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441 lines
15 KiB
441 lines
15 KiB
5 years ago
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<!DOCTYPE html>
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<html>
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<head>
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<title>Dynamic Preview of Textarea with MathJax Content</title>
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<!-- Copyright (c) 2012-2018 The MathJax Consortium -->
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<meta http-equiv="X-UA-Compatible" content="IE=edge" />
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<style>
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.changed { color: red }
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</style>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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TeX: {
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equationNumbers: {autoNumber: "AMS"},
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extensions: ["begingroup.js"],
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noErrors: {disabled: true}
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},
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showProcessingMessages: false,
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tex2jax: { inlineMath: [['$','$'],['\\(','\\)']] }
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});
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//MathJax.Hub.signal.Interest(function (message) {console.log(message)});
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</script>
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<script type="text/javascript" src="../MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<script>
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var Preview = {
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typeset: null, // the typeset preview area (filled in by Init below)
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preview: null, // the untypeset preview (filled in by Init below)
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buffer: null, // the new preview to be typeset (filled in by Init below)
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data: [], // paragraph-specific data
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oldtext: '', // used to see if an update is needed
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pending: false, // true when a restart is in the MathJax queue
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colorDelay: 400, // how long to leave changed paragraphs colored
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ctimeout: null, // timeout for changed style remover
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labelDelay: 1250, // how long to wait before reprocessing for label changes
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ltimeout: null, // timeout for changed labels
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keytimes: [], // tracks the times between keypresses
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keyrate: 100, // the average of the keytimes (default value)
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keyn: 0, // key index to replace next
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keysize: 10, // use this many keypresses
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//
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// Get the preview and buffer DIV's
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//
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Init: function () {
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this.typeset = document.getElementById("MathPreview");
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this.buffer = document.createElement("div");
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this.preview = document.createElement("div");
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for (var i = 0; i < this.keysize; i++) {this.keytimes[i] = this.keyrate}
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},
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//
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// This gets called when a key is pressed in the textarea.
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//
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Update: function (up) {
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if (up) {
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//
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// Determine the typing speed as a rolling average of the last few keystrokes
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//
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var time = new Date().getTime();
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if (this.lasttime) {
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var delta = time - this.lasttime;
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if (delta < 4*this.keyrate) {
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this.keyrate = (this.keysize*this.keyrate+delta-this.keytimes[this.keyn])/this.keysize;
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this.keytimes[this.keyn++] = delta;
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if (this.keyn === this.keysize) {this.keyn = 0}
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}
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}
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this.lasttime = time;
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}
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var text = document.getElementById("MathInput").value;
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text = text.replace(/^\s+/,'').replace(/\s+$/,'').replace(/\r\n?/g,"\n");
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if (text !== this.oldtext) {
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this.oldtext = text;
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if (!this.pending) {
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this.pending = true;
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MathJax.Hub.Queue(
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// allow a little time for additional typing
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["Delay",MathJax.Callback,Math.min(200,Math.floor(this.keyrate/2)+1)],
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["Restart",this]
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);
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}
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}
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},
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Restart: function (from) {
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this.pending = false;
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var text = this.oldtext.replace(/&/g,'&').replace(/</g,'<').replace(/>/g,'>');
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// var text = "<p>"+text.replace(/\n\n+/g,"</p><p>")+"</p>";
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var text = text.replace(/\n\n+/g,"<p>");
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this.buffer.innerHTML = text;
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if (this.ctimeout) {clearTimeout(this.ctimeout); this.ctimeout = null}
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if (this.ltimeout) {clearTimeout(this.ltimeout); this.ltimeout = null}
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var update = this.CompareBuffers(from);
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if (update.needed) {
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MathJax.Hub.Queue(
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["PreTypeset",this,update],
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["Typeset",this,update],
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["PostTypeset",this,update]
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);
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}
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},
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CompareBuffers: function (from) {
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var b1 = this.buffer.childNodes,
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b2 = this.preview.childNodes,
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i, m1 = b1.length, m2 = b2.length;
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//
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// Make sure all top-level elements are containers
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//
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for (i = 0; i < m1; i++) {
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var node = b1[i];
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if (typeof(node.innerHTML) === "undefined") {
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this.buffer.replaceChild(document.createElement("span"),node);
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b1[i].appendChild(node);
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}
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}
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//
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// Determine the range of elements to update
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//
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if (from != null) {
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//
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// If from a starting point to the end, return the proper range
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//
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i = from; m1--; m2--;
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} else {
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//
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// Find first non-matching element, if any,
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// and the last non-matching element
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//
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m = Math.min(m1,m2);
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for (i = 0; i < m; i++) {if (b1[i].innerHTML !== b2[i].innerHTML) break}
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if (i === m && m1 === m2) {return {needed: false}}
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while (m1 > i && m2 > i) {if (b1[--m1].innerHTML !== b2[--m2].innerHTML) break}
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}
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return {needed:true, start:i, end1:m1, end2:m2};
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},
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Typeset: function (update) {
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return MathJax.Hub.Typeset(update.nodes,{});
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},
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PreTypeset: function (update) {
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var TEX = MathJax.InputJax.TeX;
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var i, m, n = 0, defs = [], m1 = update.end1, m2 = update.end2;
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var b1 = this.buffer.childNodes,
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b2 = this.typeset.childNodes;
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//
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// Determine the starting equation number
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//
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for (i = 0, m = update.start; i < m; i++) {
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n += this.data[i].number;
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defs = defs.concat(this.data[i].defs);
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}
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TEX.resetEquationNumbers(n,true);
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//
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// Pop any left over \begingroups and push a new one
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// Then define any macros from previous paragraphs
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//
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while (TEX.rootStack.top > 1) {TEX.rootStack.stack.pop(); TEX.rootStack.top--}
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TEX.rootStack.Push(TEX.nsStack.nsFrame());
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for (i = 0, m = defs.length; i < m; i++) {TEX.rootStack.Def.apply(TEX.rootStack,defs[i])}
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i = this.i = update.start; this.refs = [];
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//
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// Remove differing elements from typeset copy
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// and add in the new (untypeset) elements.
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//
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this.recordOldData(this.data.splice(i,m2+1-i),n);
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var tail = b2[m2+1]; update.nodes = [];
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while (m2 >= i && b2[i]) {this.typeset.removeChild(b2[i]); m2--}
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while (i <= m1 && b1[i]) {
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this.data.splice(i,0,{number:0, labels:[], defs:[]});
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var node = b1[i++].cloneNode(true); update.nodes.push(node);
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if (tail) {this.typeset.insertBefore(node,tail)} else {this.typeset.appendChild(node)}
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if (node.className && node.className != "")
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{node.className += " changed"} else {node.className = "changed"}
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}
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//
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// Swap buffers and set up the new buffer for the next change
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//
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this.preview = this.buffer; this.buffer = document.createElement("div");
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this.incremental = true;
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},
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recordOldData: function (data,top) {
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var AMS = MathJax.Extension["TeX/AMSmath"];
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var labels = [], defs = [];
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this.oldtop = this.newtop = top;
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for (var i = 0, m = data.length; i < m; i++) {
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this.oldtop += data[i].number;
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defs.push(data[i].defs.all);
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for (var j = 0, n = data[i].labels.length; j < n; j++) {
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delete AMS.labels[data[i].labels[j].split(/=/)[0]];
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labels.push(data[i].labels[j]);
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}
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}
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this.oldlabels = labels.join(''); this.newlabels = [];
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this.olddefs = defs.join(''); this.newdefs = [];
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},
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getTime: function (i) {
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var time = 0;
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for (var m = this.data.length; i < m; i++) {time += this.data[i].time}
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return time;
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},
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PostTypeset: function (update) {
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var time, delay, incremental = this.incremental; this.incremental = false;
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if (incremental && this.refs.length) {
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var refs = this.refs; this.refs = [];
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var queue = MathJax.Callback.Queue(["Reprocess",MathJax.Hub,refs,{}]);
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return queue.Push(["PostTypeset",this,update]);
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}
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this.ctimeout = setTimeout(this.Unmark,this.colorDelay);
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if (update.nodes.length !== this.preview.childNodes.length) {
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if (this.needsRefresh || this.newlabels && this.newlabels.join('') !== this.oldlabels) {
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this.needsRefresh = true;
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time = this.getTime(0); delay = Math.min(this.labelDelay,3*this.keyrate);
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if (time < this.keyrate) {this.Refresh()}
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else {this.ltimeout = setTimeout(this.Refresh,delay)}
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} else {
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if (this.newtop != this.oldtop || this.newdefs.join('') !== this.olddefs) {
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if (this.needsRenumber == null) {this.needsRenumber = this.i}
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else {this.needsRenumber = Math.min(this.needsRenumber,this.i)}
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}
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if (this.needsRenumber != null) {
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time = this.getTime(this.needsRenumber);
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delay = Math.min(this.labelDelay,3*this.keyRate);
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if (time < this.keyrate) {this.Renumber()}
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else {this.ltimeout = setTimeout(this.Renumber,delay)}
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}
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}
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}
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},
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Unmark: function () {
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Preview.ctimeout = null; var nodes = Preview.typeset.childNodes;
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for (var i = 0, m = nodes.length; i < m; i++) {Preview.removeChanged(nodes[i])}
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},
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Refresh: function () {
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Preview.pending = true; Preview.needsRefresh = false; delete Preview.needsRenumber;
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MathJax.Hub.Queue(["Restart",Preview,0]);
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},
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Renumber: function () {
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if (Preview.needsRenumber < Preview.preview.childNodes.length) {
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var n = Preview.needsRenumber;
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Preview.pending = true; delete Preview.needsRenumber;
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MathJax.Hub.Queue(["Restart",Preview,n]);
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}
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},
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//
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// Remove the "changed" class from an element (leaving all other classes)
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//
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removeChanged: function (node) {
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if (node.className) {
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node.className = node.className.toString()
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.replace(/(^|\s+)changed(\s|$)/,"$2")
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.replace(/^\s+/,"");
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}
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}
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};
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MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
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MathJax.InputJax.TeX.postfilterHooks.Add(function (data) {
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if (Preview.incremental) {
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var AMS = MathJax.Extension["TeX/AMSmath"];
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var labels = Preview.data[Preview.i].labels;
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for (var id in AMS.eqlabels) {if (AMS.eqlabels.hasOwnProperty(id)) {
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labels.push(id+"="+AMS.eqlabels[id])
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}}
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Preview.newlabels = Preview.newlabels.concat(labels);
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}
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});
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});
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MathJax.Hub.Register.MessageHook("Begin Math Input",function () {
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if (Preview.incremental) {Preview.eqDefs = []; Preview.eqDefs.all = []}
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});
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MathJax.Hub.Register.MessageHook("End Math Input",function () {
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if (Preview.incremental) {
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var AMS = MathJax.Extension["TeX/AMSmath"];
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var data = Preview.data[Preview.i]||{};
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Preview.refs = Preview.refs.concat(AMS.refs); AMS.refs = [];
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Preview.eqDefs.all = Preview.eqDefs.all.join("");
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Preview.newdefs.push(Preview.eqDefs.all);
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data.defs = Preview.eqDefs;
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data.number = AMS.startNumber - Preview.newtop;
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Preview.newtop = AMS.startNumber;
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}
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},5); // priority = 5 to make sure it is before AMS runs.
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MathJax.Hub.Register.MessageHook("Begin Math",function () {
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if (Preview.incremental) {Preview.time = new Date().getTime()}
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});
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MathJax.Hub.Register.MessageHook("End Math",function () {
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if (Preview.incremental) {
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var time = new Date().getTime();
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(Preview.data[Preview.i]||{}).time = time - Preview.time;
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Preview.time = time;
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Preview.i++;
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}
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});
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MathJax.Hub.Register.StartupHook("TeX begingroup Ready",function () {
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var STACK = MathJax.InputJax.TeX.eqnStack;
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var DEF = STACK.Def;
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STACK.Def = function () {
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if (Preview.incremental) {
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Preview.eqDefs.push([].slice.call(arguments,0));
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Preview.eqDefs.all.push(arguments[0]+"{"+arguments[1]+"}");
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}
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DEF.apply(this,arguments);
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}
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//
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// Temporary hack to fix typo in begingroup.js
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//
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MathJax.InputJax.TeX.rootStack.stack[0].environments =
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MathJax.InputJax.TeX.Definitions.environment;
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});
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</script>
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</head>
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<body>
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Type text with embedded TeX in the box below:<br/>
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<textarea id="MathInput" cols="60" rows="10" onkeyup="Preview.Update(true)" onkeydown="Preview.Update()" style="margin-top:5px">
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This is a test.
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</textarea>
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<br/><br/>
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<div id="MoreMath"></div>
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Preview is shown here:
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<!--
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| There must be some missing constraints. If $\alpha_n$ is allowed to be negative, we get the following counterexample. $\smash{\rlap{\phantom{\Bigg(}}}$
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| Define
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| $$
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| u_{n+1}=(1-\alpha_n)u_n+\beta_n\tag{1}
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| $$
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| and
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| $$
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| A_n=\prod_{k=1}^{n-1}(1-\alpha_k)\tag{2}
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| $$
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| By induction, it can be verified that
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| $$
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| u_n=A_n\left(u_1+\sum_{k=1}^{n-1}\frac{\beta_k}{A_{k+1}}\right)\tag{3}
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| $$
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| For $j\ge1$, define
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| $$
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| n_j=\left\{\begin{array}{}
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| 2^{j(j-1)/2}&\text{when }j\text{ is odd}\\
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| 2^{j(j-1)/2+1}&\text{when }j\text{ is even}
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| \end{array}\right.\tag{4}
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| $$
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| and for $n\ge1$,
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| $$
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| \alpha_n=\left\{\begin{array}{}
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| \frac{1}{n+1}&\text{for }n_j\le n< n_{j+1}\text{ when }j\text{ is odd}\\
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| -\frac1n&\text{for }n_j\le n< n_{j+1}\text{ when }j\text{ is even}
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| \end{array}\right.\tag{5}
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| $$
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| Obviously, $\displaystyle\lim_{n\to\infty}\alpha_n=0$.
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| Using telescoping products, it is not difficult to show that
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| $$
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| \frac{A_{n_{j+1}}}{A_{n_j}}=\left\{\begin{array}{}
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| \frac{n_j}{n_{j+1}}=2^{-j-1}&\text{when }j\text{ is odd}\\
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| \frac{n_{j+1}}{n_j}=2^{j-1}&\text{when }j\text{ is even}
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| \end{array}\right.\tag{6}
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| $$
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| Equation $(6)$ yields
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| $$
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| A_{n_j}=\left\{\begin{array}{}
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| 2^{-(j-1)/2}&\text{when }j\text{ is odd}\\
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| 2^{-(3j-2)/2}&\text{when }j\text{ is even}
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| \end{array}\right.\tag{7}
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| $$
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| Furthermore, using the standard formula for the partial harmonic series, when $j$ is odd,
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| $$
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| \begin{align}
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| \sum_{n=n_j}^{n_{j+1}-1}\alpha_n
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| &=\log\left(\frac{n_{j+1}}{n_j}\right)+O\left(\frac{1}{n_j}\right)\\
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| &=(j+1)\log(2)+O\left(2^{-j(j-1)/2}\right)\tag{8}
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| \end{align}
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| $$
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| and when $j$ is even,
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| $$
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| \begin{align}
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| \sum_{n=n_j}^{n_{j+1}-1}\alpha_n
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| &=-\log\left(\frac{n_{j+1}}{n_j}\right)+O\left(\frac{1}{n_j}\right)\\
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| &=-(j-1)\log(2)+O\left(2^{-j(j-1)/2}\right)\tag{9}
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| \end{align}
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| $$
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| Combining $(8)$ and $(9)$ yields
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| $$
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| \sum_{n=1}^{n_j-1}\alpha_n=\left\{\begin{array}{}
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| \frac{j-1}{2}\log(2)+O(1)&\text{when }j\text{ is odd}\\
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| \frac{3j-2}{2}\log(2)+O(1)&\text{when }j\text{ is even}
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| \end{array}\right.\tag{10}
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| $$
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| Equation $(10)$ says that $\displaystyle\sum_{n=1}^\infty\alpha_n=\infty$.
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|
|
| Define
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|
|
| $$
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|
|
| \beta_n=\left\{\begin{array}{}
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|
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| 2^{-j}&\text{when }n=n_j-1\text{ for }j\text{ even}\\
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| 0&\text{otherwise}
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| \end{array}\right.\tag{11}
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|
| $$
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| Summing the geometric series yields $\displaystyle\sum_{n=1}^\infty\beta_n=\frac13$.
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|
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| Using $(3)$, we get
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|
|
| $$
|
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|
|
| \begin{align}
|
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|
|
| u_{n_{j+1}}
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|
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| &=A_{n_{j+1}}\left(u_1+\sum_{k=1}^{n_{j+1}-1}\frac{\beta_k}{A_{k+1}}\right)\\
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|
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| &\ge\frac{A_{n_{j+1}}}{A_{n_j}}\beta_{n_j-1}\\
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| &=2^{j-1}\cdot2^{-j}\\
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| &=\frac12\tag{12}
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|
| \end{align}
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|
| $$
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| when $j$ is even. $(12)$ says that $\displaystyle\lim_{n\to\infty}u_n\not=0$.
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-->
|