mathjax
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Beautiful math in all browsers. MathJax is an open-source JavaScript display engine for LaTeX, MathML, and AsciiMath notation that works in all browsers.
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JavaScript
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goog.defineClass.applyProperties_=function(a,b){for(var c in b)Object.prototype.hasOwnProperty.call(b,c)&&(a[c]=b[c]);for(var d=0;d<goog.defineClass.OBJECT_PROTOTYPE_FIELDS_.length;d++)c=goog.defineClass.OBJECT_PROTOTYPE_FIELDS_[d],Object.prototype.hasOwnProperty.call(b,c)&&(a[c]=b[c])};goog.tagUnsealableClass=function(a){!COMPILED&&goog.defineClass.SEAL_CLASS_INSTANCES&&(a.prototype[goog.UNSEALABLE_CONSTRUCTOR_PROPERTY_]=!0)};goog.UNSEALABLE_CONSTRUCTOR_PROPERTY_="goog_defineClass_legacy_unsealable";
goog.createRequiresTranspilation_=function(){function a(a,b){d?c[a]=!0:b()?c[a]=!1:d=c[a]=!0}function b(a){try{return!!eval(a)}catch(g){return!1}}var c={es3:!1},d=!1,e=goog.global.navigator&&goog.global.navigator.userAgent?goog.global.navigator.userAgent:"";a("es5",function(){return b("[1,].length==1")});a("es6",function(){var a=e.match(/Edge\/(\d+)(\.\d)*/i);return a&&15>Number(a[1])?!1:b('(()=>{"use strict";class X{constructor(){if(new.target!=String)throw 1;this.x=42}}let q=Reflect.construct(X,[],String);if(q.x!=42||!(q instanceof String))throw 1;for(const a of[2,3]){if(a==2)continue;function f(z={a}){let a=0;return z.a}{function f(){return 0;}}return f()==3}})()')});
a("es6-impl",function(){return!0});a("es7",function(){return b("2 ** 2 == 4")});a("es8",function(){return b("async () => 1, true")});return c};var sre={SystemExternal:function(){}};sre.SystemExternal.require=function(a){return"undefined"!==typeof require?require(a):null};sre.SystemExternal.documentSupported=function(){return"undefined"!=typeof document};sre.SystemExternal.process=sre.SystemExternal.require("process");sre.SystemExternal.xmldom=sre.SystemExternal.documentSupported()?window:sre.SystemExternal.require("xmldom");
sre.SystemExternal.document=sre.SystemExternal.documentSupported()?document:(new sre.SystemExternal.xmldom.DOMImplementation).createDocument("","",0);sre.SystemExternal.xpath=sre.SystemExternal.documentSupported()?document:sre.SystemExternal.require("xpath");sre.SystemExternal.commander=sre.SystemExternal.documentSupported()?null:sre.SystemExternal.require("commander");sre.SystemExternal.fs=sre.SystemExternal.documentSupported()?null:sre.SystemExternal.require("fs");
sre.SystemExternal.xm=sre.SystemExternal.documentSupported()?null:sre.SystemExternal.require("xml-mapping");sre.SystemExternal.locationSupported=function(){return"undefined"!=typeof location};sre.SystemExternal.url=sre.SystemExternal.locationSupported()?location.protocol+"//progressiveaccess.com/content":"https://progressiveaccess.com/content";
sre.SystemExternal.jsonPath=function(){return(sre.SystemExternal.process&&"undefined"!==typeof global?sre.SystemExternal.process.env.SRE_JSON_PATH||global.SRE_JSON_PATH||sre.SystemExternal.process.cwd():sre.SystemExternal.url+"/mathmaps")+"/"}();sre.SystemExternal.WGXpath=sre.SystemExternal.url+"/wgxpath.install.js";sre.SystemExternal.wgxpath=null;sre.BrowserUtil={};sre.BrowserUtil.detectIE=function(){if(!("undefined"!==typeof window&&"ActiveXObject"in window&&"clipboardData"in window))return!1;sre.BrowserUtil.loadMapsForIE_();sre.BrowserUtil.loadWGXpath_();return!0};sre.BrowserUtil.detectEdge=function(){if(!("undefined"!==typeof window&&"MSGestureEvent"in window&&"chrome"in window&&null==window.chrome.loadTimes))return!1;document.evaluate=null;sre.BrowserUtil.loadWGXpath_(!0);return!0};sre.BrowserUtil.mapsForIE=null;
sre.BrowserUtil.loadWGXpath_=function(a){sre.BrowserUtil.loadScript(sre.SystemExternal.WGXpath);sre.BrowserUtil.installWGXpath_(a)};
sre.BrowserUtil.installWGXpath_=function(a,b){var c=b||1;"undefined"===typeof wgxpath&&10>c?setTimeout(function(){sre.BrowserUtil.installWGXpath_(a,c++)},200):10<=c||(sre.SystemExternal.wgxpath=wgxpath,a?sre.SystemExternal.wgxpath.install({document:document}):sre.SystemExternal.wgxpath.install(),sre.XpathUtil.xpathEvaluate=document.evaluate,sre.XpathUtil.xpathResult=XPathResult,sre.XpathUtil.createNSResolver=document.createNSResolver)};
sre.BrowserUtil.loadMapsForIE_=function(){sre.BrowserUtil.loadScript(sre.SystemExternal.jsonPath+"mathmaps_ie.js")};sre.BrowserUtil.loadScript=function(a){var b=sre.SystemExternal.document.createElement("script");b.type="text/javascript";b.src=a;sre.SystemExternal.document.head?sre.SystemExternal.document.head.appendChild(b):sre.SystemExternal.document.body.appendChild(b)};sre.DynamicProperties=function(a,b){this.properties_=a;this.order_=b||Object.keys(a)};sre.DynamicProperties.prototype.getProperties=function(){return this.properties_};sre.DynamicProperties.prototype.getOrder=function(){return this.order_};sre.DynamicProperties.prototype.getAxes=function(){return this.order_};sre.DynamicProperties.prototype.getProperty=function(a){return this.properties_[a]};
sre.DynamicProperties.prototype.toString=function(){var a=[];this.order_.forEach(goog.bind(function(b){a.push(b+": "+this.getProperty(b).toString())},this));return a.join("\n")};sre.DynamicCstr=function(a,b){this.components_=a;var c={},d;for(d in a){var e=a[d];c[d]=[e];sre.DynamicCstr.Values_.getInstance().add(d,e)}sre.DynamicProperties.call(this,c,b)};goog.inherits(sre.DynamicCstr,sre.DynamicProperties);sre.DynamicCstr.prototype.getComponents=function(){return this.components_};
sre.DynamicCstr.prototype.getValue=function(a){return this.components_[a]};sre.DynamicCstr.prototype.getValues=function(){var a=[];this.order_.forEach(goog.bind(function(b){a.push(this.getValue(b))},this));return a};sre.DynamicCstr.prototype.toString=function(){return this.getValues().join(".")};sre.DynamicCstr.prototype.equal=function(a){var b=a.getAxes();if(this.order_.length!==b.length)return!1;for(var c=0,d;d=b[c];c++){var e=this.getValue(d);if(!e||a.getValue(d)!==e)return!1}return!0};
sre.DynamicCstr.Axis={DOMAIN:"domain",STYLE:"style",LANGUAGE:"language",TOPIC:"topic",MODALITY:"modality"};sre.DynamicCstr.Values_=function(){this.axisToValues=sre.DynamicCstr.Values_.makeAxisValueObject_()};goog.addSingletonGetter(sre.DynamicCstr.Values_);sre.DynamicCstr.Values_.prototype.add=function(a,b){this.axisToValues[a][b]=!0};sre.DynamicCstr.Values_.prototype.get=function(){var a={},b=sre.DynamicCstr.Values_.getInstance().axisToValues,c;for(c in b)a[c]=Object.keys(b[c]);return a};
sre.DynamicCstr.Values_.makeAxisValueObject_=function(){var a={},b;for(b in sre.DynamicCstr.Axis)a[sre.DynamicCstr.Axis[b]]={};return a};sre.DynamicCstr.getAxisValues=function(){return sre.DynamicCstr.Values_.getInstance().get()};sre.DynamicCstr.DEFAULT_ORDER=[sre.DynamicCstr.Axis.DOMAIN,sre.DynamicCstr.Axis.STYLE,sre.DynamicCstr.Axis.LANGUAGE,sre.DynamicCstr.Axis.TOPIC,sre.DynamicCstr.Axis.MODALITY];sre.DynamicCstr.DEFAULT_VALUE="default";sre.DynamicCstr.Parser=function(a){this.order_=a};
sre.DynamicCstr.Parser.prototype.parse=function(a){a=a.split(".");var b={};if(a.length>this.order_.length)throw Error("Invalid dynamic constraint: "+b);for(var c=0,d;d=this.order_[c],a.length;c++){var e=a.shift();b[d]=e}return new sre.DynamicCstr(b,this.order_.slice(0,c))};sre.DynamicCstr.Comparator=function(){};sre.DynamicCstr.Comparator.prototype.getReference=function(){};sre.DynamicCstr.Comparator.prototype.setReference=function(a,b){};sre.DynamicCstr.Comparator.prototype.match=function(a){};
sre.DynamicCstr.Comparator.prototype.compare=function(a,b){};sre.DynamicCstr.DefaultComparator=function(a,b){this.reference_=a;this.fallback_=b||new sre.DynamicProperties(a.getProperties(),a.getOrder());this.order_=this.reference_.getOrder()};sre.DynamicCstr.DefaultComparator.prototype.getReference=function(){return this.reference_};
sre.DynamicCstr.DefaultComparator.prototype.setReference=function(a,b){this.reference_=a;this.fallback_=b||new sre.DynamicProperties(a.getProperties(),a.getOrder());this.order_=this.reference_.getOrder()};sre.DynamicCstr.DefaultComparator.prototype.match=function(a){var b=a.getAxes();return b.length===this.reference_.getAxes().length&&b.every(goog.bind(function(b){var c=a.getValue(b);return c===this.reference_.getValue(b)||-1!==this.fallback_.getProperty(b).indexOf(c)},this))};
sre.DynamicCstr.DefaultComparator.prototype.compare=function(a,b){for(var c=!1,d=0,e;e=this.order_[d];d++){var f=a.getValue(e),g=b.getValue(e);if(!c){var h=this.reference_.getValue(e);if(h===f&&h!==g)return-1;if(h===g&&h!==f)return 1;if(h===f&&h===g)continue;h!==f&&h!==g&&(c=!0)}e=this.fallback_.getProperty(e);f=e.indexOf(f);g=e.indexOf(g);if(f<g)return-1;if(g<f)return 1}return 0};
sre.DynamicProperties.create=function(a){for(var b=sre.DynamicCstr.DEFAULT_ORDER,c={},d=Array.prototype.slice.call(arguments,0),e=0,f=d.length,g=b.length;e<f&&e<g;e++)c[b[e]]=d[e];return new sre.DynamicProperties(c)};sre.DynamicCstr.create=function(a){for(var b=sre.DynamicCstr.DEFAULT_ORDER,c={},d=Array.prototype.slice.call(arguments,0),e=0,f=d.length,g=b.length;e<f&&e<g;e++)c[b[e]]=d[e];return new sre.DynamicCstr(c)};
sre.DynamicCstr.defaultCstr=function(){return sre.DynamicCstr.create.apply(null,sre.DynamicCstr.defaults_())};sre.DynamicCstr.defaults_=function(){return Array.apply(null,Array(sre.DynamicCstr.DEFAULT_ORDER.length+1)).map(function(){return sre.DynamicCstr.DEFAULT_VALUE})};sre.DynamicCstr.validOrder=function(a){var b=sre.DynamicCstr.DEFAULT_ORDER.slice();return a.every(function(a){a=b.indexOf(a);return-1!==a&&b.splice(a,1)})};sre.Engine=function(){this.alternativeHost=this.activeHost=null;this.evaluator=sre.Engine.defaultEvaluator;this.dynamicCstr=sre.DynamicCstr.defaultCstr();this.comparator=null;this.domain="default";this.style="short";this.walker="Syntax";this.semantics=!0;this.mode=sre.Engine.Mode.SYNC;this.speech=sre.Engine.Speech.NONE;this.ruleSets=[];this.cache=!0;this.markup=sre.Engine.Markup.NONE;this.isEdge=this.isIE=this.strict=!1;this.setupTests_=[]};goog.addSingletonGetter(sre.Engine);
sre.Engine.personalityProps={PITCH:"pitch",RATE:"rate",VOLUME:"volume",PAUSE:"pause"};sre.Engine.Mode={SYNC:"sync",ASYNC:"async",HTTP:"http"};sre.Engine.Speech={NONE:"none",SHALLOW:"shallow",DEEP:"deep"};sre.Engine.Markup={NONE:"none",SSML:"ssml",ACSS:"acss",SABLE:"sable",VOICEXML:"voicexml"};sre.Engine.registerTest=function(a){sre.Engine.getInstance().setupTests_.push(a)};sre.Engine.isReady=function(){return sre.Engine.getInstance().setupTests_.every(function(a){return a()})};
sre.Engine.prototype.setupBrowsers=function(){this.isIE=sre.BrowserUtil.detectIE();this.isEdge=sre.BrowserUtil.detectEdge()};sre.Engine.prototype.getAxisValues=function(){return sre.DynamicCstr.getAxisValues()};sre.Engine.defaultEvaluator=function(a,b){return a};sre.AudioUtil={};sre.AudioUtil.mergePause=function(a,b,c){return a?{pause:(c||function(a,b){return a+b}).call(null,a.pause,b.pause)}:b};sre.AudioUtil.mergeMarkup=function(a,b){delete a.open;b.close.forEach(function(b){delete a[b]});b.open.forEach(function(c){a[c]=b[c]});var c=Object.keys(a);a.open=c};
sre.AudioUtil.sortClose=function(a,b){if(1>=a.length)return a;for(var c=[],d=0,e;e=b[d],a.length;d++)e.close&&e.close.length&&e.close.forEach(function(b){var d=a.indexOf(b);-1!==d&&(c.unshift(b),a.splice(d,1))});return c};sre.AudioUtil.PersonalityRanges_={};sre.AudioUtil.LastOpen_=[];
sre.AudioUtil.personalityMarkup=function(a){sre.AudioUtil.PersonalityRanges_={};sre.AudioUtil.LastOpen_=[];for(var b=[],c={},d=0,e;e=a[d];d++){var f=null,g=e.descriptionString();e=e.personality;void 0!==e[sre.Engine.personalityProps.PAUSE]&&(f={},f[sre.Engine.personalityProps.PAUSE]=e[sre.Engine.personalityProps.PAUSE],delete e[sre.Engine.personalityProps.PAUSE]);e=sre.AudioUtil.personalityDiff_(e,c);sre.AudioUtil.appendMarkup_(b,g,e,f,!0)}return b};
sre.AudioUtil.isMarkupElement=function(a){return"object"===typeof a&&a.open};sre.AudioUtil.isPauseElement=function(a){return"object"===typeof a&&1===Object.keys(a).length&&Object.keys(a)[0]===sre.Engine.personalityProps.PAUSE};sre.AudioUtil.isStringElement=function(a){return"object"===typeof a&&1===Object.keys(a).length&&"string"===Object.keys(a)[0]};
sre.AudioUtil.appendMarkup_=function(a,b,c,d,e){if(e){if((e=a[a.length-1])&&!b&&d&&sre.AudioUtil.isPauseElement(e)){var f=sre.Engine.personalityProps.PAUSE;e[f]+=d[f];d=null}e&&b&&0===Object.keys(c).length&&sre.AudioUtil.isStringElement(e)&&(e.string+=" "+b,b="")}0!==Object.keys(c).length&&a.push(c);b&&a.push({string:b});d&&a.push(d)};
sre.AudioUtil.personalityDiff_=function(a,b){if(!b)return a;var c={};for(h in sre.Engine.personalityProps){var d=sre.Engine.personalityProps[h],e=a[d],f=b[d];if(!(!e&&!f||e&&f&&e===f)){var g=e||0;sre.AudioUtil.isMarkupElement(c)||(c.open=[],c.close=[]);e||c.close.push(d);f||c.open.push(d);f&&e&&(c.close.push(d),c.open.push(d));b[d]=g;c[d]=g;sre.AudioUtil.PersonalityRanges_[d]?sre.AudioUtil.PersonalityRanges_[d].push(g):sre.AudioUtil.PersonalityRanges_[d]=[g]}}if(sre.AudioUtil.isMarkupElement(c)){for(a=
c.close.slice();0<a.length;){var h=sre.AudioUtil.LastOpen_.pop();d=sre.BaseUtil.setdifference(h,a);a=sre.BaseUtil.setdifference(a,h);h=d;if(0===a.length)0!==h.length&&sre.AudioUtil.LastOpen_.push(h);else if(0!==h.length)for(c.close=c.close.concat(h),c.open=c.open.concat(h),d=0;e=h[d];d++)c[e]=b[e]}sre.AudioUtil.LastOpen_.push(c.open)}return c};sre.AudioRenderer=function(){};sre.AudioRenderer.prototype.setSeparator=function(a){};sre.AudioRenderer.prototype.getSeparator=function(){};sre.AudioRenderer.prototype.markup=function(a){};sre.AudioRenderer.prototype.error=function(a){};sre.AudioRenderer.prototype.merge=function(a){};sre.AbstractAudioRenderer=function(){this.separator_=" "};sre.AbstractAudioRenderer.prototype.setSeparator=function(a){this.separator_=a};sre.AbstractAudioRenderer.prototype.getSeparator=function(){return this.separator_};sre.AbstractAudioRenderer.prototype.markup=goog.abstractMethod;sre.AbstractAudioRenderer.prototype.error=function(a){return null};sre.AbstractAudioRenderer.prototype.merge=function(a){return a.join(" ")};sre.MarkupRenderer=function(){sre.AbstractAudioRenderer.call(this);this.scaleFunction_=null};goog.inherits(sre.MarkupRenderer,sre.AbstractAudioRenderer);sre.MarkupRenderer.prototype.setScaleFunction=function(a,b,c,d,e){var f=e||0;this.scaleFunction_=function(e){e=(e-a)/(b-a);return+(Math.round(c*(1-e)+d*e+"e+"+f)+"e-"+f)}};sre.MarkupRenderer.prototype.applyScaleFunction=function(a){return this.scaleFunction_?this.scaleFunction_(a):a};sre.MarkupRenderer.prototype.pause=goog.abstractMethod;
sre.MarkupRenderer.prototype.prosodyElement=goog.abstractMethod;sre.AcssRenderer=function(){sre.MarkupRenderer.call(this)};goog.inherits(sre.AcssRenderer,sre.MarkupRenderer);
sre.AcssRenderer.prototype.markup=function(a){this.setScaleFunction(-2,2,0,10,0);a=sre.AudioUtil.personalityMarkup(a);for(var b=[],c={open:[]},d=null,e=!1,f=0,g;g=a[f];f++)if(sre.AudioUtil.isMarkupElement(g))sre.AudioUtil.mergeMarkup(c,g);else if(sre.AudioUtil.isPauseElement(g))e&&(d=sre.AudioUtil.mergePause(d,g,Math.max));else{g='"'+g.string+'"';e=!0;d&&(b.push(this.pause(d)),d=null);var h=this.prosody_(c);b.push(h?"(text ("+h+") "+g+")":g)}return"(exp "+b.join(this.getSeparator())+")"};
sre.AcssRenderer.prototype.merge=function(a){return"(exp "+a.map(function(a){return a.replace(/^\(exp /,"").replace(/\)$/,"")}).join(" ")+")"};sre.AcssRenderer.prototype.error=function(a){return'(error "'+a+'")'};sre.AcssRenderer.prototype.prosody_=function(a){for(var b=a.open,c=[],d=0,e;e=b[d];d++)c.push(this.prosodyElement(e,a[e]));return c.join(" ")};
sre.AcssRenderer.prototype.prosodyElement=function(a,b){b=this.applyScaleFunction(b);switch(a){case sre.Engine.personalityProps.RATE:return"(richness . "+b+")";case sre.Engine.personalityProps.PITCH:return"(average-pitch . "+b+")";case sre.Engine.personalityProps.VOLUME:return"(stress . "+b+")"}return"(value . "+b+")"};sre.AcssRenderer.prototype.pause=function(a){return"(pause . "+a[sre.Engine.personalityProps.PAUSE]+")"};sre.XmlRenderer=function(){sre.MarkupRenderer.call(this)};goog.inherits(sre.XmlRenderer,sre.MarkupRenderer);
sre.XmlRenderer.prototype.markup=function(a){this.setScaleFunction(-2,2,-100,100,2);a=sre.AudioUtil.personalityMarkup(a);for(var b=[],c=[],d=0,e;e=a[d];d++)if(e.string)b.push(e.string);else if(sre.AudioUtil.isPauseElement(e))b.push(this.pause(e));else{if(e.close.length)for(var f=0;f<e.close.length;f++){var g=c.pop();if(-1===e.close.indexOf(g))throw Error("Unknown closing markup element: "+g);b.push(this.closeTag(g))}e.open.length&&sre.AudioUtil.sortClose(e.open.slice(),a.slice(d+1)).forEach(goog.bind(function(a){b.push(this.prosodyElement(a,
e[a]));c.push(a)},this))}return b.join(this.getSeparator())};sre.XmlRenderer.prototype.closeTag=goog.abstractMethod;sre.SableRenderer=function(){sre.XmlRenderer.call(this)};goog.inherits(sre.SableRenderer,sre.XmlRenderer);sre.SableRenderer.prototype.pause=function(a){return'<BREAK MSEC="'+a[sre.Engine.personalityProps.PAUSE]+'"/>'};
sre.SableRenderer.prototype.prosodyElement=function(a,b){b=this.applyScaleFunction(b);switch(a){case sre.Engine.personalityProps.PITCH:return'<PITCH BASE="'+b+'%">';case sre.Engine.personalityProps.RATE:return'<RATE SPEED="'+b+'%">';case sre.Engine.personalityProps.VOLUME:return'<VOLUME LEVEL="'+b+'%">';default:return"<"+a.toUpperCase()+' VALUE="'+b+'">'}};sre.SableRenderer.prototype.closeTag=function(a){return"</"+a.toUpperCase()+">"};sre.SsmlRenderer=function(){sre.XmlRenderer.call(this)};goog.inherits(sre.SsmlRenderer,sre.XmlRenderer);sre.SsmlRenderer.prototype.pause=function(a){return'<BREAK TIME="'+a[sre.Engine.personalityProps.PAUSE]+'ms"/>'};sre.SsmlRenderer.prototype.prosodyElement=function(a,b){b=this.applyScaleFunction(b);b=0>b?b.toString():"+"+b;return"<PROSODY "+a.toUpperCase()+'="'+b+(a===sre.Engine.personalityProps.VOLUME?">":'%">')};sre.SsmlRenderer.prototype.closeTag=function(a){return"</PROSODY>"};sre.BaseUtil={};sre.BaseUtil.removeEmpty=function(a){return a.filter(function(a){return a})};sre.BaseUtil.interleaveLists=function(a,b){for(var c=[];a.length||b.length;)a.length&&c.push(a.shift()),b.length&&c.push(b.shift());return c};sre.BaseUtil.setdifference=function(a,b){return a?b?a.filter(function(a){return 0>b.indexOf(a)}):a:[]};sre.BaseUtil.union=function(a,b){return a&&b?a.concat(sre.BaseUtil.setdifference(b,a)):a||b||[]};sre.BaseUtil.makePath=function(a){return a.match("/$")?a:a+"/"};sre.StringRenderer=function(){sre.AbstractAudioRenderer.call(this)};goog.inherits(sre.StringRenderer,sre.AbstractAudioRenderer);sre.StringRenderer.prototype.markup=function(a){return sre.BaseUtil.removeEmpty(a.map(function(a){return a.descriptionString()})).join(this.getSeparator())};sre.AuralRendering=function(){};goog.addSingletonGetter(sre.AuralRendering);sre.AuralRendering.prototype.setSeparator=function(a){var b=sre.AuralRendering.rendererMapping_[sre.Engine.getInstance().markup];b&&b.setSeparator(a)};sre.AuralRendering.prototype.getSeparator=function(){var a=sre.AuralRendering.rendererMapping_[sre.Engine.getInstance().markup];return a?a.getSeparator():""};
sre.AuralRendering.prototype.markup=function(a){var b=sre.AuralRendering.rendererMapping_[sre.Engine.getInstance().markup];return b?b.markup(a):""};sre.AuralRendering.prototype.merge=function(a){var b=sre.AuralRendering.rendererMapping_[sre.Engine.getInstance().markup];return b?b.merge(a):a.join()};sre.AuralRendering.prototype.error=function(a){var b=sre.AuralRendering.rendererMapping_[sre.Engine.getInstance().markup];return b?b.error(a):""};
sre.AuralRendering.registerRenderer=function(a,b){sre.AuralRendering.rendererMapping_[a]=b};sre.AuralRendering.rendererMapping_={};sre.AuralRendering.registerRenderer(sre.Engine.Markup.NONE,new sre.StringRenderer);sre.AuralRendering.registerRenderer(sre.Engine.Markup.ACSS,new sre.AcssRenderer);sre.AuralRendering.registerRenderer(sre.Engine.Markup.SABLE,new sre.SableRenderer);sre.AuralRendering.xmlInstance=new sre.SsmlRenderer;sre.AuralRendering.registerRenderer(sre.Engine.Markup.VOICEXML,sre.AuralRendering.xmlInstance);
sre.AuralRendering.registerRenderer(sre.Engine.Markup.SSML,sre.AuralRendering.xmlInstance);sre.Debugger=function(){this.isActive_=!1;this.outputFunction_=console.log;this.stream_=null};goog.addSingletonGetter(sre.Debugger);sre.Debugger.prototype.init=function(a){a&&this.startDebugFile_(a);this.isActive_=!0};
sre.Debugger.prototype.startDebugFile_=function(a){this.stream_=sre.SystemExternal.fs.createWriteStream(a);this.outputFunction_=goog.bind(function(a){var b=Array.prototype.slice.call(arguments,0);this.stream_.write(b.join(" "));this.stream_.write("\n")},this);this.stream_.on("error",goog.bind(function(a){console.log("Invalid log file. Debug information sent to console.");this.outputFunction_=console.log},this));this.stream_.on("finish",function(){console.log("Finalizing debug file.")})};
sre.Debugger.prototype.output_=function(a){this.outputFunction_.apply(console.log===this.outputFunction_?console:this.outputFunction_,["Speech Rule Engine Debugger:"].concat(a))};sre.Debugger.prototype.output=function(a){this.isActive_&&this.output_(Array.prototype.slice.call(arguments,0))};sre.Debugger.prototype.generateOutput=function(a){this.isActive_&&this.output_(a.apply(a,[]))};
sre.Debugger.prototype.exit=function(a){this.isActive_&&this.stream_&&this.stream_.end("","",a||function(){});this.isActive_=!1};sre.XpathUtil={};sre.XpathUtil.xpathSupported=function(){return"undefined"==typeof XPathResult?!1:!0};sre.XpathUtil.currentDocument=null;sre.XpathUtil.xpathEvaluate=sre.XpathUtil.xpathSupported()?document.evaluate:sre.SystemExternal.xpath.evaluate;sre.XpathUtil.xpathResult=sre.XpathUtil.xpathSupported()?XPathResult:sre.SystemExternal.xpath.XPathResult;sre.XpathUtil.createNSResolver=sre.XpathUtil.xpathSupported()?document.createNSResolver:sre.SystemExternal.xpath.createNSResolver;
sre.XpathUtil.nameSpaces_={xhtml:"http://www.w3.org/1999/xhtml",mathml:"http://www.w3.org/1998/Math/MathML",svg:"http://www.w3.org/2000/svg"};sre.XpathUtil.resolveNameSpace=function(a){return sre.XpathUtil.nameSpaces_[a]||null};sre.XpathUtil.resolver_=function(){this.lookupNamespaceURI=sre.XpathUtil.resolveNameSpace};
sre.XpathUtil.evaluateXpath_=function(a,b,c){var d=sre.Engine.getInstance();return d.mode!==sre.Engine.Mode.HTTP||d.isIE||d.isEdge?sre.XpathUtil.xpathEvaluate(a,b,new sre.XpathUtil.resolver_,c,null):sre.XpathUtil.currentDocument.evaluate(a,b,sre.XpathUtil.resolveNameSpace,c,null)};sre.XpathUtil.evalXPath=function(a,b){try{var c=sre.XpathUtil.evaluateXpath_(a,b,sre.XpathUtil.xpathResult.ORDERED_NODE_ITERATOR_TYPE)}catch(d){return[]}a=[];for(b=c.iterateNext();b;b=c.iterateNext())a.push(b);return a};
sre.XpathUtil.getLeafNodes=function(a){return sre.XpathUtil.evalXPath(".//*[count(*)=0]",a)};sre.XpathUtil.evaluateBoolean=function(a,b){try{var c=sre.XpathUtil.evaluateXpath_(a,b,sre.XpathUtil.xpathResult.BOOLEAN_TYPE)}catch(d){return!1}return c.booleanValue};sre.XpathUtil.evaluateString=function(a,b){try{var c=sre.XpathUtil.evaluateXpath_(a,b,sre.XpathUtil.xpathResult.STRING_TYPE)}catch(d){return""}return c.stringValue};sre.DomUtil={};sre.DomUtil.toArray=function(a){for(var b=[],c=0,d=a.length;c<d;c++)b.push(a[c]);return b};sre.DomUtil.trimInput_=function(a){a=a.replace(/ /g," ");return a.replace(/>\s+</g,"><").trim()};
sre.DomUtil.parseInput=function(a,b){b=b||Error;var c=new sre.SystemExternal.xmldom.DOMParser;a=sre.DomUtil.trimInput_(a);if(!a)throw new b("Empty input!");try{var d=c.parseFromString(a,"text/xml");sre.Engine.getInstance().mode===sre.Engine.Mode.HTTP&&(sre.XpathUtil.currentDocument=d);return d.documentElement}catch(e){throw new b("Illegal input: "+e.message);}};
sre.DomUtil.NodeType={ELEMENT_NODE:1,ATTRIBUTE_NODE:2,TEXT_NODE:3,CDATA_SECTION_NODE:4,ENTITY_REFERENCE_NODE:5,ENTITY_NODE:6,PROCESSING_INSTRUCTION_NODE:7,COMMENT_NODE:8,DOCUMENT_NODE:9,DOCUMENT_TYPE_NODE:10,DOCUMENT_FRAGMENT_NODE:11,NOTATION_NODE:12};sre.DomUtil.replaceNode=function(a,b){a.parentNode&&(a.parentNode.insertBefore(b,a),a.parentNode.removeChild(a))};sre.DomUtil.createElement=function(a){return sre.SystemExternal.document.createElement(a)};sre.DomUtil.createTextNode=function(a){return sre.SystemExternal.document.createTextNode(a)};
sre.DomUtil.formatXml=function(a){var b=/(>)(<)(\/*)/g;a=a.replace(b,"$1\r\n$2$3");b=/(>)(.+)(<c)/g;a=a.replace(b,"$1\r\n$2\r\n$3");var c="",d="";a.split("\r\n").forEach(function(a){a.match(/.+<\/\w[^>]*>$/)?c+=d+a+"\r\n":a.match(/^<\/\w/)?d&&(d=d.slice(2),c+=d+a+"\r\n"):a.match(/^<\w[^>]*[^\/]>.*$/)?(c+=d+a+"\r\n",d+=" "):c+=d+a+"\r\n"});return c};sre.DomUtil.dataAttribute=function(a){a.match(/^data-/)&&(a=a.substr(5));return a.replace(/-([a-z])/g,function(a,c){return c.toUpperCase()})};
sre.DomUtil.getDataAttribute=function(a,b){return a.dataset?a.dataset[sre.DomUtil.dataAttribute(b)]:a.getAttribute(b)};sre.DomUtil.querySelectorAllByAttr=function(a,b){return a.querySelectorAll?sre.DomUtil.toArray(a.querySelectorAll("["+b+"]")):sre.XpathUtil.evalXPath(".//*[@"+b+"]",a)};sre.DomUtil.querySelectorAllByAttrValue=function(a,b,c){return a.querySelectorAll?sre.DomUtil.toArray(a.querySelectorAll("["+b+'="'+c+'"]')):sre.XpathUtil.evalXPath(".//*[@"+b+'="'+c+'"]',a)};
sre.DomUtil.querySelectorAll=function(a,b){return a.querySelectorAll?sre.DomUtil.toArray(a.querySelectorAll(b)):sre.XpathUtil.evalXPath(".//"+b,a)};sre.DomUtil.tagName=function(a){return a.tagName.toUpperCase()};sre.EnrichCase=function(){};sre.EnrichCase.prototype.getMathml=function(){};sre.AbstractEnrichCase=function(a){this.semantic=a};sre.AbstractEnrichCase.prototype.getMathml=goog.abstractMethod;sre.AbstractEnrichCase.test=goog.abstractMethod;sre.EnrichCaseFactory=function(){};sre.EnrichCaseFactory.getEmbellishedCase=function(a){return new sre.EnrichCaseFactory.embellishedCase(a)};sre.EnrichCaseFactory.cases=[];sre.EnrichCaseFactory.getCase=function(a){for(var b=0,c;c=sre.EnrichCaseFactory.cases[b];b++)if(c.test(a))return new c.constr(a);return null};sre.SemanticUtil=function(){};sre.SemanticUtil.objectsToKeys=function(a){a=Array.prototype.slice.call(arguments,0);var b=[];return b.concat.apply(b,a.map(Object.keys))};sre.SemanticUtil.objectsToValues=function(a){a=Array.prototype.slice.call(arguments,0);var b=[];a.forEach(function(a){for(var c in a)b.push(a[c])});return b};
sre.SemanticUtil.unicodeToNumber=function(a){if(!a||2<a.length)return null;if(2==a.length){var b=a.charCodeAt(0);a=a.charCodeAt(1);return 55296<=b&&56319>=b&&!isNaN(a)?1024*(b-55296)+(a-56320)+65536:null}return a.charCodeAt(0)};sre.SemanticUtil.numberToUnicode=function(a){return 65536>a?String.fromCharCode(a):String.fromCharCode((a-65536)/1024+55296,(a-65536)%1024+56320)};
sre.SemanticUtil.splitUnicode=function(a){a=a.split("");for(var b=[],c=0,d;d=a[c];c++)"\ud800"<=d&&"\udbff">=d&&a[c+1]?b.push(d+a[++c]):b.push(d);return b};sre.SemanticUtil.LEAFTAGS=["MO","MI","MN","MTEXT","MS"];sre.SemanticUtil.IGNORETAGS="MERROR MPHANTOM MSPACE MALIGNGROUP MALIGNMARK MPRESCRIPTS ANNOTATION ANNOTATION-XML".split(" ");sre.SemanticUtil.EMPTYTAGS="MATH MROW MPADDED MACTION NONE MSTYLE SEMANTICS".split(" ");sre.SemanticUtil.hasMathTag=function(a){return!!a&&"MATH"===sre.DomUtil.tagName(a)};
sre.SemanticUtil.hasIgnoreTag=function(a){return!!a&&-1!==sre.SemanticUtil.IGNORETAGS.indexOf(sre.DomUtil.tagName(a))};sre.SemanticUtil.hasEmptyTag=function(a){return!!a&&-1!==sre.SemanticUtil.EMPTYTAGS.indexOf(sre.DomUtil.tagName(a))};sre.SemanticUtil.purgeNodes=function(a){for(var b=[],c=0,d;d=a[c];c++){var e=sre.DomUtil.tagName(d);-1==sre.SemanticUtil.IGNORETAGS.indexOf(e)&&(-1!=sre.SemanticUtil.EMPTYTAGS.indexOf(e)&&0==d.childNodes.length||b.push(d))}return b};
sre.SemanticUtil.isZeroLength=function(a){return a?-1!=="negativeveryverythinmathspace negativeverythinmathspace negativethinmathspace negativemediummathspace negativethickmathspace negativeverythickmathspace negativeveryverythickmathspace".split(" ").indexOf(a)?!0:(a=a.match(/[0-9\.]+/))?0===parseFloat(a)?!0:!1:!1:!1};sre.SemanticAttr=function(){this.generalPunctuations='!"#%&:;?@\\\u00a1\u00a7\u00b6\u00bf\u2017\u2020\u2021\u2022\u2023\u2024\u2025\u2027\u2030\u2031\u2038\u203b\u203c\u203d\u203e\u2041\u2042\u2043\u2047\u2048\u2049\u204b\u204c\u204d\u204e\u204f\u2050\u2051\u2053\u2055\u2056\u2058\u2059\u205a\u205b\u205c\u205d\u205e\ufe10\ufe13\ufe14\ufe15\ufe16\ufe30\ufe45\ufe46\ufe49\ufe4a\ufe4b\ufe4c\ufe50\ufe54\ufe55\ufe56\ufe57\ufe5f\ufe60\ufe61\ufe68\ufe6a\ufe6b\uff01\uff02\uff03\uff05\uff06\uff07\uff0a\uff0c\uff0f\uff1a\uff1b\uff1f\uff20\uff3c'.split("");
this.invisibleComma_=sre.SemanticUtil.numberToUnicode(8291);this.commas=["