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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": [
      "%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": [],
     "prompt_number": 1
    },
    {
     "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>$\\left[\\begin{matrix}5 + 4 i & 2 + i\\end{matrix}\\right]^{\\dagger}$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb38204c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "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>$\\left[\\begin{matrix}5 - 4 i\\\\2 - i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb2c19ec>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "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>$\\left[\\begin{matrix}i & 3 + i\\\\2 + 3 i & 5 i\\end{matrix}\\right] - \\left[\\begin{matrix}2 + 2 i & 4 + 2 i\\\\4 + 2 i & 3 + 5 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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>$\\left[\\begin{matrix}5 + 10 i & 3 + 4 i\\\\4 + i & 8 + 6 i\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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 object>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "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 $\\left[\\begin{matrix}5\\\\4\\end{matrix}\\right]$ 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 0xb38792c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}9\\\\1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb39072c>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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(1,1)/sqrt(2), vector(1,-1)/sqrt(2), vector(2,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}2\\\\3\\end{matrix}\\right]$, 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 object>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}5\\\\-1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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+9tlnw/1fL1my5NczZ85cYfdMgbd33nmnJCcn59Njx471t3uWYDdd16u3bds2\n2u45DOPcG1dXXXXVFwcOHMg8c+ZMkpPenDQMQw4cOJDp1DcnfT6fds899yz/7W9/u9juWTrejh07\n1v/777/vaxiGnDp16qLx48e//957702we66ON4/H87NbbrllnZlj2P4P0dltyJAhXzopuKdOnbo6\nNzd3Z35+ft0dd9zx2jfffJNm90yBt2HDhu0fPHjwVwUFBbUFBQW1Dz744At2z+S/vf7667enp6fX\nJycnnx4wYEBjSUnJO3bPZBiGrF+//uYRI0bsGzp06Ofl5eXz7J7Hf5s+ffrKn/zkJ0eSkpLOpKen\n11dUVNxv90yBtw8++GCcpmm+/Pz8Ov/r7Z133imxey7DMGTHjh15bre7Jj8/vy4vL2/HU089Ncfu\nmTq7eTyen5ndVcIp7wCgGMfsKgEAhIbgBgDFENwAoBiCGwAUQ3ADgGIIbgBQDMENAIr5f29G1cu1\n7ckSAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa656e0c>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(1/sqrt(2)*vector(1,1), 1/sqrt(2)*vector(1,-1), vector(2,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}2\\\\3\\end{matrix}\\right]$, 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 object>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\frac{1}{\\sqrt{2}}\\left[\\begin{matrix}5\\\\-1\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xa5906ec>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(vector(-1,0), vector(0,-1), vector(2,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}2\\\\3\\end{matrix}\\right]$, 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 object>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\left[\\begin{matrix}-2\\\\-3\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xa5b7a4c>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_projections(1/sqrt(5)*vector(2,1), 1/sqrt(5)*vector(-1,2), vector(2,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The vector $\\left[\\begin{matrix}2\\\\3\\end{matrix}\\right]$, 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 object>"
       ]
      },
      {
       "html": [
        "<font size=4>The vector in this basis is: $\\frac{1}{\\sqrt{5}}\\left[\\begin{matrix}7\\\\4\\end{matrix}\\right]$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i77zzjkyZMkVsNptf93f9i0tmlcwSEcIavbFpw3T82baD2bSDPS3S0tIiN910k5w/f97n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\nAKAQQhsAFEJoA4BCCG0AUAihDQAK+X80opHQXk+MGQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa65aecc>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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: $\\;-\\dfrac{1}{\\sqrt{5}}| +z \\rangle-\\dfrac{2}{\\sqrt{5}}| -z \\rangle$\n",
        "<br><br>\n",
        "If you do a measurment in the $x$ basis.\n",
        "<br><br>\n",
        "What is the probability of getting $|+x\\rangle$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb2210ec>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "answer = 10/23\n",
      "prob.check(answer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<font size=4>The answer is: $\\;\\frac{9}{10}$, or approximately $\\;0.9000$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0xb38be0c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "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: $\\;-\\dfrac{2 + 3 i}{3 \\sqrt{7}}| +x \\rangle-\\dfrac{5 + 5 i}{3 \\sqrt{7}}| -x \\rangle$\n",
        "<br><br>\n",
        "If you do a measurment in the $z$ basis.\n",
        "<br><br>\n",
        "What is the probability of getting $|-z\\rangle$</font>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML object>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(prob.latex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Given the input state: $\\;-\\dfrac{2 + 3 i}{3 \\sqrt{7}}| +x \\rangle-\\dfrac{5 + 5 i}{3 \\sqrt{7}}| -x \\rangle$\n",
        "<br><br>\n",
        "If you do a measurment in the $z$ basis.\n",
        "<br><br>\n",
        "What is the probability of getting $|-z\\rangle$\n"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}