Accessing Old Gists

readme.md

Accessing Old Gists

Example gist SHA 0c37e47f24531557decd

1. List the commits from the gist

   https://gist.github.com/ICBacon/0c37e47f24531557decd/commits

2. Open the console

3. Parse the request

   // Deserialize API request into the console
   eval('var data = ' + document.getElementsByTagName('pre')[0].innerText )
   // Get the last Gist 
   gistUrl = data.slice(-1)[0]['url']

4. Open the Github Gist

   // Replace the api location with the html uri location
   // Open that bad boy
   window.open(gistUrl.replace('https://api.github.com/gists/','https://gist.github.com/'))

5. Open the Raw API

   ```javascript
   

   // Open that bad boy window.open(gistUrl)

   
   1. Parse the request again
   
   ```javascript
   // Deserialize API request into the console
   eval('var data = ' + document.getElementsByTagName('pre')[0].innerText )
   

   2. Copy homeboy into the clipboard

   copy(data['files']['MyFirstNotebook.ipynb']['content'])

References

• copy function in the console

firstnb.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Definition of a Field F in Mathematics (Field Axioms):\n",
    "\n",
    "* ### Closure of F under addition and multiplication (i.e. + and · are binary operations on F)\n",
    "\n",
    "    $\\forall$ a, b $\\epsilon$ F,\n",
    "    $$a + b\\; \\epsilon\\; F$$\n",
    "    $$a · b\\; \\epsilon\\; F$$\n",
    "\n",
    "* ### Commutativity of addition and multiplication\n",
    "\n",
    "     $\\forall$ a, b $\\epsilon$ F, the following equalities hold:\n",
    "     $$b + a = a + b$$\n",
    "     $$b · a = a · b$$\n",
    "\n",
    "* ### Associativity of addition and multiplication\n",
    "    \n",
    "    $\\forall$ a, b, and c $\\epsilon$ F, the following equalities hold:\n",
    "    $$a + (b + c) = (a + b) + c$$\n",
    "    $$a · (b · c) = (a · b) · c$$\n",
    "\n",
    "* ### Distributivity of multiplication over addition\n",
    "\n",
    "    $\\forall$ a, b, and c $\\epsilon$ F, the following equality holds:\n",
    "    \n",
    "    $$a · (b + c) = (a · b) + (a · c)$$\n",
    "\n",
    "* ### Existence of additive and multiplicative identity elements\n",
    "\n",
    "     $\\forall$ a $\\epsilon$ F, $\\exists$ 0 $\\epsilon$ F, called the additive identity element, s.t.\n",
    "    \n",
    "    $$a + 0 = a$$\n",
    "    \n",
    "    Likewise, $\\exists$ 1 $\\epsilon$ F, called the multiplicative identity element, s.t. $\\forall$ a $\\epsilon$ F,\n",
    "    \n",
    "    $$a · 1 = a$$\n",
    "\n",
    "* ### Existence of additive inverses and multiplicative inverses\n",
    "\n",
    "    $\\forall$ a $\\epsilon$ F, $\\exists$ (−a) $\\epsilon$ F, s.t.\n",
    "    \n",
    "    $$a + (−a) = 0$$\n",
    "    \n",
    "    Similarly, $\\forall$ a $\\epsilon$ F, with a $\\neq$ 0, $\\exists$ $a^{−1}$ $\\epsilon$ F, s.t.\n",
    "    \n",
    "    $$a · a^{−1} = 1$$\n",
    "    \n",
    "    (The elements a + (−b) and a · $b^{−1}$ are also denoted a − b and $\\dfrac{a}{b}$, respectively.) In other words, subtraction and division operations exist.\n",
    "\n",
    "* ### Nontrivial Field\n",
    "\n",
    "    To exclude the trivial ring, let's require the additive identity and the multiplicative identity to be distinct:\n",
    "    \n",
    "    $$0 \\neq 1$$\n",
    "\n",
    "* ### Summary\n",
    "\n",
    "    A *field* is therefore an algebraic structure〈F, +, ·, −, −1, 0, 1〉; of type〈2, 2, 1, 1, 0, 0〉, consisting of two abelian groups:\n",
    "    \n",
    "    * F under +, −, and 0\n",
    "    * F ∖ {0} under ·, −1, and 1, where 0 $\\neq$ 1, along with · distributing over +"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Show that the set of all real numbers $\\mathbb{R}$ is a field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall the set $\\mathbb{R}$ = {...,-3,-2,-1,0,1,2,3,...}\n",
    "\n",
    "Suppose $\\exists$ a, b, and c $\\epsilon$ $\\mathbb{R}$. To show that $\\mathbb{R}$ is a field by using the definition above, let's show that all of the field axioms hold true.\n",
    "\n",
    "#### Axiom 1 (Closure).  $\\forall$ $a, b$ $\\epsilon$ $\\mathbb{R}$,\n",
    "$$a + b\\; \\epsilon\\; \\mathbb{R}$$\n",
    "$$a · b\\; \\epsilon\\; \\mathbb{R}$$\n",
    "\n",
    "#### Axiom 2 (Commutativity).  $\\forall$ $a, b$ $\\epsilon$ $\\mathbb{R}$,\n",
    "$$b + a = a + b$$\n",
    "$$b · a = a · b$$\n",
    "\n",
    "#### Axiom 3 (Associativity). $\\forall$ $a,b,c$ $\\epsilon$ $\\mathbb{R}$,\n",
    "$$a + (b + c) = (a + b) + c$$\n",
    "$$a · (b · c) = (a · b) · c$$\n",
    "\n",
    "#### Axiom 4 (Distributivity). $\\forall$ $a,b,c$ $\\epsilon$ $\\mathbb{R}$,\n",
    "$$a · (b + c) = (a · b) + (a · c)$$\n",
    "\n",
    "#### Axiom 5 (Identities). $\\forall$ $b$ $\\epsilon$ $\\mathbb{R}$, $\\exists$ $0,1$ $\\epsilon$ $\\mathbb{R}$, $s.t.$\n",
    "$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad b + 0 = 0 + b = b\\qquad\\qquad(Additive\\, Identity)$$\n",
    "$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad b · 1 = 1 · b = b\\qquad\\quad\\;\\,(Multiplicative\\, Identity)$$\n",
    "\n",
    "#### Axiom 6 (Inverses). $\\forall$ $a$ $\\epsilon$ $\\mathbb{R}$, $\\exists$ $b,c$ $\\epsilon$ $\\mathbb{R}$, $and\\,\\, c\\neq0$ $s.t.$\n",
    "$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad a + b = b + a = 0\\qquad\\qquad (Additive\\, Inverse)$$\n",
    "$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad a · c = c · a = 1\\qquad\\quad\\;\\,(Multiplicative\\, Inverse)$$\n",
    "\n",
    "#### Axiom 7 (Non-Trivial Field). $$0 \\neq 1$$\n",
    "\n",
    "####Axioms (1-7) imply that $\\mathbb{R}$ is a field."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take three real numbers a,b,c $\\epsilon$ $\\mathbb{R}$ to show this result. Suppose we take a,b,c to be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 2\n",
    "b = -4\n",
    "c = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + (b + c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a + b) + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-40"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * (b * c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-40"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a * b) * c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b * a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + (-a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * (a ** (-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * (b + c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a * b) + (a * c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}