ZhuJiaHao
/
zdqy_firm_former


			
				
					
						
						
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							<!DOCTYPE html>
<html>
<head>
<title>Dynamic Preview of Textarea with MathJax Content</title>
<!-- Copyright (c) 2012-2018 The MathJax Consortium -->
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />

<style>
.changed { color: red }
</style>

<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    TeX: {
      equationNumbers: {autoNumber: "AMS"},
      extensions: ["begingroup.js"],
      noErrors: {disabled: true}
    },
    showProcessingMessages: false,
    tex2jax: { inlineMath: [['$','$'],['\\(','\\)']] }
  });
//MathJax.Hub.signal.Interest(function (message) {console.log(message)});
</script>
<script type="text/javascript" src="../MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>

<script>
var Preview = {
  typeset: null,     // the typeset preview area (filled in by Init below)
  preview: null,     // the untypeset preview    (filled in by Init below)
  buffer: null,      // the new preview to be typeset (filled in by Init below)
  data: [],          // paragraph-specific data

  oldtext: '',       // used to see if an update is needed
  pending: false,    // true when a restart is in the MathJax queue

  colorDelay: 400,   // how long to leave changed paragraphs colored
  ctimeout: null,    // timeout for changed style remover
  labelDelay: 1250,  // how long to wait before reprocessing for label changes
  ltimeout: null,    // timeout for changed labels

  keytimes: [],      // tracks the times between keypresses
  keyrate: 100,      // the average of the keytimes (default value)
  keyn: 0,           // key index to replace next
  keysize:  10,      // use this many keypresses

  //
  //  Get the preview and buffer DIV's
  //
  Init: function () {
    this.typeset = document.getElementById("MathPreview");
    this.buffer = document.createElement("div");
    this.preview = document.createElement("div");
    for (var i = 0; i < this.keysize; i++) {this.keytimes[i] = this.keyrate}
  },

  //
  //  This gets called when a key is pressed in the textarea.
  //
  Update: function (up) {
    if (up) {
      //
      //  Determine the typing speed as a rolling average of the last few keystrokes
      //
      var time = new Date().getTime();
      if (this.lasttime) {
        var delta = time - this.lasttime;
        if (delta < 4*this.keyrate) {
          this.keyrate = (this.keysize*this.keyrate+delta-this.keytimes[this.keyn])/this.keysize;
          this.keytimes[this.keyn++] = delta;
          if (this.keyn === this.keysize) {this.keyn = 0}
        }
      }
      this.lasttime = time;
    }
    var text = document.getElementById("MathInput").value;
    text = text.replace(/^\s+/,'').replace(/\s+$/,'').replace(/\r\n?/g,"\n");
    if (text !== this.oldtext) {
      this.oldtext = text;
      if (!this.pending) {
        this.pending = true;
        MathJax.Hub.Queue(
          // allow a little time for additional typing
          ["Delay",MathJax.Callback,Math.min(200,Math.floor(this.keyrate/2)+1)],
          ["Restart",this]
        );
      }
    }
  },

  Restart: function (from) {
    this.pending = false;
    var text = this.oldtext.replace(/&/g,'&amp;').replace(/</g,'&lt;').replace(/>/g,'&gt;');
//    var text = "<p>"+text.replace(/\n\n+/g,"</p><p>")+"</p>";
    var text = text.replace(/\n\n+/g,"<p>");
    this.buffer.innerHTML = text;
    if (this.ctimeout) {clearTimeout(this.ctimeout); this.ctimeout = null}
    if (this.ltimeout) {clearTimeout(this.ltimeout); this.ltimeout = null}
    var update = this.CompareBuffers(from);
    if (update.needed) {
      MathJax.Hub.Queue(
        ["PreTypeset",this,update],
        ["Typeset",this,update],
        ["PostTypeset",this,update]
      );
    }
  },

  CompareBuffers: function (from) {
    var b1 = this.buffer.childNodes,
        b2 = this.preview.childNodes,
        i, m1 = b1.length, m2 = b2.length;
    //
    //  Make sure all top-level elements are containers
    //
    for (i = 0; i < m1; i++) {
      var node = b1[i];
      if (typeof(node.innerHTML) === "undefined") {
        this.buffer.replaceChild(document.createElement("span"),node);
        b1[i].appendChild(node);
      }
    }
    //
    //  Determine the range of elements to update
    //
    if (from != null) {
      //
      //  If from a starting point to the end, return the proper range
      //
      i = from; m1--; m2--;
    } else {
      //
      //  Find first non-matching element, if any,
      //    and the last non-matching element
      //
      m = Math.min(m1,m2);
      for (i = 0; i < m; i++) {if (b1[i].innerHTML !== b2[i].innerHTML) break}
      if (i === m && m1 === m2) {return {needed: false}}
      while (m1 > i && m2 > i) {if (b1[--m1].innerHTML !== b2[--m2].innerHTML) break}
    }
    return {needed:true, start:i, end1:m1, end2:m2};
  },

  Typeset: function (update) {
    return MathJax.Hub.Typeset(update.nodes,{});
  },

  PreTypeset: function (update) {
    var TEX = MathJax.InputJax.TeX;
    var i, m, n = 0, defs = [], m1 = update.end1, m2 = update.end2;
    var b1 = this.buffer.childNodes,
        b2 = this.typeset.childNodes;

    //
    //  Determine the starting equation number
    //
    for (i = 0, m = update.start; i < m; i++) {
      n += this.data[i].number;
      defs = defs.concat(this.data[i].defs);
    }
    TEX.resetEquationNumbers(n,true);
    //
    //  Pop any left over \begingroups and push a new one
    //  Then define any macros from previous paragraphs
    //
    while (TEX.rootStack.top > 1) {TEX.rootStack.stack.pop(); TEX.rootStack.top--}
    TEX.rootStack.Push(TEX.nsStack.nsFrame());
    for (i = 0, m = defs.length; i < m; i++) {TEX.rootStack.Def.apply(TEX.rootStack,defs[i])}
    i = this.i = update.start; this.refs = [];

    //
    //  Remove differing elements from typeset copy
    //  and add in the new (untypeset) elements.
    //
    this.recordOldData(this.data.splice(i,m2+1-i),n);
    var tail = b2[m2+1]; update.nodes = [];
    while (m2 >= i && b2[i]) {this.typeset.removeChild(b2[i]); m2--}
    while (i <= m1 && b1[i]) {
      this.data.splice(i,0,{number:0, labels:[], defs:[]});
      var node = b1[i++].cloneNode(true); update.nodes.push(node);
      if (tail) {this.typeset.insertBefore(node,tail)} else {this.typeset.appendChild(node)}
      if (node.className && node.className != "")
        {node.className += " changed"} else {node.className = "changed"}
    }
    //
    //  Swap buffers and set up the new buffer for the next change
    //
    this.preview = this.buffer; this.buffer = document.createElement("div");
    this.incremental = true;
  },

  recordOldData: function (data,top) {
    var AMS = MathJax.Extension["TeX/AMSmath"];
    var labels = [], defs = [];
    this.oldtop = this.newtop = top;
    for (var i = 0, m = data.length; i < m; i++) {
      this.oldtop += data[i].number;
      defs.push(data[i].defs.all);
      for (var j = 0, n = data[i].labels.length; j < n; j++) {
        delete AMS.labels[data[i].labels[j].split(/=/)[0]];
        labels.push(data[i].labels[j]);
      }
    }
    this.oldlabels = labels.join(''); this.newlabels = [];
    this.olddefs = defs.join(''); this.newdefs = [];
  },

  getTime: function (i) {
    var time = 0;
    for (var m = this.data.length; i < m; i++) {time += this.data[i].time}
    return time;
  },

  PostTypeset: function (update) {
    var time, delay, incremental = this.incremental; this.incremental = false;
    if (incremental && this.refs.length) {
      var refs = this.refs; this.refs = [];
      var queue = MathJax.Callback.Queue(["Reprocess",MathJax.Hub,refs,{}]);
      return queue.Push(["PostTypeset",this,update]);
    }
    this.ctimeout = setTimeout(this.Unmark,this.colorDelay);
    if (update.nodes.length !== this.preview.childNodes.length) {
      if (this.needsRefresh || this.newlabels && this.newlabels.join('') !== this.oldlabels) {
        this.needsRefresh = true;
        time = this.getTime(0); delay = Math.min(this.labelDelay,3*this.keyrate);
        if (time < this.keyrate) {this.Refresh()}
          else {this.ltimeout = setTimeout(this.Refresh,delay)}
      } else {
        if (this.newtop != this.oldtop || this.newdefs.join('') !== this.olddefs) {
          if (this.needsRenumber == null) {this.needsRenumber = this.i}
            else {this.needsRenumber = Math.min(this.needsRenumber,this.i)}
        }
        if (this.needsRenumber != null) {
          time = this.getTime(this.needsRenumber);
          delay = Math.min(this.labelDelay,3*this.keyRate);
          if (time < this.keyrate) {this.Renumber()}
            else {this.ltimeout = setTimeout(this.Renumber,delay)}
        }
      }
    }
  },
  Unmark: function () {
    Preview.ctimeout = null; var nodes = Preview.typeset.childNodes;
    for (var i = 0, m = nodes.length; i < m; i++) {Preview.removeChanged(nodes[i])}
  },
  Refresh: function () {
    Preview.pending = true; Preview.needsRefresh = false; delete Preview.needsRenumber;
    MathJax.Hub.Queue(["Restart",Preview,0]);
  },
  Renumber: function () {
    if (Preview.needsRenumber < Preview.preview.childNodes.length) {
      var n = Preview.needsRenumber;
      Preview.pending = true; delete Preview.needsRenumber;
      MathJax.Hub.Queue(["Restart",Preview,n]);
    }
  },

  //
  //  Remove the "changed" class from an element (leaving all other classes)
  //
  removeChanged: function (node) {
    if (node.className) {
      node.className = node.className.toString()
                           .replace(/(^|\s+)changed(\s|$)/,"$2")
                           .replace(/^\s+/,"");
    }
  }

};

MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
  MathJax.InputJax.TeX.postfilterHooks.Add(function (data) {
    if (Preview.incremental) {
      var AMS = MathJax.Extension["TeX/AMSmath"];
      var labels = Preview.data[Preview.i].labels;
      for (var id in AMS.eqlabels) {if (AMS.eqlabels.hasOwnProperty(id)) {
        labels.push(id+"="+AMS.eqlabels[id])
      }}
      Preview.newlabels = Preview.newlabels.concat(labels);
    }
  });
});
MathJax.Hub.Register.MessageHook("Begin Math Input",function () {
  if (Preview.incremental) {Preview.eqDefs = []; Preview.eqDefs.all = []}
});
MathJax.Hub.Register.MessageHook("End Math Input",function () {
  if (Preview.incremental) {
    var AMS = MathJax.Extension["TeX/AMSmath"];
    var data = Preview.data[Preview.i]||{};
    Preview.refs = Preview.refs.concat(AMS.refs); AMS.refs = [];
    Preview.eqDefs.all = Preview.eqDefs.all.join("");
    Preview.newdefs.push(Preview.eqDefs.all);
    data.defs = Preview.eqDefs;
    data.number = AMS.startNumber - Preview.newtop;
    Preview.newtop = AMS.startNumber;
  }
},5); // priority = 5 to make sure it is before AMS runs.

MathJax.Hub.Register.MessageHook("Begin Math",function () {
  if (Preview.incremental) {Preview.time = new Date().getTime()}
});
MathJax.Hub.Register.MessageHook("End Math",function () {
  if (Preview.incremental) {
    var time = new Date().getTime();
    (Preview.data[Preview.i]||{}).time = time - Preview.time;
    Preview.time = time;
    Preview.i++;
  }
});

MathJax.Hub.Register.StartupHook("TeX begingroup Ready",function () {
  var STACK = MathJax.InputJax.TeX.eqnStack;
  var DEF = STACK.Def;
  STACK.Def = function () {
    if (Preview.incremental) {
      Preview.eqDefs.push([].slice.call(arguments,0));
      Preview.eqDefs.all.push(arguments[0]+"{"+arguments[1]+"}");
    }
    DEF.apply(this,arguments);
  }
  //
  //  Temporary hack to fix typo in begingroup.js
  //
  MathJax.InputJax.TeX.rootStack.stack[0].environments =
    MathJax.InputJax.TeX.Definitions.environment;
});

</script>
</head>
<body>

Type text with embedded TeX in the box below:<br/>

<textarea id="MathInput" cols="60" rows="10" onkeyup="Preview.Update(true)" onkeydown="Preview.Update()" style="margin-top:5px">
This is a test.
</textarea>
<br/><br/>
<div id="MoreMath"></div>
Preview is shown here:
<div id="MathPreview" style="border:1px solid; padding: 3px; width:50%; margin-top:5px"></div>
<div style="display:none">Force loading: $x$</div>
<script>
Preview.Init();
MathJax.Hub.Queue(["Update",Preview]);
</script>

</body>
</html>

<!--
 | There must be some missing constraints. If $\alpha_n$ is allowed to be negative, we get the following counterexample. $\smash{\rlap{\phantom{\Bigg(}}}$
 | 
 | Define
 | $$
 | u_{n+1}=(1-\alpha_n)u_n+\beta_n\tag{1}
 | $$
 | and
 | $$
 | A_n=\prod_{k=1}^{n-1}(1-\alpha_k)\tag{2}
 | $$
 | By induction, it can be verified that
 | $$
 | u_n=A_n\left(u_1+\sum_{k=1}^{n-1}\frac{\beta_k}{A_{k+1}}\right)\tag{3}
 | $$
 | For $j\ge1$, define
 | $$
 | n_j=\left\{\begin{array}{}
 | 2^{j(j-1)/2}&\text{when }j\text{ is odd}\\
 | 2^{j(j-1)/2+1}&\text{when }j\text{ is even}
 | \end{array}\right.\tag{4}
 | $$
 | and for $n\ge1$,
 | $$
 | \alpha_n=\left\{\begin{array}{}
 | \frac{1}{n+1}&\text{for }n_j\le n< n_{j+1}\text{ when }j\text{ is odd}\\
 | -\frac1n&\text{for }n_j\le n< n_{j+1}\text{ when }j\text{ is even}
 | \end{array}\right.\tag{5}
 | $$
 | Obviously, $\displaystyle\lim_{n\to\infty}\alpha_n=0$.
 | 
 | Using telescoping products, it is not difficult to show that
 | $$
 | \frac{A_{n_{j+1}}}{A_{n_j}}=\left\{\begin{array}{}
 | \frac{n_j}{n_{j+1}}=2^{-j-1}&\text{when }j\text{ is odd}\\
 | \frac{n_{j+1}}{n_j}=2^{j-1}&\text{when }j\text{ is even}
 | \end{array}\right.\tag{6}
 | $$
 | Equation $(6)$ yields
 | $$
 | A_{n_j}=\left\{\begin{array}{}
 | 2^{-(j-1)/2}&\text{when }j\text{ is odd}\\
 | 2^{-(3j-2)/2}&\text{when }j\text{ is even}
 | \end{array}\right.\tag{7}
 | $$
 | Furthermore, using the standard formula for the partial harmonic series, when $j$ is odd,
 | $$
 | \begin{align}
 | \sum_{n=n_j}^{n_{j+1}-1}\alpha_n
 | &=\log\left(\frac{n_{j+1}}{n_j}\right)+O\left(\frac{1}{n_j}\right)\\
 | &=(j+1)\log(2)+O\left(2^{-j(j-1)/2}\right)\tag{8}
 | \end{align}
 | $$
 | and when $j$ is even,
 | $$
 | \begin{align}
 | \sum_{n=n_j}^{n_{j+1}-1}\alpha_n
 | &=-\log\left(\frac{n_{j+1}}{n_j}\right)+O\left(\frac{1}{n_j}\right)\\
 | &=-(j-1)\log(2)+O\left(2^{-j(j-1)/2}\right)\tag{9}
 | \end{align}
 | $$
 | Combining $(8)$ and $(9)$ yields
 | $$
 | \sum_{n=1}^{n_j-1}\alpha_n=\left\{\begin{array}{}
 | \frac{j-1}{2}\log(2)+O(1)&\text{when }j\text{ is odd}\\
 | \frac{3j-2}{2}\log(2)+O(1)&\text{when }j\text{ is even}
 | \end{array}\right.\tag{10}
 | $$
 | Equation $(10)$ says that $\displaystyle\sum_{n=1}^\infty\alpha_n=\infty$.
 | 
 | Define
 | $$
 | \beta_n=\left\{\begin{array}{}
 | 2^{-j}&\text{when }n=n_j-1\text{ for }j\text{ even}\\
 | 0&\text{otherwise}
 | \end{array}\right.\tag{11}
 | $$
 | Summing the geometric series yields $\displaystyle\sum_{n=1}^\infty\beta_n=\frac13$.
 | 
 | Using $(3)$, we get
 | $$
 | \begin{align}
 | u_{n_{j+1}}
 | &=A_{n_{j+1}}\left(u_1+\sum_{k=1}^{n_{j+1}-1}\frac{\beta_k}{A_{k+1}}\right)\\
 | &\ge\frac{A_{n_{j+1}}}{A_{n_j}}\beta_{n_j-1}\\
 | &=2^{j-1}\cdot2^{-j}\\
 | &=\frac12\tag{12}
 | \end{align}
 | $$
 | when $j$ is even. $(12)$ says that $\displaystyle\lim_{n\to\infty}u_n\not=0$.
-->