From 6b38396b680e51c47ae0c73d40f0faa4a949b37a Mon Sep 17 00:00:00 2001
From: john <jjj.may377@gmail.com>
Date: Fri, 10 May 2019 01:37:45 -0400
Subject: [PATCH 1/2] fixed padding error

---
 Palindromic-Mnemonic-Tool.html | 251 ++++++++++++++++++++++++++++++++-
 bignumber.js                   |   2 +
 2 files changed, 248 insertions(+), 5 deletions(-)
 create mode 100644 bignumber.js

diff --git a/Palindromic-Mnemonic-Tool.html b/Palindromic-Mnemonic-Tool.html
index 0a2e1a6..18d9f3b 100644
--- a/Palindromic-Mnemonic-Tool.html
+++ b/Palindromic-Mnemonic-Tool.html
@@ -64,6 +64,7 @@
 b){var c={},d;for(d=0;d<b.length;d++)void 0!==a[b[d]]&&(c[b[d]]=a[b[d]]);return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.pa={};sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.pa,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=void 0===b.salt?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};
 "undefined"!==typeof module&&module.exports&&(module.exports=sjcl);"function"===typeof define&&define([],function(){return sjcl});
     </script>
+    <script src='./bignumber.js'></script>
     <script type="text/javascript">
     // bip39 Valid Mnemonic Generator Javascript App
     /*
@@ -104,7 +105,9 @@
         const wordCount = document.getElementById('wordLength').value;
         addElementToOutput('Number of mnemonic words:',wordCount)
         var entropy = document.getElementById('entropy').value;
+        console.log(entropy+ 'init entropy')
         const checksumBitCount = Math.floor(wordCount/3)
+	   
         const totalBitCount = wordCount * 11
         const generatedBitCount = totalBitCount - checksumBitCount
         const generatedCharCount = Math.floor(generatedBitCount/4)
@@ -113,16 +116,27 @@
           alert('check the correctness of entropy inserted and generate again.')
           return
         }
+        console.log(TestHash(entropy, generatedCharCount, checksumBitCount))
+        while(TestHash(entropy, generatedCharCount, checksumBitCount)===false){
+            console.log(TestHash(entropy, generatedCharCount, checksumBitCount))
+            entropy = generateEntropy(generatedBitCount)
+            if(entropy == null) {
+                alert('check the correctness of entropy inserted and generate again.')
+                return
+             }
+        }
         const entropyWithChecksum = getHash(entropy, generatedCharCount, checksumBitCount)
         const words = pickWords(entropyWithChecksum)
         output += 'mnemonic is valid.<br />'
         output = addWordsToOutput(words) + output
         document.getElementById('output').innerHTML = output;
     }
-
+   
     function generateBIP39Palindromic() {
         var palindromic = false
         var firstTimeEntropy = true
+        
+        
         var countMnemonic = 0
         const wordCountPal = document.getElementById('wordLengthPal').value;
         var entropyPal = document.getElementById('entropyPal').value;
@@ -255,6 +269,15 @@
         }
         return byteArray
     }
+    function HexstringToByteArray(data) {
+        var byteArray = []
+        
+        for(var i=0; i<data.length; i=i+2) {
+           // console.log(data.slice(i,i+2))  
+          byteArray.push(parseInt(data.slice(i,i+2),16))
+        }
+        return byteArray
+    }
 
     // Pad a numeric string on the left with zero digits until the given width
     // is reached.
@@ -277,23 +300,32 @@
     }
 
     function getHash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic') {
+       
         const entropyBinary = byteArrayToBinaryString(entropyBytearray)
         const data = byteArrayToWordArray(entropyBytearray)
+        
         const hexData = '0x' + sjcl.codec.hex.fromBits(data)
         const hexDataNoPadding = hexData.slice(2)
-        // sha256
         const hash = sjcl.hash.sha256.hash(data)
         const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+    
         const c = zfill(hexStringToBinaryString(hashHex), 256)
         const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+        
         const checksumCharCount = Math.floor(checksumBitCount/4)
         const bit = hashHex.slice(0,checksumCharCount)
         // final entropy + checksum bits
         const b = entropyBinary + checksum;
+        const hatNotation= base64en(b)
+       
         addElementToOutput('Initial entropy:', entropyBinary, mode)
         addElementToOutput('Length of initial entropy:', entropyBinary.length, mode)
         addElementToOutput('Initial entropy as hex:', hexData, mode)
         addElementToOutput('Length of entropy as hex:', hexData.length, mode)
+        addElementToOutput('Entropy as Base64:', hatNotation, mode)
         addElementToOutput('gcc:', generatedCharCount, mode)
         addElementToOutput('Entropy length as hex without 0x pad:', hexDataNoPadding.length, mode)
         addElementToOutput('Initial entropy as hex without pad:', hexDataNoPadding, mode)
@@ -310,7 +342,86 @@
         addElementToOutput('Hash digest of initial entropy bytes:', hashHex, mode)
         return b
     }
-
+    function TestHash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic') {
+        
+        const entropyBinary = byteArrayToBinaryString(entropyBytearray)
+        const data = byteArrayToWordArray(entropyBytearray)
+       
+        const hexData = '0x' + sjcl.codec.hex.fromBits(data)
+        const hexDataNoPadding = hexData.slice(2)
+        const hash = sjcl.hash.sha256.hash(data)
+        const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+       
+        const c = zfill(hexStringToBinaryString(hashHex), 256)
+        const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+       
+        const checksumCharCount = Math.floor(checksumBitCount/4)
+        const bit = hashHex.slice(0,checksumCharCount)
+        // final entropy + checksum bits
+        const b = entropyBinary + checksum;
+        const hatNotation= base64en(b)
+        console.log(hatNotation)
+        const bool=(hatNotation.length===22)
+        console.log(bool)
+        return bool
+        
+    }
+    function getDecodedhash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic'){
+        console.log(generatedCharCount)
+        console.log(entropyBytearray)
+        console.log(checksumBitCount)
+        const entropyBinary = byteArrayToBinaryString(entropyBytearray)
+        const data = byteArrayToWordArray(entropyBytearray)
+        const hexData = '0x' + sjcl.codec.hex.fromBits(data)
+        const hexDataNoPadding = hexData.slice(2)
+        // sha256
+        const hash = sjcl.hash.sha256.hash(data)
+        const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+       
+        const c = zfill(hexStringToBinaryString(hashHex), 256)
+        const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+        const checksumCharCount = Math.floor(checksumBitCount/4)
+        const bit = hashHex.slice(0,checksumCharCount)
+        // final entropy + checksum bits
+        const b = entropyBinary + checksum;
+        
+      
+        return b
+    }
+    function Decrypt(){
+        var entropy64 = document.getElementById('base64entropy').value;
+        
+        var hex=decodeAsHex(entropy64)
+        var bin=decodeAsBin(entropy64)
+        console.log(hex.length+'hex length')
+        if(hex.length>32){
+            
+            var words=pickWords(bin) 
+            console.log(words)
+        document.getElementById('result').innerHTML=words
+        } 
+        else{
+        var bytes=HexstringToByteArray(hex)
+        var wordCount=12
+        const checksumBitCount = Math.floor(wordCount/3)
+	   
+        const totalBitCount = wordCount * 11
+        const generatedBitCount = totalBitCount - checksumBitCount
+        const generatedCharCount = Math.floor(generatedBitCount/4)
+        const entropyWithChecksum = getDecodedhash(bytes, generatedCharCount, checksumBitCount)
+        var words=pickWords(entropyWithChecksum) 
+            
+        document.getElementById('result').innerHTML=words
+        }
+        
+       
+    }
     function pickWords(entropyHash) {
         var result = [];
         const blen = entropyHash.length / 11;
@@ -367,8 +478,8 @@
         "adjust",
         "admit",
         "adult",
-        "advance",
-        "advice",
+        "advance",   
+        "advice",   
         "aerobic",
         "affair",
         "afford",
@@ -2385,6 +2496,130 @@
         "zone",
         "zoo"
     ]
+    const base64library=["0",
+    "1",
+    "2",
+    "3",
+    "4",
+    "5",
+    "6",
+    "7",
+    "8",
+    "9",
+    "A",
+    "B",
+    "C",
+    "D",
+    "E",
+    "F",
+    "G",
+    "H",
+    "I",
+    "J",
+    "K",
+    "L",
+    "M",
+    "N",
+    "O",
+    "P",
+    "Q",
+    "R",
+    "S",
+    "T",
+    "U",
+    "V",
+    "W",
+    "X",
+    "Y",
+    "Z",
+    "!",
+    '"',
+    "#",
+    "$",
+    "%",
+    "&",
+    "'",
+    "(",
+    ")",
+    "*",
+    "+",
+    ",",
+    "-",
+    ".",
+    "{",
+    ":",
+    ";",
+    "<",
+    "=",
+    ">",
+    "?",
+    "@",
+    "[",
+    "}",
+    "]",
+    "^",
+    "_",
+    "`"]
+    var b64dict= {};
+    for(var i=0;i<base64library.length;i++) {
+        b64dict[base64library[i]] = i;
+    }
+
+    
+
+    function decodeAsBin(string) {
+        var output = [];
+        var s='';
+        for(var j=0;j<string.length;j++) {
+            if(string[j] != ' ') {
+                console.log(string[j] +'symbol '+j)
+                console.log(zfill(b64dict[string[j].toUpperCase()].toString(2)))
+                console.log(zfill(b64dict[string[j].toUpperCase()].toString(2), 6))
+                output.push(zfill(b64dict[string[j].toUpperCase()].toString(2), 6));
+            }
+        }
+        return output.join('');
+    }
+
+    function decodeAsHex(string) {
+    var bin = decodeAsBin(string);
+    console.log(bin+ 'bin')
+    var output = [];
+    var s='';
+    // Pad with 0 for binaries not divisible by 4, for hex conversion
+    var binModule = bin.length % 4;
+    console.log(binModule+'aofijeow***********************************************************************************************************************')
+    if(binModule != 0) {
+        bin = zfill(bin, bin.length + 4 - binModule);
+    }
+    for(var i=0;i<bin.length;i=i+4) {
+        console.log(parseInt(bin.slice(i,i+4), 2).toString(16)+ 'first character')
+        output.push(parseInt(bin.slice(i,i+4), 2).toString(16));
+    }
+    return output.join('');
+    }
+
+    function base64en(address_hex) {  // important never to rename base64en to "base64" which can corrupt the Python installation.
+    // (renamed alphabet to base64library below) alphabet = string.digits+string.ascii_uppercase+string.punctuation
+    
+    var b64_string = '';
+    // Convert hex to decimal
+    var x= new BigNumber(address_hex,2);
+    
+    // Append digits to the start of string
+    
+
+    while(x > 0) {
+       var digit = x.mod(64)
+	     //console.log(digit,'digit')
+       var digit_char = base64library[digit];
+         b64_string = digit_char + b64_string;
+        x =x.idiv(64)  ;
+	    //console.log(x,'new address int')    
+    }
+    return b64_string;
+}
+
 
     </script>
   </head>
@@ -2419,5 +2654,11 @@ <h2>REVERSIBLE: BIP39 Palindromic Mnemonic Tool</h2>
      <br>
      <br>
      <div id='outputPal'></div>
+     <h2>Decode Base64 Entropy </h2>
+     <input id="base64entropy">
+     <button onclick="Decrypt()"> Get Seed Words</button>
+     <br>
+     <p id='result'></p>
+     <br>
   </body>
 </html>
diff --git a/bignumber.js b/bignumber.js
new file mode 100644
index 0000000..79d2f66
--- /dev/null
+++ b/bignumber.js
@@ -0,0 +1,2 @@
+/* bignumber.js v8.1.1 https://github.com/MikeMcl/bignumber.js/LICENCE */
+!function(e){"use strict";var r,x=/^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,L="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator,U=Math.ceil,I=Math.floor,T="[BigNumber Error] ",C=T+"Number primitive has more than 15 significant digits: ",M=1e14,G=14,k=9007199254740991,F=[1,10,100,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10,1e11,1e12,1e13],j=1e7,q=1e9;function $(e){var r=0|e;return 0<e||e===r?r:r-1}function z(e){for(var r,n,t=1,i=e.length,o=e[0]+"";t<i;){for(r=e[t++]+"",n=G-r.length;n--;r="0"+r);o+=r}for(i=o.length;48===o.charCodeAt(--i););return o.slice(0,i+1||1)}function H(e,r){var n,t,i=e.c,o=r.c,s=e.s,f=r.s,u=e.e,l=r.e;if(!s||!f)return null;if(n=i&&!i[0],t=o&&!o[0],n||t)return n?t?0:-f:s;if(s!=f)return s;if(n=s<0,t=u==l,!i||!o)return t?0:!i^n?1:-1;if(!t)return l<u^n?1:-1;for(f=(u=i.length)<(l=o.length)?u:l,s=0;s<f;s++)if(i[s]!=o[s])return i[s]>o[s]^n?1:-1;return u==l?0:l<u^n?1:-1}function V(e,r,n,t){if(e<r||n<e||e!==I(e))throw Error(T+(t||"Argument")+("number"==typeof e?e<r||n<e?" 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From 737f3040892500b3f08c2cc3474210023fe90b14 Mon Sep 17 00:00:00 2001
From: johhonn <35551051+johhonn@users.noreply.github.com>
Date: Tue, 7 Jul 2020 21:59:33 -0400
Subject: [PATCH 2/2] Created using Colaboratory

---
 Markdown_Guide.ipynb | 220 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 220 insertions(+)
 create mode 100644 Markdown_Guide.ipynb

diff --git a/Markdown_Guide.ipynb b/Markdown_Guide.ipynb
new file mode 100644
index 0000000..a473c28
--- /dev/null
+++ b/Markdown_Guide.ipynb
@@ -0,0 +1,220 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "Markdown Guide",
+      "provenance": [],
+      "collapsed_sections": [],
+      "toc_visible": true,
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/johhonn/BIP39-Mnemonic-Tools/blob/master/Markdown_Guide.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "uTnBkRyvGvhW"
+      },
+      "source": [
+        "Formatting text in Colaboratory: A guide to Colaboratory markdown\n",
+        "==="
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "70pYkR9LiOV0"
+      },
+      "source": [
+        "## What is markdown?\n",
+        "\n",
+        "Colaboratory has two types of cells: text and code. The text cells are formatted using a simple markup language called markdown, based on [the original](https://daringfireball.net/projects/markdown/syntax).\n",
+        "\n",
+        "## Quick reference\n",
+        "\n",
+        "To see the markdown source, double-click a text cell, showing both the markdown source (above) and the rendered version (below). Above the markdown source there is a toolbar to assist editing.\n",
+        "\n",
+        "Headers are created using \\#. Use multiple \\#\\#\\# for less emphasis. For example:\n",
+        ">\\# This is equivalent to an &lt;h1> tag\n",
+        "\n",
+        ">\\##### This is equivalent to an &lt;h5> tag\n",
+        "\n",
+        "To make text **bold** surround it with \\*\\*two asterisks\\*\\*. To make text *italic* use a \\*single asterisk\\* or \\_underscore\\_. \\\n",
+        "_**Bold** inside italics_ and **vice-_versa_** also work. ~~Strikethrough~~ uses \\~\\~two tildes\\~\\~ while `monospace` (such as code) uses \\`backtick\\`.\n",
+        "\n",
+        "Blocks are indented with \\>, and multiple levels of indentation are indicated by repetition: \\>\\>\\> indents three levels.\n",
+        "\n",
+        "Ordered lists are created by typing any number followed by a period at the beginning of a line. Unordered lists are \\* or - at the beginning of a line. Lists can be nested by indenting using two spaces for each level of nesting.\n",
+        "\n",
+        "[Links](https://research.google.com/colaboratory) are created with \\[brackets around the linked text\\](and-parentheses-around-the-url.html). Naked URLs, like https://google.com, will automatically be linkified.\n",
+        "Another way to create links is using references, which look like [brackets around the linked text][an-arbitrary-reference-id] and then, later anywhere in the cell on its own line, \\[an-arbitrary-reference-id]: followed-by-a-URL.html\n",
+        "\n",
+        "A '!' character in front of a link turns it into an inline image link: !\\[Alt text]\\(link-to-an-image.png).\n",
+        "\n",
+        "$\\LaTeX$ equations are surrounded by `$`. For example, `$y = 0.1 x$` renders as the following inline equation: $y = 0.1 x$. Double the `$` to set the contents off on its own centered line.\n",
+        "\n",
+        "Horizontal rules are created with three or more hyphens, underscores, or asterisks (\\-\\-\\-, \\_\\_\\_, or \\*\\*\\*) on their own line.\n",
+        "\n",
+        "Tables are created using \\-\\-\\- for the boundary between the column header and columns and \\| between the columns.\n",
+        "\n",
+        "Please see also [GitHub's documentation](https://help.github.com/articles/basic-writing-and-formatting-syntax/) for a similar (but not identical) version of markdown."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "eYaIiIaJOPqi"
+      },
+      "source": [
+        "## Examples"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "tPqPXAKKkzaM"
+      },
+      "source": [
+        "Examples of markdown text with tags repeated, escaped the second time, to clarify their function:\n",
+        "\n",
+        "##### \\#\\#\\#\\#\\#This text is treated as an <h5> because it has five hashes at the beginning\n",
+        "\n",
+        "\\**italics*\\* and \\__italics_\\_\n",
+        "\n",
+        "**\\*\\*bold\\*\\***\n",
+        "\n",
+        "\\~\\~~~strikethrough~~\\~\\~\n",
+        "\n",
+        "\\``monospace`\\`\n",
+        "\n",
+        "No indent\n",
+        ">\\>One level of indentation\n",
+        ">>\\>\\>Two levels of indentation\n",
+        "\n",
+        "An ordered list:\n",
+        "1. 1\\. One\n",
+        "1. 1\\. Two\n",
+        "1. 1\\. Three\n",
+        "\n",
+        "An unordered list:\n",
+        "* \\* One\n",
+        "* \\* Two\n",
+        "* \\* Three\n",
+        "\n",
+        "A naked URL: https://google.com\n",
+        "\n",
+        "Linked URL: \\[[Colaboratory](https://research.google.com/colaboratory)]\\(https://research.google.com/colaboratory)\n",
+        "\n",
+        "A linked URL using references:\n",
+        "\n",
+        ">\\[[Colaboratory][colaboratory-label]]\\[colaboratory-label]\n",
+        "\n",
+        ">\\[colaboratory-label]: https://research.google.com/colaboratory\n",
+        "[colaboratory-label]: https://research.google.com/colaboratory\n",
+        "\n",
+        "An inline image: !\\[Google's logo](https://www.google.com/images/logos/google_logo_41.png)\n",
+        ">![Google's logo](https://www.google.com/images/logos/google_logo_41.png)\n",
+        "\n",
+        "Equations:\n",
+        "\n",
+        ">$y=x^2$\n",
+        "\n",
+        ">$e^{i\\pi} + 1 = 0$\n",
+        "\n",
+        ">$e^x=\\sum_{i=0}^\\infty \\frac{1}{i!}x^i$\n",
+        "\n",
+        ">$\\frac{n!}{k!(n-k)!} = {n \\choose k}$\n",
+        "\n",
+        ">$A_{m,n} =\n",
+        " \\begin{pmatrix}\n",
+        "  a_{1,1} & a_{1,2} & \\cdots & a_{1,n} \\\\\n",
+        "  a_{2,1} & a_{2,2} & \\cdots & a_{2,n} \\\\\n",
+        "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
+        "  a_{m,1} & a_{m,2} & \\cdots & a_{m,n}\n",
+        " \\end{pmatrix}$\n",
+        "\n",
+        "Tables:\n",
+        ">```\n",
+        "First column name | Second column name\n",
+        "--- | ---\n",
+        "Row 1, Col 1 | Row 1, Col 2\n",
+        "Row 2, Col 1 | Row 2, Col 2\n",
+        "```\n",
+        "\n",
+        "becomes:\n",
+        "\n",
+        ">First column name | Second column name\n",
+        ">--- | ---\n",
+        ">Row 1, Col 1 | Row 1, Col 2\n",
+        ">Row 2, Col 1 | Row 2, Col 2\n",
+        "\n",
+        "Horizontal rule done with three dashes (\\-\\-\\-):\n",
+        "\n",
+        "---\n",
+        "\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "w86a4I4fmkvD"
+      },
+      "source": [
+        "## Differences between Colaboratory markdown and other markdown dialects\n",
+        "\n",
+        "Colaboratory uses [marked.js](https://github.com/chjj/marked) and so is similar but not quite identical to the markdown used by Jupyter and Github.\n",
+        "\n",
+        "The biggest differences are that Colaboratory supports (MathJax) $\\LaTeX$ equations like Jupyter, but does not allow HTML tags in the markdown unlike most other markdowns.\n",
+        "\n",
+        "Smaller differences are that Colaboratory does not support syntax highlighting in code blocks, nor does it support some GitHub additions like emojis and to-do checkboxes.\n",
+        "\n",
+        "If HTML must be included in a Colaboratory notebook, see the [%%html magic](/notebooks/basic_features_overview.ipynb#scrollTo=qM4myQGfQboQ)."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "uSx6SUb1Komv"
+      },
+      "source": [
+        "## Useful references"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "colab_type": "text",
+        "id": "5Y3CStVkLxqt"
+      },
+      "source": [
+        "* [Github markdown basics](https://help.github.com/articles/markdown-basics/)\n",
+        "* [Github flavored markdown](https://help.github.com/articles/github-flavored-markdown/)\n",
+        "* [Original markdown spec: Syntax](http://daringfireball.net/projects/markdown/syntax)\n",
+        "* [Original markdown spec: Basics](http://daringfireball.net/projects/markdown/basics)\n",
+        "* [marked.js library used by Colaboratory](https://github.com/chjj/marked)\n",
+        "* [LaTex mathematics for equations](https://en.wikibooks.org/wiki/LaTeX/Mathematics)"
+      ]
+    }
+  ]
+}
\ No newline at end of file