From 1698f9c33cac4298d5da365e91941185df9ee72c Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Fri, 10 Feb 2012 08:21:42 -0500 Subject: [PATCH] Make a separate routine to get the contents of a script, and make it work in IE for XHTML files. --- MathJax.js | 2 +- config/AM_HTMLorMML-full.js | 2 +- config/AM_HTMLorMML.js | 2 +- config/Accessible-full.js | 4 ++-- config/Accessible.js | 4 ++-- config/MML_HTMLorMML-full.js | 2 +- config/MML_HTMLorMML.js | 2 +- config/TeX-AMS-MML_HTMLorMML-full.js | 4 ++-- config/TeX-AMS-MML_HTMLorMML.js | 4 ++-- config/TeX-AMS-MML_SVG-full.js | 4 ++-- config/TeX-AMS-MML_SVG.js | 4 ++-- config/TeX-AMS_HTML-full.js | 2 +- config/TeX-AMS_HTML.js | 2 +- config/TeX-MML-AM_HTMLorMML-full.js | 6 +++--- config/TeX-MML-AM_HTMLorMML.js | 6 +++--- jax/input/AsciiMath/jax.js | 2 +- jax/input/MathML/jax.js | 2 +- jax/input/TeX/jax.js | 2 +- unpacked/MathJax.js | 10 +++++++--- unpacked/jax/input/AsciiMath/jax.js | 2 +- unpacked/jax/input/MathML/jax.js | 4 +--- unpacked/jax/input/TeX/jax.js | 5 +---- 22 files changed, 38 insertions(+), 39 deletions(-) diff --git a/MathJax.js b/MathJax.js index 05436a133..27959d9dd 100644 --- 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;i0&&priorityf){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=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{if(i){delete this.loading[h]}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;k1?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.ithis.processUpdateTime&&a.i1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.jthis.processUpdateTime&&h.i=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=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('');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;i0&&priorityf){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=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{if(i){delete this.loading[h]}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;k1?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.ithis.processUpdateTime&&a.i1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.jthis.processUpdateTime&&h.i=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=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('');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/AM_HTMLorMML-full.js b/config/AM_HTMLorMML-full.js index dcfb21ba6..c370c4b99 100644 --- a/config/AM_HTMLorMML-full.js +++ b/config/AM_HTMLorMML-full.js @@ -53,7 +53,7 @@ MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version 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")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}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+""},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;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[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\n"+g.join("\n")+"\n"+h+""}});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\n"+g.join("\n")+"\n"+h+""}});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+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});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(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=c.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); +(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{".MathJax_mmlExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex",padding:0,border:0,margin:0}}},settings:b.config.menuSettings,Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}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+""},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;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[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\n"+g.join("\n")+"\n"+h+""}});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\n"+g.join("\n")+"\n"+h+""}});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+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});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(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=c.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); +(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); MathJax.Ajax.loadComplete("[MathJax]/config/AM_HTMLorMML.js"); diff --git a/config/Accessible-full.js b/config/Accessible-full.js index 1ec4c5642..3cae924db 100644 --- a/config/Accessible-full.js +++ b/config/Accessible-full.js @@ -80,13 +80,13 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"2.0",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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 span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}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+""},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;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[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\n"+g.join("\n")+"\n"+h+""}});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\n"+g.join("\n")+"\n"+h+""}});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+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});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(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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 span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}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+""},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;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[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\n"+g.join("\n")+"\n"+h+""}});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\n"+g.join("\n")+"\n"+h+""}});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+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});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(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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 span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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=p.SVGlast+p.SVGchunk){this.postTranslate(p);p.SVGchunk=Math.floor(p.SVGchunk*this.config.EqnChunkFactor);p.SVGdelay=true}}},postTranslate:function(q){var l=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.SVGlast,k=q.SVGeqn;o=55296&&o<56319){t++;o=(((o-55296)<<10)+(B.charCodeAt(t)-56320))+65536;if(this.FONTDATA.RemapPlane1){var v=this.FONTDATA.RemapPlane1(o,s);o=v.n;s=v.variant}}else{k=this.FONTDATA.RANGES;for(l=0,x=k.length;l=k[l].low&&o<=k[l].high){if(k[l].remap&&k[l].remap[o]){o=w+k[l].remap[o]}else{o=o-k[l].low+w;if(k[l].add){o+=k[l].add}}if(s["variant"+k[l].offset]){s=this.FONTDATA.VARIANT[s["variant"+k[l].offset]]}break}}}if(s.remap&&s.remap[o]){if(s.remap[o] instanceof Array){var A=s.remap[o];o=A[0];s=this.FONTDATA.VARIANT[A[1]]}else{if(typeof(s.remap[o])==="string"){B=s.remap[o]+B.substr(t+1);t=0;q=B.length;o=B.charCodeAt(0)}else{o=s.remap[o];if(s.remap.variant){s=this.FONTDATA.VARIANT[s.remap.variant]}}}}if(this.FONTDATA.REMAP[o]&&!s.noRemap){o=this.FONTDATA.REMAP[o];if(o instanceof Array){s=this.FONTDATA.VARIANT[o[1]];o=o[0]}if(typeof(o)==="string"){B=o+B.substr(t+1);t=0;q=B.length;o=o.charCodeAt(0)}}p=this.lookupChar(s,o);y=p[o];if(y){y=[r,p.id+"-"+o.toString(16).toUpperCase()].concat(y);u.Add(i.GLYPH.apply(i,y),u.w,0)}else{if(this.FONTDATA.DELIMITERS[o]){u.Add(this.createDelimiter(o,0,1,p),u.w,0)}else{if(o<=65535){y=String.fromCharCode(o)}else{w=o-65536;y=String.fromCharCode((w>>10)+55296)+String.fromCharCode((w&1023)+56320)}B=i.TEXT(r,y,{"font-family":s.defaultFamily||a.config.MISSINGFONT,"font-style":(s.italic?"italic":""),"font-weight":(s.bold?"bold":"")});if(s.h!=null){B.h=s.h}if(s.d!=null){B.d=s.d}y=i.G();y.Add(B);u.Add(y,u.w,0);B="";c.signal.Post(["SVG Jax - unknown char",o,s])}}}if(B.length==1&&p.skew&&p.skew[o]){u.skew=p.skew[o]*1000}if(u.element.childNodes.length===1){u.element=u.element.firstChild;u.removeable=false;u.scale=r}return u},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){c.RestartAfter(h.Require(this.fontDir+"/"+k))},createDelimiter:function(k,n,q,o){if(!q){q=1}var s=i.G();if(!k){s.Clean();delete s.element;s.w=s.r=this.TeX.nulldelimiterspace*q;return s}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){c.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var r=0,p=l.HW.length;r=n-10-a.config.blacker||(r==p-1&&!l.stretch)){if(l.HW[r][2]){q*=l.HW[r][2]}if(l.HW[r][3]){k=l.HW[r][3]}return this.createChar(q,[k,l.HW[r][1]],o).With({stretched:true})}}if(l.stretch){this["extendDelimiter"+l.dir](s,t,l.stretch,q,o)}return s},createChar:function(s,q,n){var r="",p={fonts:[q[1]],noRemap:true};if(n&&n===g.VARIANT.BOLD){p.fonts=[q[1]+"-bold",q[1]]}if(typeof(q[1])!=="string"){p=q[1]}if(q[0] instanceof Array){for(var o=0,k=q[0].length;oq){var l=this.createChar(o,m.ext,n);var p=(m.mid?2:1),v=(A-q)/p,B=(v+100)/(l.h+l.d);while(p-->0){var t=a.Element("g",{transform:"translate("+l.y+","+(w-B*l.h+50+l.y)+") scale(1,"+B+")"});t.appendChild(l.element.cloneNode(false));r.element.appendChild(t);w-=v;if(m.mid&&p){r.Add(z,0,w-z.h);w-=(z.h+z.d)}}}else{if(m.mid){w+=(q-A)/2;r.Add(z,0,w-z.h);w+=-(z.h+z.d)+(q-A)/2}else{w+=(q-A)}}r.Add(u,0,w-u.h);r.Clean();r.scale=o;r.isMultiChar=true},extendDelimiterH:function(t,o,m,q,n){var p=this.createChar(q,(m.left||m.rep),n);var C=this.createChar(q,(m.right||m.rep),n);t.Add(p,-p.l,0);var B=(p.r-p.l)+(C.r-C.l),z=p.r-p.l;if(m.mid){var A=this.createChar(q,m.mid,n);B+=A.w}if(o>B){var y=this.createChar(q,m.rep,n),l=m.fuzz||0;var r=(m.mid?2:1),v=(o-B)/r,E=(v+l)/(y.r-y.l);while(r-->0){var u=a.Element("g",{transform:"translate("+(z-l/2-E*y.l+y.x)+","+y.y+") scale("+E+",1)"});u.appendChild(y.element.cloneNode(false));t.element.appendChild(u);z+=v;if(m.mid&&r){t.Add(A,z,0);z+=A.w}}}else{if(m.mid){var D=Math.min(B-o,p.w/2);z-=D/2;t.Add(A,z,0);z+=A.w-D/2}else{z-=(B-o)}}t.Add(C,z-C.l,0);t.Clean();t.scale=q;t.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:100,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var i=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(k){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,k)}},With:function(k){return c.Insert(this,k)},Add:function(n,m,l,p,o){if(m){n.x+=m}if(l){n.y+=l}if(n.element){if(n.removeable&&n.element.childNodes.length===1&&n.n===1){var r=n.element.firstChild;if(r.nodeName==="use"||r.nodeName==="rect"){n.element=r;n.scale=n.childScale;var k=n.childX,q=n.childY;n.x+=k;n.y+=q;n.h-=q;n.d+=q;n.H-=q;n.D+=q;n.w-=k;n.r-=k;n.l+=k;n.removeable=false}}if(Math.abs(n.x)<1&&Math.abs(n.y)<1){n.remove=n.removeable}else{if(n.element.nodeName==="g"){if(!n.element.firstChild){n.remove=n.removeable}else{n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}}else{if(n.element.nodeName==="line"||n.element.nodeName==="polygon"||n.element.nodeName==="path"||n.element.nodeName==="a"){n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}else{n.element.setAttribute("x",Math.floor(n.x/n.scale));n.element.setAttribute("y",Math.floor(n.y/n.scale))}}}if(n.remove){this.n+=n.n;while(n.element.firstChild){if(o&&this.element.firstChild){this.element.insertBefore(n.element.firstChild,this.element.firstChild)}else{this.element.appendChild(n.element.firstChild)}}}else{if(o){this.element.insertBefore(n.element,this.element.firstChild)}else{this.element.appendChild(n.element)}}delete n.element}if(n.d-n.y>this.d){this.d=n.d-n.y;if(this.d>this.D){this.D=this.d}}if(n.y+n.h>this.h){this.h=n.y+n.h;if(this.h>this.H){this.H=this.h}}if(n.D-n.y>this.D){this.D=n.D-n.y}if(n.y+n.H>this.H){this.H=n.y+n.H}if(n.x+n.lthis.r){this.r=n.x+n.r}if(p||n.x+n.w+(n.X||0)>this.w){this.w=n.x+n.w+(n.X||0)}this.childScale=n.scale;this.childX=n.x;this.childY=n.y;this.n++;return n},Align:function(m,n,l,k){l=({left:l,center:(this.w-m.w)/2,right:this.w-m.w-l})[n]||0;this.Add(m,l,k)},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});i.ROW=i.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(l){var k=l.toSVG();this.svg.push(k);if(l.SVGcanStretch("Vertical")){k.mml=l}if(k.h>this.sh){this.sh=k.h}if(k.d>this.sd){this.sd=k.d}},Stretch:function(){for(var n=0,k=this.svg.length;nl.w&&p.length===1&&!o.noIC){l.ic=l.r-l.w;l.w=l.r}this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGdataStretched:function(l,k,m){this.SVGdata={HW:k,D:m};if(m!=null){return this.data[l].SVGstretchV(k,m)}if(k!=null){return this.data[l].SVGstretchH(k)}return this.data[l].toSVG()},SVGsaveData:function(l){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=l.w,this.SVGdata.x=l.x;if(l.X!=null){this.SVGdata.X=l.X}if(this["class"]){l.removeable=false;a.Element(l.element,{"class":this["class"]})}if(this.id){l.removeable=false;a.Element(l.element,{id:this.id})}if(this.href){var k=a.Element("a");k.setAttributeNS(j,"href",this.href);a.addElement(k,"rect",{width:l.w,height:l.h+l.d,y:-l.d,fill:"none",stroke:"none","pointer-events":"all"});if(l.type==="svg"){var n=l.element.firstChild;while(n.firstChild){k.appendChild(n.firstChild)}n.appendChild(k)}else{if(l.removeable&&l.element.nodeName==="g"){while(l.element.firstChild){k.appendChild(l.element.firstChild)}}else{k.appendChild(l.element)}l.element=k}l.removeable=false}if(a.config.addMMLclasses){l.removeable=false;l.element.setAttribute("className","mjx-svg-"+this.type)}var m=this.Get("style");if(m){l.element.style.cssText=m;if(l.element.style.fontSize){l.element.style.fontSize=""}l.element.style.border=l.element.style.padding="";if(l.removeable){l.removeable=l.element.style.cssText===""}}},SVGgetStyles:function(){var l=this.Get("style");if(l){var k=e.Element("span");k.style.cssText=l;this.styles={border:a.getBorders(k),padding:a.getPadding(k)};if(k.style.fontSize){this.styles.fontSize=k.style.fontSize}if(k.style.color){this.styles.color=k.style.color}if(k.style.backgroundColor){this.styles.background=k.style.backgroundColor}if(k.style.fontStyle){this.styles.fontStyle=k.style.fontStyle}if(k.style.fontWeight){this.styles.fontWeight=k.style.fontWeight}if(k.style.fontFamily){this.styles.fontFamily=k.style.fontFamily}if(this.styles.fontWeight&&this.styles.fontWeight.match(/^\d+$/)){this.styles.fontWeight=(parseInt(this.styles.fontWeight)>600?"bold":"normal")}}},SVGhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.SVGgetMu(n);m.lspace=Math.max(0,a.length2em(m.lspace,l));m.rspace=Math.max(0,a.length2em(m.rspace,l));var k=this,o=this.Parent();while(o&&o.isEmbellished()&&o.Core()===k){k=o;o=o.Parent()}if(m.lspace){n.x+=m.lspace}if(m.rspace){n.X=m.rspace}}}else{var p=this.texSpacing();if(p!==""){n.x+=a.length2em(p,this.SVGgetScale())/n.scale}}},SVGhandleColor:function(o){var w=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!w.color){w.color=this.styles.color}if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.mathcolor){a.Element(o.element,{fill:w.mathcolor,stroke:w.mathcolor});o.removeable=false}var s=(this.styles||{}).border,u=(this.styles||{}).padding,t=((s||{}).left||0),q=((u||{}).left||0),k;w.background=(this.mathbackground||this.background||(this.styles||{}).background||g.COLOR.TRANSPARENT);if(t+q){var l=i();for(k in o){if(o.hasOwnProperty(k)){l[k]=o[k]}}l.x=0;l.y=0;o.element=a.Element("g");o.removeable=true;o.Add(l,t+q,0)}if(u){o.w+=u.right;o.h+=u.top;o.d+=u.bottom}if(s){o.w+=s.right;o.h+=s.top;o.d+=s.bottom}if(w.background!==g.COLOR.TRANSPARENT){if(o.element.nodeName!=="g"&&o.element.nodeName!=="svg"){var p=a.Element("g");p.appendChild(o.element);o.element=p;o.removable=true}o.Add(i.RECT(o.h,o.d,o.w,{fill:w.background}),0,0,false,true)}if(s){var v=5;var m={left:["V",o.h+o.d,-v,-o.d],right:["V",o.h+o.d,o.w-s.right+v,-o.d],top:["H",o.w,0,o.h-s.top+v],bottom:["H",o.w,0,-o.d-v]};for(k in m){if(m.hasOwnProperty(k)){if(s[k]){var r=m[k],n=i[r[0]+"LINE"];o.Add(n(r[1],s[k],s[k+"Style"],s[k+"Color"]),r[2],r[3])}}}}},SVGhandleVariant:function(k,m,l){return a.HandleVariant(k,m,l)},SVGgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var l=k.mathvariant;if(this.variantForm){l="-TeX-variant"}k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.styles){if(!k.style&&this.styles.fontStyle){k.style=this.styles.fontStyle}if(!k.weight&&this.styles.fontWeight){k.weight=this.styles.fontWeight}if(!k.family&&this.styles.fontFamily){k.family=this.styles.fontFamily}}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}l={forceFamily:true,font:{"font-family":k.family}};if(k.style){l.font["font-style"]=k.style}if(k.weight){l.font["font-weight"]=k.weight}return l}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}return a.FONTDATA.VARIANT[l]},SVGgetScale:function(){var l=1,k=this.getValues("mathsize","scriptlevel","fontsize");if((this.styles||{}).fontSize&&!k.fontsize){k.fontsize=this.styles.fontSize}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(l2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},SVGnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},SVGcanStretch:function(k){if(this.isEmbellished()){return this.Core().SVGcanStretch(k)}return false},SVGstretchV:function(k,l){return this.toSVG(k,l)},SVGstretchH:function(k){return this.toSVG(k)},SVGlineBreaks:function(){return false}},{SVGautoload:function(){var k=a.autoloadDir+"/"+this.type+".js";c.RestartAfter(h.Require(k))},SVGautoloadFile:function(k){var l=a.autoloadDir+"/"+k+".js";c.RestartAfter(h.Require(l))}});g.chars.Augment({toSVG:function(l,o,k,m){var n=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(k){n=k(n,m)}return this.SVGhandleVariant(l,o,n)}});g.entity.Augment({toSVG:function(k,l){return this.SVGhandleVariant(k,l,this.toString().replace(/[\u2061-\u2064]/g,""))}});g.mo.Augment({toSVG:function(){this.SVGgetStyles();var r=this.svg=this.SVG();this.SVGhandleSpace(r);if(this.data.length==0){r.Clean();this.SVGsaveData(r);return r}var n=this.SVGgetScale(),p=this.SVGgetVariant();var w=this.getValues("largeop","displaystyle");if(w.largeop){p=a.FONTDATA.VARIANT[w.displaystyle?"-largeOp":"-smallOp"]}var v=this.CoreParent(),o=(v&&v.isa(g.msubsup)&&this!==v.data[0]),k=(o?this.SVGremapChars:null);if(this.data.join("").length===1&&v&&v.isa(g.munderover)&&this.CoreText(v.data[v.base]).length===1){var s=v.data[v.over],u=v.data[v.under];if(s&&this===s.CoreMO()&&v.Get("accent")){k=a.FONTDATA.REMAPACCENT}else{if(u&&this===u.CoreMO()&&v.Get("accentunder")){k=a.FONTDATA.REMAPACCENTUNDER}}}for(var q=0,l=this.data.length;q10*y.w){t+=-y.l}r.Add(y,t,0,true);if(y.skew){r.skew=y.skew}}}r.Clean();if(this.data.join("").length!==1){delete r.skew}if(w.largeop){r.y=(r.h-r.d)/2/n-a.TeX.axis_height;if(r.r>r.w){r.ic=r.r-r.w;r.w=r.r}}this.SVGhandleColor(r);this.SVGsaveData(r);return r},CoreParent:function(){var k=this;while(k&&k.isEmbellished()&&k.CoreMO()===this&&!k.isa(g.math)){k=k.Parent()}return k},CoreText:function(k){if(!k){return""}if(k.isEmbellished()){return k.CoreMO().data.join("")}while(k.isa(g.mrow)&&k.data.length===1&&k.data[0]){k=k.data[0]}if(!k.isToken){return""}else{return k.data.join("")}},SVGremapChars:{"*":"\u2217",'"':"\u2033","\u00B0":"\u2218","\u00B2":"2","\u00B3":"3","\u00B4":"\u2032","\u00B9":"1"},SVGremap:function(l,k){l=l.replace(/-/g,"\u2212");if(k){l=l.replace(/'/g,"\u2032").replace(/`/g,"\u2035");if(l.length===1){l=k[l]||l}}return l},SVGcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var l=this.CoreParent();if(l&&l.isa(g.munderover)&&this.CoreText(l.data[l.base]).length===1){var n=l.data[l.over],k=l.data[l.under];if(n&&this===n.CoreMO()&&l.Get("accent")){p=a.FONTDATA.REMAPACCENT[p]||p}else{if(k&&this===k.CoreMO()&&l.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=a.FONTDATA.DELIMITERS[p.charCodeAt(0)];var m=(p&&p.dir==o.substr(0,1));if(!m){delete this.svg}return m},SVGstretchV:function(p,q){var m=this.svg||this.toSVG();var l=this.getValues("symmetric","maxsize","minsize");var o=a.TeX.axis_height,k=this.SVGgetMu(m),n;if(l.symmetric){n=2*Math.max(p-o,q+o)}else{n=p+q}l.maxsize=a.length2em(l.maxsize,k,m.h+m.d);l.minsize=a.length2em(l.minsize,k,m.h+m.d);n=Math.max(l.minsize,Math.min(l.maxsize,n));m=a.createDelimiter(this.data.join("").charCodeAt(0),n,m.scale);if(l.symmetric){n=(m.h+m.d)/2+o}else{n=(m.h+m.d)*p/(p+q)}m.y=n-m.h;this.SVGhandleSpace(m);this.SVGhandleColor(m);delete this.svg;this.SVGsaveData(m);return m},SVGstretchH:function(l){var n=this.svg||this.toSVG(),k=this.SVGgetMu(n);var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}m.maxsize=a.length2em(m.maxsize,k,n.w);m.minsize=a.length2em(m.minsize,k,n.w);l=Math.max(m.minsize,Math.min(m.maxsize,l));n=a.createDelimiter(this.data.join("").charCodeAt(0),l,n.scale,m.mathvariant);this.SVGhandleSpace(n);this.SVGhandleColor(n);delete this.svg;this.SVGsaveData(n);return n}});g.mtext.Augment({toSVG:function(){this.SVGgetStyles();var k,m,l=this.SVGgetScale();if(this.Parent().type==="merror"){k=this.SVG();this.SVGhandleSpace(k);m=i.G();m.Add(i.TEXT(0.9*l,this.data.join(""),{fill:"#C00"}));k.Add(i.RECT(m.h+100,m.d+100,m.w+200,{fill:"#FF8",stroke:"#C00","stroke-width":50}),0,0);k.Add(m,150,0);k.H+=150;k.D+=50;k.Clean();this.SVGsaveData(k);return k}else{if(a.config.mtextFontInherit){k=this.SVG();this.SVGhandleSpace(k);k.Add(i.TEXT(l,this.data.join("")));k.Clean();this.SVGhandleColor(k);this.SVGsaveData(k);return k}else{return this.SUPER(arguments).toSVG.call(this)}}}});g.ms.Augment({toSVG:g.mbase.SVGautoload});g.mglyph.Augment({toSVG:g.mbase.SVGautoload});g.mspace.Augment({toSVG:function(){this.SVGgetStyles();var m=this.getValues("height","depth","width");m.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){m.mathbackground=this.background}var l=this.SVG(),k=this.SVGgetMu(l);l.h=a.length2em(m.height,k)/l.scale;l.d=a.length2em(m.depth,k)/l.scale;l.w=l.r=a.length2em(m.width,k)/l.scale;if(l.w<0){l.x=l.w;l.w=l.r=0}l.l=0;l.Clean();this.SVGhandleColor(l);this.SVGsaveData(l);return l}});g.mphantom.Augment({toSVG:function(k,m){this.SVGgetStyles();var l=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(l);l.Add(this.SVGdataStretched(0,k,m));l.Clean();while(l.element.firstChild){l.element.removeChild(l.element.firstChild)}}this.SVGhandleColor(l);if(!l.element.firstChild){delete l.element}this.SVGsaveData(l);return l}});g.mpadded.Augment({toSVG:function(l,k){this.SVGgetStyles();var o=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(o);var m=this.SVGdataStretched(0,l,k),u=this.SVGgetMu(o);var t=this.getValues("height","depth","width","lspace","voffset"),r=0,q=0;if(t.lspace){r=this.SVGlength2em(m,t.lspace,u)}if(t.voffset){q=this.SVGlength2em(m,t.voffset,u)}var n=m.h,p=m.d,s=m.w;o.Add(m,r,q);o.Clean();o.h=n;o.d=p;o.w=s;o.removeable=false;if(t.height!==""){o.h=this.SVGlength2em(o,t.height,u,"h",0)}if(t.depth!==""){o.d=this.SVGlength2em(o,t.depth,u,"d",0)}if(t.width!==""){o.w=this.SVGlength2em(o,t.width,u,"w",0)}if(o.h>o.H){o.H=o.h}if(o.d>o.D){o.D=o.d}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGlength2em:function(o,r,l,s,k){if(k==null){k=-a.BIGDIMEN}var p=String(r).match(/width|height|depth/);var q=(p?o[p[0].charAt(0)]:(s?o[s]:0));var n=a.length2em(r,l,q);if(s&&String(r).match(/^\s*[-+]/)){return Math.max(k,o[s]+n)}else{return n}}});g.mrow.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);for(var n=0,k=this.data.length;na.linebreakWidth)||this.hasNewline()},SVGmultiline:function(k){g.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(k){var l=this.data[this.core].SVGstretchH(k);this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGstretchV:function(l,m){var k=this.data[this.core].SVGstretchV(l,m);this.SVGhandleColor(k);this.SVGsaveData(k);return k}});g.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(k);var l=k.Add(this.data[0].toSVG());k.Clean();if(l.ic){k.ic=l.ic}this.SVGhandleColor(k)}this.SVGsaveData(k);return k},SVGstretchH:function(k){return(this.data[0]!=null?this.data[0].SVGstretchH(k):i.NULL())},SVGstretchV:function(k,l){return(this.data[0]!=null?this.data[0].SVGstretchV(k,l):i.NULL())}});g.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var w=this.SVG();this.SVGhandleSpace(w);var s=this.data[0].toSVG(),y=this.data[1].toSVG();var C=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var r=w.scale=this.SVGgetScale(),n=C.displaystyle;var x=a.TeX.axis_height*r;if(C.bevelled){var B=(n?400:150);var A=Math.max(s.h+s.d,y.h+y.d)+2*B;var F=a.createDelimiter(47,A);w.Add(s,0,(s.d-s.h)/2+x+B);w.Add(F,s.w-B/2,(F.d-F.h)/2+x);w.Add(y,s.w+F.w-B,(y.d-y.h)/2+x-B)}else{var o=Math.max(s.w,y.w);var E=a.thickness2em(C.linethickness,r),m,l,D,z;var k=a.TeX.min_rule_thickness/a.em*1000;if(n){D=a.TeX.num1;z=a.TeX.denom1}else{D=(E===0?a.TeX.num3:a.TeX.num2);z=a.TeX.denom2}D*=r;z*=r;if(E===0){m=Math.max((n?7:3)*a.TeX.rule_thickness,2*k);l=(D-s.d)-(y.h-z);if(lv){k=((o.h+o.d)-(v-w))/2}s=i.RECT(w,0,m.w);v=m.h+k+w;u=this.SVGaddRoot(r,o,u,o.h+o.d-v,n);r.Add(o,u,v-o.h);r.Add(s,u+o.w,v-s.h);r.Add(m,u+o.w,0);r.Clean();r.h+=w;r.H+=w;this.SVGhandleColor(r);this.SVGsaveData(r);return r},SVGaddRoot:function(l,m,k,o,n){return k}});g.mroot.Augment({toSVG:g.msqrt.prototype.toSVG,SVGaddRoot:function(n,l,q,o,k){var s=(l.isMultiChar?0.55:0.65)*l.w;if(this.data[1]){var p=this.data[1].toSVG();p.x=0;var m=this.SVGrootHeight(l.h+l.d,k,p)-o;var r=Math.min(p.w,p.r);q=Math.max(r,s);n.Add(p,q-r,m)}else{s=q}return q-s},SVGrootHeight:function(m,l,k){return 0.45*(m-900*l)+600*l+Math.max(0,k.d-75)}});g.mfenced.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);if(this.data.open){l.Check(this.data.open)}if(this.data[0]!=null){l.Check(this.data[0])}for(var n=1,k=this.data.length;nI){I=p[J].w}if(!K[J]&&I>n){n=I}}}if(C==null&&F!=null){n=F}else{if(n==-a.BIGDIMEN){n=I}}for(J=I=0,G=this.data.length;JI){I=p[J].w}}}var B=a.TeX.rule_thickness;var o=p[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,scale:M};var s,q,w,v,r,A,H,L=0;if(o.ic){L=1.3*o.ic+0.05}for(J=0,G=this.data.length;Ju.H){u.H=u.h}}else{if(J==this.under){if(z){H=3*B*M;r=0}else{w=a.TeX.big_op_spacing2*M;v=a.TeX.big_op_spacing4*M;H=Math.max(w,v-u.h)}H=Math.max(H,1500/a.em);s-=L/2;q=-(o.d+u.h+H);u.d+=r;if(u.d>u.D){u.D=u.d}}}E.Add(u,s,q)}}E.Clean();this.SVGhandleColor(E);this.SVGsaveData(E);return E}});g.msubsup.Augment({toSVG:function(G,z){this.SVGgetStyles();var B=this.SVG();this.SVGhandleSpace(B);var K=B.scale=this.SVGgetScale(),E=this.SVGgetMu(B);var m=B.Add(this.SVGdataStretched(this.base,G,z));var l=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var I=a.TeX.x_height*K,y=a.TeX.scriptspace*K;var k,n;if(this.SVGnotEmpty(this.data[this.sup])){k=this.data[this.sup].toSVG();k.w+=y;k.r=Math.max(k.w,k.r)}if(this.SVGnotEmpty(this.data[this.sub])){n=this.data[this.sub].toSVG();n.w+=y;n.r=Math.max(n.w,n.r)}var C=a.TeX.sup_drop*l,A=a.TeX.sub_drop*l;var w=m.h-C,o=m.d+A,J=0,F;if(m.ic){m.w-=m.ic;J=1.3*m.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&m.scale===1&&!m.stretched&&!this.data[this.base].Get("largeop")){w=o=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:a.length2em(H.subscriptshift,E));H.superscriptshift=(H.superscriptshift===""?0:a.length2em(H.superscriptshift,E));if(!k){if(n){o=Math.max(o,a.TeX.sub1*K,n.h-(4/5)*I,H.subscriptshift);B.Add(n,m.w,-o)}}else{if(!n){values=this.getValues("displaystyle","texprimestyle");F=a.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];w=Math.max(w,F*K,k.d+(1/4)*I,H.superscriptshift);B.Add(k,m.w+J,w)}else{o=Math.max(o,a.TeX.sub2*K);var x=a.TeX.rule_thickness*K;if((w-k.d)-(n.h-o)<3*x){o=3*x-w+k.d+n.h;C=(4/5)*I-(w-k.d);if(C>0){w+=C;o-=C}}B.Add(k,m.w+J,Math.max(w,H.superscriptshift));B.Add(n,m.w,-Math.max(o,H.subscriptshift))}}B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B}});g.mmultiscripts.Augment({toSVG:g.mbase.SVGautoload});g.mtable.Augment({toSVG:g.mbase.SVGautoload});g["annotation-xml"].Augment({toSVG:g.mbase.SVGautoload});g.math.Augment({SVG:i.Subclass({type:"svg",removeable:false}),toSVG:function(t,m){if(this.data[0]){this.SVGgetStyles();g.mbase.prototype.displayAlign=c.config.displayAlign;g.mbase.prototype.displayIndent=c.config.displayIndent;var q=i.G({stroke:"black",fill:"black","stroke-thickness":0,transform:"matrix(1 0 0 -1 0 0)"}).With({removeable:false});q.Add(this.data[0].toSVG(),0,0,true);q.Clean();this.SVGhandleColor(q);var s=this.SVG();s.element.setAttribute("xmlns:xlink",j);s.Add(q);s.Clean();this.SVGsaveData(s);var p=Math.max(-s.l,0),k=Math.max(s.r-s.w,0);var n=s.element.style;n.width=a.Ex(p+s.w+k);n.height=a.Ex(s.H+s.D);n.verticalAlign=a.Ex(-s.D-2*a.em);n.marginLeft=a.Ex(-p);n.marginRight=a.Ex(-k);s.element.setAttribute("viewBox",(-p)+" "+(-s.H)+" "+(p+s.w+k)+" "+(s.H+s.D));s.element.style.margin="1px 0px";if(s.H>s.h||s.D>s.d){var o=e.Element("span",{style:{display:"inline-block","white-space":"nowrap",padding:"1px 0px"},isMathJax:true},[["span",{style:{display:"inline-block",position:"relative",isMathJax:true,width:a.Ex(s.w),height:a.Ex(s.h+s.d),"vertical-align":a.Ex(-s.d)}}]]);o.firstChild.appendChild(s.element);s.element=o;n.verticalAlign="";n.position="absolute";n.bottom=a.Ex(s.d-s.D);n.left=0}t.appendChild(s.element);s.element=null;if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===g.INDENTALIGN.AUTO){u.indentalign=this.displayAlign}m.style.textAlign=u.indentalign;if(u.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift=this.displayIndent}if(u.indentshift&&u.indentalign!==g.INDENTALIGN.CENTER){t.style[{left:"marginLeft",right:"marginRight"}[u.indentalign]]=a.Ex(a.length2em(u.indentshift))}}}return t}});g.TeXAtom.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(this.data[0]!=null){var l=this.data[0].toSVG(),m=0;if(this.texClass===g.TEXCLASS.VCENTER){m=a.TeX.axis_height-(l.h+l.d)/2+l.d}k.Add(l,0,m);k.ic=l.ic}this.SVGhandleColor(k);this.SVGsaveData(k);return k}});c.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(k,l){var m=(typeof(k)==="string"?document.createElement("svg:"+k):k);m.isMathJax=true;if(l){for(var n in l){if(l.hasOwnProperty(n)){m.setAttribute(n,l[n].toString())}}}return m}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); diff --git a/config/TeX-AMS-MML_SVG.js b/config/TeX-AMS-MML_SVG.js index be7da99fd..d6c6b3858 100644 --- a/config/TeX-AMS-MML_SVG.js +++ b/config/TeX-AMS-MML_SVG.js @@ -57,12 +57,12 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"2.0",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=c.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); +(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{".MathJax_mmlExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex",padding:0,border:0,margin:0}}},settings:b.config.menuSettings,Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=c.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); +(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_HTMLorMML.js"); diff --git a/jax/input/AsciiMath/jax.js b/jax/input/AsciiMath/jax.js index 21e0b0af1..72f8fdd48 100644 --- a/jax/input/AsciiMath/jax.js +++ b/jax/input/AsciiMath/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=c.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); +(function(ae){var j;var Z=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.childNodes.push(ag);ag.parent=this;this.lastChild=ag;return ag},removeChild:function(ai){for(var ah=0,ag=this.childNodes.length;ah=ag-1){this.lastChild=aj}this.childNodes[ai]=aj;aj.nextSibling=ah.nextSibling;ah.nextSibling=ah.parent=null;return ah},toString:function(){return"{"+this.childNodes.join("")+"}"}});var D=function(){j=MathJax.ElementJax.mml;var ag=j.mbase.prototype.Init;j.mbase.Augment({firstChild:null,lastChild:null,nodeValue:"",nextSibling:null,Init:function(){var ah=ag.apply(this,arguments)||this;ah.childNodes=ah.data;ah.nodeName=ah.type;return ah},appendChild:function(ak){if(ak.parent){ak.parent.removeChild(ak)}var ai=arguments;if(ak.isa(Z)){ai=ak.childNodes;ak.data=ak.childNodes=[];ak.firstChild=ak.lastChild=null}for(var aj=0,ah=ai.length;aj=ah-1){this.lastChild=ak}this.SetData(aj,ak);ak.nextSibling=ai.nextSibling;this.nodeValue="";for(aj=0,ah=this.childNodes.length;aj=",tag:"mo",output:"\u2265",tex:"ge",ttype:d},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:d},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:d},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:d},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:d},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:d},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:d},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:d},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:d},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:d},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:d},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:d},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:d},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:d},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:d},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:d},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:d},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:d},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:d},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:d},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:d},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:d},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:d},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:d},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:k},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:k},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:k},{input:"|",tag:"mo",output:"|",tex:null,ttype:q},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:k},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:k},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:k,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:d},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:Y},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:Y},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:Y},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:Y},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:d},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:d},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:d},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:d},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:d},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:d},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:d},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:d},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:d},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:d},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:d},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:d},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:d},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:d},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:d},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:d},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:d},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:d},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:d},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:d},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:d},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:d},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:d},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:d},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:d},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:d},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:d},{input:"f",tag:"mi",output:"f",tex:null,ttype:G,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:G,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:O},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:O},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:G,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:G,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:G,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:G,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:G,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:G,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:G,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:G,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:G,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:G,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:G,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:G,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:d},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:d},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:G,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:G,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:d},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:d},{input:"min",tag:"mo",output:"min",tex:null,ttype:O},{input:"max",tag:"mo",output:"max",tex:null,ttype:O},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:d},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:d},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:d},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:d},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:d},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:d},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:d},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:d},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:d},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:d},i,ad,z,P,n,r,h,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:G,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:G,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:G,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:G,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:G,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:G,acc:true},af,w,o,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:G},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:G},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:G},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:G},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:G,codes:C},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:G,codes:C},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:G,codes:I},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:G,codes:I},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:G},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:G},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:G,codes:M},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:G,codes:M}];function V(ah,ag){if(ah.input>ag.input){return 1}else{return -1}}var T=[];function u(){var ah=[],ag;for(ag=0;ag>1;if(ah[ag]=T[ag]}x=E;if(ak!=""){E=F[aj].ttype;return F[aj]}E=d;ag=1;ap=am.slice(0,1);var an=true;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}if(ap==f){ap=am.slice(ag,ag+1);if("0"<=ap&&ap<="9"){an=false;ag++;while("0"<=ap&&ap<="9"&&ag<=am.length){ap=am.slice(ag,ag+1);ag++}}}if((an&&ag>1)||ag>2){ap=am.slice(0,ag-1);ao="mn"}else{ag=2;ap=am.slice(0,1);ao=(("A">ap||ap>"Z")&&("a">ap||ap>"z")?"mo":"mi")}if(ap=="-"&&x==l){return{input:ap,tag:ao,output:ap,ttype:G,func:true}}return{input:ap,tag:ao,output:ap,ttype:d}}function S(ah){var ag;if(ah.nodeName=="mrow"){ag=ah.firstChild.firstChild.nodeValue;if(ag=="("||ag=="["||ag=="{"){ah.removeChild(ah.firstChild)}}if(ah.nodeName=="mrow"){ag=ah.lastChild.firstChild.nodeValue;if(ag==")"||ag=="]"||ag=="}"){ah.removeChild(ah.lastChild)}}}var J,x,E;function K(am){var ai,ah,ap,ak,ao,al=g.createDocumentFragment();am=t(am,0);ai=m(am);if(ai==null||ai.ttype==k&&J>0){return[null,am]}if(ai.ttype==Y){am=ai.output+t(am,ai.input.length);ai=m(am)}switch(ai.ttype){case O:case d:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am];case b:J++;am=t(am,ai.input.length);ap=v(am,true);J--;if(typeof ai.invisible=="boolean"&&ai.invisible){ah=L("mrow",ap[0])}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0])}return[ah,ap[1]];case aa:if(ai!=o){am=t(am,ai.input.length)}if(am.charAt(0)=="{"){ak=am.indexOf("}")}else{if(am.charAt(0)=="("){ak=am.indexOf(")")}else{if(am.charAt(0)=="["){ak=am.indexOf("]")}else{if(ai==o){ak=am.slice(1).indexOf('"')+1}else{ak=0}}}}if(ak==-1){ak=am.length}ao=am.slice(1,ak);if(ao.charAt(0)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}al.appendChild(L(ai.tag,g.createTextNode(ao)));if(ao.charAt(ao.length-1)==" "){ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah)}am=t(am,ak+1);return[L("mrow",al),am];case G:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L(ai.tag,g.createTextNode(ai.output)),am]}if(typeof ai.func=="boolean"&&ai.func){ao=am.charAt(0);if(ao=="^"||ao=="_"||ao=="/"||ao=="|"||ao==","){return[L(ai.tag,g.createTextNode(ai.output)),am]}else{ah=L("mrow",L(ai.tag,g.createTextNode(ai.output)));ah.appendChild(ap[0]);return[ah,ap[1]]}}S(ap[0]);if(ai.input=="sqrt"){return[L(ai.tag,ap[0]),ap[1]]}else{if(typeof ai.acc=="boolean"&&ai.acc){ah=L(ai.tag,ap[0]);ah.appendChild(L("mo",g.createTextNode(ai.output)));return[ah,ap[1]]}else{if(!p&&typeof ai.codes!="undefined"){for(ak=0;ak64&&ao.charCodeAt(aj)<91){an=an+String.fromCharCode(ai.codes[ao.charCodeAt(aj)-65])}else{an=an+ao.charAt(aj)}}if(ap[0].nodeName=="mi"){ap[0]=Q("mo").appendChild(g.createTextNode(an))}else{ap[0].replaceChild(Q("mo").appendChild(g.createTextNode(an)),ap[0].childNodes[ak])}}}}ah=L(ai.tag,ap[0]);ah.setAttribute(ai.atname,ai.atval);return[ah,ap[1]]}}case W:am=t(am,ai.input.length);ap=K(am);if(ap[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ap[0]);var ag=K(ap[1]);if(ag[0]==null){return[L("mo",g.createTextNode(ai.input)),am]}S(ag[0]);if(ai.input=="root"||ai.input=="stackrel"){al.appendChild(ag[0])}al.appendChild(ap[0]);if(ai.input=="frac"){al.appendChild(ag[0])}return[L(ai.tag,al),ag[1]];case l:am=t(am,ai.input.length);return[L("mo",g.createTextNode(ai.output)),am];case a:am=t(am,ai.input.length);ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);al.appendChild(L(ai.tag,g.createTextNode(ai.output)));ah=Q("mspace");ah.setAttribute("width","1ex");al.appendChild(ah);return[L("mrow",al),am];case q:J++;am=t(am,ai.input.length);ap=v(am,false);J--;ao="";if(ap[0].lastChild!=null){ao=ap[0].lastChild.firstChild.nodeValue}if(ao=="|"){ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);ah.appendChild(ap[0]);return[ah,ap[1]]}else{ah=L("mo",g.createTextNode(ai.output));ah=L("mrow",ah);return[ah,am]}default:am=t(am,ai.input.length);return[L(ai.tag,g.createTextNode(ai.output)),am]}}function y(am){var ak,an,al,aj,ag,ai;am=t(am,0);an=m(am);ag=K(am);aj=ag[0];am=ag[1];ak=m(am);if(ak.ttype==l&&ak.input!="/"){am=t(am,ak.input.length);ag=K(am);if(ag[0]==null){ag[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ag[0])}am=ag[1];if(ak.input=="_"){al=m(am);ai=(an.ttype==O);if(al.input=="^"){am=t(am,al.input.length);var ah=K(am);S(ah[0]);am=ah[1];aj=L((ai?"munderover":"msubsup"),aj);aj.appendChild(ag[0]);aj.appendChild(ah[0]);aj=L("mrow",aj)}else{aj=L((ai?"munder":"msub"),aj);aj.appendChild(ag[0])}}else{aj=L(ak.tag,aj);aj.appendChild(ag[0])}}return[aj,am]}function v(ao,an){var at,ap,ak,aw,al=g.createDocumentFragment();do{ao=t(ao,0);ak=y(ao);ap=ak[0];ao=ak[1];at=m(ao);if(at.ttype==l&&at.input=="/"){ao=t(ao,at.input.length);ak=y(ao);if(ak[0]==null){ak[0]=L("mo",g.createTextNode("\u25A1"))}else{S(ak[0])}ao=ak[1];S(ap);ap=L(at.tag,ap);ap.appendChild(ak[0]);al.appendChild(ap);at=m(ao)}else{if(ap!=undefined){al.appendChild(ap)}}}while((at.ttype!=k&&(at.ttype!=q||an)||J==0)&&at!=null&&at.output!="");if(at.ttype==k||at.ttype==q){var ax=al.childNodes.length;if(ax>0&&al.childNodes[ax-1].nodeName=="mrow"&&ax>1&&al.childNodes[ax-2].nodeName=="mo"&&al.childNodes[ax-2].firstChild.nodeValue==","){var az=al.childNodes[ax-1].lastChild.firstChild.nodeValue;if(az==")"||az=="]"){var ah=al.childNodes[ax-1].firstChild.firstChild.nodeValue;if(ah=="("&&az==")"&&at.output!="}"||ah=="["&&az=="]"){var ai=[];var au=true;var aq=al.childNodes.length;for(aw=0;au&&aw1){au=ai[aw].length==ai[aw-2].length}}if(au){var aj,ag,am,ar,ay=g.createDocumentFragment();for(aw=0;aw2){al.removeChild(al.firstChild);al.removeChild(al.firstChild)}ay.appendChild(L("mtr",aj))}ap=L("mtable",ay);if(typeof at.invisible=="boolean"&&at.invisible){ap.setAttribute("columnalign","left")}al.replaceChild(ap,al.firstChild)}}}}ao=t(ao,at.input.length);if(typeof at.invisible!="boolean"||!at.invisible){ap=L("mo",g.createTextNode(at.output));al.appendChild(ap)}}return[al,ao]}function e(ai){var ah=Q("mstyle");if(H!=""){ah.setAttribute("mathcolor",H)}if(s){ah.setAttribute("displaystyle","true")}if(ab!=""){ah.setAttribute("fontfamily",ab)}J=0;ah.appendChild(v(ai.replace(/^\s+/g,""),false)[0]);ah=L("math",ah);if(B){ah.setAttribute("title",ai.replace(/\s+/g," "))}if(ab!=""&&(p||ab!="serif")){var ag=U("font");ag.setAttribute("face",ab);ag.appendChild(ah);return ag}return ah}B=false;ab="";H="";(function(){for(var ah=0,ag=F.length;ah",tex:null,ttype:d},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:d},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:d},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:d},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:d},{input:"arcsin",tag:"mi",output:"arcsin",tex:null,ttype:G,func:true},{input:"arccos",tag:"mi",output:"arccos",tex:null,ttype:G,func:true},{input:"arctan",tag:"mi",output:"arctan",tex:null,ttype:G,func:true},{input:"coth",tag:"mi",output:"coth",tex:null,ttype:G,func:true},{input:"sech",tag:"mi",output:"sech",tex:null,ttype:G,func:true},{input:"csch",tag:"mi",output:"csch",tex:null,ttype:G,func:true},{input:"abs",tag:"mi",output:"abs",tex:null,ttype:G,func:true},{input:"exp",tag:"mi",output:"exp",tex:null,ttype:G,func:true},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:G,acc:true});ae.Augment({AM:{Init:function(){s=ae.config.displaystyle;decimal=ae.config.decimal;D();u()},Augment:function(ag){for(var ah in ag){if(ag.hasOwnProperty(ah)){switch(ah){case"displaystyle":s=ag[ah];break;case"decimal":decimal=ag[ah];break;case"parseMath":e=ag[ah];break;case"parseExpr":v=ag[ah];break;case"parseIexpr":y=ag[ah];break;case"parseSexpr":K=ag[ah];break;case"removeBrackets":S=ag[ah];break;case"getSymbol":m=ag[ah];break;case"position":c=ag[ah];break;case"removeCharsAndBlanks":t=ag[ah];break;case"createMmlNode":L=ag[ah];break;case"createElementMathML":Q=ag[ah];break;case"createElementXHTML":U=ag[ah];break;case"initSymbols":u=ag[ah];break;case"compareNames":comareNames=ag[ah];break}this[ah]=ag[ah]}}},parseMath:e,parseExpr:v,parseIexpr:y,parseSexr:K,removeBrackets:S,getSymbol:m,position:c,removeCharsAndBlanks:t,createMmlNode:L,createElementMathML:Q,createElementXHTML:U,initSymbols:u,compareNames:V,createDocumentFragment:Z,document:g,define:A,symbols:F,names:T,TOKEN:{CONST:d,UNARY:G,BINARY:W,INFIX:l,LEFTBRACKET:b,RIGHTBRACKET:k,SPACE:a,UNDEROVER:O,DEFINITION:Y,LEFTRIGHT:q,TEXT:aa}}});var ac=[R,N];ac=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:"AsciiMath Input",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};this.prefilterHooks.Execute(g);f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.merror(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath); diff --git a/jax/input/MathML/jax.js b/jax/input/MathML/jax.js index c0eae3735..a844d5226 100644 --- a/jax/input/MathML/jax.js +++ b/jax/input/MathML/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(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(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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").replace(/&/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>");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]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?\s*$/,"$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 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]*)\/>/g,"<$1$2>");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":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p").replace(/&/g,"&")} data.math = math; this.prefilterHooks.Execute(data); math = data.math; } try { diff --git a/unpacked/jax/input/TeX/jax.js b/unpacked/jax/input/TeX/jax.js index 87e4c0b4c..cf50a7288 100644 --- a/unpacked/jax/input/TeX/jax.js +++ b/unpacked/jax/input/TeX/jax.js @@ -1980,7 +1980,7 @@ // Convert TeX to ElementJax // Translate: function (script) { - var mml, isError = false, math = script.innerHTML.replace(/^\s+/,"").replace(/\s+$/,""); + var mml, isError = false, math = MathJax.HTML.getScript(script); var display = (script.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/) != null); var data = {math:math, display:display, script:script}; this.prefilterHooks.Execute(data); math = data.math; @@ -1999,9 +1999,6 @@ return data.math; }, prefilterMath: function (math,displaystyle,script) { - // Konqueror incorrectly quotes these characters in script.innerHTML - if (HUB.Browser.isKonqueror) - {math = math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")} return math; }, postfilterMath: function (math,displaystyle,script) {