just leave the outer parens and brackets as is, and enter the rows you need. \n",
      "    <br><br>\n",
      "        Example: the matrix\n",
      "    $\\left[\\begin{smallmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{smallmatrix}\\right]$\n",
      "    <br><br>\n",
      "    would be entered as: \n",
      "        <br><br>\n",
      "        <code>Matrix([ (1,2,3), (4,5,6), (7,8,9) ])</code></li>\n",
      "<br>\n",
      "<li> You can use the \"Matrix Test\" cell below to see the results of a particular\n",
      "    matrix command.</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob = matrix_problem(max_dim=2, max_int=5, complex=True)\n",
      "prob.new()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>$\\left[\\begin{matrix}3 + 5 i & 3 + 3 i\\\\1 + 4 i & 4 i\\end{matrix}\\right] \\left[\\begin{matrix}1 + 3 i\\\\2 + 2 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb7eb16c>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "answer = Matrix([ (4,8), (7,27) ])\n",
      "prob.check(answer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The correct answer is:\n"
       ]
      },
      {
       "html": [
        "<font size=4>$\\left[\\begin{matrix}-12 + 26 i\\\\-19 + 15 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9269cc>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b><font color=brown>Matrix Test</font></b>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = Matrix([ (1,2,3), (4,5,6), (7,8,9) ])\n",
      "Print('$%s$'%sy.latex(M))  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>$\\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9d504c>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=basis></a>\n",
      "<h2><a href=\"#top\">^</a> Basis Problems</h2>\n",
      "<ul class=sp>\n",
      "<li>In all of these problems, the original vector is given in the\n",
      "            \"standard\" basis (1, 0) and (0, 1).</li>\n",
      "<li> All vectors in these problems are column vectors.</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob = change_basis_problem(max_int=5, complex=False)\n",
      "prob.new()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>Transform the vector $\\left[\\begin{matrix}5\\\\2\\end{matrix}\\right]$ to the basis $\\left(\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}1\\\\1\\end{matrix}\\right],\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}1\\\\-1\\end{matrix}\\right]\\right)$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb7d3b4c>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "answer = col(0,0)\n",
      "prob.check(answer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The correct answer is: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}7\\\\3\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9d592c>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=projections></a>\n",
      "<h2><a href=\"#top\">^</a> Draw Projections</h2>\n",
      "<ul class=sp>\n",
      "<li> Pick the cell below that is closest to the problem you're interested in and then modify it for your problem.</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(vector(1,0), vector(0,1), vector(-4,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}-4\\\\1\\end{matrix}\\right]$, and its projection on the basis: $\\left[\\begin{matrix}1\\\\0\\end{matrix}\\right],\\left[\\begin{matrix}0\\\\1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9d5b0c>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\left[\\begin{matrix}-4\\\\1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9f4c0c>"
       ]
      },
      {
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       "text": [
        "<matplotlib.figure.Figure at 0xb9d6fec>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(vector(-1,0), vector(0,-1), vector(-4,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}-4\\\\1\\end{matrix}\\right]$, and its projection on the basis: $\\left[\\begin{matrix}-1\\\\0\\end{matrix}\\right],\\left[\\begin{matrix}0\\\\-1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9eb4ac>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\left[\\begin{matrix}4\\\\-1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9eb84c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb78a4ac>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(1/sqrt(2)*vector(1,1), 1/sqrt(2)*vector(1,-1), vector(-4,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}-4\\\\1\\end{matrix}\\right]$, and its projection on the basis: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}1\\\\1\\end{matrix}\\right],\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}1\\\\-1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb764fec>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}-3\\\\-5\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb952d2c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb862b6c>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(1/sqrt(5)*vector(2,1), 1/sqrt(5)*vector(-1,2), vector(-4,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}-4\\\\1\\end{matrix}\\right]$, and its projection on the basis: $\\frac{1}{\\sqrt{5}}\\left[\\begin{matrix}2\\\\1\\end{matrix}\\right],\\frac{1}{\\sqrt{5}}\\left[\\begin{matrix}-1\\\\2\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb677a6c>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\frac{1}{\\sqrt{5}}\\left[\\begin{matrix}-7\\\\6\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb7e94ec>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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B9EC4MwDBBtIL4U5jBBtIT4Q7DRFsIL0R7jRCsIHMQLgN47quDl4+qNnjZus2321RPYdg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\nhBsALEO4AcAyhBsALEO4AcAyhBsALPP/o0V7v6EC+toAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb85ca2c>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=electron1></a>\n",
      "<h2><a href=\"#top\">^</a> Electron Spin</h2>\n",
      "<ul class=sp>\n",
      "<li>The \"use_y\" flag will determine whether y spin states are included.</li>\n",
      "<li>The \"complex\" flag tells whether to include complex amplitudes.</li>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sglib\n",
      "reload(sglib)\n",
      "from sglib import *\n",
      "#\n",
      "set_font_size(3) # Font size of 3 or 4 works pretty well\n",
      "z=1; x=2; y=3 # Don't change this line!!!\n",
      "prob = electron_problem(\n",
      "    min_int=0, max_int=5, use_y=False, complex=False)\n",
      "#prob.set_debug(True) # Probably leave this commented out\n",
      "prob.new()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>Given the input state: $\\;-| +z \\rangle$\n",
        "<br><br>\n",
        "If you do the observation associated with the matrix $\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$\n",
        "<br><br>\n",
        "What is the probability of seeing the $1$ eigenvalue\n",
        "<br><br>\n",
        "</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb783dec>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "answer = 10/23\n",
      "prob.check(answer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The answer is: $\\;\\frac{1}{2}$, or approximately $\\;0.5000$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb683aec>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<p>\n",
      "You can ignore everything below this point.\n",
      "</p>\n",
      "<hr size=3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Print(prob.latex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>Given the input state: $\\;-| +z \\rangle$\n",
        "<br><br>\n",
        "If you do the observation associated with the matrix $\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$\n",
        "<br><br>\n",
        "What is the probability of seeing the $1$ eigenvalue\n",
        "<br><br>\n",
        "</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb9ec12c>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(prob.latex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Given the input state: $\\;-| +z \\rangle$\n",
        "<br><br>\n",
        "If you do the observation associated with the matrix $\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$\n",
        "<br><br>\n",
        "What is the probability of seeing the $1$ eigenvalue\n",
        "<br><br>\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 42
    }
   ],
   "metadata": {}
  }
 ]
}