www

Unnamed repository; edit this file 'description' to name the repository.
Log | Files | Refs | README | LICENSE

commit 30e35cc72919b8cc97a384eadd6088481ed4a7e5
parent 02909ecba44e4e889ce6bdcd3f735082ea898a07
Author: Davide P. Cervone <dpvc@union.edu>
Date:   Wed, 25 Jan 2012 09:45:20 -0500

Add menu control for showing TeX hints in MathML, and make TeXAtom not show extra mrow when it contains a single element

Diffstat:
MMathJax.js | 2+-
Mconfig/Accessible-full.js | 4++--
Mconfig/Accessible.js | 4++--
Mconfig/MML_HTMLorMML-full.js | 4++--
Mconfig/MML_HTMLorMML.js | 4++--
Mconfig/TeX-AMS-MML_HTMLorMML-full.js | 4++--
Mconfig/TeX-AMS-MML_HTMLorMML.js | 4++--
Mconfig/TeX-AMS_HTML-full.js | 4++--
Mconfig/TeX-AMS_HTML.js | 4++--
Mextensions/MathMenu.js | 2+-
Mextensions/toMathML.js | 2+-
Munpacked/MathJax.js | 5++++-
Munpacked/extensions/MathMenu.js | 4+++-
Munpacked/extensions/toMathML.js | 7++++---
14 files changed, 30 insertions(+), 24 deletions(-)

diff --git a/MathJax.js b/MathJax.js @@ -26,5 +26,5 @@ if (!window.MathJax) {window.MathJax = {}} MathJax.isPacked = true; -if(document.getElementById&&document.childNodes&&document.createElement){if(!window.MathJax){window.MathJax={}}if(!MathJax.Hub){MathJax.version="2.0";MathJax.fileversion="2.0";(function(d){var b=window[d];if(!b){b=window[d]={}}var f=[];var c=function(g){var h=g.constructor;if(!h){h=new Function("")}for(var i in g){if(i!=="constructor"&&g.hasOwnProperty(i)){h[i]=g[i]}}return h};var a=function(){return new Function("return arguments.callee.Init.call(this,arguments)")};var e=a();e.prototype={bug_test:1};if(!e.prototype.bug_test){a=function(){return function(){return arguments.callee.Init.call(this,arguments)}}}b.Object=c({constructor:a(),Subclass:function(g,i){var h=a();h.SUPER=this;h.Init=this.Init;h.Subclass=this.Subclass;h.Augment=this.Augment;h.protoFunction=this.protoFunction;h.can=this.can;h.has=this.has;h.isa=this.isa;h.prototype=new this(f);h.prototype.constructor=h;h.Augment(g,i);return h},Init:function(g){var h=this;if(g.length===1&&g[0]===f){return h}if(!(h instanceof g.callee)){h=new g.callee(f)}return h.Init.apply(h,g)||h},Augment:function(g,h){var i;if(g!=null){for(i in g){if(g.hasOwnProperty(i)){this.protoFunction(i,g[i])}}if(g.toString!==this.prototype.toString&&g.toString!=={}.toString){this.protoFunction("toString",g.toString)}}if(h!=null){for(i in h){if(h.hasOwnProperty(i)){this[i]=h[i]}}}return this},protoFunction:function(h,g){this.prototype[h]=g;if(typeof g==="function"){g.SUPER=this.SUPER.prototype}},prototype:{Init:function(){},SUPER:function(g){return g.callee.SUPER},can:function(g){return typeof(this[g])==="function"},has:function(g){return typeof(this[g])!=="undefined"},isa:function(g){return(g instanceof Object)&&(this instanceof g)}},can:function(g){return this.prototype.can.call(this,g)},has:function(g){return this.prototype.has.call(this,g)},isa:function(h){var g=this;while(g){if(g===h){return true}else{g=g.SUPER}}return false},SimpleSUPER:c({constructor:function(g){return this.SimpleSUPER.define(g)},define:function(g){var i={};if(g!=null){for(var h in g){if(g.hasOwnProperty(h)){i[h]=this.wrap(h,g[h])}}if(g.toString!==this.prototype.toString&&g.toString!=={}.toString){i.toString=this.wrap("toString",g.toString)}}return i},wrap:function(i,h){if(typeof(h)==="function"&&h.toString().match(/\.\s*SUPER\s*\(/)){var g=new Function(this.wrapper);g.label=i;g.original=h;h=g;g.toString=this.stringify}return h},wrapper:function(){var h=arguments.callee;this.SUPER=h.SUPER[h.label];try{var g=h.original.apply(this,arguments)}catch(i){delete this.SUPER;throw i}delete this.SUPER;return g}.toString().replace(/^\s*function \(\)\s*\{\s*/i,"").replace(/\s*\}\s*$/i,""),toString:function(){return this.original.toString.apply(this.original,arguments)}})})})("MathJax");(function(BASENAME){var BASE=window[BASENAME];if(!BASE){BASE=window[BASENAME]={}}var CALLBACK=function(data){var cb=new Function("return arguments.callee.execute.apply(arguments.callee,arguments)");for(var id in CALLBACK.prototype){if(CALLBACK.prototype.hasOwnProperty(id)){if(typeof(data[id])!=="undefined"){cb[id]=data[id]}else{cb[id]=CALLBACK.prototype[id]}}}cb.toString=CALLBACK.prototype.toString;return cb};CALLBACK.prototype={isCallback:true,hook:function(){},data:[],object:window,execute:function(){if(!this.called||this.autoReset){this.called=!this.autoReset;return this.hook.apply(this.object,this.data.concat([].slice.call(arguments,0)))}},reset:function(){delete this.called},toString:function(){return this.hook.toString.apply(this.hook,arguments)}};var ISCALLBACK=function(f){return(typeof(f)==="function"&&f.isCallback)};var EVAL=function(code){return eval.call(window,code)};EVAL("var __TeSt_VaR__ = 1");if(window.__TeSt_VaR__){try{delete window.__TeSt_VaR__}catch(error){window.__TeSt_VaR__=null}}else{if(window.execScript){EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";window.execScript(code);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}else{EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";var head=(document.getElementsByTagName("head"))[0];if(!head){head=document.body}var script=document.createElement("script");script.appendChild(document.createTextNode(code));head.appendChild(script);head.removeChild(script);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}}var USING=function(args,i){if(arguments.length>1){if(arguments.length===2&&!(typeof arguments[0]==="function")&&arguments[0] instanceof Object&&typeof arguments[1]==="number"){args=[].slice.call(args,i)}else{args=[].slice.call(arguments,0)}}if(args instanceof Array&&args.length===1){args=args[0]}if(typeof args==="function"){if(args.execute===CALLBACK.prototype.execute){return args}return CALLBACK({hook:args})}else{if(args instanceof Array){if(typeof(args[0])==="string"&&args[1] instanceof Object&&typeof args[1][args[0]]==="function"){return CALLBACK({hook:args[1][args[0]],object:args[1],data:args.slice(2)})}else{if(typeof args[0]==="function"){return CALLBACK({hook:args[0],data:args.slice(1)})}else{if(typeof args[1]==="function"){return CALLBACK({hook:args[1],object:args[0],data:args.slice(2)})}}}}else{if(typeof(args)==="string"){return CALLBACK({hook:EVAL,data:[args]})}else{if(args instanceof Object){return CALLBACK(args)}else{if(typeof(args)==="undefined"){return CALLBACK({})}}}}}throw Error("Can't make callback from given data")};var DELAY=function(time,callback){callback=USING(callback);callback.timeout=setTimeout(callback,time);return callback};var WAITFOR=function(callback,signal){callback=USING(callback);if(!callback.called){WAITSIGNAL(callback,signal);signal.pending++}};var WAITEXECUTE=function(){var signals=this.signal;delete this.signal;this.execute=this.oldExecute;delete this.oldExecute;var result=this.execute.apply(this,arguments);if(ISCALLBACK(result)&&!result.called){WAITSIGNAL(result,signals)}else{for(var i=0,m=signals.length;i<m;i++){signals[i].pending--;if(signals[i].pending<=0){signals[i].call()}}}};var WAITSIGNAL=function(callback,signals){if(!(signals instanceof Array)){signals=[signals]}if(!callback.signal){callback.oldExecute=callback.execute;callback.execute=WAITEXECUTE;callback.signal=signals}else{if(signals.length===1){callback.signal.push(signals[0])}else{callback.signal=callback.signal.concat(signals)}}};var AFTER=function(callback){callback=USING(callback);callback.pending=0;for(var i=1,m=arguments.length;i<m;i++){if(arguments[i]){WAITFOR(arguments[i],callback)}}if(callback.pending===0){var result=callback();if(ISCALLBACK(result)){callback=result}}return callback};var HOOKS=MathJax.Object.Subclass({Init:function(reset){this.hooks=[];this.reset=reset},Add:function(hook,priority){if(priority==null){priority=10}if(!ISCALLBACK(hook)){hook=USING(hook)}hook.priority=priority;var i=this.hooks.length;while(i>0&&priority<this.hooks[i-1].priority){i--}this.hooks.splice(i,0,hook);return hook},Remove:function(hook){for(var i=0,m=this.hooks.length;i<m;i++){if(this.hooks[i]===hook){this.hooks.splice(i,1);return}}},Execute:function(){var callbacks=[{}];for(var i=0,m=this.hooks.length;i<m;i++){if(this.reset){this.hooks[i].reset()}var result=this.hooks[i].apply(window,arguments);if(ISCALLBACK(result)&&!result.called){callbacks.push(result)}}if(callbacks.length===1){return null}if(callbacks.length===2){return callbacks[1]}return AFTER.apply({},callbacks)}});var EXECUTEHOOKS=function(hooks,data,reset){if(!hooks){return null}if(!(hooks instanceof Array)){hooks=[hooks]}if(!(data instanceof Array)){data=(data==null?[]:[data])}var handler=HOOKS(reset);for(var i=0,m=hooks.length;i<m;i++){handler.Add(hooks[i])}return handler.Execute.apply(handler,data)};var QUEUE=BASE.Object.Subclass({Init:function(){this.pending=0;this.running=0;this.queue=[];this.Push.apply(this,arguments)},Push:function(){var callback;for(var i=0,m=arguments.length;i<m;i++){callback=USING(arguments[i]);if(callback===arguments[i]&&!callback.called){callback=USING(["wait",this,callback])}this.queue.push(callback)}if(!this.running&&!this.pending){this.Process()}return callback},Process:function(queue){while(!this.running&&!this.pending&&this.queue.length){var callback=this.queue[0];queue=this.queue.slice(1);this.queue=[];this.Suspend();var result=callback();this.Resume();if(queue.length){this.queue=queue.concat(this.queue)}if(ISCALLBACK(result)&&!result.called){WAITFOR(result,this)}}},Suspend:function(){this.running++},Resume:function(){if(this.running){this.running--}},call:function(){this.Process.apply(this,arguments)},wait:function(callback){return callback}});var SIGNAL=QUEUE.Subclass({Init:function(name){QUEUE.prototype.Init.call(this);this.name=name;this.posted=[];this.listeners=HOOKS(true)},Post:function(message,callback,forget){callback=USING(callback);if(this.posting||this.pending){this.Push(["Post",this,message,callback,forget])}else{this.callback=callback;callback.reset();if(!forget){this.posted.push(message)}this.Suspend();this.posting=true;var result=this.listeners.Execute(message);if(ISCALLBACK(result)&&!result.called){WAITFOR(result,this)}this.Resume();delete this.posting;if(!this.pending){this.call()}}return callback},Clear:function(callback){callback=USING(callback);if(this.posting||this.pending){callback=this.Push(["Clear",this,callback])}else{this.posted=[];callback()}return callback},call:function(){this.callback(this);this.Process()},Interest:function(callback,ignorePast,priority){callback=USING(callback);this.listeners.Add(callback,priority);if(!ignorePast){for(var i=0,m=this.posted.length;i<m;i++){callback.reset();var result=callback(this.posted[i]);if(ISCALLBACK(result)&&i===this.posted.length-1){WAITFOR(result,this)}}}return callback},NoInterest:function(callback){this.listeners.Remove(callback)},MessageHook:function(msg,callback,priority){callback=USING(callback);if(!this.hooks){this.hooks={};this.Interest(["ExecuteHooks",this])}if(!this.hooks[msg]){this.hooks[msg]=HOOKS(true)}this.hooks[msg].Add(callback,priority);for(var i=0,m=this.posted.length;i<m;i++){if(this.posted[i]==msg){callback.reset();callback(this.posted[i])}}return callback},ExecuteHooks:function(msg,more){var type=((msg instanceof Array)?msg[0]:msg);if(!this.hooks[type]){return null}return this.hooks[type].Execute(msg)}},{signals:{},find:function(name){if(!SIGNAL.signals[name]){SIGNAL.signals[name]=new SIGNAL(name)}return SIGNAL.signals[name]}});BASE.Callback=BASE.CallBack=USING;BASE.Callback.Delay=DELAY;BASE.Callback.After=AFTER;BASE.Callback.Queue=QUEUE;BASE.Callback.Signal=SIGNAL.find;BASE.Callback.Hooks=HOOKS;BASE.Callback.ExecuteHooks=EXECUTEHOOKS})("MathJax");(function(d){var a=window[d];if(!a){a=window[d]={}}var c=(navigator.vendor==="Apple Computer, Inc."&&typeof navigator.vendorSub==="undefined");var f=0;var g=function(h){if(document.styleSheets&&document.styleSheets.length>f){f=document.styleSheets.length}if(!h){h=(document.getElementsByTagName("head"))[0];if(!h){h=document.body}}return h};var e=[];var b=function(){for(var j=0,h=e.length;j<h;j++){a.Ajax.head.removeChild(e[j])}e=[]};a.Ajax={loaded:{},loading:{},loadHooks:{},timeout:15*1000,styleDelay:1,config:{root:""},STATUS:{OK:1,ERROR:-1},rootPattern:new RegExp("^\\["+d+"\\]"),fileURL:function(h){return h.replace(this.rootPattern,this.config.root)},Require:function(j,m){m=a.Callback(m);var k;if(j instanceof Object){for(var h in j){}k=h.toUpperCase();j=j[h]}else{k=j.split(/\./).pop().toUpperCase()}j=this.fileURL(j);if(this.loaded[j]){m(this.loaded[j])}else{var l={};l[k]=j;this.Load(l,m)}return m},Load:function(j,l){l=a.Callback(l);var k;if(j instanceof Object){for(var h in j){}k=h.toUpperCase();j=j[h]}else{k=j.split(/\./).pop().toUpperCase()}j=this.fileURL(j);if(this.loading[j]){this.addHook(j,l)}else{this.head=g(this.head);if(this.loader[k]){this.loader[k].call(this,j,l)}else{throw Error("Can't load files of type "+k)}}return l},LoadHook:function(k,l,j){l=a.Callback(l);if(k instanceof Object){for(var h in k){k=k[h]}}k=this.fileURL(k);if(this.loaded[k]){l(this.loaded[k])}else{this.addHook(k,l,j)}return l},addHook:function(i,j,h){if(!this.loadHooks[i]){this.loadHooks[i]=MathJax.Callback.Hooks()}this.loadHooks[i].Add(j,h)},Preloading:function(){for(var k=0,h=arguments.length;k<h;k++){var j=this.fileURL(arguments[k]);if(!this.loading[j]){this.loading[j]={preloaded:true}}}},loader:{JS:function(i,k){var h=document.createElement("script");var j=a.Callback(["loadTimeout",this,i]);this.loading[i]={callback:k,message:a.Message.File(i),timeout:setTimeout(j,this.timeout),status:this.STATUS.OK,script:h};h.onerror=j;h.type="text/javascript";h.src=i;this.head.appendChild(h)},CSS:function(h,j){var i=document.createElement("link");i.rel="stylesheet";i.type="text/css";i.href=h;this.loading[h]={callback:j,message:a.Message.File(h),status:this.STATUS.OK};this.head.appendChild(i);this.timer.create.call(this,[this.timer.file,h],i)}},timer:{create:function(i,h){i=a.Callback(i);if(h.nodeName==="STYLE"&&h.styleSheet&&typeof(h.styleSheet.cssText)!=="undefined"){i(this.STATUS.OK)}else{if(window.chrome&&typeof(window.sessionStorage)!=="undefined"&&h.nodeName==="STYLE"){i(this.STATUS.OK)}else{if(c){this.timer.start(this,[this.timer.checkSafari2,f++,i],this.styleDelay)}else{this.timer.start(this,[this.timer.checkLength,h,i],this.styleDelay)}}}return i},start:function(i,h,j,k){h=a.Callback(h);h.execute=this.execute;h.time=this.time;h.STATUS=i.STATUS;h.timeout=k||i.timeout;h.delay=h.total=0;if(j){setTimeout(h,j)}else{h()}},time:function(h){this.total+=this.delay;this.delay=Math.floor(this.delay*1.05+5);if(this.total>=this.timeout){h(this.STATUS.ERROR);return 1}return 0},file:function(i,h){if(h<0){a.Ajax.loadTimeout(i)}else{a.Ajax.loadComplete(i)}},execute:function(){this.hook.call(this.object,this,this.data[0],this.data[1])},checkSafari2:function(h,i,j){if(h.time(j)){return}if(document.styleSheets.length>i&&document.styleSheets[i].cssRules&&document.styleSheets[i].cssRules.length){j(h.STATUS.OK)}else{setTimeout(h,h.delay)}},checkLength:function(h,k,m){if(h.time(m)){return}var l=0;var i=(k.sheet||k.styleSheet);try{if((i.cssRules||i.rules||[]).length>0){l=1}}catch(j){if(j.message.match(/protected variable|restricted URI/)){l=1}else{if(j.message.match(/Security error/)){l=1}}}if(l){setTimeout(a.Callback([m,h.STATUS.OK]),0)}else{setTimeout(h,h.delay)}}},loadComplete:function(h){h=this.fileURL(h);var i=this.loading[h];if(i&&!i.preloaded){a.Message.Clear(i.message);clearTimeout(i.timeout);if(i.script){if(e.length===0){setTimeout(b,0)}e.push(i.script)}this.loaded[h]=i.status;delete this.loading[h];this.addHook(h,i.callback)}else{this.loaded[h]=this.STATUS.OK;i={status:this.STATUS.OK}}if(!this.loadHooks[h]){return null}return this.loadHooks[h].Execute(i.status)},loadTimeout:function(h){if(this.loading[h].timeout){clearTimeout(this.loading[h].timeout)}this.loading[h].status=this.STATUS.ERROR;this.loadError(h);this.loadComplete(h)},loadError:function(h){a.Message.Set("File failed to load: "+h,null,2000);a.Hub.signal.Post(["file load error",h])},Styles:function(j,k){var h=this.StyleString(j);if(h===""){k=a.Callback(k);k()}else{var i=document.createElement("style");i.type="text/css";this.head=g(this.head);this.head.appendChild(i);if(i.styleSheet&&typeof(i.styleSheet.cssText)!=="undefined"){i.styleSheet.cssText=h}else{i.appendChild(document.createTextNode(h))}k=this.timer.create.call(this,k,i)}return k},StyleString:function(m){if(typeof(m)==="string"){return m}var j="",n,l;for(n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="string"){j+=n+" {"+m[n]+"}\n"}else{if(m[n] instanceof Array){for(var k=0;k<m[n].length;k++){l={};l[n]=m[n][k];j+=this.StyleString(l)}}else{if(n.substr(0,6)==="@media"){j+=n+" {"+this.StyleString(m[n])+"}\n"}else{if(m[n]!=null){l=[];for(var h in m[n]){if(m[n].hasOwnProperty(h)){if(m[n][h]!=null){l[l.length]=h+": "+m[n][h]}}}j+=n+" {"+l.join("; ")+"}\n"}}}}}}return j}}})("MathJax");MathJax.HTML={Element:function(c,e,d){var f=document.createElement(c);if(e){if(e.style){var b=e.style;e.style={};for(var g in b){if(b.hasOwnProperty(g)){e.style[g.replace(/-([a-z])/g,this.ucMatch)]=b[g]}}}MathJax.Hub.Insert(f,e)}if(d){for(var a=0;a<d.length;a++){if(d[a] instanceof Array){f.appendChild(this.Element(d[a][0],d[a][1],d[a][2]))}else{f.appendChild(document.createTextNode(d[a]))}}}return f},ucMatch:function(a,b){return b.toUpperCase()},addElement:function(b,a,d,c){return b.appendChild(this.Element(a,d,c))},TextNode:function(a){return document.createTextNode(a)},addText:function(a,b){return a.appendChild(this.TextNode(b))},setScript:function(a,b){if(this.setScriptBug){a.text=b}else{while(a.firstChild){a.removeChild(a.firstChild)}this.addText(a,b)}},Cookie:{prefix:"mjx",expires:365,Set:function(a,d){var c=[];if(d){for(var f in d){if(d.hasOwnProperty(f)){c.push(f+":"+d[f].toString().replace(/&/g,"&&"))}}}var b=this.prefix+"."+a+"="+escape(c.join("&;"));if(this.expires){var e=new Date();e.setDate(e.getDate()+this.expires);b+="; expires="+e.toGMTString()}document.cookie=b+"; path=/"},Get:function(c,h){if(!h){h={}}var g=new RegExp("(?:^|;\\s*)"+this.prefix+"\\."+c+"=([^;]*)(?:;|$)");var b=g.exec(document.cookie);if(b&&b[1]!==""){var e=unescape(b[1]).split("&;");for(var d=0,a=e.length;d<a;d++){b=e[d].match(/([^:]+):(.*)/);var f=b[2].replace(/&&/g,"&");if(f==="true"){f=true}else{if(f==="false"){f=false}else{if(f.match(/^-?(\d+(\.\d+)?|\.\d+)$/)){f=parseFloat(f)}}}h[b[1]]=f}}return h}}};MathJax.Message={ready:false,log:[{}],current:null,textNodeBug:(navigator.vendor==="Apple Computer, Inc."&&typeof navigator.vendorSub==="undefined")||(window.hasOwnProperty&&window.hasOwnProperty("konqueror")),styles:{"#MathJax_Message":{position:"fixed",left:"1px",bottom:"2px","background-color":"#E6E6E6",border:"1px solid #959595",margin:"0px",padding:"2px 8px","z-index":"102",color:"black","font-size":"80%",width:"auto","white-space":"nowrap"},"#MathJax_MSIE_Frame":{position:"absolute",top:0,left:0,width:"0px","z-index":101,border:"0px",margin:"0px",padding:"0px"}},browsers:{MSIE:function(a){MathJax.Hub.config.styles["#MathJax_Message"].position="absolute";MathJax.Message.quirks=(document.compatMode==="BackCompat")},Chrome:function(a){MathJax.Hub.config.styles["#MathJax_Message"].bottom="1.5em";MathJax.Hub.config.styles["#MathJax_Message"].left="1em"}},Init:function(a){if(a){this.ready=true}if(!document.body||!this.ready){return false}if(this.div&&this.div.parentNode==null){this.div=document.getElementById("MathJax_Message");if(this.div){this.text=this.div.firstChild}}if(!this.div){var b=document.body;if(MathJax.Hub.Browser.isMSIE){b=this.frame=this.addDiv(document.body);b.removeAttribute("id");b.style.position="absolute";b.style.border=b.style.margin=b.style.padding="0px";b.style.zIndex="101";b.style.height="0px";b=this.addDiv(b);b.id="MathJax_MSIE_Frame";window.attachEvent("onscroll",this.MoveFrame);window.attachEvent("onresize",this.MoveFrame);this.MoveFrame()}this.div=this.addDiv(b);this.div.style.display="none";this.text=this.div.appendChild(document.createTextNode(""))}return true},addDiv:function(a){var b=document.createElement("div");b.id="MathJax_Message";if(a.firstChild){a.insertBefore(b,a.firstChild)}else{a.appendChild(b)}return b},MoveFrame:function(){var a=(MathJax.Message.quirks?document.body:document.documentElement);var b=MathJax.Message.frame;b.style.left=a.scrollLeft+"px";b.style.top=a.scrollTop+"px";b.style.width=a.clientWidth+"px";b=b.firstChild;b.style.height=a.clientHeight+"px"},filterText:function(a,b){if(MathJax.Hub.config.messageStyle==="simple"){if(a.match(/^Loading /)){if(!this.loading){this.loading="Loading "}a=this.loading;this.loading+="."}else{if(a.match(/^Processing /)){if(!this.processing){this.processing="Processing "}a=this.processing;this.processing+="."}else{if(a.match(/^Typesetting /)){if(!this.typesetting){this.typesetting="Typesetting "}a=this.typesetting;this.typesetting+="."}}}}return a},Set:function(b,c,a){if(this.timer){clearTimeout(this.timer);delete this.timeout}if(c==null){c=this.log.length;this.log[c]={}}this.log[c].text=b;this.log[c].filteredText=b=this.filterText(b,c);if(typeof(this.log[c].next)==="undefined"){this.log[c].next=this.current;if(this.current!=null){this.log[this.current].prev=c}this.current=c}if(this.current===c&&MathJax.Hub.config.messageStyle!=="none"){if(this.Init()){if(this.textNodeBug){this.div.innerHTML=b}else{this.text.nodeValue=b}this.div.style.display="";if(this.status){window.status="";delete this.status}}else{window.status=b;this.status=true}}if(a){setTimeout(MathJax.Callback(["Clear",this,c]),a)}else{if(a==0){this.Clear(c,0)}}return c},Clear:function(b,a){if(this.log[b].prev!=null){this.log[this.log[b].prev].next=this.log[b].next}if(this.log[b].next!=null){this.log[this.log[b].next].prev=this.log[b].prev}if(this.current===b){this.current=this.log[b].next;if(this.text){if(this.div.parentNode==null){this.Init()}if(this.current==null){if(this.timer){clearTimeout(this.timer);delete this.timer}if(a==null){a=600}if(a===0){this.Remove()}else{this.timer=setTimeout(MathJax.Callback(["Remove",this]),a)}}else{if(MathJax.Hub.config.messageStyle!=="none"){if(this.textNodeBug){this.div.innerHTML=this.log[this.current].filteredText}else{this.text.nodeValue=this.log[this.current].filteredText}}}if(this.status){window.status="";delete this.status}}else{if(this.status){window.status=(this.current==null?"":this.log[this.current].text)}}}delete this.log[b].next;delete this.log[b].prev;delete this.log[b].filteredText},Remove:function(){this.text.nodeValue="";this.div.style.display="none"},File:function(b){var a=MathJax.Ajax.config.root;if(b.substr(0,a.length)===a){b="[MathJax]"+b.substr(a.length)}return this.Set("Loading "+b)},Log:function(){var b=[];for(var c=1,a=this.log.length;c<a;c++){b[c]=this.log[c].text}return b.join("\n")}};MathJax.Hub={config:{root:"",config:[],styleSheets:[],styles:{".MathJax_Preview":{color:"#888"}},jax:[],extensions:[],preJax:null,postJax:null,displayAlign:"center",displayIndent:"0",preRemoveClass:"MathJax_Preview",showProcessingMessages:true,messageStyle:"normal",delayStartupUntil:"none",skipStartupTypeset:false,"v1.0-compatible":true,elements:[],positionToHash:true,showMathMenu:true,showMathMenuMSIE:true,menuSettings:{zoom:"None",CTRL:false,ALT:false,CMD:false,Shift:false,discoverable:false,zscale:"200%",renderer:"",font:"Auto",context:"MathJax"},errorSettings:{message:["[Math Processing Error]"],style:{color:"#CC0000","font-style":"italic"}}},preProcessors:MathJax.Callback.Hooks(true),inputJax:{},outputJax:{order:{}},processUpdateTime:250,processUpdateDelay:10,signal:MathJax.Callback.Signal("Hub"),Config:function(a){this.Insert(this.config,a);if(this.config.Augment){this.Augment(this.config.Augment)}},CombineConfig:function(c,f){var b=this.config,g,e;c=c.split(/\./);for(var d=0,a=c.length;d<a;d++){g=c[d];if(!b[g]){b[g]={}}e=b;b=b[g]}e[g]=b=this.Insert(f,b);return b},Register:{PreProcessor:function(){MathJax.Hub.preProcessors.Add.apply(MathJax.Hub.preProcessors,arguments)},MessageHook:function(){return MathJax.Hub.signal.MessageHook.apply(MathJax.Hub.signal,arguments)},StartupHook:function(){return MathJax.Hub.Startup.signal.MessageHook.apply(MathJax.Hub.Startup.signal,arguments)},LoadHook:function(){return MathJax.Ajax.LoadHook.apply(MathJax.Ajax,arguments)}},getAllJax:function(e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax){c.push(b[d].MathJax.elementJax)}}return c},getJaxByType:function(f,e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax&&b[d].MathJax.elementJax.mimeType===f){c.push(b[d].MathJax.elementJax)}}return c},getJaxByInputType:function(f,e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax&&b[d].type&&b[d].type.replace(/ *;(.|\s)*/,"")===f){c.push(b[d].MathJax.elementJax)}}return c},getJaxFor:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a&&a.MathJax){return a.MathJax.elementJax}if(a&&a.isMathJax){while(a&&!a.jaxID){a=a.parentNode}if(a){return MathJax.OutputJax[a.jaxID].getJaxFromMath(a)}}return null},isJax:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a&&a.isMathJax){return 1}if(a&&a.tagName!=null&&a.tagName.toLowerCase()==="script"){if(a.MathJax){return(a.MathJax.state===MathJax.ElementJax.STATE.PROCESSED?1:-1)}if(a.type&&this.inputJax[a.type.replace(/ *;(.|\s)*/,"")]){return -1}}return 0},setRenderer:function(d,c){if(!d){return}if(!MathJax.OutputJax[d]){this.config.menuSettings.renderer="";var b="[MathJax]/jax/output/"+d+"/config.js";return MathJax.Ajax.Require(b,["setRenderer",this,d,c])}else{this.config.menuSettings.renderer=d;if(c==null){c="jax/mml"}var a=this.outputJax;if(a[c]&&a[c].length){if(d!==a[c][0].id){a[c].unshift(MathJax.OutputJax[d]);return this.signal.Post(["Renderer Selected",d])}}return null}},Queue:function(){return this.queue.Push.apply(this.queue,arguments)},Typeset:function(e,f){if(!MathJax.isReady){return null}var c=this.elementCallback(e,f);var b=MathJax.Callback.Queue();for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){b.Push(["PreProcess",this,c.elements[d]],["Process",this,c.elements[d]])}}return b.Push(c.callback)},PreProcess:function(e,f){var c=this.elementCallback(e,f);var b=MathJax.Callback.Queue();for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){b.Push(["Post",this.signal,["Begin PreProcess",c.elements[d]]],(arguments.callee.disabled?{}:["Execute",this.preProcessors,c.elements[d]]),["Post",this.signal,["End PreProcess",c.elements[d]]])}}return b.Push(c.callback)},Process:function(a,b){return this.takeAction("Process",a,b)},Update:function(a,b){return this.takeAction("Update",a,b)},Reprocess:function(a,b){return this.takeAction("Reprocess",a,b)},Rerender:function(a,b){return this.takeAction("Rerender",a,b)},takeAction:function(g,e,h){var c=this.elementCallback(e,h);var b=MathJax.Callback.Queue(["Clear",this.signal]);for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){var f={scripts:[],start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]};b.Push(["Post",this.signal,["Begin "+g,c.elements[d]]],["Post",this.signal,["Begin Math",c.elements[d],g]],["prepareScripts",this,g,c.elements[d],f],["Post",this.signal,["Begin Math Input",c.elements[d],g]],["processInput",this,f],["Post",this.signal,["End Math Input",c.elements[d],g]],["prepareOutput",this,f,"preProcess"],["Post",this.signal,["Begin Math Output",c.elements[d],g]],["processOutput",this,f],["Post",this.signal,["End Math Output",c.elements[d],g]],["prepareOutput",this,f,"postProcess"],["Post",this.signal,["End Math",c.elements[d],g]],["Post",this.signal,["End "+g,c.elements[d]]])}}return b.Push(c.callback)},scriptAction:{Process:function(a){},Update:function(b){var a=b.MathJax.elementJax;if(a&&a.needsUpdate()){a.Remove(true);b.MathJax.state=a.STATE.UPDATE}else{b.MathJax.state=a.STATE.PROCESSED}},Reprocess:function(b){var a=b.MathJax.elementJax;if(a){a.Remove(true);b.MathJax.state=a.STATE.UPDATE}},Rerender:function(b){var a=b.MathJax.elementJax;if(a){a.Remove(true);b.MathJax.state=a.STATE.OUTPUT}}},prepareScripts:function(h,e,g){if(arguments.callee.disabled){return}var b=this.elementScripts(e);var f=MathJax.ElementJax.STATE;for(var d=0,a=b.length;d<a;d++){var c=b[d];if(c.type&&this.inputJax[c.type.replace(/ *;(.|\n)*/,"")]){if(c.MathJax){if(c.MathJax.elementJax&&c.MathJax.elementJax.hover){MathJax.Extension.MathEvents.Hover.ClearHover(c.MathJax.elementJax)}if(c.MathJax.state!==f.PENDING){this.scriptAction[h](c)}}if(!c.MathJax){c.MathJax={state:f.PENDING}}if(c.MathJax.state!==f.PROCESSED){g.scripts.push(c)}}}},checkScriptSiblings:function(a){if(a.MathJax.checked){return}var b=this.config,f=a.previousSibling;if(f&&f.nodeName==="#text"){var d,e,c=a.nextSibling;if(c&&c.nodeName!=="#text"){c=null}if(b.preJax){if(typeof(b.preJax)==="string"){b.preJax=new RegExp(b.preJax+"$")}d=f.nodeValue.match(b.preJax)}if(b.postJax&&c){if(typeof(b.postJax)==="string"){b.postJax=new RegExp("^"+b.postJax)}e=c.nodeValue.match(b.postJax)}if(d&&(!b.postJax||e)){f.nodeValue=f.nodeValue.replace(b.preJax,(d.length>1?d[1]:""));f=null}if(e&&(!b.preJax||d)){c.nodeValue=c.nodeValue.replace(b.postJax,(e.length>1?e[1]:""))}if(f&&!f.nodeValue.match(/\S/)){f=f.previousSibling}}if(b.preRemoveClass&&f&&f.className===b.preRemoveClass){a.MathJax.preview=f}a.MathJax.checked=1},processInput:function(a){var b,i=MathJax.ElementJax.STATE;var h,e,d=a.scripts.length;try{while(a.i<d){h=a.scripts[a.i];if(!h){a.i++;continue}e=h.previousSibling;if(e&&e.className==="MathJax_Error"){e.parentNode.removeChild(e)}if(!h.MathJax||h.MathJax.state===i.PROCESSED){a.i++;continue}if(!h.MathJax.elementJax||h.MathJax.state===i.UPDATE){this.checkScriptSiblings(h);var g=h.type.replace(/ *;(.|\s)*/,"");b=this.inputJax[g].Process(h,a);if(typeof b==="function"){if(b.called){continue}this.RestartAfter(b)}b.Attach(h,this.inputJax[g].id);this.saveScript(b,a,h,i)}else{if(h.MathJax.state===i.OUTPUT){this.saveScript(h.MathJax.elementJax,a,h,i)}}a.i++;var c=new Date().getTime();if(c-a.start>this.processUpdateTime&&a.i<a.scripts.length){a.start=c;this.RestartAfter(MathJax.Callback.Delay(1))}}}catch(f){return this.processError(f,a,"Input")}if(a.scripts.length&&this.config.showProcessingMessages){MathJax.Message.Set("Processing math: 100%",0)}a.start=new Date().getTime();a.i=a.j=0;return null},saveScript:function(a,d,b,c){if(!this.outputJax[a.mimeType]){b.MathJax.state=c.UPDATE;throw Error("No output jax registered for "+a.mimeType)}a.outputJax=this.outputJax[a.mimeType][0].id;if(!d.jax[a.outputJax]){if(d.jaxIDs.length===0){d.jax[a.outputJax]=d.scripts}else{if(d.jaxIDs.length===1){d.jax[d.jaxIDs[0]]=d.scripts.slice(0,d.i)}d.jax[a.outputJax]=[]}d.jaxIDs.push(a.outputJax)}if(d.jaxIDs.length>1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.j<c.jaxIDs.length){var e=c.jaxIDs[c.j],d=MathJax.OutputJax[e];if(d[f]){try{var a=d[f](c);if(typeof a==="function"){if(a.called){continue}this.RestartAfter(a)}}catch(b){if(!b.restart){MathJax.Message.Set("Error preparing "+e+" output ("+f+")",null,600);MathJax.Hub.lastPrepError=b;c.j++}return MathJax.Callback.After(["prepareOutput",this,c,f],b.restart)}}c.j++}return null},processOutput:function(h){var b,g=MathJax.ElementJax.STATE,d,a=h.scripts.length;try{while(h.i<a){d=h.scripts[h.i];if(!d||!d.MathJax){h.i++;continue}var c=d.MathJax.elementJax;if(!c){h.i++;continue}b=MathJax.OutputJax[c.outputJax].Process(d,h);d.MathJax.state=g.PROCESSED;h.i++;if(d.MathJax.preview){d.MathJax.preview.style.display="none";d.MathJax.preview.style.visibility="hidden"}this.signal.Post(["New Math",c.inputID]);var e=new Date().getTime();if(e-h.start>this.processUpdateTime&&h.i<h.scripts.length){h.start=e;this.RestartAfter(MathJax.Callback.Delay(this.processUpdateDelay))}}}catch(f){return this.processError(f,h,"Output")}if(h.scripts.length&&this.config.showProcessingMessages){MathJax.Message.Set("Typesetting math: 100%",0);MathJax.Message.Clear(0)}h.i=h.j=0;return null},processMessage:function(d,b){var a=Math.floor(d.i/(d.scripts.length)*100);var c=(b==="Output"?"Typesetting":"Processing");if(this.config.showProcessingMessages){MathJax.Message.Set(c+" math: "+a+"%",0)}},processError:function(b,c,a){if(!b.restart){if(!this.config.errorSettings.message){throw b}this.formatError(c.scripts[c.i],b);c.i++}this.processMessage(c,a);return MathJax.Callback.After(["process"+a,this,c],b.restart)},formatError:function(a,c){var b=MathJax.HTML.Element("span",{className:"MathJax_Error"},this.config.errorSettings.message);b.jaxID="Error";if(MathJax.Extension.MathEvents){b.oncontextmenu=MathJax.Extension.MathEvents.Event.Menu;b.onmousedown=MathJax.Extension.MathEvents.Event.Mousedown}else{MathJax.Ajax.Require("[MathJax]/extensions/MathEvents.js",function(){b.oncontextmenu=MathJax.Extension.MathEvents.Event.Menu;b.onmousedown=MathJax.Extension.MathEvents.Event.Mousedown})}a.parentNode.insertBefore(b,a);if(a.MathJax.preview){a.MathJax.preview.style.display="none";a.MathJax.preview.style.visibility="hidden"}this.lastError=c},RestartAfter:function(a){throw this.Insert(Error("restart"),{restart:MathJax.Callback(a)})},elementCallback:function(c,f){if(f==null&&(c instanceof Array||typeof c==="function")){try{MathJax.Callback(c);f=c;c=null}catch(d){}}if(c==null){c=this.config.elements||[]}if(!(c instanceof Array)){c=[c]}c=[].concat(c);for(var b=0,a=c.length;b<a;b++){if(typeof(c[b])==="string"){c[b]=document.getElementById(c[b])}}if(c.length==0){c.push(document.body)}if(!f){f={}}return{elements:c,callback:f}},elementScripts:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a==null){a=document.body}if(a.tagName!=null&&a.tagName.toLowerCase()==="script"){return[a]}return a.getElementsByTagName("script")},Insert:function(c,a){for(var b in a){if(a.hasOwnProperty(b)){if(typeof a[b]==="object"&&!(a[b] instanceof Array)&&(typeof c[b]==="object"||typeof c[b]==="function")){this.Insert(c[b],a[b])}else{c[b]=a[b]}}}return c}};MathJax.Hub.Insert(MathJax.Hub.config.styles,MathJax.Message.styles);MathJax.Hub.Insert(MathJax.Hub.config.styles,{".MathJax_Error":MathJax.Hub.config.errorSettings.style});MathJax.Extension={};MathJax.Hub.Configured=MathJax.Callback({});MathJax.Hub.Startup={script:"",queue:MathJax.Callback.Queue(),signal:MathJax.Callback.Signal("Startup"),params:{},Config:function(){this.queue.Push(["Post",this.signal,"Begin Config"]);var b=MathJax.HTML.Cookie.Get("user");if(b.URL||b.Config){if(confirm("MathJax has found a user-configuration cookie that includes code to be run. Do you want to run it?\n\n(You should press Cancel unless you set up the cookie yourself.)")){if(b.URL){this.queue.Push(["Require",MathJax.Ajax,b.URL])}if(b.Config){this.queue.Push(new Function(b.Config))}}else{MathJax.HTML.Cookie.Set("user",{})}}if(this.params.config){var d=this.params.config.split(/,/);for(var c=0,a=d.length;c<a;c++){if(!d[c].match(/\.js$/)){d[c]+=".js"}this.queue.Push(["Require",MathJax.Ajax,this.URL("config",d[c])])}}if(this.script.match(/\S/)){this.queue.Push(this.script+";\n1;")}this.queue.Push(["ConfigDelay",this],["ConfigBlocks",this],["ConfigDefault",this],[function(e){return e.loadArray(MathJax.Hub.config.config,"config",null,true)},this],["Post",this.signal,"End Config"])},ConfigDelay:function(){var a=this.params.delayStartupUntil||MathJax.Hub.config.delayStartupUntil;if(a==="onload"){return this.onload}if(a==="configured"){return MathJax.Hub.Configured}return a},ConfigBlocks:function(){var c=document.getElementsByTagName("script");var f=null,b=MathJax.Callback.Queue();for(var d=0,a=c.length;d<a;d++){var e=String(c[d].type).replace(/ /g,"");if(e.match(/^text\/x-mathjax-config(;.*)?$/)&&!e.match(/;executed=true/)){c[d].type+=";executed=true";f=b.Push(c[d].innerHTML+";\n1;")}}return f},ConfigDefault:function(){var a=MathJax.Hub.config;if(a["v1.0-compatible"]&&(a.jax||[]).length===0&&!this.params.config&&(a.config||[]).length===0){return MathJax.Ajax.Require(this.URL("extensions","v1.0-warning.js"))}},Cookie:function(){return this.queue.Push(["Post",this.signal,"Begin Cookie"],["Get",MathJax.HTML.Cookie,"menu",MathJax.Hub.config.menuSettings],[function(d){var f=d.menuSettings.renderer,b=d.jax;if(f){var c="output/"+f;b.sort();for(var e=0,a=b.length;e<a;e++){if(b[e].substr(0,7)==="output/"){break}}if(e==a-1){b.pop()}else{while(e<a){if(b[e]===c){b.splice(e,1);break}e++}}b.unshift(c)}},MathJax.Hub.config],["Post",this.signal,"End Cookie"])},Styles:function(){return this.queue.Push(["Post",this.signal,"Begin Styles"],["loadArray",this,MathJax.Hub.config.styleSheets,"config"],["Styles",MathJax.Ajax,MathJax.Hub.config.styles],["Post",this.signal,"End Styles"])},Jax:function(){var e=MathJax.Hub.config,c=MathJax.Hub.outputJax;for(var f=0,b=e.jax.length,d=0;f<b;f++){if(e.jax[f].substr(0,7)==="output/"){c.order[e.jax[f].substr(7)]=d;d++}}var a=MathJax.Callback.Queue();return a.Push(["Post",this.signal,"Begin Jax"],["loadArray",this,e.jax,"jax","config.js"],["Post",this.signal,"End Jax"])},Extensions:function(){var a=MathJax.Callback.Queue();return a.Push(["Post",this.signal,"Begin Extensions"],["loadArray",this,MathJax.Hub.config.extensions,"extensions"],["Post",this.signal,"End Extensions"])},Message:function(){MathJax.Message.Init(true)},Menu:function(){var b=MathJax.Hub.config.menuSettings,a=MathJax.Hub.outputJax,d;for(var c in a){if(a.hasOwnProperty(c)){if(a[c].length){d=a[c];break}}}if(d&&d.length){if(b.renderer&&b.renderer!==d[0].id){d.unshift(MathJax.OutputJax[b.renderer])}b.renderer=d[0].id}},Hash:function(){if(MathJax.Hub.config.positionToHash&&document.location.hash){setTimeout("document.location = document.location.hash",1)}},MenuZoom:function(){if(!MathJax.Extension.MathMenu){setTimeout(MathJax.Callback(["Require",MathJax.Ajax,"[MathJax]/extensions/MathMenu.js"]),1000)}if(!MathJax.Extension.MathZoom){setTimeout(MathJax.Callback(["Require",MathJax.Ajax,"[MathJax]/extensions/MathZoom.js"]),2000)}},onLoad:function(a){var b=this.onload=MathJax.Callback(function(){MathJax.Hub.Startup.signal.Post("onLoad")});if(document.body&&document.readyState&&document.readyState!=="loading"){return[b]}if(window.addEventListener){window.addEventListener("load",b,false);if(!this.params.noDOMContentEvent){window.addEventListener("DOMContentLoaded",b,false)}}else{if(window.attachEvent){window.attachEvent("onload",b)}else{window.onload=b}}return b},Typeset:function(a,b){if(MathJax.Hub.config.skipStartupTypeset){return function(){}}return this.queue.Push(["Post",this.signal,"Begin Typeset"],["Typeset",MathJax.Hub,a,b],["Post",this.signal,"End Typeset"])},URL:function(b,a){if(!a.match(/^([a-z]+:\/\/|\[|\/)/)){a="[MathJax]/"+b+"/"+a}return a},loadArray:function(b,f,c,a){if(b){if(!(b instanceof Array)){b=[b]}if(b.length){var h=MathJax.Callback.Queue(),j={},e;for(var g=0,d=b.length;g<d;g++){e=this.URL(f,b[g]);if(c){e+="/"+c}if(a){h.Push(["Require",MathJax.Ajax,e,j])}else{h.Push(MathJax.Ajax.Require(e,j))}}return h.Push({})}}return null}};(function(d){var b=window[d],e="["+d+"]";var c=b.Hub,a=b.Ajax,f=b.Callback;var g=MathJax.Object.Subclass({JAXFILE:"jax.js",require:null,config:{},Init:function(i,h){if(arguments.length===0){return this}return(this.constructor.Subclass(i,h))()},Augment:function(k,j){var i=this.constructor,h={};if(k!=null){for(var l in k){if(k.hasOwnProperty(l)){if(typeof k[l]==="function"){i.protoFunction(l,k[l])}else{h[l]=k[l]}}}if(k.toString!==i.prototype.toString&&k.toString!=={}.toString){i.protoFunction("toString",k.toString)}}c.Insert(i.prototype,h);i.Augment(null,j);return this},preProcess:function(i){var j,h=this.directory+"/"+this.JAXFILE;this.constructor.prototype.preProcess=function(k){if(!j.called){return j}throw Error(h+" failed to load properly")};j=a.Require(h);return j},Translate:function(h){throw Error(this.directory+"/"+this.JAXFILE+" failed to redefine the Translate() method")},Register:function(h){},Config:function(){this.config=c.CombineConfig(this.id,this.config);if(this.config.Augment){this.Augment(this.config.Augment)}},Startup:function(){},loadComplete:function(i){if(i==="config.js"){return a.loadComplete(this.directory+"/"+i)}else{var h=f.Queue();h.Push(c.Register.StartupHook("End Config",{}),["Post",c.Startup.signal,this.id+" Jax Config"],["Config",this],["Post",c.Startup.signal,this.id+" Jax Require"],[function(j){return MathJax.Hub.Startup.loadArray(j.require,this.directory)},this],[function(j,k){return MathJax.Hub.Startup.loadArray(j.extensions,"extensions/"+k)},this.config||{},this.id],["Post",c.Startup.signal,this.id+" Jax Startup"],["Startup",this],["Post",c.Startup.signal,this.id+" Jax Ready"],[function(j){j.preProcess=j.preTranslate;j.Process=j.Translate;j.postProcess=j.postTranslate},this.constructor.prototype]);return h.Push(["loadComplete",a,this.directory+"/"+i])}}},{id:"Jax",version:"2.0",directory:e+"/jax",extensionDir:e+"/extensions"});b.InputJax=g.Subclass({elementJax:"mml",Process:function(o){var j=f.Queue();var k=this.elementJax;if(!(k instanceof Array)){k=[k]}for(var n=0,h=k.length;n<h;n++){var l=b.ElementJax.directory+"/"+k[n]+"/"+this.JAXFILE;if(!this.require){this.require=[]}else{if(!(this.require instanceof Array)){this.require=[this.require]}}this.require.push(l);j.Push(a.Require(l))}var p=j.Push(a.Require(this.directory+"/"+this.JAXFILE));if(!p.called){this.constructor.prototype.Process=function(){return p}}k=c.outputJax["jax/"+k[0]];if(k){j.Push(a.Require(k[0].directory+"/"+this.JAXFILE))}return j.Push({})},needsUpdate:function(h){var i=h.SourceElement();return(h.originalText!==(i.text==""?i.innerHTML:i.text))},Register:function(h){if(!c.inputJax){c.inputJax={}}c.inputJax[h]=this}},{id:"InputJax",version:"2.0",directory:g.directory+"/input",extensionDir:g.extensionDir});b.OutputJax=g.Subclass({Register:function(i){var h=c.outputJax;if(!h[i]){h[i]=[]}if(h[i].length&&(this.id===c.config.menuSettings.renderer||(h.order[this.id]||0)<(h.order[h[i][0].id]||0))){h[i].unshift(this)}else{h[i].push(this)}if(!this.require){this.require=[]}else{if(!(this.require instanceof Array)){this.require=[this.require]}}this.require.push(b.ElementJax.directory+"/"+(i.split(/\//)[1])+"/"+this.JAXFILE)},Remove:function(h){}},{id:"OutputJax",version:"2.0",directory:g.directory+"/output",extensionDir:g.extensionDir,fontDir:e+(b.isPacked?"":"/..")+"/fonts",imageDir:e+(b.isPacked?"":"/..")+"/images"});b.ElementJax=g.Subclass({Init:function(i,h){return this.constructor.Subclass(i,h)},inputJax:null,outputJax:null,inputID:null,originalText:"",mimeType:"",Text:function(i,j){var h=this.SourceElement();b.HTML.setScript(h,i);h.MathJax.state=this.STATE.UPDATE;return c.Update(h,j)},Reprocess:function(i){var h=this.SourceElement();h.MathJax.state=this.STATE.UPDATE;return c.Reprocess(h,i)},Update:function(h){return this.Rerender(h)},Rerender:function(i){var h=this.SourceElement();h.MathJax.state=this.STATE.OUTPUT;return c.Process(h,i)},Remove:function(h){if(this.hover){this.hover.clear(this)}b.OutputJax[this.outputJax].Remove(this);if(!h){c.signal.Post(["Remove Math",this.inputID]);this.Detach()}},needsUpdate:function(){return b.InputJax[this.inputJax].needsUpdate(this)},SourceElement:function(){return document.getElementById(this.inputID)},Attach:function(i,j){var h=i.MathJax.elementJax;if(i.MathJax.state===this.STATE.UPDATE){h.Clone(this)}else{h=i.MathJax.elementJax=this;if(i.id){this.inputID=i.id}else{i.id=this.inputID=b.ElementJax.GetID();this.newID=1}}h.originalText=(i.text==""?i.innerHTML:i.text);h.inputJax=j;if(h.root){h.root.inputID=h.inputID}return h},Detach:function(){var h=this.SourceElement();if(!h){return}try{delete h.MathJax}catch(i){h.MathJax=null}if(this.newID){h.id=""}},Clone:function(h){var i;for(i in this){if(!this.hasOwnProperty(i)){continue}if(typeof(h[i])==="undefined"&&i!=="newID"){delete this[i]}}for(i in h){if(!h.hasOwnProperty(i)){continue}if(typeof(this[i])==="undefined"||(this[i]!==h[i]&&i!=="inputID")){this[i]=h[i]}}}},{id:"ElementJax",version:"2.0",directory:g.directory+"/element",extensionDir:g.extensionDir,ID:0,STATE:{PENDING:1,PROCESSED:2,UPDATE:3,OUTPUT:4},GetID:function(){this.ID++;return"MathJax-Element-"+this.ID},Subclass:function(){var h=g.Subclass.apply(this,arguments);h.loadComplete=this.prototype.loadComplete;return h}});b.ElementJax.prototype.STATE=b.ElementJax.STATE;b.OutputJax.Error={id:"Error",version:"2.0",config:{},ContextMenu:function(){return b.Extension.MathEvents.Event.ContextMenu.apply(b.Extension.MathEvents.Event,arguments)},Mousedown:function(){return b.Extension.MathEvents.Event.AltContextMenu.apply(b.Extension.MathEvents.Event,arguments)},getJaxFromMath:function(){return{inputJax:"Error",outputJax:"Error",originalText:"Math Processing Error"}}};b.InputJax.Error={id:"Error",version:"2.0",config:{},sourceMenuTitle:"Error Message"}})("MathJax");(function(l){var f=window[l];if(!f){f=window[l]={}}var c=f.Hub;var q=c.Startup;var u=c.config;var e=document.getElementsByTagName("head")[0];if(!e){e=document.childNodes[0]}var b=(document.documentElement||document).getElementsByTagName("script");var d=new RegExp("(^|/)"+l+"\\.js(\\?.*)?$");for(var o=b.length-1;o>=0;o--){if(b[o].src.match(d)){q.script=b[o].innerHTML;if(RegExp.$2){var r=RegExp.$2.substr(1).split(/\&/);for(var n=0,h=r.length;n<h;n++){var k=r[n].match(/(.*)=(.*)/);if(k){q.params[unescape(k[1])]=unescape(k[2])}}}u.root=b[o].src.replace(/(^|\/)[^\/]*(\?.*)?$/,"");break}}f.Ajax.config=u;var a={isMac:(navigator.platform.substr(0,3)==="Mac"),isPC:(navigator.platform.substr(0,3)==="Win"),isMSIE:(window.ActiveXObject!=null&&window.clipboardData!=null),isFirefox:(window.netscape!=null&&document.ATTRIBUTE_NODE!=null&&!window.opera),isSafari:(navigator.userAgent.match(/ (Apple)?WebKit\//)!=null&&(!window.chrome||window.chrome.loadTimes==null)),isChrome:(window.chrome!=null&&window.chrome.loadTimes!=null),isOpera:(window.opera!=null&&window.opera.version!=null),isKonqueror:(window.hasOwnProperty&&window.hasOwnProperty("konqueror")&&navigator.vendor=="KDE"),versionAtLeast:function(x){var w=(this.version).split(".");x=(new String(x)).split(".");for(var y=0,j=x.length;y<j;y++){if(w[y]!=x[y]){return parseInt(w[y]||"0")>=parseInt(x[y])}}return true},Select:function(j){var i=j[c.Browser];if(i){return i(c.Browser)}return null}};var g=navigator.userAgent.replace(/^Mozilla\/(\d+\.)+\d+ /,"").replace(/[a-z][-a-z0-9._: ]+\/\d+[^ ]*-[^ ]*\.([a-z][a-z])?\d+ /i,"").replace(/Gentoo |Ubuntu\/(\d+\.)*\d+ (\([^)]*\) )?/,"");c.Browser=c.Insert(c.Insert(new String("Unknown"),{version:"0.0"}),a);for(var t in a){if(a.hasOwnProperty(t)){if(a[t]&&t.substr(0,2)==="is"){t=t.slice(2);if(t==="Mac"||t==="PC"){continue}c.Browser=c.Insert(new String(t),a);var p=new RegExp(".*(Version)/((?:\\d+\\.)+\\d+)|.*("+t+")"+(t=="MSIE"?" ":"/")+"((?:\\d+\\.)*\\d+)|(?:^|\\(| )([a-z][-a-z0-9._: ]+|(?:Apple)?WebKit)/((?:\\d+\\.)+\\d+)");var s=p.exec(g)||["","","","unknown","0.0"];c.Browser.name=(s[1]=="Version"?t:(s[3]||s[5]));c.Browser.version=s[2]||s[4]||s[6];break}}}c.Browser.Select({Safari:function(j){var i=parseInt((String(j.version).split("."))[0]);if(i>85){j.webkit=j.version}if(i>=534){j.version="5.1"}else{if(i>=533){j.version="5.0"}else{if(i>=526){j.version="4.0"}else{if(i>=525){j.version="3.1"}else{if(i>500){j.version="3.0"}else{if(i>400){j.version="2.0"}else{if(i>85){j.version="1.0"}}}}}}}j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);j.noContextMenu=j.isMobile},Firefox:function(j){if((j.version==="0.0"||navigator.userAgent.match(/Firefox/)==null)&&navigator.product==="Gecko"){var m=navigator.userAgent.match(/[\/ ]rv:(\d+\.\d.*?)[\) ]/);if(m){j.version=m[1]}else{var i=(navigator.buildID||navigator.productSub||"0").substr(0,8);if(i>="20111220"){j.version="9.0"}else{if(i>="20111120"){j.version="8.0"}else{if(i>="20110927"){j.version="7.0"}else{if(i>="20110816"){j.version="6.0"}else{if(i>="20110621"){j.version="5.0"}else{if(i>="20110320"){j.version="4.0"}else{if(i>="20100121"){j.version="3.6"}else{if(i>="20090630"){j.version="3.5"}else{if(i>="20080617"){j.version="3.0"}else{if(i>="20061024"){j.version="2.0"}}}}}}}}}}}}j.isMobile=(navigator.appVersion.match(/Android/i)!=null||navigator.userAgent.match(/ Fennec\//)!=null)},Opera:function(i){i.version=opera.version()},MSIE:function(j){j.isIE9=!!(document.documentMode&&(window.performance||window.msPerformance));MathJax.HTML.setScriptBug=!j.isIE9||document.documentMode<9;var v=false;try{new ActiveXObject("MathPlayer.Factory.1");v=true}catch(m){}if(v){var i=document.createElement("object");i.id="mathplayer";i.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(i);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");j.hasMathPlayer=true;if(document.readyState&&(document.readyState==="loading"||document.readyState==="interactive")){document.write('<?import namespace="m" implementation="#MathPlayer">');j.mpImported=true}}}});c.Browser.Select(MathJax.Message.browsers);c.queue=f.Callback.Queue();c.queue.Push(["Post",q.signal,"Begin"],["Config",q],["Cookie",q],["Styles",q],["Message",q],function(){var i=f.Callback.Queue(q.Jax(),q.Extensions());return i.Push({})},["Menu",q],q.onLoad(),function(){MathJax.isReady=true},["Typeset",q],["Hash",q],["MenuZoom",q],["Post",q.signal,"End"])})("MathJax")}}; +if(document.getElementById&&document.childNodes&&document.createElement){if(!window.MathJax){window.MathJax={}}if(!MathJax.Hub){MathJax.version="2.0";MathJax.fileversion="2.0";(function(d){var b=window[d];if(!b){b=window[d]={}}var f=[];var c=function(g){var h=g.constructor;if(!h){h=new Function("")}for(var i in g){if(i!=="constructor"&&g.hasOwnProperty(i)){h[i]=g[i]}}return h};var a=function(){return new Function("return arguments.callee.Init.call(this,arguments)")};var e=a();e.prototype={bug_test:1};if(!e.prototype.bug_test){a=function(){return function(){return arguments.callee.Init.call(this,arguments)}}}b.Object=c({constructor:a(),Subclass:function(g,i){var h=a();h.SUPER=this;h.Init=this.Init;h.Subclass=this.Subclass;h.Augment=this.Augment;h.protoFunction=this.protoFunction;h.can=this.can;h.has=this.has;h.isa=this.isa;h.prototype=new this(f);h.prototype.constructor=h;h.Augment(g,i);return h},Init:function(g){var h=this;if(g.length===1&&g[0]===f){return h}if(!(h instanceof g.callee)){h=new g.callee(f)}return h.Init.apply(h,g)||h},Augment:function(g,h){var i;if(g!=null){for(i in g){if(g.hasOwnProperty(i)){this.protoFunction(i,g[i])}}if(g.toString!==this.prototype.toString&&g.toString!=={}.toString){this.protoFunction("toString",g.toString)}}if(h!=null){for(i in h){if(h.hasOwnProperty(i)){this[i]=h[i]}}}return this},protoFunction:function(h,g){this.prototype[h]=g;if(typeof g==="function"){g.SUPER=this.SUPER.prototype}},prototype:{Init:function(){},SUPER:function(g){return g.callee.SUPER},can:function(g){return typeof(this[g])==="function"},has:function(g){return typeof(this[g])!=="undefined"},isa:function(g){return(g instanceof Object)&&(this instanceof g)}},can:function(g){return this.prototype.can.call(this,g)},has:function(g){return this.prototype.has.call(this,g)},isa:function(h){var g=this;while(g){if(g===h){return true}else{g=g.SUPER}}return false},SimpleSUPER:c({constructor:function(g){return this.SimpleSUPER.define(g)},define:function(g){var i={};if(g!=null){for(var h in g){if(g.hasOwnProperty(h)){i[h]=this.wrap(h,g[h])}}if(g.toString!==this.prototype.toString&&g.toString!=={}.toString){i.toString=this.wrap("toString",g.toString)}}return i},wrap:function(i,h){if(typeof(h)==="function"&&h.toString().match(/\.\s*SUPER\s*\(/)){var g=new Function(this.wrapper);g.label=i;g.original=h;h=g;g.toString=this.stringify}return h},wrapper:function(){var h=arguments.callee;this.SUPER=h.SUPER[h.label];try{var g=h.original.apply(this,arguments)}catch(i){delete this.SUPER;throw i}delete this.SUPER;return g}.toString().replace(/^\s*function \(\)\s*\{\s*/i,"").replace(/\s*\}\s*$/i,""),toString:function(){return this.original.toString.apply(this.original,arguments)}})})})("MathJax");(function(BASENAME){var BASE=window[BASENAME];if(!BASE){BASE=window[BASENAME]={}}var CALLBACK=function(data){var cb=new Function("return arguments.callee.execute.apply(arguments.callee,arguments)");for(var id in CALLBACK.prototype){if(CALLBACK.prototype.hasOwnProperty(id)){if(typeof(data[id])!=="undefined"){cb[id]=data[id]}else{cb[id]=CALLBACK.prototype[id]}}}cb.toString=CALLBACK.prototype.toString;return cb};CALLBACK.prototype={isCallback:true,hook:function(){},data:[],object:window,execute:function(){if(!this.called||this.autoReset){this.called=!this.autoReset;return this.hook.apply(this.object,this.data.concat([].slice.call(arguments,0)))}},reset:function(){delete this.called},toString:function(){return this.hook.toString.apply(this.hook,arguments)}};var ISCALLBACK=function(f){return(typeof(f)==="function"&&f.isCallback)};var EVAL=function(code){return eval.call(window,code)};EVAL("var __TeSt_VaR__ = 1");if(window.__TeSt_VaR__){try{delete window.__TeSt_VaR__}catch(error){window.__TeSt_VaR__=null}}else{if(window.execScript){EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";window.execScript(code);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}else{EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";var head=(document.getElementsByTagName("head"))[0];if(!head){head=document.body}var script=document.createElement("script");script.appendChild(document.createTextNode(code));head.appendChild(script);head.removeChild(script);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}}var USING=function(args,i){if(arguments.length>1){if(arguments.length===2&&!(typeof arguments[0]==="function")&&arguments[0] instanceof Object&&typeof arguments[1]==="number"){args=[].slice.call(args,i)}else{args=[].slice.call(arguments,0)}}if(args instanceof Array&&args.length===1){args=args[0]}if(typeof args==="function"){if(args.execute===CALLBACK.prototype.execute){return args}return CALLBACK({hook:args})}else{if(args instanceof Array){if(typeof(args[0])==="string"&&args[1] instanceof Object&&typeof args[1][args[0]]==="function"){return CALLBACK({hook:args[1][args[0]],object:args[1],data:args.slice(2)})}else{if(typeof args[0]==="function"){return CALLBACK({hook:args[0],data:args.slice(1)})}else{if(typeof args[1]==="function"){return CALLBACK({hook:args[1],object:args[0],data:args.slice(2)})}}}}else{if(typeof(args)==="string"){return CALLBACK({hook:EVAL,data:[args]})}else{if(args instanceof Object){return CALLBACK(args)}else{if(typeof(args)==="undefined"){return CALLBACK({})}}}}}throw Error("Can't make callback from given data")};var DELAY=function(time,callback){callback=USING(callback);callback.timeout=setTimeout(callback,time);return callback};var WAITFOR=function(callback,signal){callback=USING(callback);if(!callback.called){WAITSIGNAL(callback,signal);signal.pending++}};var WAITEXECUTE=function(){var signals=this.signal;delete this.signal;this.execute=this.oldExecute;delete this.oldExecute;var result=this.execute.apply(this,arguments);if(ISCALLBACK(result)&&!result.called){WAITSIGNAL(result,signals)}else{for(var i=0,m=signals.length;i<m;i++){signals[i].pending--;if(signals[i].pending<=0){signals[i].call()}}}};var WAITSIGNAL=function(callback,signals){if(!(signals instanceof Array)){signals=[signals]}if(!callback.signal){callback.oldExecute=callback.execute;callback.execute=WAITEXECUTE;callback.signal=signals}else{if(signals.length===1){callback.signal.push(signals[0])}else{callback.signal=callback.signal.concat(signals)}}};var AFTER=function(callback){callback=USING(callback);callback.pending=0;for(var i=1,m=arguments.length;i<m;i++){if(arguments[i]){WAITFOR(arguments[i],callback)}}if(callback.pending===0){var result=callback();if(ISCALLBACK(result)){callback=result}}return callback};var HOOKS=MathJax.Object.Subclass({Init:function(reset){this.hooks=[];this.reset=reset},Add:function(hook,priority){if(priority==null){priority=10}if(!ISCALLBACK(hook)){hook=USING(hook)}hook.priority=priority;var i=this.hooks.length;while(i>0&&priority<this.hooks[i-1].priority){i--}this.hooks.splice(i,0,hook);return hook},Remove:function(hook){for(var i=0,m=this.hooks.length;i<m;i++){if(this.hooks[i]===hook){this.hooks.splice(i,1);return}}},Execute:function(){var callbacks=[{}];for(var i=0,m=this.hooks.length;i<m;i++){if(this.reset){this.hooks[i].reset()}var result=this.hooks[i].apply(window,arguments);if(ISCALLBACK(result)&&!result.called){callbacks.push(result)}}if(callbacks.length===1){return null}if(callbacks.length===2){return callbacks[1]}return AFTER.apply({},callbacks)}});var EXECUTEHOOKS=function(hooks,data,reset){if(!hooks){return null}if(!(hooks instanceof Array)){hooks=[hooks]}if(!(data instanceof Array)){data=(data==null?[]:[data])}var handler=HOOKS(reset);for(var i=0,m=hooks.length;i<m;i++){handler.Add(hooks[i])}return handler.Execute.apply(handler,data)};var QUEUE=BASE.Object.Subclass({Init:function(){this.pending=0;this.running=0;this.queue=[];this.Push.apply(this,arguments)},Push:function(){var callback;for(var i=0,m=arguments.length;i<m;i++){callback=USING(arguments[i]);if(callback===arguments[i]&&!callback.called){callback=USING(["wait",this,callback])}this.queue.push(callback)}if(!this.running&&!this.pending){this.Process()}return callback},Process:function(queue){while(!this.running&&!this.pending&&this.queue.length){var callback=this.queue[0];queue=this.queue.slice(1);this.queue=[];this.Suspend();var result=callback();this.Resume();if(queue.length){this.queue=queue.concat(this.queue)}if(ISCALLBACK(result)&&!result.called){WAITFOR(result,this)}}},Suspend:function(){this.running++},Resume:function(){if(this.running){this.running--}},call:function(){this.Process.apply(this,arguments)},wait:function(callback){return callback}});var SIGNAL=QUEUE.Subclass({Init:function(name){QUEUE.prototype.Init.call(this);this.name=name;this.posted=[];this.listeners=HOOKS(true)},Post:function(message,callback,forget){callback=USING(callback);if(this.posting||this.pending){this.Push(["Post",this,message,callback,forget])}else{this.callback=callback;callback.reset();if(!forget){this.posted.push(message)}this.Suspend();this.posting=true;var result=this.listeners.Execute(message);if(ISCALLBACK(result)&&!result.called){WAITFOR(result,this)}this.Resume();delete this.posting;if(!this.pending){this.call()}}return callback},Clear:function(callback){callback=USING(callback);if(this.posting||this.pending){callback=this.Push(["Clear",this,callback])}else{this.posted=[];callback()}return callback},call:function(){this.callback(this);this.Process()},Interest:function(callback,ignorePast,priority){callback=USING(callback);this.listeners.Add(callback,priority);if(!ignorePast){for(var i=0,m=this.posted.length;i<m;i++){callback.reset();var result=callback(this.posted[i]);if(ISCALLBACK(result)&&i===this.posted.length-1){WAITFOR(result,this)}}}return callback},NoInterest:function(callback){this.listeners.Remove(callback)},MessageHook:function(msg,callback,priority){callback=USING(callback);if(!this.hooks){this.hooks={};this.Interest(["ExecuteHooks",this])}if(!this.hooks[msg]){this.hooks[msg]=HOOKS(true)}this.hooks[msg].Add(callback,priority);for(var i=0,m=this.posted.length;i<m;i++){if(this.posted[i]==msg){callback.reset();callback(this.posted[i])}}return callback},ExecuteHooks:function(msg,more){var type=((msg instanceof Array)?msg[0]:msg);if(!this.hooks[type]){return null}return this.hooks[type].Execute(msg)}},{signals:{},find:function(name){if(!SIGNAL.signals[name]){SIGNAL.signals[name]=new SIGNAL(name)}return SIGNAL.signals[name]}});BASE.Callback=BASE.CallBack=USING;BASE.Callback.Delay=DELAY;BASE.Callback.After=AFTER;BASE.Callback.Queue=QUEUE;BASE.Callback.Signal=SIGNAL.find;BASE.Callback.Hooks=HOOKS;BASE.Callback.ExecuteHooks=EXECUTEHOOKS})("MathJax");(function(d){var a=window[d];if(!a){a=window[d]={}}var c=(navigator.vendor==="Apple Computer, Inc."&&typeof navigator.vendorSub==="undefined");var f=0;var g=function(h){if(document.styleSheets&&document.styleSheets.length>f){f=document.styleSheets.length}if(!h){h=(document.getElementsByTagName("head"))[0];if(!h){h=document.body}}return h};var e=[];var b=function(){for(var j=0,h=e.length;j<h;j++){a.Ajax.head.removeChild(e[j])}e=[]};a.Ajax={loaded:{},loading:{},loadHooks:{},timeout:15*1000,styleDelay:1,config:{root:""},STATUS:{OK:1,ERROR:-1},rootPattern:new RegExp("^\\["+d+"\\]"),fileURL:function(h){return h.replace(this.rootPattern,this.config.root)},Require:function(j,m){m=a.Callback(m);var k;if(j instanceof Object){for(var h in j){}k=h.toUpperCase();j=j[h]}else{k=j.split(/\./).pop().toUpperCase()}j=this.fileURL(j);if(this.loaded[j]){m(this.loaded[j])}else{var l={};l[k]=j;this.Load(l,m)}return m},Load:function(j,l){l=a.Callback(l);var k;if(j instanceof Object){for(var h in j){}k=h.toUpperCase();j=j[h]}else{k=j.split(/\./).pop().toUpperCase()}j=this.fileURL(j);if(this.loading[j]){this.addHook(j,l)}else{this.head=g(this.head);if(this.loader[k]){this.loader[k].call(this,j,l)}else{throw Error("Can't load files of type "+k)}}return l},LoadHook:function(k,l,j){l=a.Callback(l);if(k instanceof Object){for(var h in k){k=k[h]}}k=this.fileURL(k);if(this.loaded[k]){l(this.loaded[k])}else{this.addHook(k,l,j)}return l},addHook:function(i,j,h){if(!this.loadHooks[i]){this.loadHooks[i]=MathJax.Callback.Hooks()}this.loadHooks[i].Add(j,h)},Preloading:function(){for(var k=0,h=arguments.length;k<h;k++){var j=this.fileURL(arguments[k]);if(!this.loading[j]){this.loading[j]={preloaded:true}}}},loader:{JS:function(i,k){var h=document.createElement("script");var j=a.Callback(["loadTimeout",this,i]);this.loading[i]={callback:k,message:a.Message.File(i),timeout:setTimeout(j,this.timeout),status:this.STATUS.OK,script:h};h.onerror=j;h.type="text/javascript";h.src=i;this.head.appendChild(h)},CSS:function(h,j){var i=document.createElement("link");i.rel="stylesheet";i.type="text/css";i.href=h;this.loading[h]={callback:j,message:a.Message.File(h),status:this.STATUS.OK};this.head.appendChild(i);this.timer.create.call(this,[this.timer.file,h],i)}},timer:{create:function(i,h){i=a.Callback(i);if(h.nodeName==="STYLE"&&h.styleSheet&&typeof(h.styleSheet.cssText)!=="undefined"){i(this.STATUS.OK)}else{if(window.chrome&&typeof(window.sessionStorage)!=="undefined"&&h.nodeName==="STYLE"){i(this.STATUS.OK)}else{if(c){this.timer.start(this,[this.timer.checkSafari2,f++,i],this.styleDelay)}else{this.timer.start(this,[this.timer.checkLength,h,i],this.styleDelay)}}}return i},start:function(i,h,j,k){h=a.Callback(h);h.execute=this.execute;h.time=this.time;h.STATUS=i.STATUS;h.timeout=k||i.timeout;h.delay=h.total=0;if(j){setTimeout(h,j)}else{h()}},time:function(h){this.total+=this.delay;this.delay=Math.floor(this.delay*1.05+5);if(this.total>=this.timeout){h(this.STATUS.ERROR);return 1}return 0},file:function(i,h){if(h<0){a.Ajax.loadTimeout(i)}else{a.Ajax.loadComplete(i)}},execute:function(){this.hook.call(this.object,this,this.data[0],this.data[1])},checkSafari2:function(h,i,j){if(h.time(j)){return}if(document.styleSheets.length>i&&document.styleSheets[i].cssRules&&document.styleSheets[i].cssRules.length){j(h.STATUS.OK)}else{setTimeout(h,h.delay)}},checkLength:function(h,k,m){if(h.time(m)){return}var l=0;var i=(k.sheet||k.styleSheet);try{if((i.cssRules||i.rules||[]).length>0){l=1}}catch(j){if(j.message.match(/protected variable|restricted URI/)){l=1}else{if(j.message.match(/Security error/)){l=1}}}if(l){setTimeout(a.Callback([m,h.STATUS.OK]),0)}else{setTimeout(h,h.delay)}}},loadComplete:function(h){h=this.fileURL(h);var i=this.loading[h];if(i&&!i.preloaded){a.Message.Clear(i.message);clearTimeout(i.timeout);if(i.script){if(e.length===0){setTimeout(b,0)}e.push(i.script)}this.loaded[h]=i.status;delete this.loading[h];this.addHook(h,i.callback)}else{this.loaded[h]=this.STATUS.OK;i={status:this.STATUS.OK}}if(!this.loadHooks[h]){return null}return this.loadHooks[h].Execute(i.status)},loadTimeout:function(h){if(this.loading[h].timeout){clearTimeout(this.loading[h].timeout)}this.loading[h].status=this.STATUS.ERROR;this.loadError(h);this.loadComplete(h)},loadError:function(h){a.Message.Set("File failed to load: "+h,null,2000);a.Hub.signal.Post(["file load error",h])},Styles:function(j,k){var h=this.StyleString(j);if(h===""){k=a.Callback(k);k()}else{var i=document.createElement("style");i.type="text/css";this.head=g(this.head);this.head.appendChild(i);if(i.styleSheet&&typeof(i.styleSheet.cssText)!=="undefined"){i.styleSheet.cssText=h}else{i.appendChild(document.createTextNode(h))}k=this.timer.create.call(this,k,i)}return k},StyleString:function(m){if(typeof(m)==="string"){return m}var j="",n,l;for(n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="string"){j+=n+" {"+m[n]+"}\n"}else{if(m[n] instanceof Array){for(var k=0;k<m[n].length;k++){l={};l[n]=m[n][k];j+=this.StyleString(l)}}else{if(n.substr(0,6)==="@media"){j+=n+" {"+this.StyleString(m[n])+"}\n"}else{if(m[n]!=null){l=[];for(var h in m[n]){if(m[n].hasOwnProperty(h)){if(m[n][h]!=null){l[l.length]=h+": "+m[n][h]}}}j+=n+" {"+l.join("; ")+"}\n"}}}}}}return j}}})("MathJax");MathJax.HTML={Element:function(c,e,d){var f=document.createElement(c);if(e){if(e.style){var b=e.style;e.style={};for(var g in b){if(b.hasOwnProperty(g)){e.style[g.replace(/-([a-z])/g,this.ucMatch)]=b[g]}}}MathJax.Hub.Insert(f,e)}if(d){for(var a=0;a<d.length;a++){if(d[a] instanceof Array){f.appendChild(this.Element(d[a][0],d[a][1],d[a][2]))}else{f.appendChild(document.createTextNode(d[a]))}}}return f},ucMatch:function(a,b){return b.toUpperCase()},addElement:function(b,a,d,c){return b.appendChild(this.Element(a,d,c))},TextNode:function(a){return document.createTextNode(a)},addText:function(a,b){return a.appendChild(this.TextNode(b))},setScript:function(a,b){if(this.setScriptBug){a.text=b}else{while(a.firstChild){a.removeChild(a.firstChild)}this.addText(a,b)}},Cookie:{prefix:"mjx",expires:365,Set:function(a,d){var c=[];if(d){for(var f in d){if(d.hasOwnProperty(f)){c.push(f+":"+d[f].toString().replace(/&/g,"&&"))}}}var b=this.prefix+"."+a+"="+escape(c.join("&;"));if(this.expires){var e=new Date();e.setDate(e.getDate()+this.expires);b+="; expires="+e.toGMTString()}document.cookie=b+"; path=/"},Get:function(c,h){if(!h){h={}}var g=new RegExp("(?:^|;\\s*)"+this.prefix+"\\."+c+"=([^;]*)(?:;|$)");var b=g.exec(document.cookie);if(b&&b[1]!==""){var e=unescape(b[1]).split("&;");for(var d=0,a=e.length;d<a;d++){b=e[d].match(/([^:]+):(.*)/);var f=b[2].replace(/&&/g,"&");if(f==="true"){f=true}else{if(f==="false"){f=false}else{if(f.match(/^-?(\d+(\.\d+)?|\.\d+)$/)){f=parseFloat(f)}}}h[b[1]]=f}}return h}}};MathJax.Message={ready:false,log:[{}],current:null,textNodeBug:(navigator.vendor==="Apple Computer, Inc."&&typeof navigator.vendorSub==="undefined")||(window.hasOwnProperty&&window.hasOwnProperty("konqueror")),styles:{"#MathJax_Message":{position:"fixed",left:"1px",bottom:"2px","background-color":"#E6E6E6",border:"1px solid #959595",margin:"0px",padding:"2px 8px","z-index":"102",color:"black","font-size":"80%",width:"auto","white-space":"nowrap"},"#MathJax_MSIE_Frame":{position:"absolute",top:0,left:0,width:"0px","z-index":101,border:"0px",margin:"0px",padding:"0px"}},browsers:{MSIE:function(a){MathJax.Hub.config.styles["#MathJax_Message"].position="absolute";MathJax.Message.quirks=(document.compatMode==="BackCompat")},Chrome:function(a){MathJax.Hub.config.styles["#MathJax_Message"].bottom="1.5em";MathJax.Hub.config.styles["#MathJax_Message"].left="1em"}},Init:function(a){if(a){this.ready=true}if(!document.body||!this.ready){return false}if(this.div&&this.div.parentNode==null){this.div=document.getElementById("MathJax_Message");if(this.div){this.text=this.div.firstChild}}if(!this.div){var b=document.body;if(MathJax.Hub.Browser.isMSIE){b=this.frame=this.addDiv(document.body);b.removeAttribute("id");b.style.position="absolute";b.style.border=b.style.margin=b.style.padding="0px";b.style.zIndex="101";b.style.height="0px";b=this.addDiv(b);b.id="MathJax_MSIE_Frame";window.attachEvent("onscroll",this.MoveFrame);window.attachEvent("onresize",this.MoveFrame);this.MoveFrame()}this.div=this.addDiv(b);this.div.style.display="none";this.text=this.div.appendChild(document.createTextNode(""))}return true},addDiv:function(a){var b=document.createElement("div");b.id="MathJax_Message";if(a.firstChild){a.insertBefore(b,a.firstChild)}else{a.appendChild(b)}return b},MoveFrame:function(){var a=(MathJax.Message.quirks?document.body:document.documentElement);var b=MathJax.Message.frame;b.style.left=a.scrollLeft+"px";b.style.top=a.scrollTop+"px";b.style.width=a.clientWidth+"px";b=b.firstChild;b.style.height=a.clientHeight+"px"},filterText:function(a,b){if(MathJax.Hub.config.messageStyle==="simple"){if(a.match(/^Loading /)){if(!this.loading){this.loading="Loading "}a=this.loading;this.loading+="."}else{if(a.match(/^Processing /)){if(!this.processing){this.processing="Processing "}a=this.processing;this.processing+="."}else{if(a.match(/^Typesetting /)){if(!this.typesetting){this.typesetting="Typesetting "}a=this.typesetting;this.typesetting+="."}}}}return a},Set:function(b,c,a){if(this.timer){clearTimeout(this.timer);delete this.timeout}if(c==null){c=this.log.length;this.log[c]={}}this.log[c].text=b;this.log[c].filteredText=b=this.filterText(b,c);if(typeof(this.log[c].next)==="undefined"){this.log[c].next=this.current;if(this.current!=null){this.log[this.current].prev=c}this.current=c}if(this.current===c&&MathJax.Hub.config.messageStyle!=="none"){if(this.Init()){if(this.textNodeBug){this.div.innerHTML=b}else{this.text.nodeValue=b}this.div.style.display="";if(this.status){window.status="";delete this.status}}else{window.status=b;this.status=true}}if(a){setTimeout(MathJax.Callback(["Clear",this,c]),a)}else{if(a==0){this.Clear(c,0)}}return c},Clear:function(b,a){if(this.log[b].prev!=null){this.log[this.log[b].prev].next=this.log[b].next}if(this.log[b].next!=null){this.log[this.log[b].next].prev=this.log[b].prev}if(this.current===b){this.current=this.log[b].next;if(this.text){if(this.div.parentNode==null){this.Init()}if(this.current==null){if(this.timer){clearTimeout(this.timer);delete this.timer}if(a==null){a=600}if(a===0){this.Remove()}else{this.timer=setTimeout(MathJax.Callback(["Remove",this]),a)}}else{if(MathJax.Hub.config.messageStyle!=="none"){if(this.textNodeBug){this.div.innerHTML=this.log[this.current].filteredText}else{this.text.nodeValue=this.log[this.current].filteredText}}}if(this.status){window.status="";delete this.status}}else{if(this.status){window.status=(this.current==null?"":this.log[this.current].text)}}}delete this.log[b].next;delete this.log[b].prev;delete this.log[b].filteredText},Remove:function(){this.text.nodeValue="";this.div.style.display="none"},File:function(b){var a=MathJax.Ajax.config.root;if(b.substr(0,a.length)===a){b="[MathJax]"+b.substr(a.length)}return this.Set("Loading "+b)},Log:function(){var b=[];for(var c=1,a=this.log.length;c<a;c++){b[c]=this.log[c].text}return b.join("\n")}};MathJax.Hub={config:{root:"",config:[],styleSheets:[],styles:{".MathJax_Preview":{color:"#888"}},jax:[],extensions:[],preJax:null,postJax:null,displayAlign:"center",displayIndent:"0",preRemoveClass:"MathJax_Preview",showProcessingMessages:true,messageStyle:"normal",delayStartupUntil:"none",skipStartupTypeset:false,"v1.0-compatible":true,elements:[],positionToHash:true,showMathMenu:true,showMathMenuMSIE:true,menuSettings:{zoom:"None",CTRL:false,ALT:false,CMD:false,Shift:false,discoverable:false,zscale:"200%",renderer:"",font:"Auto",context:"MathJax",mpContext:false,mpMouse:false,texHints:true},errorSettings:{message:["[Math Processing Error]"],style:{color:"#CC0000","font-style":"italic"}}},preProcessors:MathJax.Callback.Hooks(true),inputJax:{},outputJax:{order:{}},processUpdateTime:250,processUpdateDelay:10,signal:MathJax.Callback.Signal("Hub"),Config:function(a){this.Insert(this.config,a);if(this.config.Augment){this.Augment(this.config.Augment)}},CombineConfig:function(c,f){var b=this.config,g,e;c=c.split(/\./);for(var d=0,a=c.length;d<a;d++){g=c[d];if(!b[g]){b[g]={}}e=b;b=b[g]}e[g]=b=this.Insert(f,b);return b},Register:{PreProcessor:function(){MathJax.Hub.preProcessors.Add.apply(MathJax.Hub.preProcessors,arguments)},MessageHook:function(){return MathJax.Hub.signal.MessageHook.apply(MathJax.Hub.signal,arguments)},StartupHook:function(){return MathJax.Hub.Startup.signal.MessageHook.apply(MathJax.Hub.Startup.signal,arguments)},LoadHook:function(){return MathJax.Ajax.LoadHook.apply(MathJax.Ajax,arguments)}},getAllJax:function(e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax){c.push(b[d].MathJax.elementJax)}}return c},getJaxByType:function(f,e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax&&b[d].MathJax.elementJax.mimeType===f){c.push(b[d].MathJax.elementJax)}}return c},getJaxByInputType:function(f,e){var c=[],b=this.elementScripts(e);for(var d=0,a=b.length;d<a;d++){if(b[d].MathJax&&b[d].MathJax.elementJax&&b[d].type&&b[d].type.replace(/ *;(.|\s)*/,"")===f){c.push(b[d].MathJax.elementJax)}}return c},getJaxFor:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a&&a.MathJax){return a.MathJax.elementJax}if(a&&a.isMathJax){while(a&&!a.jaxID){a=a.parentNode}if(a){return MathJax.OutputJax[a.jaxID].getJaxFromMath(a)}}return null},isJax:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a&&a.isMathJax){return 1}if(a&&a.tagName!=null&&a.tagName.toLowerCase()==="script"){if(a.MathJax){return(a.MathJax.state===MathJax.ElementJax.STATE.PROCESSED?1:-1)}if(a.type&&this.inputJax[a.type.replace(/ *;(.|\s)*/,"")]){return -1}}return 0},setRenderer:function(d,c){if(!d){return}if(!MathJax.OutputJax[d]){this.config.menuSettings.renderer="";var b="[MathJax]/jax/output/"+d+"/config.js";return MathJax.Ajax.Require(b,["setRenderer",this,d,c])}else{this.config.menuSettings.renderer=d;if(c==null){c="jax/mml"}var a=this.outputJax;if(a[c]&&a[c].length){if(d!==a[c][0].id){a[c].unshift(MathJax.OutputJax[d]);return this.signal.Post(["Renderer Selected",d])}}return null}},Queue:function(){return this.queue.Push.apply(this.queue,arguments)},Typeset:function(e,f){if(!MathJax.isReady){return null}var c=this.elementCallback(e,f);var b=MathJax.Callback.Queue();for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){b.Push(["PreProcess",this,c.elements[d]],["Process",this,c.elements[d]])}}return b.Push(c.callback)},PreProcess:function(e,f){var c=this.elementCallback(e,f);var b=MathJax.Callback.Queue();for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){b.Push(["Post",this.signal,["Begin PreProcess",c.elements[d]]],(arguments.callee.disabled?{}:["Execute",this.preProcessors,c.elements[d]]),["Post",this.signal,["End PreProcess",c.elements[d]]])}}return b.Push(c.callback)},Process:function(a,b){return this.takeAction("Process",a,b)},Update:function(a,b){return this.takeAction("Update",a,b)},Reprocess:function(a,b){return this.takeAction("Reprocess",a,b)},Rerender:function(a,b){return this.takeAction("Rerender",a,b)},takeAction:function(g,e,h){var c=this.elementCallback(e,h);var b=MathJax.Callback.Queue(["Clear",this.signal]);for(var d=0,a=c.elements.length;d<a;d++){if(c.elements[d]){var f={scripts:[],start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]};b.Push(["Post",this.signal,["Begin "+g,c.elements[d]]],["Post",this.signal,["Begin Math",c.elements[d],g]],["prepareScripts",this,g,c.elements[d],f],["Post",this.signal,["Begin Math Input",c.elements[d],g]],["processInput",this,f],["Post",this.signal,["End Math Input",c.elements[d],g]],["prepareOutput",this,f,"preProcess"],["Post",this.signal,["Begin Math Output",c.elements[d],g]],["processOutput",this,f],["Post",this.signal,["End Math Output",c.elements[d],g]],["prepareOutput",this,f,"postProcess"],["Post",this.signal,["End Math",c.elements[d],g]],["Post",this.signal,["End "+g,c.elements[d]]])}}return b.Push(c.callback)},scriptAction:{Process:function(a){},Update:function(b){var a=b.MathJax.elementJax;if(a&&a.needsUpdate()){a.Remove(true);b.MathJax.state=a.STATE.UPDATE}else{b.MathJax.state=a.STATE.PROCESSED}},Reprocess:function(b){var a=b.MathJax.elementJax;if(a){a.Remove(true);b.MathJax.state=a.STATE.UPDATE}},Rerender:function(b){var a=b.MathJax.elementJax;if(a){a.Remove(true);b.MathJax.state=a.STATE.OUTPUT}}},prepareScripts:function(h,e,g){if(arguments.callee.disabled){return}var b=this.elementScripts(e);var f=MathJax.ElementJax.STATE;for(var d=0,a=b.length;d<a;d++){var c=b[d];if(c.type&&this.inputJax[c.type.replace(/ *;(.|\n)*/,"")]){if(c.MathJax){if(c.MathJax.elementJax&&c.MathJax.elementJax.hover){MathJax.Extension.MathEvents.Hover.ClearHover(c.MathJax.elementJax)}if(c.MathJax.state!==f.PENDING){this.scriptAction[h](c)}}if(!c.MathJax){c.MathJax={state:f.PENDING}}if(c.MathJax.state!==f.PROCESSED){g.scripts.push(c)}}}},checkScriptSiblings:function(a){if(a.MathJax.checked){return}var b=this.config,f=a.previousSibling;if(f&&f.nodeName==="#text"){var d,e,c=a.nextSibling;if(c&&c.nodeName!=="#text"){c=null}if(b.preJax){if(typeof(b.preJax)==="string"){b.preJax=new RegExp(b.preJax+"$")}d=f.nodeValue.match(b.preJax)}if(b.postJax&&c){if(typeof(b.postJax)==="string"){b.postJax=new RegExp("^"+b.postJax)}e=c.nodeValue.match(b.postJax)}if(d&&(!b.postJax||e)){f.nodeValue=f.nodeValue.replace(b.preJax,(d.length>1?d[1]:""));f=null}if(e&&(!b.preJax||d)){c.nodeValue=c.nodeValue.replace(b.postJax,(e.length>1?e[1]:""))}if(f&&!f.nodeValue.match(/\S/)){f=f.previousSibling}}if(b.preRemoveClass&&f&&f.className===b.preRemoveClass){a.MathJax.preview=f}a.MathJax.checked=1},processInput:function(a){var b,i=MathJax.ElementJax.STATE;var h,e,d=a.scripts.length;try{while(a.i<d){h=a.scripts[a.i];if(!h){a.i++;continue}e=h.previousSibling;if(e&&e.className==="MathJax_Error"){e.parentNode.removeChild(e)}if(!h.MathJax||h.MathJax.state===i.PROCESSED){a.i++;continue}if(!h.MathJax.elementJax||h.MathJax.state===i.UPDATE){this.checkScriptSiblings(h);var g=h.type.replace(/ *;(.|\s)*/,"");b=this.inputJax[g].Process(h,a);if(typeof b==="function"){if(b.called){continue}this.RestartAfter(b)}b.Attach(h,this.inputJax[g].id);this.saveScript(b,a,h,i)}else{if(h.MathJax.state===i.OUTPUT){this.saveScript(h.MathJax.elementJax,a,h,i)}}a.i++;var c=new Date().getTime();if(c-a.start>this.processUpdateTime&&a.i<a.scripts.length){a.start=c;this.RestartAfter(MathJax.Callback.Delay(1))}}}catch(f){return this.processError(f,a,"Input")}if(a.scripts.length&&this.config.showProcessingMessages){MathJax.Message.Set("Processing math: 100%",0)}a.start=new Date().getTime();a.i=a.j=0;return null},saveScript:function(a,d,b,c){if(!this.outputJax[a.mimeType]){b.MathJax.state=c.UPDATE;throw Error("No output jax registered for "+a.mimeType)}a.outputJax=this.outputJax[a.mimeType][0].id;if(!d.jax[a.outputJax]){if(d.jaxIDs.length===0){d.jax[a.outputJax]=d.scripts}else{if(d.jaxIDs.length===1){d.jax[d.jaxIDs[0]]=d.scripts.slice(0,d.i)}d.jax[a.outputJax]=[]}d.jaxIDs.push(a.outputJax)}if(d.jaxIDs.length>1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.j<c.jaxIDs.length){var e=c.jaxIDs[c.j],d=MathJax.OutputJax[e];if(d[f]){try{var a=d[f](c);if(typeof a==="function"){if(a.called){continue}this.RestartAfter(a)}}catch(b){if(!b.restart){MathJax.Message.Set("Error preparing "+e+" output ("+f+")",null,600);MathJax.Hub.lastPrepError=b;c.j++}return MathJax.Callback.After(["prepareOutput",this,c,f],b.restart)}}c.j++}return null},processOutput:function(h){var b,g=MathJax.ElementJax.STATE,d,a=h.scripts.length;try{while(h.i<a){d=h.scripts[h.i];if(!d||!d.MathJax){h.i++;continue}var c=d.MathJax.elementJax;if(!c){h.i++;continue}b=MathJax.OutputJax[c.outputJax].Process(d,h);d.MathJax.state=g.PROCESSED;h.i++;if(d.MathJax.preview){d.MathJax.preview.style.display="none";d.MathJax.preview.style.visibility="hidden"}this.signal.Post(["New Math",c.inputID]);var e=new Date().getTime();if(e-h.start>this.processUpdateTime&&h.i<h.scripts.length){h.start=e;this.RestartAfter(MathJax.Callback.Delay(this.processUpdateDelay))}}}catch(f){return this.processError(f,h,"Output")}if(h.scripts.length&&this.config.showProcessingMessages){MathJax.Message.Set("Typesetting math: 100%",0);MathJax.Message.Clear(0)}h.i=h.j=0;return null},processMessage:function(d,b){var a=Math.floor(d.i/(d.scripts.length)*100);var c=(b==="Output"?"Typesetting":"Processing");if(this.config.showProcessingMessages){MathJax.Message.Set(c+" math: "+a+"%",0)}},processError:function(b,c,a){if(!b.restart){if(!this.config.errorSettings.message){throw b}this.formatError(c.scripts[c.i],b);c.i++}this.processMessage(c,a);return MathJax.Callback.After(["process"+a,this,c],b.restart)},formatError:function(a,c){var b=MathJax.HTML.Element("span",{className:"MathJax_Error"},this.config.errorSettings.message);b.jaxID="Error";if(MathJax.Extension.MathEvents){b.oncontextmenu=MathJax.Extension.MathEvents.Event.Menu;b.onmousedown=MathJax.Extension.MathEvents.Event.Mousedown}else{MathJax.Ajax.Require("[MathJax]/extensions/MathEvents.js",function(){b.oncontextmenu=MathJax.Extension.MathEvents.Event.Menu;b.onmousedown=MathJax.Extension.MathEvents.Event.Mousedown})}a.parentNode.insertBefore(b,a);if(a.MathJax.preview){a.MathJax.preview.style.display="none";a.MathJax.preview.style.visibility="hidden"}this.lastError=c},RestartAfter:function(a){throw this.Insert(Error("restart"),{restart:MathJax.Callback(a)})},elementCallback:function(c,f){if(f==null&&(c instanceof Array||typeof c==="function")){try{MathJax.Callback(c);f=c;c=null}catch(d){}}if(c==null){c=this.config.elements||[]}if(!(c instanceof Array)){c=[c]}c=[].concat(c);for(var b=0,a=c.length;b<a;b++){if(typeof(c[b])==="string"){c[b]=document.getElementById(c[b])}}if(c.length==0){c.push(document.body)}if(!f){f={}}return{elements:c,callback:f}},elementScripts:function(a){if(typeof(a)==="string"){a=document.getElementById(a)}if(a==null){a=document.body}if(a.tagName!=null&&a.tagName.toLowerCase()==="script"){return[a]}return a.getElementsByTagName("script")},Insert:function(c,a){for(var b in a){if(a.hasOwnProperty(b)){if(typeof a[b]==="object"&&!(a[b] instanceof Array)&&(typeof c[b]==="object"||typeof c[b]==="function")){this.Insert(c[b],a[b])}else{c[b]=a[b]}}}return c}};MathJax.Hub.Insert(MathJax.Hub.config.styles,MathJax.Message.styles);MathJax.Hub.Insert(MathJax.Hub.config.styles,{".MathJax_Error":MathJax.Hub.config.errorSettings.style});MathJax.Extension={};MathJax.Hub.Configured=MathJax.Callback({});MathJax.Hub.Startup={script:"",queue:MathJax.Callback.Queue(),signal:MathJax.Callback.Signal("Startup"),params:{},Config:function(){this.queue.Push(["Post",this.signal,"Begin Config"]);var b=MathJax.HTML.Cookie.Get("user");if(b.URL||b.Config){if(confirm("MathJax has found a user-configuration cookie that includes code to be run. Do you want to run it?\n\n(You should press Cancel unless you set up the cookie yourself.)")){if(b.URL){this.queue.Push(["Require",MathJax.Ajax,b.URL])}if(b.Config){this.queue.Push(new Function(b.Config))}}else{MathJax.HTML.Cookie.Set("user",{})}}if(this.params.config){var d=this.params.config.split(/,/);for(var c=0,a=d.length;c<a;c++){if(!d[c].match(/\.js$/)){d[c]+=".js"}this.queue.Push(["Require",MathJax.Ajax,this.URL("config",d[c])])}}if(this.script.match(/\S/)){this.queue.Push(this.script+";\n1;")}this.queue.Push(["ConfigDelay",this],["ConfigBlocks",this],["ConfigDefault",this],[function(e){return e.loadArray(MathJax.Hub.config.config,"config",null,true)},this],["Post",this.signal,"End Config"])},ConfigDelay:function(){var a=this.params.delayStartupUntil||MathJax.Hub.config.delayStartupUntil;if(a==="onload"){return this.onload}if(a==="configured"){return MathJax.Hub.Configured}return a},ConfigBlocks:function(){var c=document.getElementsByTagName("script");var f=null,b=MathJax.Callback.Queue();for(var d=0,a=c.length;d<a;d++){var e=String(c[d].type).replace(/ /g,"");if(e.match(/^text\/x-mathjax-config(;.*)?$/)&&!e.match(/;executed=true/)){c[d].type+=";executed=true";f=b.Push(c[d].innerHTML+";\n1;")}}return f},ConfigDefault:function(){var a=MathJax.Hub.config;if(a["v1.0-compatible"]&&(a.jax||[]).length===0&&!this.params.config&&(a.config||[]).length===0){return MathJax.Ajax.Require(this.URL("extensions","v1.0-warning.js"))}},Cookie:function(){return this.queue.Push(["Post",this.signal,"Begin Cookie"],["Get",MathJax.HTML.Cookie,"menu",MathJax.Hub.config.menuSettings],[function(d){var f=d.menuSettings.renderer,b=d.jax;if(f){var c="output/"+f;b.sort();for(var e=0,a=b.length;e<a;e++){if(b[e].substr(0,7)==="output/"){break}}if(e==a-1){b.pop()}else{while(e<a){if(b[e]===c){b.splice(e,1);break}e++}}b.unshift(c)}},MathJax.Hub.config],["Post",this.signal,"End Cookie"])},Styles:function(){return this.queue.Push(["Post",this.signal,"Begin Styles"],["loadArray",this,MathJax.Hub.config.styleSheets,"config"],["Styles",MathJax.Ajax,MathJax.Hub.config.styles],["Post",this.signal,"End Styles"])},Jax:function(){var e=MathJax.Hub.config,c=MathJax.Hub.outputJax;for(var f=0,b=e.jax.length,d=0;f<b;f++){if(e.jax[f].substr(0,7)==="output/"){c.order[e.jax[f].substr(7)]=d;d++}}var a=MathJax.Callback.Queue();return a.Push(["Post",this.signal,"Begin Jax"],["loadArray",this,e.jax,"jax","config.js"],["Post",this.signal,"End Jax"])},Extensions:function(){var a=MathJax.Callback.Queue();return a.Push(["Post",this.signal,"Begin Extensions"],["loadArray",this,MathJax.Hub.config.extensions,"extensions"],["Post",this.signal,"End Extensions"])},Message:function(){MathJax.Message.Init(true)},Menu:function(){var b=MathJax.Hub.config.menuSettings,a=MathJax.Hub.outputJax,d;for(var c in a){if(a.hasOwnProperty(c)){if(a[c].length){d=a[c];break}}}if(d&&d.length){if(b.renderer&&b.renderer!==d[0].id){d.unshift(MathJax.OutputJax[b.renderer])}b.renderer=d[0].id}},Hash:function(){if(MathJax.Hub.config.positionToHash&&document.location.hash){setTimeout("document.location = document.location.hash",1)}},MenuZoom:function(){if(!MathJax.Extension.MathMenu){setTimeout(MathJax.Callback(["Require",MathJax.Ajax,"[MathJax]/extensions/MathMenu.js"]),1000)}if(!MathJax.Extension.MathZoom){setTimeout(MathJax.Callback(["Require",MathJax.Ajax,"[MathJax]/extensions/MathZoom.js"]),2000)}},onLoad:function(a){var b=this.onload=MathJax.Callback(function(){MathJax.Hub.Startup.signal.Post("onLoad")});if(document.body&&document.readyState&&document.readyState!=="loading"){return[b]}if(window.addEventListener){window.addEventListener("load",b,false);if(!this.params.noDOMContentEvent){window.addEventListener("DOMContentLoaded",b,false)}}else{if(window.attachEvent){window.attachEvent("onload",b)}else{window.onload=b}}return b},Typeset:function(a,b){if(MathJax.Hub.config.skipStartupTypeset){return function(){}}return this.queue.Push(["Post",this.signal,"Begin Typeset"],["Typeset",MathJax.Hub,a,b],["Post",this.signal,"End Typeset"])},URL:function(b,a){if(!a.match(/^([a-z]+:\/\/|\[|\/)/)){a="[MathJax]/"+b+"/"+a}return a},loadArray:function(b,f,c,a){if(b){if(!(b instanceof Array)){b=[b]}if(b.length){var h=MathJax.Callback.Queue(),j={},e;for(var g=0,d=b.length;g<d;g++){e=this.URL(f,b[g]);if(c){e+="/"+c}if(a){h.Push(["Require",MathJax.Ajax,e,j])}else{h.Push(MathJax.Ajax.Require(e,j))}}return h.Push({})}}return null}};(function(d){var b=window[d],e="["+d+"]";var c=b.Hub,a=b.Ajax,f=b.Callback;var g=MathJax.Object.Subclass({JAXFILE:"jax.js",require:null,config:{},Init:function(i,h){if(arguments.length===0){return this}return(this.constructor.Subclass(i,h))()},Augment:function(k,j){var i=this.constructor,h={};if(k!=null){for(var l in k){if(k.hasOwnProperty(l)){if(typeof k[l]==="function"){i.protoFunction(l,k[l])}else{h[l]=k[l]}}}if(k.toString!==i.prototype.toString&&k.toString!=={}.toString){i.protoFunction("toString",k.toString)}}c.Insert(i.prototype,h);i.Augment(null,j);return this},preProcess:function(i){var j,h=this.directory+"/"+this.JAXFILE;this.constructor.prototype.preProcess=function(k){if(!j.called){return j}throw Error(h+" failed to load properly")};j=a.Require(h);return j},Translate:function(h){throw Error(this.directory+"/"+this.JAXFILE+" failed to redefine the Translate() method")},Register:function(h){},Config:function(){this.config=c.CombineConfig(this.id,this.config);if(this.config.Augment){this.Augment(this.config.Augment)}},Startup:function(){},loadComplete:function(i){if(i==="config.js"){return a.loadComplete(this.directory+"/"+i)}else{var h=f.Queue();h.Push(c.Register.StartupHook("End Config",{}),["Post",c.Startup.signal,this.id+" Jax Config"],["Config",this],["Post",c.Startup.signal,this.id+" Jax Require"],[function(j){return MathJax.Hub.Startup.loadArray(j.require,this.directory)},this],[function(j,k){return MathJax.Hub.Startup.loadArray(j.extensions,"extensions/"+k)},this.config||{},this.id],["Post",c.Startup.signal,this.id+" Jax Startup"],["Startup",this],["Post",c.Startup.signal,this.id+" Jax Ready"],[function(j){j.preProcess=j.preTranslate;j.Process=j.Translate;j.postProcess=j.postTranslate},this.constructor.prototype]);return h.Push(["loadComplete",a,this.directory+"/"+i])}}},{id:"Jax",version:"2.0",directory:e+"/jax",extensionDir:e+"/extensions"});b.InputJax=g.Subclass({elementJax:"mml",Process:function(o){var j=f.Queue();var k=this.elementJax;if(!(k instanceof Array)){k=[k]}for(var n=0,h=k.length;n<h;n++){var l=b.ElementJax.directory+"/"+k[n]+"/"+this.JAXFILE;if(!this.require){this.require=[]}else{if(!(this.require instanceof Array)){this.require=[this.require]}}this.require.push(l);j.Push(a.Require(l))}var p=j.Push(a.Require(this.directory+"/"+this.JAXFILE));if(!p.called){this.constructor.prototype.Process=function(){return p}}k=c.outputJax["jax/"+k[0]];if(k){j.Push(a.Require(k[0].directory+"/"+this.JAXFILE))}return j.Push({})},needsUpdate:function(h){var i=h.SourceElement();return(h.originalText!==(i.text==""?i.innerHTML:i.text))},Register:function(h){if(!c.inputJax){c.inputJax={}}c.inputJax[h]=this}},{id:"InputJax",version:"2.0",directory:g.directory+"/input",extensionDir:g.extensionDir});b.OutputJax=g.Subclass({Register:function(i){var h=c.outputJax;if(!h[i]){h[i]=[]}if(h[i].length&&(this.id===c.config.menuSettings.renderer||(h.order[this.id]||0)<(h.order[h[i][0].id]||0))){h[i].unshift(this)}else{h[i].push(this)}if(!this.require){this.require=[]}else{if(!(this.require instanceof Array)){this.require=[this.require]}}this.require.push(b.ElementJax.directory+"/"+(i.split(/\//)[1])+"/"+this.JAXFILE)},Remove:function(h){}},{id:"OutputJax",version:"2.0",directory:g.directory+"/output",extensionDir:g.extensionDir,fontDir:e+(b.isPacked?"":"/..")+"/fonts",imageDir:e+(b.isPacked?"":"/..")+"/images"});b.ElementJax=g.Subclass({Init:function(i,h){return this.constructor.Subclass(i,h)},inputJax:null,outputJax:null,inputID:null,originalText:"",mimeType:"",Text:function(i,j){var h=this.SourceElement();b.HTML.setScript(h,i);h.MathJax.state=this.STATE.UPDATE;return c.Update(h,j)},Reprocess:function(i){var h=this.SourceElement();h.MathJax.state=this.STATE.UPDATE;return c.Reprocess(h,i)},Update:function(h){return this.Rerender(h)},Rerender:function(i){var h=this.SourceElement();h.MathJax.state=this.STATE.OUTPUT;return c.Process(h,i)},Remove:function(h){if(this.hover){this.hover.clear(this)}b.OutputJax[this.outputJax].Remove(this);if(!h){c.signal.Post(["Remove Math",this.inputID]);this.Detach()}},needsUpdate:function(){return b.InputJax[this.inputJax].needsUpdate(this)},SourceElement:function(){return document.getElementById(this.inputID)},Attach:function(i,j){var h=i.MathJax.elementJax;if(i.MathJax.state===this.STATE.UPDATE){h.Clone(this)}else{h=i.MathJax.elementJax=this;if(i.id){this.inputID=i.id}else{i.id=this.inputID=b.ElementJax.GetID();this.newID=1}}h.originalText=(i.text==""?i.innerHTML:i.text);h.inputJax=j;if(h.root){h.root.inputID=h.inputID}return h},Detach:function(){var h=this.SourceElement();if(!h){return}try{delete h.MathJax}catch(i){h.MathJax=null}if(this.newID){h.id=""}},Clone:function(h){var i;for(i in this){if(!this.hasOwnProperty(i)){continue}if(typeof(h[i])==="undefined"&&i!=="newID"){delete this[i]}}for(i in h){if(!h.hasOwnProperty(i)){continue}if(typeof(this[i])==="undefined"||(this[i]!==h[i]&&i!=="inputID")){this[i]=h[i]}}}},{id:"ElementJax",version:"2.0",directory:g.directory+"/element",extensionDir:g.extensionDir,ID:0,STATE:{PENDING:1,PROCESSED:2,UPDATE:3,OUTPUT:4},GetID:function(){this.ID++;return"MathJax-Element-"+this.ID},Subclass:function(){var h=g.Subclass.apply(this,arguments);h.loadComplete=this.prototype.loadComplete;return h}});b.ElementJax.prototype.STATE=b.ElementJax.STATE;b.OutputJax.Error={id:"Error",version:"2.0",config:{},ContextMenu:function(){return b.Extension.MathEvents.Event.ContextMenu.apply(b.Extension.MathEvents.Event,arguments)},Mousedown:function(){return b.Extension.MathEvents.Event.AltContextMenu.apply(b.Extension.MathEvents.Event,arguments)},getJaxFromMath:function(){return{inputJax:"Error",outputJax:"Error",originalText:"Math Processing Error"}}};b.InputJax.Error={id:"Error",version:"2.0",config:{},sourceMenuTitle:"Error Message"}})("MathJax");(function(l){var f=window[l];if(!f){f=window[l]={}}var c=f.Hub;var q=c.Startup;var u=c.config;var e=document.getElementsByTagName("head")[0];if(!e){e=document.childNodes[0]}var b=(document.documentElement||document).getElementsByTagName("script");var d=new RegExp("(^|/)"+l+"\\.js(\\?.*)?$");for(var o=b.length-1;o>=0;o--){if(b[o].src.match(d)){q.script=b[o].innerHTML;if(RegExp.$2){var r=RegExp.$2.substr(1).split(/\&/);for(var n=0,h=r.length;n<h;n++){var k=r[n].match(/(.*)=(.*)/);if(k){q.params[unescape(k[1])]=unescape(k[2])}}}u.root=b[o].src.replace(/(^|\/)[^\/]*(\?.*)?$/,"");break}}f.Ajax.config=u;var a={isMac:(navigator.platform.substr(0,3)==="Mac"),isPC:(navigator.platform.substr(0,3)==="Win"),isMSIE:(window.ActiveXObject!=null&&window.clipboardData!=null),isFirefox:(window.netscape!=null&&document.ATTRIBUTE_NODE!=null&&!window.opera),isSafari:(navigator.userAgent.match(/ (Apple)?WebKit\//)!=null&&(!window.chrome||window.chrome.loadTimes==null)),isChrome:(window.chrome!=null&&window.chrome.loadTimes!=null),isOpera:(window.opera!=null&&window.opera.version!=null),isKonqueror:(window.hasOwnProperty&&window.hasOwnProperty("konqueror")&&navigator.vendor=="KDE"),versionAtLeast:function(x){var w=(this.version).split(".");x=(new String(x)).split(".");for(var y=0,j=x.length;y<j;y++){if(w[y]!=x[y]){return parseInt(w[y]||"0")>=parseInt(x[y])}}return true},Select:function(j){var i=j[c.Browser];if(i){return i(c.Browser)}return null}};var g=navigator.userAgent.replace(/^Mozilla\/(\d+\.)+\d+ /,"").replace(/[a-z][-a-z0-9._: ]+\/\d+[^ ]*-[^ ]*\.([a-z][a-z])?\d+ /i,"").replace(/Gentoo |Ubuntu\/(\d+\.)*\d+ (\([^)]*\) )?/,"");c.Browser=c.Insert(c.Insert(new String("Unknown"),{version:"0.0"}),a);for(var t in a){if(a.hasOwnProperty(t)){if(a[t]&&t.substr(0,2)==="is"){t=t.slice(2);if(t==="Mac"||t==="PC"){continue}c.Browser=c.Insert(new String(t),a);var p=new RegExp(".*(Version)/((?:\\d+\\.)+\\d+)|.*("+t+")"+(t=="MSIE"?" ":"/")+"((?:\\d+\\.)*\\d+)|(?:^|\\(| )([a-z][-a-z0-9._: ]+|(?:Apple)?WebKit)/((?:\\d+\\.)+\\d+)");var s=p.exec(g)||["","","","unknown","0.0"];c.Browser.name=(s[1]=="Version"?t:(s[3]||s[5]));c.Browser.version=s[2]||s[4]||s[6];break}}}c.Browser.Select({Safari:function(j){var i=parseInt((String(j.version).split("."))[0]);if(i>85){j.webkit=j.version}if(i>=534){j.version="5.1"}else{if(i>=533){j.version="5.0"}else{if(i>=526){j.version="4.0"}else{if(i>=525){j.version="3.1"}else{if(i>500){j.version="3.0"}else{if(i>400){j.version="2.0"}else{if(i>85){j.version="1.0"}}}}}}}j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);j.noContextMenu=j.isMobile},Firefox:function(j){if((j.version==="0.0"||navigator.userAgent.match(/Firefox/)==null)&&navigator.product==="Gecko"){var m=navigator.userAgent.match(/[\/ ]rv:(\d+\.\d.*?)[\) ]/);if(m){j.version=m[1]}else{var i=(navigator.buildID||navigator.productSub||"0").substr(0,8);if(i>="20111220"){j.version="9.0"}else{if(i>="20111120"){j.version="8.0"}else{if(i>="20110927"){j.version="7.0"}else{if(i>="20110816"){j.version="6.0"}else{if(i>="20110621"){j.version="5.0"}else{if(i>="20110320"){j.version="4.0"}else{if(i>="20100121"){j.version="3.6"}else{if(i>="20090630"){j.version="3.5"}else{if(i>="20080617"){j.version="3.0"}else{if(i>="20061024"){j.version="2.0"}}}}}}}}}}}}j.isMobile=(navigator.appVersion.match(/Android/i)!=null||navigator.userAgent.match(/ Fennec\//)!=null)},Opera:function(i){i.version=opera.version()},MSIE:function(j){j.isIE9=!!(document.documentMode&&(window.performance||window.msPerformance));MathJax.HTML.setScriptBug=!j.isIE9||document.documentMode<9;var v=false;try{new ActiveXObject("MathPlayer.Factory.1");v=true}catch(m){}if(v){var i=document.createElement("object");i.id="mathplayer";i.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(i);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");j.hasMathPlayer=true;if(document.readyState&&(document.readyState==="loading"||document.readyState==="interactive")){document.write('<?import namespace="m" implementation="#MathPlayer">');j.mpImported=true}}}});c.Browser.Select(MathJax.Message.browsers);c.queue=f.Callback.Queue();c.queue.Push(["Post",q.signal,"Begin"],["Config",q],["Cookie",q],["Styles",q],["Message",q],function(){var i=f.Callback.Queue(q.Jax(),q.Extensions());return i.Push({})},["Menu",q],q.onLoad(),function(){MathJax.isReady=true},["Typeset",q],["Hash",q],["MenuZoom",q],["Post",q.signal,"End"])})("MathJax")}}; diff --git a/config/Accessible-full.js b/config/Accessible-full.js @@ -69,11 +69,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/config/Accessible.js b/config/Accessible.js @@ -66,11 +66,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/config/MML_HTMLorMML-full.js b/config/MML_HTMLorMML-full.js @@ -47,11 +47,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(g){var h;if(typeof g!=="string"){h=g.parentNode}else{if(g.match(/^<[a-z]+:/i)&&!g.match(/^<[^<>]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");g=g.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);h=b.ParseXML(g);if(h==null){b.Error("Error parsing MathML")}}var f=h.getElementsByTagName("parsererror")[0];if(f){b.Error("Error parsing MathML: "+f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(h.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(h.firstChild.nodeName.toLowerCase()==="html"){var e=h.getElementsByTagName("h1")[0];if(e&&e.textContent==="XML parsing error"&&e.nextSibling){b.Error("Error parsing MathML: "+String(e.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(h.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+h.firstChild.nodeName+">")}this.mml=this.MakeMML(h.firstChild)},MakeMML:function(g){var h=String(g.getAttribute("class")||"");var e,f=g.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var d=(h.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(d){e=this.TeXAtom(d[2])}else{if(!(a[f]&&a[f].isa&&a[f].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",f]);return a.merror("Unknown node type: "+f)}else{e=a[f]()}}this.AddAttributes(e,g);this.CheckClass(e,h);this.AddChildren(e,g);if(b.config.useMathMLspacing){e.useMMLspacing=8}return e},TeXAtom:function(e){var d=a.TeXAtom().With({texClass:a.TEXCLASS[e]});if(d.texClass===a.TEXCLASS.OP){d.movesupsub=d.movablelimits=true}return d},CheckClass:function(e,g){g=g.split(/ /);var h=[];for(var f=0,d=g.length;f<d;f++){if(g[f].substr(0,4)==="MJX-"){if(g[f]==="MJX-arrow"){e.arrow=true}else{if(g[f]==="MJX-variant"){e.variantForm=true;if(!MathJax.Extension["TeX/AMSsymbols"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}}else{if(g[f].substr(0,11)!=="MJX-TeXAtom"){e.mathvariant=g[f].substr(3);if(e.mathvariant==="-tex-caligraphic-bold"||e.mathvariant==="-tex-oldstyle-bold"){if(!MathJax.Extension["TeX/boldsymbol"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}}}}}}else{h.push(g[f])}}if(h.length){e["class"]=h.join(" ")}else{delete e["class"]}},AddAttributes:function(f,h){f.attr={};f.attrNames=[];for(var g=0,d=h.attributes.length;g<d;g++){var e=h.attributes[g].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}var j=h.attributes[g].value;if(j.toLowerCase()==="true"){j=true}else{if(j.toLowerCase()==="false"){j=false}}if(f.defaults[e]!=null||a.copyAttributes[e]){f[e]=j}else{f.attr[e]=j}f.attrNames.push(e)}},AddChildren:function(f,h){for(var g=0,d=h.childNodes.length;g<d;g++){var k=h.childNodes[g];if(k.nodeName==="#comment"){continue}if(k.nodeName==="#text"){if(f.isToken&&!f.mmlSelfClosing){var j=this.trimSpace(k.nodeValue);j=j.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);f.Append(a.chars(j))}else{if(k.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+k.nodeValue+"'")}}}else{if(f.type==="annotation-xml"){f.Append(a.xml(k))}else{var e=this.MakeMML(k);f.Append(e);if(e.mmlSelfClosing&&e.data.length){f.Append.apply(f,e.data);e.data=[]}}}}},trimSpace:function(d){return d.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f}},{loaded:[]});b.Augment({sourceMenuTitle:"Original MathML",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g,h={script:d};if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){h.math=d.firstChild;this.prefilterHooks.Execute(h);g=h.math}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/(&nbsp;)+$/,"")}else{if(c.isKonqueror){g=g.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}}h.math=g;this.prefilterHooks.Execute(h);g=h.math}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}h.math=a(e);this.postfilterHooks.Execute(h);return h.math},prefilterMath:function(e,d){return e},prefilterMathML:function(e,d){return e},formatError:function(g,f,d){var e=g.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",e,f,d]);return a.merror(e)},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true})}});b.prefilterHooks.Add(function(d){d.math=(typeof(d.math)==="string"?b.prefilterMath(d.math,d.script):b.prefilterMathML(d.math,d.script))});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/MML_HTMLorMML.js b/config/MML_HTMLorMML.js @@ -44,11 +44,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(g){var h;if(typeof g!=="string"){h=g.parentNode}else{if(g.match(/^<[a-z]+:/i)&&!g.match(/^<[^<>]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");g=g.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);h=b.ParseXML(g);if(h==null){b.Error("Error parsing MathML")}}var f=h.getElementsByTagName("parsererror")[0];if(f){b.Error("Error parsing MathML: "+f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(h.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(h.firstChild.nodeName.toLowerCase()==="html"){var e=h.getElementsByTagName("h1")[0];if(e&&e.textContent==="XML parsing error"&&e.nextSibling){b.Error("Error parsing MathML: "+String(e.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(h.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+h.firstChild.nodeName+">")}this.mml=this.MakeMML(h.firstChild)},MakeMML:function(g){var h=String(g.getAttribute("class")||"");var e,f=g.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var d=(h.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(d){e=this.TeXAtom(d[2])}else{if(!(a[f]&&a[f].isa&&a[f].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",f]);return a.merror("Unknown node type: "+f)}else{e=a[f]()}}this.AddAttributes(e,g);this.CheckClass(e,h);this.AddChildren(e,g);if(b.config.useMathMLspacing){e.useMMLspacing=8}return e},TeXAtom:function(e){var d=a.TeXAtom().With({texClass:a.TEXCLASS[e]});if(d.texClass===a.TEXCLASS.OP){d.movesupsub=d.movablelimits=true}return d},CheckClass:function(e,g){g=g.split(/ /);var h=[];for(var f=0,d=g.length;f<d;f++){if(g[f].substr(0,4)==="MJX-"){if(g[f]==="MJX-arrow"){e.arrow=true}else{if(g[f]==="MJX-variant"){e.variantForm=true;if(!MathJax.Extension["TeX/AMSsymbols"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}}else{if(g[f].substr(0,11)!=="MJX-TeXAtom"){e.mathvariant=g[f].substr(3);if(e.mathvariant==="-tex-caligraphic-bold"||e.mathvariant==="-tex-oldstyle-bold"){if(!MathJax.Extension["TeX/boldsymbol"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}}}}}}else{h.push(g[f])}}if(h.length){e["class"]=h.join(" ")}else{delete e["class"]}},AddAttributes:function(f,h){f.attr={};f.attrNames=[];for(var g=0,d=h.attributes.length;g<d;g++){var e=h.attributes[g].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}var j=h.attributes[g].value;if(j.toLowerCase()==="true"){j=true}else{if(j.toLowerCase()==="false"){j=false}}if(f.defaults[e]!=null||a.copyAttributes[e]){f[e]=j}else{f.attr[e]=j}f.attrNames.push(e)}},AddChildren:function(f,h){for(var g=0,d=h.childNodes.length;g<d;g++){var k=h.childNodes[g];if(k.nodeName==="#comment"){continue}if(k.nodeName==="#text"){if(f.isToken&&!f.mmlSelfClosing){var j=this.trimSpace(k.nodeValue);j=j.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);f.Append(a.chars(j))}else{if(k.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+k.nodeValue+"'")}}}else{if(f.type==="annotation-xml"){f.Append(a.xml(k))}else{var e=this.MakeMML(k);f.Append(e);if(e.mmlSelfClosing&&e.data.length){f.Append.apply(f,e.data);e.data=[]}}}}},trimSpace:function(d){return d.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f}},{loaded:[]});b.Augment({sourceMenuTitle:"Original MathML",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g,h={script:d};if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){h.math=d.firstChild;this.prefilterHooks.Execute(h);g=h.math}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/(&nbsp;)+$/,"")}else{if(c.isKonqueror){g=g.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}}h.math=g;this.prefilterHooks.Execute(h);g=h.math}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}h.math=a(e);this.postfilterHooks.Execute(h);return h.math},prefilterMath:function(e,d){return e},prefilterMathML:function(e,d){return e},formatError:function(g,f,d){var e=g.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",e,f,d]);return a.merror(e)},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true})}});b.prefilterHooks.Add(function(d){d.math=(typeof(d.math)==="string"?b.prefilterMath(d.math,d.script):b.prefilterMathML(d.math,d.script))});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/TeX-AMS-MML_HTMLorMML-full.js b/config/TeX-AMS-MML_HTMLorMML-full.js @@ -58,11 +58,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/config/TeX-AMS-MML_HTMLorMML.js b/config/TeX-AMS-MML_HTMLorMML.js @@ -55,11 +55,11 @@ MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/config/TeX-AMS_HTML-full.js b/config/TeX-AMS_HTML-full.js @@ -42,11 +42,11 @@ MathJax.Extension.tex2jax={version:"2.0",config:{inlineMath:[["\\(","\\)"]],disp (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/config/TeX-AMS_HTML.js b/config/TeX-AMS_HTML.js @@ -40,11 +40,11 @@ MathJax.Extension.tex2jax={version:"2.0",config:{inlineMath:[["\\(","\\)"]],disp (function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className+=" isError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var n=0,k=r.length;n<k;n++){h.addText(p,r[n]);if(n!==k-1){h.addElement(p,"br",{isMathJax:true})}}var s=h.getHD(p.parentNode),j=h.getW(p.parentNode);if(k>1){var q=(s.h+s.d)/2,o=h.TeX.x_height/2;var l=h.config.styles[".MathJax .merror"]["font-size"];if(l&&l.match(/%/)){o*=parseInt(l)/100}p.parentNode.style.verticalAlign=h.Em(s.d+(o-q));s.h=o+q;s.d=q-o}p.bbox={h:s.h,d:s.d,w:j,lw:0,rw:j};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/extensions/MathMenu.js b/extensions/MathMenu.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); +(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+s,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable.",MSIE:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(r){var q=o.settings.discoverable;if(!e){if(o.settings.mpMouse&&!confirm("This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?")){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!q&&r.name==="Menu Events"&&o.settings.mpContext){alert("The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead.")}}};c.Browser.Select({MSIE:function(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("Zoom Factor",m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU("Math Renderer",{hidden:!o.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,o.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); diff --git a/extensions/toMathML.js b/extensions/toMathML.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.arrow){e.push("MJX-arrow")}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+" "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+" ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); diff --git a/unpacked/MathJax.js b/unpacked/MathJax.js @@ -1250,7 +1250,10 @@ MathJax.Hub = { zscale: "200%", // the scaling factor for MathZoom renderer: "", // set when Jax are loaded font: "Auto", // what font HTML-CSS should use - context: "MathJax" // or "Browser" for pass-through to browser menu + context: "MathJax", // or "Browser" for pass-through to browser menu + mpContext: false, // true means pass menu events to MathPlayer in IE + mpMouse: false, // true means pass mouse events to MathPlayer in IE + texHints: true // includes class names for TeXAtom elements }, errorSettings: { diff --git a/unpacked/extensions/MathMenu.js b/unpacked/extensions/MathMenu.js @@ -896,7 +896,9 @@ MENU.menu = MENU( ITEM.SUBMENU("Show Math As", ITEM.COMMAND("MathML Code", MENU.ShowSource, {nativeTouch: true, format: "MathML"}), - ITEM.COMMAND("Original Form", MENU.ShowSource, {nativeTouch: true}) + ITEM.COMMAND("Original Form", MENU.ShowSource, {nativeTouch: true}), + ITEM.RULE(), + ITEM.CHECKBOX("Show TeX hints in MathML", "texHints") ), ITEM.RULE(), ITEM.SUBMENU("Math Settings", diff --git a/unpacked/extensions/toMathML.js b/unpacked/extensions/toMathML.js @@ -25,7 +25,8 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function () { var VERSION = "2.0"; - var MML = MathJax.ElementJax.mml; + var MML = MathJax.ElementJax.mml + SETTINGS = MathJax.Hub.config.menuSettings; MML.mbase.Augment({ @@ -73,7 +74,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function () { }, toMathMLclass: function (attr) { var CLASS = []; if (this["class"]) {CLASS.push(this["class"])} - if (this.isa(MML.TeXAtom)) { + if (this.isa(MML.TeXAtom) && SETTINGS.texHints) { var TEXCLASS = ["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass]; if (TEXCLASS) {CLASS.push("MJX-TeXAtom-"+TEXCLASS)} } @@ -89,7 +90,6 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function () { // FIXME: should take scriptlevel into account return ((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"em"; } - // FIXME: set classes for these? else if (this.toMathMLvariants[value]) {return this.toMathMLvariants[value]} return this.toMathMLquote(value); }, @@ -148,6 +148,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function () { toMathML: function (space) { // FIXME: Handle spacing using mpadded? var attr = this.toMathMLattributes(); + if (!attr && this.data[0].data.length === 1) {return space.substr(2) + this.data[0].toMathML(space)} return space+"<mrow"+attr+">\n" + this.data[0].toMathML(space+" ")+"\n"+space+"</mrow>"; } });