{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discovering Computable Math on the Web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "from operator import is_not\n",
    "from functools import partial, lru_cache\n",
    "\n",
    "from sympy import init_printing\n",
    "from sympy.plotting import plot\n",
    "from latex2sympy import process_sympy\n",
    "from pyquery import PyQuery\n",
    "from notebook.utils import url_path_join as ujoin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to do some scraping... at least do _some_ caching."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "@lru_cache(maxsize=128)\n",
    "def pq(url):\n",
    "    return PyQuery(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's a lot of crazy Latex out there, and a lot of math that `latex2sympy` can't parse yet, so here's a helper function to winnow that down some.\n",
    "\n",
    "[This PR](https://github.com/augustt198/latex2sympy/pull/38) handles the various style expressions!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "STYLE_RE = r'{\\\\(display|text|script)style (.*)\\}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "def parses(raw):\n",
    "    match = re.match(STYLE_RE, raw, re.M)\n",
    "    \n",
    "    if match is not None:\n",
    "        raw = match[2]\n",
    "    try:\n",
    "        return process_sympy(raw)\n",
    "    except:\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wikipedia (or any other MediaWiki page with the [Math](https://www.mediawiki.org/wiki/Extension:Math) extension.\n",
    "\n",
    "> _TODO: How might we search for MediaWiki pages that use a given extension?_\n",
    "\n",
    "Here are some URLs and HTML selectors that have lots of neat stuff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "WIKIPEDIA = \"https://en.wikipedia.org/wiki\"\n",
    "MEDIAWIKI_SELECTOR = \".mwe-math-fallback-image-inline[alt]\"\n",
    "MATH_WIKI = \"http://math.wikia.com/wiki\"\n",
    "WIKIA_SELECTOR = \".tex[alt]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wiki_maths(topic, wiki=WIKIPEDIA, selector=MEDIAWIKI_SELECTOR, attrib=\"alt\"):\n",
    "    url = ujoin(wiki, topic.replace(\" \", \"_\"))\n",
    "    return list(filter(partial(is_not, None), [\n",
    "        parses(img.attrib[attrib])\n",
    "        for img in pq(url)(selector)\n",
    "    ]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 🚀 Rockets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAGLMAAAAkCAYAAADWQi6GAAAABHNCSVQICAgIfAhkiAAAIABJREFU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\nQmCC\n",
      "text/latex": [
       "$$\\left [ \\Delta v = v_{e*text} \\log{\\left (\\frac{m_{0}}{m_{f}},e \\right )}, \\quad m_{0}, \\quad m_{f}, \\quad v_{e*text}, \\quad v_{e*text} = I_{text*(p*s)} g_{0}, \\quad I_{text*(p*s)}, \\quad g_{0}, \\quad t = 0, \\quad P_{1} = V \\operatorname{left}{\\left (right \\left(\\Delta m + m\\right) \\right )}, \\quad P_{2} = \\Delta V_{e} m + m \\operatorname{left}{\\left (\\Delta V right + V \\right )}, \\quad t = 0, \\quad t = 0, \\quad V_{e}, \\quad v_{e}, \\quad V_{e} = V - v_{e}, \\quad dm = - \\Delta m, \\quad \\Delta m, \\quad m \\frac{d}{d t} V = - v_{e} \\frac{d}{d t} m, \\quad m_{0}, \\quad m_{1}, \\quad v_{e}, \\quad m_{0} - m_{1}, \\quad M_{f}, \\quad \\Delta v, \\quad m_{1}, \\quad m_{0}, \\quad c, \\quad \\frac{m_{0}}{m_{1}} = left \\left(right \\frac{1 + \\frac{\\Delta v}{c}}{- \\frac{\\Delta v}{c} + 1}\\right)^{\\frac{c}{2 v_{e}}}, \\quad \\frac{m_{0}}{m_{1}}, \\quad R, \\quad \\frac{\\Delta v}{c} = \\frac{R^{\\frac{2 v_{e}}{c}} - 1}{R^{\\frac{2 v_{e}}{c}} + 1}, \\quad R^{\\frac{2 v_{e}}{c}} = exp left \\frac{2 v_{e}}{c} \\log{\\left (R right,e \\right )}, \\quad \\tanh{\\left (x \\right )} = \\frac{e^{2 x} - 1}{e^{2 x} + 1}, \\quad \\Delta v = c \\tanh{\\left (\\operatorname{left}{\\left (\\frac{v_{e}}{c} \\log{\\left (right \\frac{m_{0}}{m_{1}},e \\right )} \\right )} \\right )}, \\quad m_{0}, \\quad \\Delta m, \\quad \\frac{J}{\\Delta m} = \\frac{F}{p} = V_{rm*(e*(h*x))}, \\quad v_{e*text} = I_{text*(p*s)} g_{0}, \\quad I_{text*(p*s)}, \\quad v_{e*text}, \\quad g_{0}, \\quad \\Delta v, \\quad \\Delta v, \\quad - \\frac{1}{e^{2.15555555555556}} + 1, \\quad \\Delta v, \\quad - \\frac{1}{e^{1.11111111111111}} + 1, \\quad \\Delta v, \\quad - \\frac{1}{e^{1.04444444444444}} + 1, \\quad v_{e}, \\quad m{\\left (t \\right )}, \\quad v_{e}\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                    ⎛m_{0}   ⎞                                               \n",
       "⎢Δ⋅v = v_{e*text}⋅log⎜─────, ℯ⎟, m_{0}, m_{f}, v_{e*text}, v_{e*text} = I_{tex\n",
       "⎢                    ⎝m_{f}   ⎠                                               \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "t*(p*s)}⋅g_{0}, I_{text*(p*s)}, g_{0}, t = 0, P_{1} = V⋅left(right⋅(Δ⋅m + m)),\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " P_{2} = Δ⋅V_{e}⋅m + m⋅left(Δ⋅V⋅right + V), t = 0, t = 0, V_{e}, v_{e}, V_{e} \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                               d              d                               \n",
       "= V - v_{e}, dm = -Δ⋅m, Δ⋅m, m⋅──(V) = -v_{e}⋅──(m), m_{0}, m_{1}, v_{e}, m_{0\n",
       "                               dt             dt                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                         c    \n",
       "                                                                      ─────── \n",
       "                                                                      2⋅v_{e} \n",
       "                                                     ⎛           Δ⋅v ⎞        \n",
       "                                                     ⎜       1 + ─── ⎟        \n",
       "                                        m_{0}        ⎜            c  ⎟        \n",
       "} - m_{1}, M_{f}, Δ⋅v, m_{1}, m_{0}, c, ───── = left⋅⎜right⋅─────────⎟       ,\n",
       "                                        m_{1}        ⎜        Δ⋅v    ⎟        \n",
       "                                                     ⎜      - ─── + 1⎟        \n",
       "                                                     ⎝         c     ⎠        \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                  2⋅v_{e}                                                     \n",
       "                  ───────       2⋅v_{e}                                       \n",
       "                     c          ───────                                       \n",
       " m_{0}     Δ⋅v   R        - 1      c               2⋅v_{e}                    \n",
       " ─────, R, ─── = ────────────, R        = exp⋅left⋅───────⋅log(R⋅right, ℯ), ta\n",
       " m_{1}      c     2⋅v_{e}                             c                       \n",
       "                  ───────                                                     \n",
       "                     c                                                        \n",
       "                 R        + 1                                                 \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         2⋅x                                                                  \n",
       "        e    - 1              ⎛    ⎛v_{e}    ⎛      m_{0}   ⎞⎞⎞               \n",
       "nh(x) = ────────, Δ⋅v = c⋅tanh⎜left⎜─────⋅log⎜right⋅─────, ℯ⎟⎟⎟, m_{0}, Δ⋅m, ─\n",
       "         2⋅x                  ⎝    ⎝  c      ⎝      m_{1}   ⎠⎠⎠              Δ\n",
       "        e    + 1                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "J    F                                                                        \n",
       "── = ─ = V_{rm*(e*(h*x))}, v_{e*text} = I_{text*(p*s)}⋅g_{0}, I_{text*(p*s)}, \n",
       "⋅m   p                                                                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                -9.7               -5.0               -4.7    \n",
       "                                ─────              ─────              ─────   \n",
       "                                 4.5                4.5                4.5    \n",
       "v_{e*text}, g_{0}, Δ⋅v, Δ⋅v, - e      + 1, Δ⋅v, - e      + 1, Δ⋅v, - e      + \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                     ⎤\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "1, v_{e}, m(t), v_{e}⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎦"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki_maths(\"Tsiolkovsky rocket equation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some advanced applied concepts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABo4AAAArCAYAAABGmXoWAAAABHNCSVQICAgIfAhkiAAAIABJREFU\neJztnXm4HUWZh98sQGKCgDgjDAiXPYGghIiihl1ABEcRRAWURVGUQRjHZYARj8oiyqjBUVxQgqMo\n2yDigpBBtkFEloRAIsoSUEBQgigIkoQ7f3xVz+nbp/uc7j6939/7PP3ce6q7lq+rvqrq+moBIYQQ\nQgghhBBCCCGEEEIIIYBJVSdApOIFwD3AhsCVFadFCCGEEEIIIYQQQgghhBAtY2KE24bA74HFwE3u\nOrbMRIlYTgJ+WXUihBBCCCGEEEIIIYQQQghRCdNyCmcHujagX2F2oUMBJkc8PBnYADgF+GpOCRDD\nswUwA7gcmFVxWoQQQgghhBBCCCGEEEIIUS5zgFtyDnMCMALcD0yH6BVHbeRqYNRdK4F7gfcN8DMT\nmA/8DnjO/b0COIBkW/zNBJ4Fbs+QxuD1Unf/TOCEhGEJIYQQQgghhBBCCCGEEKJd7AtshBl78rp6\nGC+Go9lAB1gfW7nzU+Bs5x7FmzGDzxrAu5yfA4EfAqc690HMAz4PbAOsnjCNJ7k0Bq/fAW8CfuMu\nIYQQQgghhBBCCCGEEEKMPzbCbAalM4KtdDm6isgLYDNMntcF3F7i3I6MeP7l2Aqjk2LCi7TAhXgL\n8L/A2i6e7RKm8bUx90/HCsMy4E/Ak8DJoWdeCVwF/JHeVUubJUizEEIIIYQQQgghhBBCCCHqyT9i\nRwwVwQgD7EIDH2gYB2Hy/EPAbY5z2y/i+WuAO8m+GmsqcB/d1UwPAUckSONK4AUJwj8c27YuyCzg\nb8BZ2Aqn3YBHgF8Ch5DM2DUeOQE79OsvmMFN50cJIYQQQgghhBBCCCGEqCOHA68pKOwRAnah8bBV\n3RzgYcwwALb6Zh52ztECYFPgje7exsAuwOeA553bROBR4Cl3nRcIO+jX8+/ADXTPNrqLwSuO5mDn\nJj0WiOeuJMI55mHb733Q+fs5dj7Ti4DvYhkuetkV+AqmbLtjxrsF2HsTQgghhBBCCCGEEEIIIerC\nq4Cbqop8hHatOFoArMKMMc8AzwLfA17q7h8DfMz9vx8m+4yA/4nA5u56DDgxcC/oF+zdLQ+EDXbO\n0bV90jfJpfGiQDybAxskkA3gxZjBY4+Q+38w/s5Eei+Wf38CvkB6w+h0rKyEjYGiXgybz0II0QY+\nhNWFB+cQ1guxVcvLsO16Rxnbv4nj21jfaFqGOH3635HBb1xYebyLpuFX0b+76oSIgdRBZ6Eeejue\ndRakt0KIetHB6qSRcRKvGH90qK6sVRm3aCerAf9VYPgj5LBV3VX0nqOzHNv2693Ua2u0x7EVRN4Y\nExxk3gVL92+xFUKHYLJsHhGOP69o3xi/04BL3TMrA9cq7Eyi4Du5HNtu7jrgPS6Nx2WUb28X54tD\n7j/AVhvVmY2AT2NW0uXACvf3JuAMYNuU4e2J5fWT2DvZO6X/9Z2/uSn9NYF30tXV91SclmEZNp/L\nIqqeDF7zK0tZNtogzzuwtH45wbNfdc9+ttAU5c8W2Ll4t2IrbVe4vwuAD5BsS9QyaGJ5WherPy8F\n7sEmozyJrTJ+N/2N2EXI+x16J7tk5XIX1o+xvZI7wEz6D+6+Alud/aGMcZ7vwt4yo/8gad9FnFxl\n1hEvwfqIZ8XcT6PLl2JbFE/PmJaiaKKeB8k7/VXrLNRHb7O8C+ltOTRdb4NIlvrRFjk8bZGnQ/+B\n7aLkHBRv0RSZf+H2YpjviCpoS9n2dIgua2X0IeLiLoui8zLL+ENUf6qodA7qu0Hzxkt3A95eYPgj\n2Ls4GmByxkC2xz46TnGB+VU5BwLnYFu+nTxkQvNgE2zbsQVY5RzmWuAObG/AZXQNFXMjnvf3FsX4\n3QszJs3BZv55ZmCriTbBzj4CO0dnAfDhQBpvSyNYgEnu79SA2+bYYPr+GcMsgw8BpwJTsPd4IWY0\nWhvYAfgI8FHgUJIbwK5y13LgNGBH4Gcp0jQPWAj8IoWfJvBS4EvYqru6fZxmYdh8LovtMePxqTH3\nF5SYljxogzy+/h5klJ4NHIWdUfepQlOUHxOAT2IzzlcHbgQuxj5INsbaqD2wzvFOFaUxSBPL01uB\ns7GBvp8DD2Id0bdgfZ993DOjEX6LkHd7rF4fdnXxDGzF9c/oTo7xnOT+3hrh7zTsjMCzM8b775h+\n/Taj/yDbA0+T/F1s7/6G5SqzjngT1n++NOSeRZdPx861/CCWL3WhiXoeJO/0V62zUB+9Tauz3g9I\nb4um6XobRLLUj7bI4WmbPHG0Vc4i5Qq3F8N8R1RBW/M8TJvHBzxF5eUw4w9R/ami0hnXd/M0cbx0\nb2yxRRTrYraAfbFyvQFmo1gMnOuu52P8JmaEgGUpgs3c/agzeA529x4dNhE5cSCWnnX7PHNf6PcP\nsBVA78U+zLbCKvBf0CuX97sasJTux1qQF7o0HOB+r4k1EsE0Pu/cs7Au9uH1PWym4d7A3VhhqCuf\nxd7Jr4HXxjwzEzu3aZcM4e/mwv+fFH4+j52FtWmG+OrMBKyCvRdbpdMUC3oSsuRzWfh6MqtBuG60\nRZ5J2OyuJwY8dwMm70GFpyg/zqXbNr884v5UrI2qQ9vQ1PK0O7aVaXhG4HpYux5s64MUIe80bObU\n9TmE9QEsfUdF3FsK/JVembfE+i5fzyH+YfHv4oYUfuLkKrOO+Cm25eqkkHtWXV4KPBARXlU0Vc89\neae/ap2F+uhtFp0F6W0ZNF1vg0iW+tEWOTxtkqdD/IqIIuXsF+8wTANeNuCZovMv3F5k/Y6ogjaV\nbU+H6LJWRh8iLu5hSFLGodi8HGb8IawfRaYzru8G9R8vnUj0gp+v9fFzNCbHw9gijNOBbwF/du4X\nM3iXuBH624UGPvA2d/9bEfc2cPdWDkhEWZxOr2EoyIb0frSsjq10uQP4GzYr72ZsddA6MX4/jBXE\nOOPPI9iWbACvBr4fSuPd/YRIwBswI8xzwP3Y+UZZV5MVzRFYGVkC/MOAZyeQTY4RF0fUKrMovoDl\nUb/tMiZgq8uuxQyLz2BbFB4Weu4EF/exMeFsCvwdK1NhZT2AbqX2HDab80R6KzhvMPkc8ErgMmz1\nzSiwTejZ47BBgp3pNljhinBf+i8JDV7bxchVBSOky+cy8fVkvwq9SbRJnlswWTaMuX+ou9+kWVR+\n+54lDJ6EMHXA/TJoU3nynIjJ9KWIe0XI+1oX5hcj7iVtSw4gvq6/oM+9Q4HPuP/D5yt6BrVT/n7U\nVg9TsFUNS7BzKR8IpP+vWP8s6l2cBWyNbYH1B2zW2I3YwaGeMwbIBeXUEWthfYHwh9QwuvwJ57cu\n27c2Xc/zTn8/nYVkejuMzkJ99DaNzoL0tkyarrdBJEv9aIscnjbJ0yF+YLtIOfvFm5bJ2LjYd7GJ\n1fMHPF+kXHHtRRz9viOqoE1l29MhvqwV3YfoF3ca0pZxKC4vh+n7ROlHUekcpItJxkurYh3gCnrH\nnDfFbBZx5GGkHiFgF8oyKP8K9/fmiHtbub8PZAi3CE5wVxwbYwaDIM9hH0SD9q0M+j3TXXGsH/h/\nFrZELGkak/ATd9WdFwP/ic0yfAe272U/shohP+7+bootNXyqz7PzsL0hd8WMb1FMxVai7YV9+J6H\nfSDvj1XWG9DdYsIvdZ0VE9YZmHHyXzH5wD6qv+PScQ+2teHfseXKp2J6Faws/FYds7DtLX6CVbAb\nhWSYiQ0SzMPO09o9Jk1PYsum34/NFrg4cG8GVonfgG0PFx6wq5I0+Vw2vp78VaWpyI82ybMI21J0\nW+D3oXvTMR1dAfxLyenKyvpYPbESmwH11wHPP1N4igbTpvLkWeH+RrVZRcg7x/0NzspK25Y8gm0v\n8AGsY+q3BRjF2pJn3PM3YvW/51rgeKwtvykmfYPaqde7+7eH/E3DPsp2xLajmodt43Ey1qZNj/Dj\n38XG2Iff/wLfxga63wD8ENvC968uzPP6yAXl1BH7Yn2B4IrZYXX5/9zfPanH9q1N1/O80x+ls5BO\nb4fRWYDXUQ+9TaOzIL0tk6brbRDJUj/aIoenbfLEUXc5d8QG9t+GjTetwtqV8wf4K1KuqPaiH/2+\nI6qg7nmeN3UfH8haxqGYvBy27xOlH0WVuX66mHS8tCq2wXY92w/rB3v2w844jePqGPc/YOd0nYqN\nf1+SNCF5Go7WprvH3rczhHu8CyMpC7HB/GG4Ext0Xowp4ZIS/G5Ls2ay58m7sA/di+gaWPJmL+BI\n9/8E7H3HnVn0ZewQtDdjS1PXc+5PMdYIcb4L9yTG7kH+CexD+mTM8PIEXcNKeOUP2AzLA7HznP4v\n4O6NV5/BjCG+w/AR4BrsvZ1Bt4z5D/u52FZ+UQMAk4H/xizKJ0bcD3IDtvrr/ZhOdQL3PoqV7/nA\nNweEUyZp8rkKfD35GnpnrjxFf0NzHWmTPMF9jH8auvdx4J8wfYszJNeN4zFD9rlYu9QEyixPZfQt\nJmP1NNisoDBFyOvbgeAgdNq25EbsfI2PYtsldUJxrIUN1J7H2K2tpmGrT5dis936pS+unYpKP9gg\n9Y5Yu+rP0QRrzxbE+PFh7ejiC96/BNs7fjtsi7ALsfIQJZenjDpif+zdBQfAh9Vl/6G18xDpypOm\n63ne6Y8r82n0NqvOQr30No3OgvS2TNrU35Ms9aMtcnjaJk8cdZRzK+AQd/mjBm7Czp65AHgsQRhF\nyhXVXsQx6DuiCuqY50VSx/GBPMo4FJOXw/Z9ovSjqDIXp4tpxkur4gbMcHQLdjyONzBvg63az0Ju\nRuoR4reqm0B3X7xTsA+WUzBD0ePO/UfAGhniXUby7bJGSbYsT9SLX2F5t3/EvRlYeQpex6UMf01s\ntdsTWCUwCryvz/NxZasTeGY/53ZhTBjn0bvtx+P07pE6AfvYf5axS1RfhS2NjBvAeK8L/4iA21Ln\ndmSkD+NT2EyEVwfcOsQvvfyku3dgyP37zn1Oj4/qSJvPZROsJ6Oun1eXtEy0TZ5dsXSHJzhsic3y\n/h02wNYU7sbk2a3qhCSk7PK0rE9cefUtznR+o2b+FCWv307Xb2OVpS0B+0CKk/ur7t4rQu5bOvcr\n+6RvUDsVdVbJjs5PnAwPuPvhw1XvcO77RPjxg9h7Btzi5PLsSrF1xBRM9otC7nno8jPYbLKqabqe\nF5H+sM5CNr3NorNQL71Nq7MgvS2DNvX3JEv9aIscnrbJ08HSPRJyL1rOuHijWA8bsPbbio1ig9Yn\nAZukjLdIueLaizj6fUdUQdvKtqdDfFnblWL7EP3iDpJnGYfi8nKYvk+UfhSVzn66mHa8tErupjve\nPA3bxSsLk7GFL6MM3iJ5xD2X6YyjrejNxOewrRN+jM2YG3TIkhi/PI2VmfUi7n2M3rKVdvu9s52/\nd2Fb4Y0CX8maWMcPXThxhpPPu/t7Bdx+7tyClvKDndtnQv6/49zPp9dw1sG2jQt+xPsDhR8l+uBj\nsH3pV9K73WKH+IrwMndvi5D7bzCrdBZjcFEUkc954uvJ66pOSE60TZ51MHnCW+38xLmHjad1ZjqW\n5ueBF1SclqS0rTx9EJNnKfCiiPtFyDsFq5eDqyzTtiWew5z7ByPiuRnr44Xr/1c7PxfEpG9QO+Xv\nXx9y9xMBdogJ9zasrAf30fbv4t4YP+e7MDcNuMXJ5Sm6jvhnF87BAbe8dPkh6rHNSdP1PO/0R+ks\nZNPbLDoL9dHbLDoL0tsyaLreBpEs9aMtcnjaJk+H6IHtouWMizeK+92zy7ExlZcNEW+RckW1F3EM\n+o6ograVbU+H+LJWdB+iX9xB8izjUExeDtv3idKPospcnC5mGS+tkv8EvuD+fxPRE6+SkMZIPcIQ\nhqND3L0vRNwToh9r0zUIxRk8PMe45z6ZIvzdsMrrcvd7axfGDemS2cOT7orjey6eGQG3LzLWijsF\nmw37KPDCkP/HiLesB6/Xuedf435/KyY9kzGL9BJ6P647xFeED2DW+KDhdzr2ThdHPF8VReVznvh6\ncl7C56+mm88rsXLyI7p5XjVp5NmLwWX5ncUkMxUPYqv//Hatb8TSFjcTO5hHK7BDy48qOI1J2ARL\n05+rTkgK2qQfvq26i+gJEVCM/rzK/f9fAb9p2xLPPOceXsUzGZsFvzAinds5P5fFyDGonfL3w+/k\nUeBPxE9AegRr34L4d3F2jJ9fY/rhw+wnV5C0dQQkryfOxWYvrhVwy0uXlzN4n/EySKvnUC9dT5r+\nYXQWsultFp2F+uhtWp0F6W1ZtKm/N0xfo079PGhPvgzbLjQ5X6DeskD8wHbR7XlcvFH4Cb2jWHvw\nUeysvCwUWR6j2osoknxHVEHT+3BxdOhf1oocHxgUtyfPMg7F1FPD9n2i9KOodi4qrqzjpVWyG5YX\nYGPNUzKEkdZIPeKePxrSn3HktwcIW2LTMJnoWVVVnHEkyiN4INo0+n8g+VmLSQ5Gm4wp/DmYgcdv\nWXa3i3Nb7ONzNE1iHWtihp47Yu5PwvaAf4yxH8X++VnYQbfHYxX++4C/BJ6bgp0tdJ0LJwl+X/hf\nxtyfji2pBWv4oviGu+a5tK2DHXx8I2Pf02zs3Q36UC+LaRSTz3nj68nwGQBxzMbOy/o6ViY2whqr\nq7BGNMmhh0WSRp7rscMSPTdj2zwG96RdnlO6hmERtg3lFsB92GSI54g/8HI2tvftuVh98x7sTIdb\nGK49HBZ/TsVUrD5aVWFaklK2fhTVtzgeKzd3YkvH4/aZLkJ/fGfWh5mlLfFsT/fjJMjWLtyodHtZ\n1+0TJsS3U/5+UHemAP/o0hFVj8/APqqvCbn71cC3RvhZE9Px6wJh9pMrSNo6ApLVE5OwD9GrGTsp\nJQ9dnoiV9fsz+M2btHoOw+l63nqeNP1ZdRay620WnYX66G1anQXpbVm0qb+Xpa9Rx34etCdfsrYL\nbcgXqLcs/Si7Pe/HP2OrUf25L2dgqzJuxCbzXkT6c1/yLo9x7UWYpN8RVVCnPC+TOowP5FnGoZh6\napi+T5x+FNHOxcWVZby0aq7Hvhm2AlYnPt1xHIPJsgSrb3LpB4wQsCyFuN7d2zZhWBu659+OZdiz\nxO+bvYxks+78Nb9PvGnCGW9XlSxyaXjLgOeWuOdeEnKPK09nMday7PFnKmXZDxRMKVdhsw+ieLcL\nP7z93Bznfi72Qf0ktmpnUui5qXRnmSTlW85P3NZ5UzHjStR1m/N7vfv9NudnN+ce3u7tOOf+bynS\nVyRF5XPepKknN3PP7hpx7zJsJVjVpK33PWthq8OizjSrGn+GwkHYnsGjwGkxz/o8mh1w83XRoQWm\nMSn3Y2nZY8Bzg1Z6lkXZ+rGM/PoWHr+16u3Aiwc8W4T+nOPC3M79ztKWgBnb/0LvKh6wrUBHgWNj\n/D0G/DEm3EHtlL8f3H5hMjazbdkAPx8Juft3MbvHhx02P8rYD4l+cgVJU0dA8nrCt7fvjQhjWF2e\n6fxfMsB/GaQt98Pq+jLy1fMseptGZyGb3mbVWe+3DnqbVmdBelsWbervZelr1LWf15Z8ydoutCFf\n6i4LxK+IKLo9j4s3CXOwYwMedmGsxCbtHs7g1T5Flcd+7YUnzXdEFZTdhyuLDv3LWpHjA4PijmOY\nMg7F1VNZ+z5x+lFEOxcXV5bx0jpwAbY9dL+6JYrjMZkWY2PTSRlx/lJvVTcRWyUSXL43iP3oVopv\nwApj3Ey3JvNSbDbdEmy1yVsrCiNtOPOx/Dk8Y1xp8YaW+4HNY56ZjRlrohqYqPK0i3v+hxHPf8M9\n/6Yh0nyTCyO8zHYP4ClMlnClPQWr1G+mex5P+JBfzyBj2lzGGpwWYsstV0+W/DF0XFzhpZf/SnSl\n6t/fXvQyn3LLzlyy5fN8yk2nryefIVk9eRDW2EU1/O/H0h5eSjqf8mRKK08Q31hvFHN/PuXmTZC3\nurjPxfT4AeL36D0IM/56PVwPm/GzCpsFHWY+5crlDbx3M3bLTM8EbB/cCyPuzad9+lE0H3fx3pIg\n7qL05zasL7ZawC1tWwLd/aS/H/G8bxcOiwnPn70S1ZYPaqcWEv1O7iL6I8Rv5RF17zYX12r04mU4\nOMItTi5PmjoCktcTX3Ju4YkxMJwuAxzh/EfNjJxPvduNOul6Vr1Nq7OQXm+H0Vmoh96m1dmg+3jS\n2/nUu30OUrf+Xpa+RtJ+3nzqLUuQOuVL1nahLflS928JiB7YLqM9j4o3LZOwsZb52OSKUazN/VjM\n80WWx37tBaT7jvDMp/66mibP51PNGECH/mWtyPGBQXEPIm0Zh2Lrqax9nyj9KKqdG6SLUXSIHi+F\naseuwCbPP48Z85IyjJF6hIBdKE3GzMSWdd1K8gM8X44V6LcC96SIq2msxCx5CzEFuxU7SO3pfp4K\nCCNtOBMDfsrgm9hWFx/ADFtX0l1d9E+Y0WgbTMG/E+E/XJ6mYrIFty4LsijgL25P90GchFn1f4RV\nfA+78PbGGpM96V2G/CzwG2xW5vbY4WNXxYT/EXf/EmABZuybCGyAzTBYjW5FuAZWad+BLZvNCz8D\ndlHI3Tfw22D59PvAvTLLzlSs7GTJ57LLuK8nf5UwzjlYWY5ayu7zeEXIvUyZ0soTZA7wOPEr9srO\nmyC+zBzu/r4L+FvMs3Owd/AkluapWN78G6YXYcqW6yysrjkSm0lyJVb/rMAmEszFOhhRWwS0UT+K\n5DDgU3QPiI86nH4Z3dUMRejP6tg2qIsYK3uatsTjt56K2hbAbyN1qovvaWyA+CLnfglwANYWBvt3\ng9opf38hve/kdGwm1Y+xWVV/wMrvFti5J1uF0hr3LjxRW2INksuTpo7wcSWpJ96MbTfxaEQYw+gy\n2CSPVUT3d+rebtRJ17PqbVqdhfR6O4zOQvV6m0Vnk8oG7dLburfPQerW38vS10jaz6u7LEHqlC9Z\n24W25EvdvyXiaEp7vgoba7kKM1S8EVshsVnM80WWx37tRdrvCE8TdDVNntelfIcpcnxgWNKWcSi2\nnsra94nSj6LauX66mIWqy+1PMAPQ7wc96Pg4Vt/civU1c9+mdoToFUd+m4BzUoR1EfVYel82izCF\nqTqMQeHcjlms18khnjTsA1yKHZi7AvsAvA9bTXI88VbUcHk6EyuTcYd8znX3Lx4yvbtgW+M95a7F\nwCexvdjj+J6LewXRVvggO7g0/sE9/ycXx9cYO0vTb4H3tdQSGB2iLegLscYoPKPibS4tfwM+HLpX\nZtkZJp/LLuO+nvxqwucXED1zGOCzwEMR7mXKlFaeIOfT/0DqquofsIb/aUy2KwY8uwDTuc2xQbsr\n6D3gPEhVcr0Bq1cfwjp5y7GBtQuxD5Wo1b5t1I8i6dCdQR93XRN4vgj96dcOJG1LPJ8jekWt51+w\nmWTPuudODdxb3cUTPg9lUDvl78e9k2OBe7Ey/CDwZeyMwMfpHSwfFNdSbAZbeJuEfnJ50tQRkKye\n2MGF96EBYWXR5bWwmXpx5/bUvd2ok65n1dssOgvp9HYYnYXq9TarzsL409u6t89B6tbfy9LXSNrP\nq7ssQeqUL1nbhbbkSxO+JTr0rogooz2PijcvwivtPUWVx0HtRYd03xGeJuhqmjyv6lu5Q/+yVuT4\nwKC4sxJXxqH4egrS9X3i9KOIdi5p3y1Mh/gVR1WOXXlGEj53GCbHSuysrk7EdXiCuKLsQskfSMFv\niLakl8U6mIWxnyU2LRfTvwDOwQ65G4Y8whgUztqYseCzOcRTFlWXJ2E0pew0IZ2P03tmB9gs4/ux\n2RxBmiCT59fYTOQomiTH44zdHmdjbJlw1B68TZKrCWlNqx9top/+1IUTsP5i1FklefJOF094AkOd\nSFJPnIbJUcR5fMe6sHeKuCddL4cm6CxIb4PUVW+boLNBmt7fS9rPa4IsQZQv9aEJ3xId8hnYTtue\n5xVv0VTVXjSlfCfN8yrl6ZBfWUuj03nHXRRpZUpLEfoR187lHVcT9DBIh2xG6iAjlGQ4moa93LlD\nhjMMn8P2qIziREzOQVbUMNtiltSoPTxfhFlYXxNx72q6mbQC+C1wVEFhDAoHbHnjs9h2dk2gDuVJ\nGE0pO3VP5yaYLu8ecp+AzdZdjm1XE6TuMnmmY/oad8ZaU+TwebR9yP1WojsOTZEL6p/WLPrRFgbp\nT12Ygm3ZenkOYU0i+sDO12ErfR/E3ksdSVpPLMVW+ObNVGwb3bjV1dL14mmKzoL01lNnva27zgZp\nen8vTT+v7rIEUb7Uh6Z8S3QYfmA7S3ueR7xFU2V70ZTynTTPq5SnQz5lLa1O5xl3UWSRKS1560e/\ndi7vuOquh0UwQkmGo1djGVnVB8MLgCeINjTsiFm/F5HecAR2mN0xIbc1gOuI307rCWyW33qY9fbT\nmAU3OOMvjzCShNNEqi5PQuTNgVhdOwPT6S2whu9abKuanatL2tDshMmW52rPKjgQq3emhtw/gxnu\nRXG0WT8G0ST92Rn4BDa5Yxi2xTrklwGfxw40vR57D3+k+NURw1B1PTET+yAdKSGuImiDrjdJZ0F6\nC9LbvGha2Q9TdTkoCuVLfWiKLB2GH9jO0p7nEW/RNCUPq6BJfbgO+ZS1LOUhr7iLoollvOntXN0Z\noSTD0dHY0rGqOBBbbjch5L4Wtg/37tjyrLDhaAnxy7k67pmTgRsCfiZgZ9p0iGYzereF2NC5HZpj\nGEnCaSpVlych8uZ0unXLSqy++gV2ftZLKkxXHhwH/Jne+rdpnI5tkRlmDyzftik3OeOKNuvHINqi\nP2nYCvgfbI/sZ7Gz9e4CzqD++a16YjjaoOvjUWdBeiuaX/bbWg6UL/WhKbJ0GH5gO0t7nke8RdOU\nPKyCJvXhOuRT1rKUh7ziLoomlvGmt3N1Z4QSzziqknlEH5R1AfZBA9GGoy0x+ffBrObrY4ekHUnX\nAvt67PAv/3sutvJnYeAK7gV5EPAk3cPL1sOMO6uArXMMI0k4QgghhBBCCCGEEELsig1urz1O4hXj\nj12prqxVGbcQWRhhnBiOfgCcF3I7CtuncXX3+xp6DUc7YYYXvyXa5thlCwd2AAACzUlEQVT72DLw\nzMtItyzuDMzA8xQ2G28U+DtwfEL/eYUhhBBCCCGEEEIIIYQQQggRZISAXWhipUkplqnYtgmerYDT\ngEOw1UJxvBy4DzPQAGyHGWruCTzzTCCOJMwBznFhzQV+BnwD+GJC/3mFIYQQQgghhBBCCCGEEEII\nkYoR2rHi6LvAhYHfh9Pde9Nfo9jqopXAGu65r2P7dXtOAX4ZCvtVzm/SfTsfBw4L/N7YxZtmC7mk\nYWwKvDFFuEIIIYQQQgghhBBCCCGEGL+MME5WHN3O2LN/foAZWbYLXLcA33f/+1VILwMWBfxtF/oN\nMAt4GHg0QTo2AV4ELA64PeDS984YP5NCv9OEsQ9j5RZCCCGEEEIIIYQQQgghhEhEmw1HPwNmAuu6\n338G7gxdTwPL3f+j2PuYBdwRCGczzEgTZCfgioTpmIOtDFoacr8K2D/w+3LgTOA64IiMYewCfBp4\nD2ZUmpYwjUIIIYQQQgghhBBCCCGEEK02HC0GbgbensLPZpixJWg4Wgx8DFvJAzAFM9Z8I2GYc4B7\n6Z6L5LkK2BzYxv2eBfwO2Bk7yyhLGNe6tO8JzMYMY0IIIYQQQgghhBBCCCGEEJkZoR1nHAG8Hrib\n3q3fhuEY4MocwwNYE3gwp7DuyykcIYQQQgghhBBCCCGEEEK0nxHGyRlHYNvJfRnYMMcwVwDH5hge\n2GqjG3MIZ0Ps7CUhhBBCCCGEEEIIIYQQQojUTK46ASVwVs7hfT3n8MAMR4tzCGdj4JEcwhFCCCGE\nEEIIIYQQQgghxDgkasXRSuAhbFXNLe46rsxEjUO2JR/D0Z3Api6srXMITwghhBBCCCGEEEIIIYQQ\n7eOVdG1Al2J2oacqTZEQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhBBCCCGEEEIIIYQQQgghas3/A0miq6Jq8qMnAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ P_{r} = \\frac{P_{t} G_{t} A_{r} F^{4} \\sigma}{\\left(4 \\pi\\right)^{2} R_{r}^{2} R_{t}^{2}}, \\quad G_{r} \\lambda^{2} over 4 \\pi, \\quad \\lambda, \\quad F_{D}, \\quad F_{T}, \\quad V_{R}, \\quad C, \\quad F_{D} = 2 F_{T} \\operatorname{left}{\\left (right \\frac{V_{R}}{C} \\right )}, \\quad F_{D} = F_{T} \\operatorname{left}{\\left (right \\frac{V_{R}}{C} \\right )}, \\quad F_{T}, \\quad F_{R}, \\quad F_{T}, \\quad F_{R}, \\quad F_{R}, \\quad \\left|{F_{D}}\\right| < \\frac{F_{R}}{2}, \\quad F_{D}, \\quad \\left|{V_{R}}\\right| < \\frac{F_{R} \\frac{C}{F_{T}}}{4}, \\quad \\sqrt{2}\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                           4                                                 \n",
       "⎢        P_{t}⋅G_{t}⋅A_{r}⋅F ⋅σ         2                                     \n",
       "⎢P_{r} = ──────────────────────, G_{r}⋅λ ⋅over⋅4⋅π, λ, F_{D}, F_{T}, V_{R}, C,\n",
       "⎢              2      2      2                                                \n",
       "⎣         (4⋅π) ⋅R_{r} ⋅R_{t}                                                 \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                     ⎛      V_{R}⎞                    ⎛      V_{R}⎞           \n",
       " F_{D} = 2⋅F_{T}⋅left⎜right⋅─────⎟, F_{D} = F_{T}⋅left⎜right⋅─────⎟, F_{T}, F_\n",
       "                     ⎝        C  ⎠                    ⎝        C  ⎠           \n",
       "                                                                              \n",
       "\n",
       "                                                                    C      ⎤\n",
       "                                                            F_{R}⋅─────    ⎥\n",
       "                                    F_{R}                         F_{T}    ⎥\n",
       "{R}, F_{T}, F_{R}, F_{R}, │F_{D}│ < ─────, F_{D}, │V_{R}│ < ───────────, √2⎥\n",
       "                                      2                          4         ⎥\n",
       "                                                                           ⎦"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki_maths(\"Radar\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAY+UAAAA7CAYAAABNy71wAAAABHNCSVQICAgIfAhkiAAAIABJREFU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\n",
      "text/latex": [
       "$$\\left [ hat x, \\quad P_{k*(k*mid) - 1}, \\quad mathbf x, \\quad N \\mathcal{math}, \\quad mathbf w, \\quad mathbf z, \\quad mathbf v, \\quad hat mathbf x, \\quad mathbf x, \\quad hat mathbf x, \\quad P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad tilde mathbf y, \\quad S mathbf, \\quad K mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad tilde mathbf y, \\quad hat mathbf x, \\quad P mathbf, \\quad operatorname E \\xi, \\quad \\xi, \\quad F mathbf, \\quad mathbf x, \\quad dot x, \\quad mathbf x, \\quad mathbf B u, \\quad G mathbf, \\quad mathbf x, \\quad Q mathbf, \\quad \\Delta t 0 neq, \\quad N{\\left (0,Q mathbf \\right )}, \\quad mathbf w, \\quad mathbf z, \\quad R mathbf = mathrm E left, \\quad hat mathbf x, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad tilde mathbf y, \\quad P mathbf, \\quad mathbf z, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad mathbf x, \\quad P mathbf, \\quad K mathbf, \\quad P mathbf, \\quad P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad P mathbf, \\quad P mathbf, \\quad F mathbf, \\quad H mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad P mathbf, \\quad P mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad P mathbf, \\quad P mathbf, \\quad \\hat{wide} mathbf x, \\quad E left, \\quad E left, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad P mathbf, \\quad E left, \\quad E left, \\quad P mathbf, \\quad P mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad Q mathbf, \\quad R mathbf, \\quad p, \\quad p, \\quad p, \\quad x_{k - 1}, \\quad p, \\quad Z mathbf, \\quad p, \\quad p, \\quad mathbf x, \\quad Z mathbf, \\quad mathbf x, \\quad p, \\quad mathbf z, \\quad p, \\quad k = 1, \\quad mathbf x, \\quad p, \\quad mathbf z, \\quad p, \\quad p{\\left (mathbf z \\right )} = \\prod_{k=0}^{T} p, \\quad hat mathbf x, \\quad H mathbf, \\quad \\ell = \\log{\\left (p{\\left (mathbf z \\right )},10 \\right )}, \\quad \\frac{1}{\\ell} = 0, \\quad \\ell^{k} = \\ell^{k - 1} - \\frac{left}{2}, \\quad d_{y}, \\quad hat mathbf x, \\quad N, \\quad mathbf z, \\quad mathbf z, \\quad hat mathbf x, \\quad mathbf y, \\quad hat mathbf x, \\quad i = 1, \\quad K^{i} mathbf = mathbf P^{i} mathbf H^{T mathrm} \\frac{left}{mathbf R right + mathbf H mathbf P H^{T mathrm} mathbf}, \\quad P^{i} mathbf = mathbf P left \\left(right \\operatorname{left}^{T mathrm}{\\left (F mathbf - H K mathbf^{2} right \\right )}\\right)^{i}, \\quad P mathbf, \\quad K mathbf, \\quad P mathbf, \\quad P mathbf, \\quad mathbf x, \\quad - P mathbf + P mathbf, \\quad hat mathbf x, \\quad k < n, \\quad mathbf z, \\quad mathbf z, \\quad hat mathbf x, \\quad hat mathbf x, \\quad P mathbf, \\quad P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad C mathbf, \\quad mathbf x, \\quad k, \\quad mathbf x, \\quad k + 1, \\quad S mathbf, \\quad hat C mathbf, \\quad hat mathbf x, \\quad \\alpha, \\quad beta_{k}, \\quad alpha_{k}, \\quad hat mathbf y, \\quad hat mathbf y, \\quad - hat mathbf y + mathbf y, \\quad W mathbf, \\quad mathbf W \\operatorname{left}{\\left (- hat mathbf right y + mathbf y \\right )}, \\quad mathbf \\frac{hat}{W} mathbf y, \\quad W mathbf, \\quad W mathbf, \\quad mathbf x, \\quad mathbf z, \\quad f, \\quad h, \\quad left, \\quad P mathbf \\left(L + \\lambda\\right), \\quad A mathbf, \\quad B mathbf, \\quad chi_{k*(k*mid) - 1}^{i} = f i quad \\operatorname{left}{\\left (chi_{-k*mid + k - 1}^{i} right \\right )} = 0, \\quad \\frac{f}{R^{L}}, \\quad \\alpha, \\quad \\kappa, \\quad \\beta, \\quad x, \\quad \\alpha = 10^{- 3}, \\quad \\kappa = 0, \\quad \\beta = 2, \\quad x, \\quad \\beta = 2, \\quad chi_{k*(k*mid) - 1}, \\quad R mathbf, \\quad gamma_{k}^{i} = i quad h{\\left (chi_{k*(k*mid) - 1}^{i} \\right )} = 0, \\quad P mathbf, \\quad K_{k} = P mathbf, \\quad hat mathbf x, \\quad P mathbf, \\quad mathbf Q t, \\quad mathbf R t, \\quad mathbf t w, \\quad mathbf t v, \\quad mathbf K t = mathbf P t mathbf H^{T mathrm} t mathbf \\frac{t}{R}, \\quad mathbf K t, \\quad mathbf R t, \\quad t tilde mathbf y = - H hat mathbf^{2} t^{2} x + mathbf t z, \\quad mathbf x, \\quad hat mathbf x, \\quad mathbf K t = 0\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢hat⋅x, P_{k*(k*mid) - 1}, mathbf⋅x, N⋅mathcal, mathbf⋅w, mathbf⋅z, mathbf⋅v, \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "hat⋅mathbf⋅x, mathbf⋅x, hat⋅mathbf⋅x, P⋅mathbf, hat⋅mathbf⋅x, P⋅mathbf, tilde⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "mathbf⋅y, S⋅mathbf, K⋅mathbf, hat⋅mathbf⋅x, P⋅mathbf, tilde⋅mathbf⋅y, hat⋅math\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "bf⋅x, P⋅mathbf, operatorname⋅E⋅ξ, ξ, F⋅mathbf, mathbf⋅x, dot⋅x, mathbf⋅x, math\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "bf⋅B⋅u, G⋅mathbf, mathbf⋅x, Q⋅mathbf, Δ⋅t⋅0⋅neq, N(0, Q⋅mathbf), mathbf⋅w, mat\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "hbf⋅z, R⋅mathbf = mathrm⋅E⋅left, hat⋅mathbf⋅x, P⋅mathbf, P⋅mathbf, P⋅mathbf, h\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "at⋅mathbf⋅x, P⋅mathbf, tilde⋅mathbf⋅y, P⋅mathbf, mathbf⋅z, P⋅mathbf, P⋅mathbf,\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       " P⋅mathbf, P⋅mathbf, P⋅mathbf, mathbf⋅x, P⋅mathbf, K⋅mathbf, P⋅mathbf, P⋅mathb\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "f, hat⋅mathbf⋅x, P⋅mathbf, Q⋅mathbf, R⋅mathbf, P⋅mathbf, P⋅mathbf, F⋅mathbf, H\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅mathbf, Q⋅mathbf, R⋅mathbf, Q⋅mathbf, R⋅mathbf, P⋅mathbf, P⋅mathbf, Q⋅mathbf,\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       " R⋅mathbf, P⋅mathbf, P⋅mathbf, widê⋅mathbf⋅x, E⋅left, E⋅left, P⋅mathbf, P⋅mat\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "hbf, P⋅mathbf, P⋅mathbf, E⋅left, E⋅left, P⋅mathbf, P⋅mathbf, Q⋅mathbf, R⋅mathb\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "f, Q⋅mathbf, R⋅mathbf, p, p, p, x_{k - 1}, p, Z⋅mathbf, p, p, mathbf⋅x, Z⋅math\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                             ┬\n",
       "bf, mathbf⋅x, p, mathbf⋅z, p, k = 1, mathbf⋅x, p, mathbf⋅z, p, p(mathbf⋅z) = │\n",
       "                                                                             │\n",
       "                                                                             k\n",
       "\n",
       " T                                                                            \n",
       "───┬                                                         1          k     \n",
       "   │ p, hat⋅mathbf⋅x, H⋅mathbf, ell = log(p(mathbf⋅z), 10), ─── = 0, ell  = el\n",
       "   │                                                        ell               \n",
       " = 0                                                                          \n",
       "\n",
       "                                                                              \n",
       " k - 1   left                                                                 \n",
       "l      - ────, d_{y}, hat⋅mathbf⋅x, N, mathbf⋅z, mathbf⋅z, hat⋅mathbf⋅x, mathb\n",
       "          2                                                                   \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                           i                  i         T⋅mathrm              \n",
       "f⋅y, hat⋅mathbf⋅x, i = 1, K ⋅mathbf = mathbf⋅P ⋅mathbf⋅H        ⋅─────────────\n",
       "                                                                              \n",
       "                                                                 mathbf⋅R⋅righ\n",
       "\n",
       "                                                                              \n",
       "           left                          i                        ⎛          T\n",
       "──────────────────────────────────────, P ⋅mathbf = mathbf⋅P⋅left⋅⎝right⋅left \n",
       "                       T⋅mathrm                                               \n",
       "t + mathbf⋅H⋅mathbf⋅P⋅H        ⋅mathbf                                        \n",
       "\n",
       "                                      i                                       \n",
       "⋅mathrm⎛                     2      ⎞⎞                                        \n",
       "       ⎝F⋅mathbf - H⋅K⋅mathbf ⋅right⎠⎠ , P⋅mathbf, K⋅mathbf, P⋅mathbf, P⋅mathb\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "f, mathbf⋅x, -P⋅mathbf + P⋅mathbf, hat⋅mathbf⋅x, k < n, mathbf⋅z, mathbf⋅z, ha\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "t⋅mathbf⋅x, hat⋅mathbf⋅x, P⋅mathbf, P⋅mathbf, hat⋅mathbf⋅x, P⋅mathbf, hat⋅math\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "bf⋅x, P⋅mathbf, C⋅mathbf, mathbf⋅x, k, mathbf⋅x, k + 1, S⋅mathbf, hat⋅C⋅mathbf\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       ", hat⋅mathbf⋅x, α, β_{k}, α_{k}, hat⋅mathbf⋅y, hat⋅mathbf⋅y, -hat⋅mathbf⋅y + m\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                         hat⋅m\n",
       "athbf⋅y, W⋅mathbf, mathbf⋅W⋅left(-hat⋅mathbf⋅right⋅y + mathbf⋅y), mathbf⋅─────\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "athbf⋅y                                                                       \n",
       "───────, W⋅mathbf, W⋅mathbf, mathbf⋅x, mathbf⋅z, f, h, left, P⋅mathbf⋅(L + λ),\n",
       "W                                                                             \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                      i                ⎛                  i   \n",
       " A⋅mathbf, B⋅mathbf, χ_{k*(k*mid) - 1}  = f⋅i⋅quad⋅left⎝χ_{-k*mid + k - 1} ⋅ri\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "   ⎞      f                     -3                                            \n",
       "ght⎠ = 0, ──, α, κ, β, x, α = 10  , κ = 0, β = 2, x, β = 2, χ_{k*(k*mid) - 1},\n",
       "           L                                                                  \n",
       "          R                                                                   \n",
       "\n",
       "                                                                              \n",
       "                i           ⎛                 i⎞                              \n",
       " R⋅mathbf, γ_{k}  = i⋅quad⋅h⎝χ_{k*(k*mid) - 1} ⎠ = 0, P⋅mathbf, K_{k} = P⋅math\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "bf, hat⋅mathbf⋅x, P⋅mathbf, mathbf⋅Q⋅t, mathbf⋅R⋅t, mathbf⋅t⋅w, mathbf⋅t⋅v, ma\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                              T⋅mathrm          t                             \n",
       "thbf⋅K⋅t = mathbf⋅P⋅t⋅mathbf⋅H        ⋅t⋅mathbf⋅─, mathbf⋅K⋅t, mathbf⋅R⋅t, t⋅t\n",
       "                                                R                             \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                              2  2                                            \n",
       "ilde⋅mathbf⋅y = - H⋅hat⋅mathbf ⋅t ⋅x + mathbf⋅t⋅z, mathbf⋅x, hat⋅mathbf⋅x, mat\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "           ⎤\n",
       "           ⎥\n",
       "hbf⋅K⋅t = 0⎥\n",
       "           ⎥\n",
       "           ⎦"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki_maths(\"Kalman filter\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# More Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArIAAAAgCAYAAADuSJvhAAAABHNCSVQICAgIfAhkiAAACudJREFU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\na54AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ \\frac{d}{d x} y = x^{2} - x - 2, \\quad x, \\quad y{\\left (x \\right )}, \\quad x, \\quad x, \\quad y{\\left (x \\right )}, \\quad y{\\left (x \\right )}, \\quad y{\\left (x \\right )} = e^{3 x} + 2 e^{2 x}\\right ]$$"
      ],
      "text/plain": [
       "⎡d        2                                             3⋅x      2⋅x⎤\n",
       "⎢──(y) = x  - x - 2, x, y(x), x, x, y(x), y(x), y(x) = e    + 2⋅e   ⎥\n",
       "⎣dx                                                                 ⎦"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki_maths(\"Differential equation\", MATH_WIKI, WIKIA_SELECTOR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math in Jupyter Markdown\n",
    "The Jupyter Notebook uses Jupyter Markdown, which is a subset of [Github-flavored Markdown](http://jupyter-notebook.readthedocs.io/en/stable/examples/Notebook/Working%20With%20Markdown%20Cells.html#GitHub-flavored-markdown) plus [inline and block math](http://jupyter-notebook.readthedocs.io/en/stable/examples/Notebook/Working%20With%20Markdown%20Cells.html#LaTeX-equations), wrapped in `$` or `$$`. You can drop a bit of the URL for [nbviewer](https://nbviewer.org) in this function and see all the defined equations from a notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "def notebook_math(nbviewer_fragment):\n",
    "    url = ujoin(\"https://nbviewer.jupyter.org\", nbviewer_fragment)\n",
    "    r = requests.get(url)\n",
    "    matches = sum([\n",
    "        re.findall(r'\\$\\$(.*?)\\$\\$', p.text, flags=re.M) \n",
    "        for p in pq(url)(\"p\") if p.text\n",
    "    ], [])\n",
    "    return list(filter(partial(is_not, None), [\n",
    "        parses(match)\n",
    "        for match in matches\n",
    "    ]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAADAwAAAArCAYAAABGxvuuAAAABHNCSVQICAgIfAhkiAAAIABJREFU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\n",
      "text/latex": [
       "$$\\left [ \\frac{d}{d t} u = D \\frac{partial^{2} u}{partial x^{2}} + f{\\left (u \\right )}, \\quad Bigg \\frac{d}{d x} u, \\quad t_{n} = n \\Delta t, \\quad x_{j} = j \\Delta x, \\quad \\Delta t = \\frac{T}{N}, \\quad \\Delta x = \\frac{L}{J}, \\quad approx u{\\left (j \\Delta x,n \\Delta t \\right )} U{\\left (j \\Delta x,n \\Delta t \\right )}, \\quad Bigg \\frac{d}{d t} u, \\quad Bigg \\frac{partial^{2} u}{partial x^{2}}, \\quad \\frac{- U_{0}^{n} + U_{1}^{n}}{\\Delta x} = 0, \\quad \\frac{d}{d t} u = D_{u} \\frac{partial^{2} u}{partial x^{2}} + f{\\left (u,v \\right )}, \\quad \\frac{d}{d t} v = D_{v} \\frac{partial^{2} v}{partial x^{2}} - f{\\left (u,v \\right )}, \\quad Bigg \\frac{d}{d x} u, \\quad Bigg \\frac{d}{d x} v, \\quad A_{u} U^{n + 1} mathbf = B_{u} U^{n} mathbf + f^{n} mathbf, \\quad A_{v} V^{n + 1} mathbf = B_{v} V^{n} mathbf - f^{n} mathbf\\right ]$$"
      ],
      "text/plain": [
       "⎡                 2                                                           \n",
       "⎢d         partial ⋅u              d                                          \n",
       "⎢──(u) = D⋅────────── + f(u), Bigg⋅──(u), t_{n} = n⋅Δ⋅t, x_{j} = j⋅Δ⋅x, Δ⋅t = \n",
       "⎢dt                 2              dx                                         \n",
       "⎣          partial⋅x                                                          \n",
       "\n",
       "                                                                            2 \n",
       "T        L                                               d           partial ⋅\n",
       "─, Δ⋅x = ─, approx⋅u(j⋅Δ⋅x, n⋅Δ⋅t)⋅U(j⋅Δ⋅x, n⋅Δ⋅t), Bigg⋅──(u), Bigg⋅─────────\n",
       "N        J                                               dt                   \n",
       "                                                                     partial⋅x\n",
       "\n",
       "          n        n                           2                              \n",
       "u  - U_{0}  + U_{1}       d             partial ⋅u            d             pa\n",
       "─, ───────────────── = 0, ──(u) = D_{u}⋅────────── + f(u, v), ──(v) = D_{v}⋅──\n",
       "2         Δ⋅x             dt                     2            dt              \n",
       "                                        partial⋅x                           pa\n",
       "\n",
       "     2                                                                        \n",
       "rtial ⋅v                 d           d             n + 1                 n    \n",
       "──────── - f(u, v), Bigg⋅──(u), Bigg⋅──(v), A_{u}⋅U     ⋅mathbf = B_{u}⋅U ⋅mat\n",
       "       2                 dx          dx                                       \n",
       "rtial⋅x                                                                       \n",
       "\n",
       "                                                                  ⎤\n",
       "       n                n + 1                 n           n       ⎥\n",
       "hbf + f ⋅mathbf, A_{v}⋅V     ⋅mathbf = B_{v}⋅V ⋅mathbf - f ⋅mathbf⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎦"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "notebook_math(\"github/waltherg/notebooks/blob/master/2013-12-03-Crank_Nicolson.ipynb\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}