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TeX-MML-AM_HTMLorMML-full.js

TeX-MML-AM_HTMLorMML-full.js 306 KB
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  1. /*
    2. 

  2.  *  /MathJax/config/TeX-MML-AM_HTMLorMML-full.js
    3. 

  3.  *  
    4. 

  4.  *  Copyright (c) 2010-2013 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Part of the MathJax library.
    7. 

  7.  *  See http://www.mathjax.org for details.
    8. 

  8.  * 
    9. 

  9.  *  Licensed under the Apache License, Version 2.0;
    10. 

  10.  *  you may not use this file except in compliance with the License.
    11. 

  11.  *
    12. 

  12.  *      http://www.apache.org/licenses/LICENSE-2.0
    13. 

  13.  */MathJax.Hub.Config({delayJaxRegistration:!0});MathJax.Ajax.Preloading("[MathJax]/jax/input/TeX/config.js","[MathJax]/jax/input/MathML/config.js","[MathJax]/jax/input/AsciiMath/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/jax/output/NativeMML/config.js","[MathJax]/config/MMLorHTML.js","[MathJax]/extensions/tex2jax.js","[MathJax]/extensions/mml2jax.js","[MathJax]/extensions/asciimath2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/extensions/TeX/noErrors.js","[MathJax]/extensions/TeX/noUndefined.js","[MathJax]/jax/input/TeX/jax.js","[MathJax]/extensions/TeX/AMSmath.js","[MathJax]/extensions/TeX/AMSsymbols.js","[MathJax]/jax/input/MathML/jax.js","[MathJax]/jax/input/AsciiMath/jax.js","[MathJax]/jax/output/NativeMML/jax.js","[MathJax]/jax/output/HTML-CSS/jax.js","[MathJax]/jax/output/HTML-CSS/autoload/mtable.js");MathJax.Hub.Config({"v1.0-compatible":!1});MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.2.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:!0}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.2",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:!1}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.2",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{displaystyle:!0,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js");MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:!1,EqnChunk:MathJax.Hub.Browser.isMobile?10:50,EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:!1,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'true')",padding:"3px 4px","z-index":401}}}});MathJax.Hub.Browser.isMSIE&&9<=document.documentMode&&delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter;MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax["HTML-CSS"].Register("jax/mml");MathJax.Hub.Register.StartupHook("End Config",[function(a,e){var c=a.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(d){var e=a.getJaxFor(d),m=["[Math]"],l=document.createElement("span",{className:"MathJax_Preview"});"TeX"===e.inputJax&&(e.root.Get("displaystyle")?(m=c.displayMathDelimiters,m=[m[0]+e.originalText+m[1]],c.multilineDisplay&&(m=m[0].split(/\n/))):(m=c.inlineMathDelimiters,m=[m[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+m[1]]));for(var e=0,p=m.length;e<p;e++)l.appendChild(document.createTextNode(m[e])),e<p-1&&l.appendChild(document.createElement("br"));d.parentNode.insertBefore(l,d)}},a.config["HTML-CSS"]||{});"0.0"===a.Browser.version||a.Browser.versionAtLeast(c.minBrowserVersion[a.Browser]||0)||(e.Translate=c.minBrowserTranslate,a.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),a.Startup.signal.Post("MathJax not supported"))},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.2",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,minScaleAdjust:50,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.NativeMML.Register("jax/mml");MathJax.OutputJax.NativeMML.loadComplete("config.js");(function(a,e){var c=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}}),d={Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},n="0.0"===e.version||e.versionAtLeast(d[e]||0),m=e.isFirefox&&e.versionAtLeast("1.5")||e.isMSIE&&e.hasMathPlayer||e.isSafari&&e.versionAtLeast("5.0")||e.isOpera&&e.versionAtLeast("9.52");a.Register.StartupHook("End Config",function(){var d=c.prefer&&"object"===typeof c.prefer?c.prefer[MathJax.Hub.Browser]||c.prefer.other||"HTML":c.prefer;n||m?!m||"MML"!==d&&n?(MathJax.OutputJax["HTML-CSS"]?MathJax.OutputJax["HTML-CSS"].Register("jax/mml"):a.config.jax.unshift("output/HTML-CSS"),a.Startup.signal.Post("HTML-CSS output selected")):(MathJax.OutputJax.NativeMML?MathJax.OutputJax.NativeMML.Register("jax/mml"):a.config.jax.unshift("output/NativeMML"),a.Startup.signal.Post("NativeMML output selected")):(a.PreProcess.disabled=!0,a.prepareScripts.disabled=!0,MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),a.Startup.signal.Post("MathJax not supported"))})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");MathJax.Extension.tex2jax={version:"2.2",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:!0,skipTags:"script noscript style textarea pre code".split(" "),ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:!1,processEnvironments:!0,processRefs:!0,preview:"TeX"},PreProcess:function(a){this.configured||(this.config=MathJax.Hub.CombineConfig("tex2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),"undefined"===typeof this.config.previewTeX||this.config.previewTeX||(this.config.preview="none"),this.configured=!0);"string"===typeof a&&(a=document.getElementById(a));a||(a=document.body);this.createPatterns()&&this.scanElement(a,a.nextSibling)},createPatterns:function(){var a=[],e=[],c,d,n=this.config;this.match={};c=0;for(d=n.inlineMath.length;c<d;c++)a.push(this.patternQuote(n.inlineMath[c][0])),this.match[n.inlineMath[c][0]]={mode:"",end:n.inlineMath[c][1],pattern:this.endPattern(n.inlineMath[c][1])};c=0;for(d=n.displayMath.length;c<d;c++)a.push(this.patternQuote(n.displayMath[c][0])),this.match[n.displayMath[c][0]]={mode:"; mode\x3ddisplay",end:n.displayMath[c][1],pattern:this.endPattern(n.displayMath[c][1])};a.length&&e.push(a.sort(this.sortLength).join("|"));n.processEnvironments&&e.push("\\\\begin\\{([^}]*)\\}");n.processEscapes&&e.push("\\\\*\\\\\\$");n.processRefs&&e.push("\\\\(eq)?ref\\{[^}]*\\}");this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+n.skipTags.join("|")+")$","i");a=[];MathJax.Hub.config.preRemoveClass&&a.push(MathJax.Hub.config.preRemoveClass);n.ignoreClass&&a.push(n.ignoreClass);this.ignoreClass=a.length?new RegExp("(^| )("+a.join("|")+")( |$)"):/^$/;this.processClass=new RegExp("(^| )("+n.processClass+")( |$)");return 0<e.length},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(a,e){return a.length!==e.length?e.length-a.length:a==e?0:a<e?-1:1},scanElement:function(a,e,c){for(var d,n,m;a&&a!=e;)"#text"===a.nodeName.toLowerCase()?c||(a=this.scanText(a)):(d="undefined"===typeof a.className?"":a.className,n="undefined"===typeof a.tagName?"":a.tagName,"string"!==typeof d&&(d=String(d)),m=this.processClass.exec(d),!a.firstChild||d.match(/(^| )MathJax/)||!m&&this.skipTags.exec(n)||(d=(c||this.ignoreClass.exec(d))&&!m,this.scanElement(a.firstChild,e,d))),a&&(a=a.nextSibling)},scanText:function(a){if(""==a.nodeValue.replace(/\s+/,""))return a;var e,c;this.search={start:!0};for(this.pattern=this.start;a;){for(this.pattern.lastIndex=0;a&&"#text"===a.nodeName.toLowerCase()&&(e=this.pattern.exec(a.nodeValue));)a=this.search.start?this.startMatch(e,a):this.endMatch(e,a);this.search.matched&&(a=this.encloseMath(a));if(a){do c=a,a=a.nextSibling;while(a&&("br"===a.nodeName.toLowerCase()||"#comment"===a.nodeName.toLowerCase()));if(!a||"#text"!==a.nodeName)return this.search.close?this.prevEndMatch():c}}return a},startMatch:function(a,e){var c=this.match[a[0]];if(null!=c)this.search={end:c.end,mode:c.mode,pcount:0,open:e,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length},this.switchPattern(c.pattern);else if("\\begin"===a[0].substr(0,6))this.search={end:"\\end{"+a[1]+"}",mode:"; mode\x3ddisplay",pcount:0,open:e,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:!0},this.switchPattern(this.endPattern(this.search.end));else{if("\\ref"===a[0].substr(0,4)||"\\eqref"===a[0].substr(0,6))return this.search={mode:"",end:"",open:e,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length},this.endMatch([""],e);var c=a[0].substr(0,a[0].length-1),d;0===c.length%2?(d=[c.replace(/\\\\/g,"\\")],c=1):(d=[c.substr(1).replace(/\\\\/g,"\\"),"$"],c=0);d=MathJax.HTML.Element("span",null,d);var n=MathJax.HTML.TextNode(e.nodeValue.substr(0,a.index));e.nodeValue=e.nodeValue.substr(a.index+a[0].length-c);e.parentNode.insertBefore(d,e);e.parentNode.insertBefore(n,d);this.pattern.lastIndex=c}return e},endMatch:function(a,e){var c=this.search;a[0]==c.end?(c.close&&0!==c.pcount||(c.close=e,c.cpos=this.pattern.lastIndex,c.clen=c.isBeginEnd?0:a[0].length),0===c.pcount&&(c.matched=!0,e=this.encloseMath(e),this.switchPattern(this.start))):"{"===a[0]?c.pcount++:"}"===a[0]&&c.pcount&&c.pcount--;return e},prevEndMatch:function(){this.search.matched=!0;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=a===this.start},encloseMath:function(a){a=this.search;var e=a.close,c,d;(e=a.cpos===e.length?e.nextSibling:e.splitText(a.cpos))||(c=e=MathJax.HTML.addText(a.close.parentNode,""));a.close=e;for(d=a.opos?a.open.splitText(a.opos):a.open;d.nextSibling&&d.nextSibling!==e;)d.nodeValue=null!==d.nextSibling.nodeValue?"#comment"===d.nextSibling.nodeName?d.nodeValue+d.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):d.nodeValue+d.nextSibling.nodeValue:this.msieNewlineBug?d.nodeValue+("br"===d.nextSibling.nodeName.toLowerCase()?"\n":" "):d.nodeValue+" ",d.parentNode.removeChild(d.nextSibling);e=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);"none"!==this.config.preview&&this.createPreview(a.mode,e);d=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;c&&c.parentNode.removeChild(c);return d},insertNode:function(a){var e=this.search;e.close.parentNode.insertBefore(a,e.close)},createPreview:function(a,e){var c=this.config.preview;"none"!==c&&("TeX"===c&&(c=[this.filterPreview(e)]),c&&(c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c),this.insertNode(c)))},createMathTag:function(a,e){var c=document.createElement("script");c.type="math/tex"+a;MathJax.HTML.setScript(c,e);this.insertNode(c);return c},filterPreview:function(a){return a},msieNewlineBug:MathJax.Hub.Browser.isMSIE&&9>document.documentMode};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");MathJax.Extension.mml2jax={version:"2.2",config:{preview:"alttext"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(a){this.configured||(this.config=MathJax.Hub.CombineConfig("mml2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.InitBrowser(),this.configured=!0);"string"===typeof a&&(a=document.getElementById(a));a||(a=document.body);this.ProcessMathArray(a.getElementsByTagName("math"));a.getElementsByTagNameNS&&this.ProcessMathArray(a.getElementsByTagNameNS(this.MMLnamespace,"math"));var e,c;if("undefined"!==typeof document.namespaces)try{for(e=0,c=document.namespaces.length;e<c;e++){var d=document.namespaces[e];d.urn===this.MMLnamespace&&this.ProcessMathArray(a.getElementsByTagName(d.name+":math"))}}catch(m){}else if(d=document.getElementsByTagName("html")[0])for(e=0,c=d.attributes.length;e<c;e++){var n=d.attributes[e];"xmlns:"===n.nodeName.substr(0,6)&&n.nodeValue===this.MMLnamespace&&this.ProcessMathArray(a.getElementsByTagName(n.nodeName.substr(6)+":math"))}},ProcessMathArray:function(a){var e;if(a.length)if(this.MathTagBug)for(e=a.length-1;0<=e;e--)"MATH"===a[e].nodeName?this.ProcessMathFlattened(a[e]):this.ProcessMath(a[e]);else for(e=a.length-1;0<=e;e--)this.ProcessMath(a[e])},ProcessMath:function(a){var e=a.parentNode,c=document.createElement("script");c.type="math/mml";e.insertBefore(c,a);if(this.AttributeBug){var d=this.OuterHTML(a);this.CleanupHTML&&(d=d.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,""),d=d.replace(/&nbsp;/g,"\x26#xA0;"));MathJax.HTML.setScript(c,d);e.removeChild(a)}else e=MathJax.HTML.Element("span"),e.appendChild(a),MathJax.HTML.setScript(c,e.innerHTML);"none"!==this.config.preview&&this.createPreview(a,c)},ProcessMathFlattened:function(a){var e=a.parentNode,c=document.createElement("script");c.type="math/mml";e.insertBefore(c,a);for(var e="",d,n=a;a&&"/MATH"!==a.nodeName;)d=a,a=a.nextSibling,e+=this.NodeHTML(d),d.parentNode.removeChild(d);a&&"/MATH"===a.nodeName&&a.parentNode.removeChild(a);c.text=e+"\x3c/math\x3e";"none"!==this.config.preview&&this.createPreview(n,c)},NodeHTML:function(a){var e,c,d;if("#text"===a.nodeName)e=this.quoteHTML(a.nodeValue);else if("#comment"===a.nodeName)e="\x3c!--"+a.nodeValue+"--\x3e";else{e="\x3c"+a.nodeName.toLowerCase();c=0;for(d=a.attributes.length;c<d;c++){var n=a.attributes[c];if(n.specified){e+=" "+n.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"\x3d";var m=n.nodeValue;null==m&&"style"===n.nodeName&&a.style&&(m=a.style.cssText);e+='"'+this.quoteHTML(m)+'"'}}e+="\x3e";if(null!=a.outerHTML&&a.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){c=0;for(d=a.childNodes.length;c<d;c++)e+=this.OuterHTML(a.childNodes[c]);e+="\x3c/"+a.nodeName.toLowerCase()+"\x3e"}}return e},OuterHTML:function(a){if("#"===a.nodeName.charAt(0))return this.NodeHTML(a);if(!this.AttributeBug)return a.outerHTML;for(var e=this.NodeHTML(a),c=0,d=a.childNodes.length;c<d;c++)e+=this.OuterHTML(a.childNodes[c]);return e+="\x3c/"+a.nodeName.toLowerCase()+"\x3e"},quoteHTML:function(a){null==a&&(a="");return a.replace(/&/g,"\x26#x26;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;").replace(/\"/g,"\x26quot;")},createPreview:function(a,e){var c=this.config.preview;"none"!==c&&("alttext"===c&&(c=a.getAttribute("alttext"),c=null!=c?[this.filterPreview(c)]:null),c&&(c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c),e.parentNode.insertBefore(c,e)))},filterPreview:function(a){return a},InitBrowser:function(){var a=MathJax.HTML.Element("span",{id:"\x3c",className:"mathjax",innerHTML:"\x3cmath\x3e\x3cmi\x3ex\x3c/mi\x3e\x3cmspace /\x3e\x3c/math\x3e"}),e=a.outerHTML||"";this.AttributeBug=""!==e&&!(e.match(/id="&lt;"/)&&e.match(/class="mathjax"/)&&e.match(/<\/math>/));this.MathTagBug=1<a.childNodes.length;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");MathJax.Extension.asciimath2jax={version:"2.2",config:{delimiters:[["`","`"]],skipTags:"script noscript style textarea pre code".split(" 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a=MathJax.ElementJax.mml,c=MathJax.Extension["TeX/noErrors"].config,e=a.math.prototype.toNativeMML,l=a.merror.prototype.toNativeMML;a.math.Augment({toNativeMML:function(a){var c=this.data[0];return a=c&&c.data[0]&&c.data[0].isError?c.data[0].toNativeMML(a):e.call(this,a)}});a.merror.Augment({toNativeMML:function(a){if(!this.isError)return l.call(this,a);a=a.appendChild(document.createElement("span"));for(var d=this.data[0].data[0].data.join("").split(/\n/),b=0,f=d.length;b<f;b++)a.appendChild(document.createTextNode(d[b])),b!==f-1&&a.appendChild(document.createElement("br"));this.multiLine&&(a.style.display="inline-block",1<f&&(a.style.verticalAlign="middle"));for(var k in c.style)c.style.hasOwnProperty(k)&&(d=k.replace(/-./g,function(b){return b.charAt(1).toUpperCase()}),a.style[d]=c.style[k]);return a}})});a.Startup.signal.Post("TeX noErrors 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c=d.TeXAtom(this.ParseArg(b)).With(c);this.Push(c)},MmlToken:function(b){var f=this.GetArgument(b),c=this.GetBrackets(b,"").replace(/^\s+/,"");b=this.GetArgument(b);var r={attrNames:[]},g;for(d[f]&&d[f].prototype.isToken||a.Error(["NotMathMLToken","%1 is not a token element",f]);""!==c;){(g=c.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ ]*)\s*/i))||a.Error("InvalidMathMLAttr","Invalid MathML attribute: %1",c);d[f].prototype.defaults[g[1]]||this.MmlTokenAllow[g[1]]||a.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",g[1],f]);var h=this.MmlFilterAttribute(g[1],g[2].replace(/^(['"])(.*)\1$/,"$2"));h&&("true"===h.toLowerCase()?h=!0:"false"===h.toLowerCase()&&(h=!1),r[g[1]]=h,r.attrNames.push(g[1]));c=c.substr(g[0].length)}this.Push(this.mmlToken(d[f](b).With(r)))},MmlFilterAttribute:function(b,f){return f},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(b){this.Push(d.mpadded(d.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(b,f,a){b=d.mphantom(this.ParseArg(b));if(f||a)b=d.mpadded(b),a&&(b.height=b.depth=0),f&&(b.width=0);this.Push(d.TeXAtom(b))},Smash:function(b){var f=this.trimSpaces(this.GetBrackets(b,""));b=d.mpadded(this.ParseArg(b));switch(f){case "b":b.depth=0;break;case "t":b.height=0;break;default:b.height=b.depth=0}this.Push(d.TeXAtom(b))},Lap:function(b){var f=d.mpadded(this.ParseArg(b)).With({width:0});"\\llap"===b&&(f.lspace="-1 width");this.Push(d.TeXAtom(f))},RaiseLower:function(b){var f=this.GetDimen(b),a=l.position().With({name:b,move:"vertical"});"-"===f.charAt(0)&&(f=f.slice(1),b={raise:"\\lower",lower:"\\raise"}[b.substr(1)]);"\\lower"===b?(a.dh="-"+f,a.dd="+"+f):(a.dh="+"+f,a.dd="-"+f);this.Push(a)},MoveLeftRight:function(b){var f=this.GetDimen(b),a="-"===f.charAt(0)?f.slice(1):"-"+f;if("\\moveleft"===b)var c=f,f=a,a=c;this.Push(l.position().With({name:b,move:"horizontal",left:d.mspace().With({width:f,mathsize:d.SIZE.NORMAL}),right:d.mspace().With({width:a,mathsize:d.SIZE.NORMAL})}))},Hskip:function(b){this.Push(d.mspace().With({width:this.GetDimen(b),mathsize:d.SIZE.NORMAL}))},Rule:function(b,f){var a=this.GetDimen(b),c=this.GetDimen(b),g=this.GetDimen(b),h={width:a,height:c,depth:g};"blank"!==f?(parseFloat(a)&&parseFloat(c)+parseFloat(g)&&(h.mathbackground=this.stack.env.color||"black"),a=d.mpadded(d.mrow()).With(h)):a=d.mspace().With(h);this.Push(a)},MakeBig:function(b,f,a){a*=p.p_height;a=String(a).replace(/(\.\d\d\d).+/,"$1")+"em";b=this.GetDelimiter(b);this.Push(d.TeXAtom(d.mo(b).With({minsize:a,maxsize:a,fence:!0,stretchy:!0,symmetric:!0})).With({texClass:f}))},BuildRel:function(b){var f=this.ParseUpTo(b,"\\over");b=this.ParseArg(b);this.Push(d.TeXAtom(d.munderover(b,null,f)).With({mclass:d.TEXCLASS.REL}))},HBox:function(b,f){this.Push.apply(this,this.InternalMath(this.GetArgument(b),f))},FBox:function(b){this.Push(d.menclose.apply(d,this.InternalMath(this.GetArgument(b))).With({notation:"box"}))},Not:function(b){this.Push(l.not())},Dots:function(b){this.Push(l.dots().With({ldots:this.mmlToken(d.mo(d.entity("#x2026")).With({stretchy:!1})),cdots:this.mmlToken(d.mo(d.entity("#x22EF")).With({stretchy:!1}))}))},Require:function(b){b=this.GetArgument(b).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,b)},Extension:function(b,f,k){f=a.extensionDir+"/"+f;f.match(/\.js$/)||(f+=".js");c.loaded[c.fileURL(f)]||(null!=b&&delete p[k||"macros"][b.replace(/^\\/,"")],e.RestartAfter(c.Require(f)))},Macro:function(b,f,c,d){if(c){var g=[];if(null!=d){var h=this.GetBrackets(b);g.push(null==h?d:h)}for(d=g.length;d<c;d++)g.push(this.GetArgument(b));f=this.SubstituteArgs(g,f)}this.string=this.AddArgs(f,this.string.slice(this.i));this.i=0;++this.macroCount>a.config.MAXMACROS&&a.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])},Matrix:function(b,f,c,d,g,h,e,z){var n=this.GetNext();""===n&&a.Error(["MissingArgFor","Missing argument for %1",b]);"{"===n?this.i++:(this.string=n+"}"+this.string.slice(this.i+1),this.i=0);b=l.array().With({requireClose:!0,arraydef:{rowspacing:h||"4pt",columnspacing:g||"1em"}});z&&(b.isCases=!0);if(f||c)b.open=f,b.close=c;"D"===e&&(b.arraydef.displaystyle=!0);null!=d&&(b.arraydef.columnalign=d);this.Push(b)},Entry:function(b){this.Push(l.cell().With({isEntry:!0,name:b}));if(this.stack.Top().isCases){var f=this.string,c=0;b=this.i;for(var d=f.length;b<d;){var 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n=("c"+c).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");c=c.replace(/[^clr]/g,"").split("").join(" ");c=c.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");c=l.array().With({arraydef:{columnalign:c,columnspacing:g||"1em",rowspacing:h||"4pt"}});n.match(/[|:]/)&&(n.charAt(0).match(/[|:]/)&&(c.frame.push("left"),c.frame.dashed=":"===n.charAt(0)),n.charAt(n.length-1).match(/[|:]/)&&c.frame.push("right"),n=n.substr(1,n.length-2),c.arraydef.columnlines=n.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed"));f&&(c.open=this.convertDelimiter(f));a&&(c.close=this.convertDelimiter(a));"D"===d&&(c.arraydef.displaystyle=!0);"S"===d&&(c.arraydef.scriptlevel=1);e&&(c.arraydef.useHeight=!1);this.Push(b);return c},AlignedArray:function(b){var f=this.GetBrackets("\\begin{"+b.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),f)},setArrayAlign:function(b,f){f=this.trimSpaces(f||"");"t"===f?b.arraydef.align="baseline 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c=++this.i,d=1;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "\\":this.i++;break;case "{":d++;break;case "}":if(0==d&&a.Error(["ExtraClose","Extra close brace"]),0==--d)return this.string.slice(c,this.i-1)}a.Error(["MissingCloseBrace","Missing close brace"])}return this.string.charAt(this.i++)},GetBrackets:function(b,f){if("["!=this.GetNext())return f;for(var c=++this.i,d=0;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "{":d++;break;case "\\":this.i++;break;case "}":0>=d--&&a.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"]);break;case "]":if(0==d)return this.string.slice(c,this.i-1)}a.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",b])},GetDelimiter:function(b){for(;this.nextIsSpace();)this.i++;var f=this.string.charAt(this.i);if(this.i<this.string.length&&(this.i++,"\\"==f&&(f+=this.GetCS(b)),null!=p.delimiter[f]))return this.convertDelimiter(f);a.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",b])},GetDimen:function(b){var f;this.nextIsSpace()&&this.i++;if("{"==this.string.charAt(this.i)){if(f=this.GetArgument(b),f.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/))return f.replace(/ /g,"")}else if(f=this.string.slice(this.i),f=f.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/))return this.i+=f[0].length,f[1].replace(/ /g,"");a.Error(["MissingDimOrUnits","Missing dimension or its units for %1",b])},GetUpTo:function(b,f){for(;this.nextIsSpace();)this.i++;for(var c=this.i,d,g,h=0;this.i<this.string.length;){d=this.i;g=this.string.charAt(this.i++);switch(g){case "\\":g+=this.GetCS();break;case "{":h++;break;case "}":0==h&&a.Error(["ExtraCloseLooking","Extra close brace while looking for %1",f]),h--}if(0==h&&g==f)return this.string.slice(c,d)}a.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",f,b])},ParseArg:function(b){return a.Parse(this.GetArgument(b),this.stack.env).mml()},ParseUpTo:function(b,f){return a.Parse(this.GetUpTo(b,f),this.stack.env).mml()},InternalMath:function(b,f){var c={displaystyle:!1};null!=f&&(c.scriptlevel=f);this.stack.env.font&&(c.mathvariant=this.stack.env.font);if(!b.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/))return[this.InternalText(b,c)];for(var 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c=0,f=this.data.length;c<f;c++)this.data[c]?this.data[c].toNativeMML(a):a.appendChild(this.NativeMMLelement("mrow"));b.appendChild(a)},NativeMMLattributes:function(b){var a=this.defaults,c=this.attrNames||n.copyAttributeNames,f=n.skipAttributes;if(!this.attrNames){"mstyle"===this.type&&(a=n.math.prototype.defaults);for(var k in a)!f[k]&&a.hasOwnProperty(k)&&null!=this[k]&&b.setAttribute(k,this.NativeMMLattribute(this[k]))}a=0;for(f=c.length;a<f;a++)k=(this.attr||{})[c[a]],null==k&&(k=this[c[a]]),null!=k&&b.setAttribute(c[a],this.NativeMMLattribute(k));this.NativeMMLclass(b)},NativeMMLclass:function(b){var a=[];this["class"]&&a.push(this["class"]);if(this.isa(n.TeXAtom)){var c="ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" ")[this.texClass];c&&a.push("MJX-TeXAtom-"+c)}this.mathvariant&&this.NativeMMLvariants[this.mathvariant]&&a.push("MJX"+this.mathvariant);this.arrow&&a.push("MJX-arrow");this.variantForm&&a.push("MJX-variant");a.length&&b.setAttribute("class",a.join(" "))},NativeMMLattribute:function(b){b=String(b);a.NAMEDSPACE[b]?b=a.NAMEDSPACE[b]:b.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)?b=RegExp.$2+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.NativeMMLvariants[b]&&(b=this.NativeMMLvariants[b]);return b},NativeMMLvariants:{"-tex-caligraphic":n.VARIANT.SCRIPT,"-tex-caligraphic-bold":n.VARIANT.BOLDSCRIPT,"-tex-oldstyle":n.VARIANT.NORMAL,"-tex-oldstyle-bold":n.VARIANT.BOLD,"-tex-mathit":n.VARIANT.ITALIC},NativeMMLelement:function(b){b=m?document.createElement("m:"+b):document.createElementNS(a.MMLnamespace,b);b.isMathJax=!0;return b}});n.mrow.Augment({toNativeMML:function(b){var c,f;if(this.inferred&&this.parent.inferRow)for(c=0,f=this.data.length;c<f;c++)this.data[c]?this.data[c].toNativeMML(b):b.appendChild(this.NativeMMLelement("mrow"));else if(a.stretchyMoBug&&(this.open||this.close)){var k=this.NativeMMLelement("mfenced");this.NativeMMLattributes(k);c=0;f=this.data.length;this.open&&(k.setAttribute("open",this.open),c++);this.close&&(k.setAttribute("close",this.close),f--);var d=k;1<f-c+1&&(d=this.NativeMMLelement("mrow"),b.appendChild(k),b=k);for(;c<f;c++)this.data[c]?this.data[c].toNativeMML(d):d.appendChild(this.NativeMMLelement("mrow"));b.appendChild(d)}else this.SUPER(arguments).toNativeMML.call(this,b)}});n.msubsup.Augment({toNativeMML:function(b){var a=this.type;null==this.data[this.sup]&&(a="msub");null==this.data[this.sub]&&(a="msup");a=this.NativeMMLelement(a);this.NativeMMLattributes(a);delete this.data[0].inferred;for(var c=0,f=this.data.length;c<f;c++)this.data[c]&&this.data[c].toNativeMML(a);b.appendChild(a)}});n.munderover.Augment({toNativeMML:function(b){var a=this.type;null==this.data[this.under]&&(a="mover");null==this.data[this.over]&&(a="munder");a=this.NativeMMLelement(a);this.NativeMMLattributes(a);delete this.data[0].inferred;for(var c=0,f=this.data.length;c<f;c++)this.data[c]&&this.data[c].toNativeMML(a);b.appendChild(a)}});if(!m){var b=MathJax.Hub.SplitList;n.mtable.Augment({toNativeMML:function(c){var f,k;if(a.tableSpacingBug){f=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=b("0px "+f.rowspacing);this.nMMLleftPadding=b("0px "+f.columnspacing);var d=this.nMMLtopPadding,g=d.length;f=0;for(k=this.data.length;f<k;f++)this.data[f]&&(this.data[f].nMMLtopPadding=d[f<g?f:g-1])}if(a.tableLabelBug)for(f=0,k=this.data.length;f<k;f++)if(this.data[f]&&this.data[f].isa(n.mlabeledtr)){var l=e.config.displayAlign.charAt(0),m=this.Get("side").charAt(0);this.nMMLhasLabels=!0;this.nMMLlaMatch=l===m;this.nMMLforceWidth="c"===l||!!(this.width||"").match("%");break}this.width&&this.ffTableWidthBug&&(f=(this.style||"").replace(/;\s*$/,"").split(";"),""===f[0]&&f.shift(),f.push("width:"+this.width),this.style=f.join(";"));this.SUPER(arguments).toNativeMML.call(this,c);if(this.nMMLhasLabels){f=c.firstChild;if(this.nMMLforceWidth||"r"!==m)if(l=("l"!==l?1:0)+("l"===m?1:0)){var m={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"},p;for(p in m)m.hasOwnProperty(p)&&this[p]&&(k=[m[p],m[p]].slice(2-l).join(" ")+" ",f.setAttribute(p,k+f.getAttribute(p)))}!this.nMMLforceWidth&&this.nMMLlaMatch||f.setAttribute("width","100%")}}});n.mtr.Augment({toNativeMML:function(b){this.SUPER(arguments).toNativeMML.call(this,b);var c=b.lastChild;if(a.tableSpacingBug)for(var d=this.parent.nMMLleftPadding,g=d.length,r=c.firstChild,l=0;r;r=r.nextSibling,l++)k(r,this.nMMLtopPadding,d[l<g?l:g-1]);if(a.tableLabelBug&&(d=this.parent.nMMLforceWidth,g=this.parent.Get("side").charAt(0),r=e.config.displayAlign.charAt(0),this.parent.nMMLhasLabels&&c.firstChild)){if(d||"r"!==g)f("Left",c.firstChild),"l"!==r&&c.insertBefore(this.NativeMMLelement("mtd"),c.firstChild).setAttribute("style","padding:0"),"l"===g&&c.insertBefore(this.NativeMMLelement("mtd"),c.firstChild).setAttribute("style","padding:0");(d||"l"!==g)&&f("Right",c.lastChild)}}});n.mlabeledtr.Augment({toNativeMML:function(b){var c=this.NativeMMLelement("mtr");this.NativeMMLattributes(c);for(var d=1,g=this.data.length;d<g;d++)this.data[d]?this.data[d].toNativeMML(c):c.appendChild(this.NativeMMLelement("mtd"));if(a.tableSpacingBug)for(var g=this.parent.nMMLleftPadding,r=g.length,d=0,l=c.firstChild;l;l=l.nextSibling,d++)k(l,this.nMMLtopPadding,g[d<r?d:r-1]);if(a.tableLabelBug){var d=this.parent.Get("side").charAt(0),g=e.config.displayAlign.charAt(0),m=e.config.displayIndent;this.data[0].toNativeMML(c);l=r=c.lastChild;d===g?(r.setAttribute("style","width:"+m),r.setAttribute("columnalign",e.config.displayAlign)):(l=this.NativeMMLelement("mpadded"),l.setAttribute("style","width:0"),l.setAttribute("width","0px"),l.appendChild(r.firstChild),r.appendChild(l));f("",r);c.removeChild(r);var m=100,n=this.parent.nMMLforceWidth;(this.parent.width||"").match(/%/)&&(m-=parseFloat(this.parent.width));var p=m;if(n||"r"!==d)f("Left",c.firstChild),"l"!==g&&("c"===g&&(p/=2),m-=p,c.insertBefore(this.NativeMMLelement("mtd"),c.firstChild).setAttribute("style","padding:0;width:"+p+"%")),"l"===d&&c.insertBefore(r,c.firstChild);if(n||"l"!==d)f("Right",c.lastChild),"r"!==g&&c.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+m+"%"),"r"===d&&(d!==g&&l.setAttribute("lspace","-1width"),c.appendChild(r))}b.appendChild(c)}});n.mtd.Augment({toNativeMML:function(b){b=b.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(b);a.widthBug&&(b=b.appendChild(this.NativeMMLelement("mrow")));for(var c=0,f=this.data.length;c<f;c++)this.data[c]?this.data[c].toNativeMML(b):b.appendChild(this.NativeMMLelement("mrow"))}});n.mspace.Augment({toNativeMML:function(b){this.SUPER(arguments).toNativeMML.call(this,b);if(a.spaceWidthBug&&this.width){var c=b.lastChild,f=c.getAttribute("width"),k=c.getAttribute("style")||"";""!=k&&(k+=";");c.setAttribute("style",k+"width:"+f)}}});var c=MathJax.Ajax.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");a.Augment({config:{styles:{'[mathvariant\x3d"double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant\x3d"script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant\x3d"fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant\x3d"bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant\x3d"bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant\x3d"monospace"]':{"font-family":"monospace"},'[mathvariant\x3d"sans-serif"]':{"font-family":"sans-serif"},'[mathvariant\x3d"bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant\x3d"sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant\x3d"sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},'[class\x3d"MJX-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class\x3d"MJX-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[class\x3d"MJX-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class\x3d"MJX-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+c+"/MathJax_AMS-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Script-WEB",src:"url('"+c+"/MathJax_Script-Regular.otf')"},"@font-face /*3*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+c+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+c+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+c+"/MathJax_Fraktur-Bold.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+c+"/MathJax_Caligraphic-Bold.otf')"}}}})}n.math.Augment({toNativeMML:function(b){var c=this.NativeMMLelement(this.type),f=c;c.setAttribute("xmlns",a.MMLnamespace);this.NativeMMLattributes(c);a.widthBug&&(c=c.appendChild(this.NativeMMLelement("mrow")));for(var k=0,d=this.data.length;k<d;k++)this.data[k]?this.data[k].toNativeMML(c):c.appendChild(this.NativeMMLelement("mrow"));k=(this.data[0]||[]).data[0]||{};if(k.nMMLhasLabels){if(k.nMMLforceWidth||!k.nMMLlaMatch)c.setAttribute("style","width:100%"),b.style.width=b.parentNode.style.width="100%";k.nMMLlaMatch&&"div"===b.parentNode.parentNode.nodeName.toLowerCase()&&b.parentNode.parentNode.style.setProperty("margin-"+e.config.displayAlign,"0px","important")}b.appendChild(f);a.widthBug&&!k.nMMLforceWidth&&k.nMMLlaMatch&&(b.style.width=(f.firstChild.scrollWidth/a.ex).toFixed(3)+"ex")}});n.mfenced.Augment({toNativeMML:function(b){if(a.mfencedBug){var c=e.Browser.isOpera,f,k,d,g=this.getValues("open","close","separators");g.open=g.open.replace(/^\s+/,"").replace(/\s+$/,"");g.close=g.close.replace(/^\s+/,"").replace(/\s+$/,"");g.separators=g.separators.replace(/\s+/g,"").split("");if(0==g.separators.length)g.separators=null;else if(g.separators.length<this.data.length-1)for(k=g.separators[g.separators.length-1],f=this.data.length-1-g.separators.length;0<f;f--)g.separators.push(k);var r=this.NativeMMLelement(c?this.type:"mrow");this.NativeMMLattributes(r);r.removeAttribute("separators");c?(r.setAttribute("open",g.open),r.setAttribute("close",g.close),1<this.data.length&&(b.appendChild(r),b=r,r=this.NativeMMLelement("mrow"))):(r.removeAttribute("open"),r.removeAttribute("close"));c||(d=this.NativeMMLelement("mo"),d.setAttribute("fence","true"),d.textContent=g.open,r.appendChild(d));f=0;for(k=this.data.length;f<k;f++)g.separators&&0<f&&(d=this.NativeMMLelement("mo"),d.setAttribute("separator","true"),d.textContent=g.separators[f-1],r.appendChild(d)),this.data[f]?this.data[f].toNativeMML(r):r.appendChild(this.NativeMMLelement("mrow"));c||(d=this.NativeMMLelement("mo"),d.setAttribute("fence","true"),d.textContent=g.close,r.appendChild(d));b.appendChild(r)}else this.SUPER(arguments).toNativeMML.call(this,b)}});n.TeXAtom.Augment({toNativeMML:function(b){var a=this.NativeMMLelement("mrow");this.NativeMMLattributes(a);this.data[0].toNativeMML(a);b.appendChild(a)}});n.chars.Augment({toNativeMML:function(b){b.appendChild(document.createTextNode(this.toString()))}});n.entity.Augment({toNativeMML:function(b){b.appendChild(document.createTextNode(this.toString()))}});n.xml.Augment({toNativeMML:function(b){for(var a=0,c=this.data.length;a<c;a++)b.appendChild(this.data[a].cloneNode(!0))}});e.Register.StartupHook("TeX mathchoice Ready",function(){n.TeXmathchoice.Augment({toNativeMML:function(b){this.Core().toNativeMML(b)}})});setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)});e.Browser.Select({MSIE:function(b){a.msieIE8HeightBug=8===(document.documentMode||0)},Opera:function(b){a.operaPositionBug=!0;a.stretchyMoBug=!0;a.tableLabelBug=!0;a.mfencedBug=!0},Firefox:function(b){a.ffTableWidthBug=!b.versionAtLeast("13.0");a.forceReflow=!0;a.widthBug=!0;a.spaceWidthBug=!b.versionAtLeast("20.0");a.tableSpacingBug=!0;a.tableLabelBug=!0;a.mfencedBug=!0},Chrome:function(b){a.tableSpacingBug=!0;a.tableLabelBug=!0;a.mfencedBug=!0},Safari:function(b){a.tableSpacingBug=!0;a.tableLabelBug=!0;a.mfencedBug=!0}});e.Register.StartupHook("End Cookie",function(){"None"!==e.config.menuSettings.zoom&&c.Require("[MathJax]/extensions/MathZoom.js")})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML);(function(a,e,c){var d,n=function(){var b=[].slice.call(arguments,0);b[0][0]=["HTML-CSS",b[0][0]];return MathJax.Message.Set.apply(MathJax.Message,b)},m=MathJax.Object.Subclass({timeout:1E3*(e.Browser.isMobile?15:8),FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:"sans-serif monospace script Times Courier Arial Helvetica".split(" "),testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]);this.text=this.div.firstChild},findFont:function(b,a){if(a&&this.testCollection(a))return a;for(var c=0,d=b.length;c<d;c++)if(b[c]!==a&&this.testCollection(b[c]))return b[c];return null},testCollection:function(b){return this.testFont(this.FontInfo[b])},testFont:function(b){b.isWebFont&&c.FontFaceBug?this.div.style.fontWeight=this.div.style.fontStyle="normal":(this.div.style.fontWeight=b.weight||"normal",this.div.style.fontStyle=b.style||"normal");var a=this.getComparisonWidths(b.testString,b.noStyleChar);if(a){this.div.style.fontFamily="'"+b.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==a[0]&&(this.div.style.fontFamily="'"+b.family+"',"+this.comparisonFont[a[2]],this.div.offsetWidth==a[1]))return!1;if(this.div.offsetWidth!=a[3]||this.div.offsetHeight!=a[4]){if(b.noStyleChar||!c.FONTDATA||!c.FONTDATA.hasStyleChar)return!0;for(var a=0,k=this.testSize.length;a<k;a++)if(this.testStyleChar(b,this.testSize[a]))return!0}}return!1},styleChar:"\ueffd",versionChar:"\ueffe",compChar:"\uefff",testStyleChar:function(b,a){var k=3+(b.weight?2:0)+(b.style?4:0),d="",g=0,h=this.div.style.fontSize;this.div.style.fontSize=a;c.msieItalicWidthBug&&"italic"===b.style&&(this.text.nodeValue=d=this.compChar,g=this.div.offsetWidth);c.safariTextNodeBug?this.div.innerHTML=this.compChar+d:this.text.nodeValue=this.compChar+d;var e=this.div.offsetWidth-g;c.safariTextNodeBug?this.div.innerHTML=this.styleChar+d:this.text.nodeValue=this.styleChar+d;var l=Math.floor((this.div.offsetWidth-g)/e+.5);l===k&&(c.safariTextNodeBug?this.div.innerHTML=this.versionChar+d:this.text.nodeValue=this.versionChar+d,b.version=Math.floor((this.div.offsetWidth-g)/e+1.5)/2);this.div.style.fontSize=h;return l===k},getComparisonWidths:function(b,a){c.FONTDATA&&c.FONTDATA.hasStyleChar&&!a&&(b+=this.styleChar+" "+this.compChar);c.safariTextNodeBug?this.div.innerHTML=b:this.text.nodeValue=b;this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth;this.div.style.fontFamily=c.webFontDefault;for(var d=this.div.offsetWidth,g=this.div.offsetHeight,h=1,e=this.comparisonFont.length;h<e;h++)if(this.div.style.fontFamily=this.comparisonFont[h],this.div.offsetWidth!=k)return[k,this.div.offsetWidth,h,d,g];return null},loadWebFont:function(b){e.Startup.signal.Post("HTML-CSS Jax - Web-Font "+c.fontInUse+"/"+b.directory);var f=n(["LoadWebFont","Loading web-font %1",c.fontInUse+"/"+b.directory]),k=MathJax.Callback({}),f=MathJax.Callback(["loadComplete",this,b,f,k]);a.timer.start(a,[this.checkWebFont,b,f],0,this.timeout);return k},loadComplete:function(b,f,k,d){MathJax.Message.Clear(f);d===a.STATUS.OK?(this.webFontLoaded=!0,k()):(this.loadError(b),e.Browser.isFirefox&&c.allowWebFonts&&(f=document.location.protocol+"//"+document.location.hostname,""!=document.location.port&&(f+=":"+document.location.port),f+="/",a.fileURL(c.webfontDir).substr(0,f.length)!==f&&this.firefoxFontError(b)),this.webFontLoaded?k():c.loadWebFontError(b,k))},loadError:function(b){n(["CantLoadWebFont","Can't load web font %1",c.fontInUse+"/"+b.directory],null,2E3);e.Startup.signal.Post(["HTML-CSS Jax - web font error",c.fontInUse+"/"+b.directory,b])},firefoxFontError:function(b){n(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3E3);e.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(b,a,k){b.time(k)||(c.Font.testFont(a)?k(b.STATUS.OK):setTimeout(b,b.delay))},fontFace:function(b){var f=c.allowWebFonts,k=c.FONTDATA.FONTS[b];c.msieFontCSSBug&&!k.family.match(/-Web$/)&&(k.family+="-Web");var d=a.fileURL(c.webfontDir+"/"+f),g=b.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");g.match(/-/)||(g+="-Regular");var g="svg"===f?g+(".svg#"+g):g+("."+f),h={"font-family":k.family,src:"url('"+d+"/"+g+"')"};"otf"===f?(h.src+=" format('opentype')",d=a.fileURL(c.webfontDir+"/woff"),h.src="url('"+d+"/"+g.replace(/otf$/,"woff")+"') format('woff'), "+h.src):"eot"!==f&&(h.src+=" format('"+f+"')");c.FontFaceBug&&k.isWebFont||(b.match(/-bold/)&&(h["font-weight"]="bold"),b.match(/-italic/)&&(h["font-style"]="italic"));return h}}),l,p,q;c.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important","float":"none ! important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",width:"1px",height:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity\x3d0)"},".MathJax .MathJax_HitBox 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b=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=b.offsetWidth/5;this.hiddenDiv.removeChild(b);this.startMarker=this.createStrut(this.Element("span"),10,!0);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");this.operaHeightBug&&this.createStrut(this.HDspan,0);if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(c){}}else this.HDimg=this.createStrut(this.HDspan,0);this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return a.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(b){for(var a=0,c=b.length;a<c;a++)"STIX"===b[a]&&(b.splice(a,1),c--,a--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=b[0])},PreloadWebFonts:function(){if(c.allowWebFonts&&c.config.preloadWebFonts)for(var b=0,a=c.config.preloadWebFonts.length;b<a;b++){var k=c.FONTDATA.FONTS[c.config.preloadWebFonts[b]];k.available||c.Font.testFont(k)}},InitializeHTML:function(){this.PreloadWebFonts();document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(b){var a=b.jax[this.id],c,d=a.length,g,h,t,m,n,y,q=!1,u=this.config.linebreaks.automatic,v=this.config.linebreaks.width;u?((q=null!=v.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?v=v.replace(/\s*container\s*/,""):y=this.defaultWidth,""===v&&(v="100%")):y=1E5;for(c=0;c<d;c++)if(g=a[c],g.parentNode&&((h=g.previousSibling)&&String(h.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)&&h.parentNode.removeChild(h),h=g.MathJax.elementJax))h.HTMLCSS={display:"block"===h.root.Get("display")},t=m=this.Element("span",{className:"MathJax",id:h.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:l.Menu,onmousedown:l.Mousedown,onmouseover:l.Mouseover,onmouseout:l.Mouseout,onmousemove:l.Mousemove,onclick:l.Click,ondblclick:l.DblClick}),e.Browser.noContextMenu&&(t.ontouchstart=p.start,t.ontouchend=p.end),h.HTMLCSS.display?(m=this.Element("div",{className:"MathJax_Display"}),m.appendChild(t)):this.msieDisappearingBug&&(t.style.display="inline-block"),m.setAttribute("role","textbox"),m.setAttribute("aria-readonly","true"),m.className+=" 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c=b.MathJax.elementJax,r=c.root,g=document.getElementById(c.inputID+"-Frame"),h=c.HTMLCSS.display?g.parentNode:g;this.em=d.mbase.prototype.em=c.HTMLCSS.em*c.HTMLCSS.scale;this.outerEm=c.HTMLCSS.em;this.scale=c.HTMLCSS.scale;this.linebreakWidth=c.HTMLCSS.lineWidth;g.style.fontSize=c.HTMLCSS.fontSize;this.initImg(g);this.initHTML(r,g);r.setTeXclass();try{r.toHTML(g,h)}catch(t){if(t.restart)for(;g.firstChild;)g.removeChild(g.firstChild);throw t;}c.HTMLCSS.isHidden&&b.parentNode.insertBefore(h,b);h.className=h.className.split(/ /)[0];this.hideProcessedMath&&(h.className+=" MathJax_Processed",b.MathJax.preview&&(c.HTMLCSS.preview=b.MathJax.preview,delete b.MathJax.preview),a.HTMLCSSeqn+=a.i-a.HTMLCSSi,a.HTMLCSSi=a.i,a.HTMLCSSeqn>=a.HTMLCSSlast+a.HTMLCSSchunk&&(this.postTranslate(a),a.HTMLCSSchunk=Math.floor(a.HTMLCSSchunk*this.config.EqnChunkFactor),a.HTMLCSSdelay=!0))}},postTranslate:function(b){var a=b.jax[this.id];if(this.hideProcessedMath){for(var c=b.HTMLCSSlast,d=b.HTMLCSSeqn;c<d;c++){var g=a[c];if(g&&g.MathJax.elementJax){g.previousSibling.className=g.previousSibling.className.split(/ /)[0];var h=g.MathJax.elementJax.HTMLCSS;h.preview&&(h.preview.innerHTML="",g.MathJax.preview=h.preview,delete h.preview)}}this.forceReflow&&(a=(document.styleSheets||[])[0]||{},a.disabled=!0,a.disabled=!1);b.HTMLCSSlast=b.HTMLCSSeqn}},getJaxFromMath:function(b){"MathJax_Display"===b.parentNode.className&&(b=b.parentNode);do b=b.nextSibling;while(b&&"script"!==b.nodeName.toLowerCase());return e.getJaxFor(b)},getHoverSpan:function(b,a){return b.root.HTMLspanElement()},getHoverBBox:function(b,a,c){a=a.bbox;b=b.HTMLCSS.outerEm;b={w:a.w*b,h:a.h*b,d:a.d*b};a.width&&(b.width=a.width);return b},Zoom:function(b,a,k,e,g){a.className="MathJax";a.style.fontSize=b.HTMLCSS.fontSize;g=a.appendChild(this.EmExSpan.cloneNode(!0));var h=g.lastChild.firstChild.offsetHeight/60;this.em=d.mbase.prototype.em=h;this.outerEm=h/b.HTMLCSS.scale;g.parentNode.removeChild(g);this.idPostfix="-zoom";b.root.toHTML(a,a);this.idPostfix="";if(g=b.root.HTMLspanElement().bbox.width){a.style.width=Math.floor(e-1.5*c.em)+"px";a.style.display="inline-block";for(b=document.getElementById((b.root.id||"MathJax-Span-"+b.root.spanID)+"-zoom").firstChild;b&&b.style.width!==g;)b=b.nextSibling;b&&(b.style.width="100%")}a.style.position="absolute";g||(k.style.position="absolute");b=a.offsetWidth;e=a.offsetHeight;g=k.offsetHeight;h=k.offsetWidth;0===h&&(h=k.parentNode.offsetWidth);a.style.position=k.style.position="";return{Y:-l.getBBox(a).h,mW:h,mH:g,zW:b,zH:e}},initImg:function(b){},initHTML:function(b,a){},initFont:function(b){var f=c.FONTDATA.FONTS,d=c.config.availableFonts;if(d&&d.length&&c.Font.testFont(f[b]))return f[b].available=!0,null;if(!this.allowWebFonts)return null;f[b].isWebFont=!0;c.FontFaceBug&&(f[b].family=b,c.msieFontCSSBug&&(f[b].family+="-Web"));return a.Styles({"@font-face":this.Font.fontFace(b)})},Remove:function(b){var a=document.getElementById(b.inputID+"-Frame");a&&(b.HTMLCSS.display&&(a=a.parentNode),a.parentNode.removeChild(a));delete b.HTMLCSS},getHD:function(b){var a=b.style.position;b.style.position="absolute";this.HDimg.style.height="0px";b.appendChild(this.HDspan);var c={h:b.offsetHeight};this.HDimg.style.height=c.h+"px";c.d=b.offsetHeight-c.h;c.h-=c.d;c.h/=this.em;c.d/=this.em;b.removeChild(this.HDspan);b.style.position=a;return c},getW:function(b){var a,c;a=(b.bbox||{}).w;var d=b;if(b.bbox&&b.bbox.exactW)return a;if(b.bbox&&0<=a&&!this.initialSkipBug||this.negativeBBoxes||!b.firstChild)a=b.offsetWidth,c=b.parentNode.offsetHeight;else if(b.bbox&&0>a&&this.msieNegativeBBoxBug)a=-b.offsetWidth,c=b.parentNode.offsetHeight;else{if(this.initialSkipBug){var g=b.style.position;b.style.position="absolute";d=this.startMarker;b.insertBefore(d,b.firstChild)}b.appendChild(this.endMarker);a=this.endMarker.offsetLeft-d.offsetLeft;b.removeChild(this.endMarker);this.initialSkipBug&&(b.removeChild(d),b.style.position=g)}null!=c&&(b.parentNode.HH=c/this.em);return a/this.em},Measured:function(b,a){var c=b.bbox;if(null==c.width&&c.w&&!c.isMultiline){var d=this.getW(b);c.rw+=d-c.w;c.w=d;c.exactW=!0}a||(a=b.parentNode);a.bbox||(a.bbox=c);return b},Remeasured:function(b,a){a.bbox=this.Measured(b,a).bbox},MeasureSpans:function(b){var a=[],c,d,g,h,e;d=0;for(g=b.length;d<g;d++)if(c=b[d])h=c.bbox,e=this.parentNode(c),h.exactW||h.width||0===h.w||h.isMultiline?e.bbox||(e.bbox=h):this.negativeBBoxes||!c.firstChild||0<=h.w&&!this.initialSkipBug||0>h.w&&this.msieNegativeBBoxBug?a.push([c]):this.initialSkipBug?(h=this.startMarker.cloneNode(!0),e=this.endMarker.cloneNode(!0),c.insertBefore(h,c.firstChild),c.appendChild(e),a.push([c,h,e,c.style.position]),c.style.position="absolute"):(e=this.endMarker.cloneNode(!0),c.appendChild(e),a.push([c,null,e]));d=0;for(g=a.length;d<g;d++)c=a[d][0],h=c.bbox,e=this.parentNode(c),0<=h.w&&!this.initialSkipBug||this.negativeBBoxes||!c.firstChild?(b=c.offsetWidth,e.HH=e.offsetHeight/this.em):0>h.w&&this.msieNegativeBBoxBug?(b=-c.offsetWidth,e.HH=e.offsetHeight/this.em):b=a[d][2].offsetLeft-((a[d][1]||{}).offsetLeft||0),b/=this.em,h.rw+=b-h.w,h.w=b,h.exactW=!0,e.bbox||(e.bbox=h);d=0;for(g=a.length;d<g;d++)c=a[d],c[1]&&(c[1].parentNode.removeChild(c[1]),c[0].style.position=c[3]),c[2]&&c[2].parentNode.removeChild(c[2])},Em:function(b){return 6E-4>Math.abs(b)?"0em":b.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(b){b=(Math.round(b*c.em)+.05)/c.em;return 6E-4>Math.abs(b)?"0em":b.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(b){return parseFloat(b)},Px:function(b){b*=this.em;return(0>b?"-":"")+Math.abs(b).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(b){return parseFloat(b)/this.em},Percent:function(b){return(100*b).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(b,a,k){"string"!==typeof b&&(b=b.toString());if(""===b)return"";if(b===d.SIZE.NORMAL)return 1;if(b===d.SIZE.BIG)return 2;if(b===d.SIZE.SMALL)return.71;if("infinity"===b)return c.BIGDIMEN;var e=this.FONTDATA.TeX_factor;if(b.match(/mathspace$/))return c.MATHSPACE[b]*e;var g=b.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);b=parseFloat(g[1]||"1");g=g[2];null==k&&(k=1);null==a&&(a=1);return"em"===g?b*e:"ex"===g?b*c.TeX.x_height*e:"%"===g?b/100*k:"px"===g?b/c.em:"pt"===g?b/10*e:"pc"===g?1.2*b*e:"in"===g?b*this.pxPerInch/c.em:"cm"===g?b*this.pxPerInch/c.em/2.54:"mm"===g?b*this.pxPerInch/c.em/25.4:"mu"===g?b/18*e*a:b*e*k},thickness2em:function(b,a){var k=c.TeX.rule_thickness;return b===d.LINETHICKNESS.MEDIUM?k:b===d.LINETHICKNESS.THIN?.67*k:b===d.LINETHICKNESS.THICK?1.67*k:this.length2em(b,a,k)},getPadding:function(b){var a={top:0,right:0,bottom:0,left:0},c=!1,d;for(d in a)if(a.hasOwnProperty(d)){var g=b.style["padding"+d.charAt(0).toUpperCase()+d.substr(1)];g&&(a[d]=this.length2em(g),c=!0)}return c?a:!1},getBorders:function(b){var a={top:0,right:0,bottom:0,left:0},c={},d=!1,g;for(g in a)if(a.hasOwnProperty(g)){var 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t=this.Em(a+k),l=this.Em(-k);this.msieInlineBlockAlignBug&&(l=this.Em(c.getHD(b.parentNode).d-k));b.isBox||h?(h=null==b.scale?1:b.scale,b.bbox={exactW:!0,h:a*h,d:k*h,w:e*h,rw:e*h,lw:0},b.style.height=t,b.style.verticalAlign=l,b.HH=(a+k)*h):b=this.addElement(b,"span",{style:{height:t,verticalAlign:l},isMathJax:!0});0<=e?(b.style.width=this.Em(e),b.style.display="inline-block",b.style.overflow="hidden"):(this.msieNegativeSpaceBug&&(b.style.height=""),b.style.marginLeft=this.Em(e),c.safariNegativeSpaceBug&&b.parentNode.firstChild==b&&this.createBlank(b,0,!0));g&&g!==d.COLOR.TRANSPARENT&&(b.style.backgroundColor=g,b.style.position="relative");return b},createRule:function(b,a,d,e,g){a<-d&&(d=-a);var h=c.TeX.min_rule_thickness,t=1;0<e&&e*this.em<h&&(e=h/this.em);0<a+d&&(a+d)*this.em<h&&(t=1/(a+d)*(h/this.em),a*=t,d*=t);g=g?"solid "+g:"solid";g=this.Em(e)+" 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d=String(c).match(/%$/),g=d||null==c?0:c;b=this.addElement(b,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:d?"100%":this.Em(g),height:0}});a||(b.parentNode.bbox=b.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:g,lw:this.BIGDIMEN,rw:d||null==c?-this.BIGDIMEN:c},d&&(b.bbox.width=c));return b},createBox:function(b,a){var c=this.addElement(b,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});null!=a&&(c.style.width=a);return c},addBox:function(b,a){a.style.position="absolute";a.isBox=a.isMathJax=!0;return b.appendChild(a)},placeBox:function(b,a,d,e){b.isMathJax=!0;var g=c.parentNode(b),h=b.bbox,t=g.bbox;this.msiePlaceBoxBug&&this.addText(b,this.NBSP);this.imgSpaceBug&&this.addText(b,this.imgSpace);var l,m=0;l=null!=b.HH?b.HH:h?Math.max(3,h.h+h.d):b.offsetHeight/this.em;b.noAdjust||(l=Math.round((l+1)*this.em)/this.em,this.msieInlineBlockAlignBug?this.addElement(b,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:!0,style:{width:0,height:this.Em(l)}}):(this.addElement(b,"span",{isMathJax:!0,style:{display:"inline-block",width:0,height:this.Em(l)}}),c.chromeHeightBug&&(l-=(b.lastChild.offsetHeight-Math.round(l*this.em))/this.em)));if(h&&(this.initialSkipBug&&(0>h.lw&&(m=h.lw,c.createBlank(b,-m,!0)),h.rw>h.w&&c.createBlank(b,h.rw-h.w+.1)),!this.msieClipRectBug&&!h.noclip&&!e)){e=3/this.em;var n=null==h.H?h.h:h.H,p=l+(null==h.D?h.d:h.D)+e,q=h.lw-3*e,v=1E3;this.initialSkipBug&&0>h.lw&&(q=-3*e);h.isFixed&&(v=h.width-q);b.style.clip="rect("+this.Em(l-n-e)+" "+this.Em(v)+" "+this.Em(p)+" 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c=b.bbox;c&&(c.w=a,c.exactW=!0);if(c=b.parentNode.bbox)c.w=a,c.exactW=!0}else b.style.width=b.parentNode.style.width="100%",b.bbox&&(b.bbox.width=a),b.parentNode.bbox&&(b.parentNode.bbox.width=a)},createDelimiter:function(b,c,k,r,g){if(c){r||(r=1);k instanceof Array||(k=[k,k]);var h=k[1];k=k[0];for(var l={alias:c};l.alias;)c=l.alias,(l=this.FONTDATA.DELIMITERS[c])||(l={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]});l.load&&e.RestartAfter(a.Require(this.fontDir+"/fontdata-"+l.load+".js"));for(var m=0,n=l.HW.length;m<n;m++)if(l.HW[m][0]*r>=k-.01||m==n-1&&!l.stretch){l.HW[m][2]&&(r*=l.HW[m][2]);l.HW[m][3]&&(c=l.HW[m][3]);k=this.addElement(b,"span");this.createChar(k,[c,l.HW[m][1]],r,g);b.bbox=k.bbox;b.offset=.65*b.bbox.w;b.scale=r;return}if(l.stretch)this["extendDelimiter"+l.dir](b,h,l.stretch,r,g)}else b.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0},b.bbox.rw=b.bbox.w,this.createSpace(b,b.bbox.h,b.bbox.d,b.bbox.w)},extendDelimiterV:function(b,a,c,d,g){var e=this.createStack(b,!0),l=this.createBox(e),m=this.createBox(e);this.createChar(l,c.top||c.ext,d,g);this.createChar(m,c.bot||c.ext,d,g);var n={bbox:{w:0,lw:0,rw:0}},y=n,p,q=l.bbox.h+l.bbox.d+m.bbox.h+m.bbox.d,v=-l.bbox.h;this.placeBox(l,0,v,!0);v-=l.bbox.d;c.mid&&(y=this.createBox(e),this.createChar(y,c.mid,d,g),q+=y.bbox.h+y.bbox.d);c.min&&a<q*c.min&&(a=q*c.min);if(a>q){n=this.Element("span");this.createChar(n,c.ext,d,g);p=n.bbox.h+n.bbox.d;var A=p-.05,D,B,G=c.mid?2:1;B=D=Math.min(Math.ceil((a-q)/(G*A)),this.maxStretchyParts);c.fullExtenders||(A=(a-q)/(G*D));a=D/(D+1)*(p-A);A=p-a;for(v+=a+A-n.bbox.h;0<G--;){for(;0<D--;)this.msieCloneNodeBug?(p=this.Element("span"),this.createChar(p,c.ext,d,g)):p=n.cloneNode(!0),p.bbox=n.bbox,v-=A,this.placeBox(this.addBox(e,p),0,v,!0);v+=a-n.bbox.d;c.mid&&G&&(this.placeBox(y,0,v-y.bbox.h,!0),D=B,v+=-(y.bbox.h+y.bbox.d)+a+A-n.bbox.h)}}else v+=(q-a)/2,c.mid&&(this.placeBox(y,0,v-y.bbox.h,!0),v+=-(y.bbox.h+y.bbox.d)),v+=(q-a)/2;this.placeBox(m,0,v-m.bbox.h,!0);v-=m.bbox.h+m.bbox.d;b.bbox={w:Math.max(l.bbox.w,n.bbox.w,m.bbox.w,y.bbox.w),lw:Math.min(l.bbox.lw,n.bbox.lw,m.bbox.lw,y.bbox.lw),rw:Math.max(l.bbox.rw,n.bbox.rw,m.bbox.rw,y.bbox.rw),h:0,d:-v,exactW:!0};b.scale=d;b.offset=.55*b.bbox.w;b.isMultiChar=!0;this.setStackWidth(e,b.bbox.w)},extendDelimiterH:function(b,a,c,d,g){var e=this.createStack(b,!0),l=this.createBox(e),m=this.createBox(e);this.createChar(l,c.left||c.rep,d,g);this.createChar(m,c.right||c.rep,d,g);var n=this.Element("span");this.createChar(n,c.rep,d,g);var p={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},q;this.placeBox(l,-l.bbox.lw,0,!0);var u=l.bbox.rw-l.bbox.lw+(m.bbox.rw-m.bbox.lw)-.05,v=l.bbox.rw-l.bbox.lw-.025;c.mid&&(p=this.createBox(e),this.createChar(p,c.mid,d,g),u+=p.bbox.w);c.min&&a<u*c.min&&(a=u*c.min);if(a>u){q=n.bbox.rw-n.bbox.lw;var A=q-.05,D,B,G=c.mid?2:1;B=D=Math.min(Math.ceil((a-u)/(G*A)),this.maxStretchyParts);c.fillExtenders||(A=(a-u)/(G*D));a=D/(D+1)*(q-A);A=q-a;for(v-=n.bbox.lw+a;0<G--;){for(;0<D--;)this.cloneNodeBug?(q=this.Element("span"),this.createChar(q,c.rep,d,g)):q=n.cloneNode(!0),q.bbox=n.bbox,this.placeBox(this.addBox(e,q),v,0,!0),v+=A;c.mid&&G&&(this.placeBox(p,v,0,!0),v+=p.bbox.w-a,D=B)}}else v-=(u-a)/2,c.mid&&(this.placeBox(p,v,0,!0),v+=p.bbox.w),v-=(u-a)/2;this.placeBox(m,v,0,!0);b.bbox={w:v+m.bbox.rw,lw:0,rw:v+m.bbox.rw,H:Math.max(l.bbox.h,n.bbox.h,m.bbox.h,p.bbox.h),D:Math.max(l.bbox.d,n.bbox.d,m.bbox.d,p.bbox.d),h:n.bbox.h,d:n.bbox.d,exactW:!0};b.scale=d;b.isMultiChar=!0;this.setStackWidth(e,b.bbox.w)},createChar:function(b,a,c,e){b.isMathJax=!0;var g=b,h="",l={fonts:[a[1]],noRemap:!0};e&&e===d.VARIANT.BOLD&&(l.fonts=[a[1]+"-bold",a[1]]);"string"!==typeof a[1]&&(l=a[1]);if(a[0]instanceof Array){e=0;for(var m=a[0].length;e<m;e++)h+=String.fromCharCode(a[0][e])}else h=String.fromCharCode(a[0]);a[4]&&(c*=a[4]);1!==c||a[3]?(g=this.addElement(b,"span",{style:{fontSize:this.Percent(c)},scale:c,isMathJax:!0}),this.handleVariant(g,l,h),b.bbox=g.bbox):this.handleVariant(b,l,h);a[2]&&(b.style.marginLeft=this.Em(a[2]));a[3]&&(b.firstChild.style.verticalAlign=this.Em(a[3]),b.bbox.h+=a[3],0>b.bbox.h&&(b.bbox.h=0));a[5]&&(b.bbox.h+=a[5]);a[6]&&(b.bbox.d+=a[6]);this.AccentBug&&0===b.bbox.w&&(g.firstChild.nodeValue+=this.NBSP)},positionDelimiter:function(b,a){a-=b.bbox.h;b.bbox.d-=a;b.bbox.h+=a;a&&(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||this.operaVerticalAlignBug&&b.isMultiChar?(""===b.firstChild.style.display&&""!==b.style.top&&(b=b.firstChild,a-=c.unEm(b.style.top)),b.style.position="relative",b.style.top=this.Em(-a)):(b.style.verticalAlign=this.Em(a),c.ffVerticalAlignBug&&c.createRule(b.parentNode,b.bbox.h,0,0)))},handleVariant:function(b,a,c){var e="",g,h,l,m=b,n=!!b.style.fontFamily;if(0!==c.length){b.bbox||(b.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN});a||(a=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]);l=a;for(var p=0,q=c.length;p<q;p++){a=l;g=c.charCodeAt(p);c.charAt(p);if(55296<=g&&56319>g)p++,g=(g-55296<<10)+(c.charCodeAt(p)-56320)+65536,this.FONTDATA.RemapPlane1&&(a=this.FONTDATA.RemapPlane1(g,a),g=a.n,a=a.variant);else{var u,v=this.FONTDATA.RANGES;h=0;for(u=v.length;h<u;h++)if("alpha"!==v[h].name||!a.noLowerCase){var A=a["offset"+v[h].offset];if(A&&g>=v[h].low&&g<=v[h].high){v[h].remap&&v[h].remap[g]?g=A+v[h].remap[g]:(g=g-v[h].low+A,v[h].add&&(g+=v[h].add));a["variant"+v[h].offset]&&(a=this.FONTDATA.VARIANT[a["variant"+v[h].offset]]);break}}}a.remap&&a.remap[g]&&(a.remap[g]instanceof Array?(a=a.remap[g],g=a[0],a=this.FONTDATA.VARIANT[a[1]]):"string"===typeof a.remap[g]?(c=a.remap[g]+c.substr(p+1),p=0,q=c.length,g=c.charCodeAt(0)):(g=a.remap[g],a.remap.variant&&(a=this.FONTDATA.VARIANT[a.remap.variant])));this.FONTDATA.REMAP[g]&&!a.noRemap&&(g=this.FONTDATA.REMAP[g],g instanceof Array&&(a=this.FONTDATA.VARIANT[g[1]],g=g[0]),"string"===typeof g&&(c=g+c.substr(p+1),p=0,q=c.length,g=g.charCodeAt(0)));h=this.lookupChar(a,g);a=h[g];if(n||!this.checkFont(h,m.style)&&!a[5].img)e.length&&(this.addText(m,e),e=""),u=!!m.style.fontFamily||!!b.style.fontStyle||!!b.style.fontWeight||!h.directory||n,n=!1,m!==b&&(u=!this.checkFont(h,b.style),m=b),u&&(m=this.addElement(b,"span",{isMathJax:!0,subSpan:!0})),this.handleFont(m,h,m!==b);e=this.handleChar(m,h,a,g,e);(a[5]||{}).space||(a[0]/1E3>b.bbox.h&&(b.bbox.h=a[0]/1E3),a[1]/1E3>b.bbox.d&&(b.bbox.d=a[1]/1E3));b.bbox.w+a[3]/1E3<b.bbox.lw&&(b.bbox.lw=b.bbox.w+a[3]/1E3);b.bbox.w+a[4]/1E3>b.bbox.rw&&(b.bbox.rw=b.bbox.w+a[4]/1E3);b.bbox.w+=a[2]/1E3}e.length&&this.addText(m,e);b.scale&&1!==b.scale&&(b.bbox.h*=b.scale,b.bbox.d*=b.scale,b.bbox.w*=b.scale,b.bbox.lw*=b.scale,b.bbox.rw*=b.scale);1==c.length&&h.skew&&h.skew[g]&&(b.bbox.skew=h.skew[g])}},checkFont:function(b,a){var c=a.fontWeight||"normal";c.match(/^\d+$/)&&(c=600<=parseInt(c)?"bold":"normal");return b.family.replace(/'/g,"")===a.fontFamily.replace(/'/g,"")&&(b.style||"normal")===(a.fontStyle||"normal")&&(b.weight||"normal")===c},handleFont:function(b,a,d){b.style.fontFamily=a.family;a.directory||(b.style.fontSize=Math.floor(100/c.scale+.5)+"%");if(!c.FontFaceBug||!a.isWebFont){var e=a.style||"normal";a=a.weight||"normal";if("normal"!==e||d)b.style.fontStyle=e;if("normal"!==a||d)b.style.fontWeight=a}},handleChar:function(b,a,d,e,g){var h=d[5];if(h.space)return g.length&&this.addText(b,g),c.createShift(b,d[2]/1E3),"";if(h.img)return this.handleImg(b,a,d,e,g);if(h.isUnknown&&this.FONTDATA.DELIMITERS[e])return g.length&&this.addText(b,g),g=b.scale,c.createDelimiter(b,e,0,1,a),"V"===this.FONTDATA.DELIMITERS[e].dir&&(b.style.verticalAlign=this.Em(b.bbox.d),b.bbox.h+=b.bbox.d,b.bbox.d=0),b.scale=g,d[0]=1E3*b.bbox.h,d[1]=1E3*b.bbox.d,d[2]=1E3*b.bbox.w,d[3]=1E3*b.bbox.lw,d[4]=1E3*b.bbox.rw,"";null==h.c&&(65535>=e?h.c=String.fromCharCode(e):(a=e-65536,h.c=String.fromCharCode((a>>10)+55296)+String.fromCharCode((a&1023)+56320)));if(h.rfix)return this.addText(b,g+h.c),c.createShift(b,h.rfix/1E3),"";if(d[2]||!this.msieAccentBug||g.length)return g+h.c;c.createShift(b,d[3]/1E3);c.createShift(b,(d[4]-d[3])/1E3);this.addText(b,h.c);c.createShift(b,-d[4]/1E3);return""},handleImg:function(b,a,c,d,g){return g},lookupChar:function(b,a){var d,e;if(!b.FONTS){var g=this.FONTDATA.FONTS,h=b.fonts||this.FONTDATA.VARIANT.normal.fonts;h instanceof Array||(h=[h]);b.fonts!=h&&(b.fonts=h);b.FONTS=[];d=0;for(e=h.length;d<e;d++)g[h[d]]&&(b.FONTS.push(g[h[d]]),g[h[d]].name=h[d])}d=0;for(e=b.FONTS.length;d<e;d++)if(g=b.FONTS[d],"string"===typeof g&&(delete b.FONTS,this.loadFont(g)),g[a])if(5===g[a].length&&(g[a][5]={}),c.allowWebFonts&&!g.available)this.loadWebFont(g);else return g;else this.findBlock(g,a);return this.unknownChar(b,a)},unknownChar:function(b,a){var d=b.defaultFont||{family:c.config.undefinedFamily};b.bold&&(d.weight="bold");b.italic&&(d.style="italic");d[a]||(d[a]=[800,200,500,0,500,{isUnknown:!0}]);e.signal.Post(["HTML-CSS Jax - unknown char",a,b]);return d},findBlock:function(b,a){if(b.Ranges)for(var c=0,d=b.Ranges.length;c<d&&!(a<b.Ranges[c][0]);c++)if(a<=b.Ranges[c][1]){for(var g=b.Ranges[c][2],e=b.Ranges.length-1;0<=e;e--)b.Ranges[e][2]==g&&b.Ranges.splice(e,1);this.loadFont(b.directory+"/"+g+".js")}},loadFont:function(b){var f=MathJax.Callback.Queue();f.Push(["Require",a,this.fontDir+"/"+b]);this.imgFonts&&(MathJax.isPacked||(b=b.replace(/\/([^\/]*)$/,c.imgPacked+"/$1")),f.Push(["Require",a,this.webfontDir+"/png/"+b]));e.RestartAfter(f.Push({}))},loadWebFont:function(b){b.available=b.isWebFont=!0;c.FontFaceBug&&(b.family=b.name,c.msieFontCSSBug&&(b.family+="-Web"));e.RestartAfter(this.Font.loadWebFont(b))},loadWebFontError:function(b,c){e.Startup.signal.Post("HTML-CSS Jax - disable web fonts");b.isWebFont=!1;this.config.imageFont&&this.config.imageFont===this.fontInUse?(this.imgFonts=!0,e.Startup.signal.Post("HTML-CSS Jax - switch to image fonts"),e.Startup.signal.Post("HTML-CSS Jax - using image fonts"),n(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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h=d=0,l=this.HTMLgetMu(b);a.lspace&&(d=this.HTMLlength2em(g,a.lspace,l));a.voffset&&(h=this.HTMLlength2em(g,a.voffset,l));c.placeBox(g,d,h);b.bbox={h:g.bbox.h,d:g.bbox.d,w:g.bbox.w,exactW:!0,lw:Math.min(0,g.bbox.lw+d),rw:Math.max(g.bbox.w,g.bbox.rw+d),H:Math.max(null==g.bbox.H?-c.BIGDIMEN:g.bbox.H,g.bbox.h+h),D:Math.max(null==g.bbox.D?-c.BIGDIMEN:g.bbox.D,g.bbox.d-h)};""!==a.height&&(b.bbox.h=this.HTMLlength2em(g,a.height,l,"h",0));""!==a.depth&&(b.bbox.d=this.HTMLlength2em(g,a.depth,l,"d",0));""!==a.width&&(b.bbox.w=this.HTMLlength2em(g,a.width,l,"w",0));b.bbox.H<=b.bbox.h&&delete b.bbox.H;b.bbox.D<=b.bbox.d&&delete b.bbox.D;g=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;b.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||g.exec(a.height)||g.exec(a.width)||g.exec(a.depth));c.setStackWidth(e,b.bbox.w)}this.HTMLhandleSpace(b);this.HTMLhandleColor(b);return b},HTMLlength2em:function(b,a,d,e,g){null==g&&(g=-c.BIGDIMEN);var h=String(a).match(/width|height|depth/),h=h?b.bbox[h[0].charAt(0)]:e?b.bbox[e]:0;d=c.length2em(a,d,h);return e&&String(a).match(/^\s*[-+]/)?Math.max(g,b.bbox[e]+d):d},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.mrow.Augment({HTMLlineBreaks:function(b){return this.parent.linebreakContainer?c.config.linebreaks.automatic&&b.bbox.w>c.linebreakWidth||this.hasNewline():!1},HTMLstretchH:function(b,a){this.HTMLremoveColor();var c=this.HTMLspanElement();this.data[this.core].HTMLstretchH(c,a);this.HTMLcomputeBBox(c,!0);this.HTMLhandleColor(c);return c},HTMLstretchV:function(b,a,c){this.HTMLremoveColor();b=this.HTMLspanElement();this.data[this.core].HTMLstretchV(b,a,c);this.HTMLcomputeBBox(b,!0);this.HTMLhandleColor(b);return b}});d.mstyle.Augment({toHTML:function(b,a,c){b=this.HTMLcreateSpan(b);if(null!=this.data[0]){var d=this.data[0].toHTML(b);null!=c?this.data[0].HTMLstretchV(b,a,c):null!=a&&this.data[0].HTMLstretchH(b,a);b.bbox=d.bbox}this.HTMLhandleSpace(b);this.HTMLhandleColor(b);return b},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.mfrac.Augment({toHTML:function(b){b=this.HTMLcreateSpan(b);var a=c.createStack(b),d=c.createBox(a),e=c.createBox(a);c.MeasureSpans([this.HTMLboxChild(0,d),this.HTMLboxChild(1,e)]);var g=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),h=this.HTMLgetScale(),l=g.displaystyle,m=c.TeX.axis_height*h;if(g.bevelled){var g=l?.4:.15,n=Math.max(d.bbox.h+d.bbox.d,e.bbox.h+e.bbox.d)+2*g,a=c.createBox(a);c.createDelimiter(a,47,n);c.placeBox(d,0,(d.bbox.d-d.bbox.h)/2+m+g);c.placeBox(a,d.bbox.w-g/2,(a.bbox.d-a.bbox.h)/2+m);c.placeBox(e,d.bbox.w+a.bbox.w-g,(e.bbox.d-e.bbox.h)/2+m-g)}else{var n=Math.max(d.bbox.w,e.bbox.w),p=c.thickness2em(g.linethickness,h),q,u,v=c.TeX.min_rule_thickness/this.em;l?(q=c.TeX.num1,u=c.TeX.denom1):(q=0===p?c.TeX.num3:c.TeX.num2,u=c.TeX.denom2);q*=h;u*=h;0===p?(h=Math.max((l?7:3)*c.TeX.rule_thickness,2*v),l=q-d.bbox.d-(e.bbox.h-u),l<h&&(q+=(h-l)/2,u+=(h-l)/2)):(h=Math.max((l?2:0)*v+p,p/2+1.5*v),l=q-d.bbox.d-(m+p/2),l<h&&(q+=h-l),l=m-p/2-(e.bbox.h-u),l<h&&(u+=h-l),a=c.createBox(a),c.createRule(a,p,0,n+2*p),c.placeBox(a,0,m-p/2));c.alignBox(d,g.numalign,q);c.alignBox(e,g.denomalign,-u)}this.HTMLhandleSpace(b);this.HTMLhandleColor(b);return b},HTMLcanStretch:function(b){return!1},HTMLhandleSpace:function(b){if(!this.texWithDelims){var a=(this.useMMLspacing?0:c.length2em(this.texSpacing()||0))+.12;b.style.paddingLeft=c.Em(a);b.style.paddingRight=c.Em(.12)}}});d.msqrt.Augment({toHTML:function(b){b=this.HTMLcreateSpan(b);var a=c.createStack(b),d=c.createBox(a),e=c.createBox(a),g=c.createBox(a),h=this.HTMLgetScale(),l=c.TeX.rule_thickness*h,m,n,p;m=this.Get("displaystyle")?c.TeX.x_height*h:l;m=Math.max(l+m/4,1.5*c.TeX.min_rule_thickness/this.em);var q=this.HTMLboxChild(0,d);n=q.bbox.h+q.bbox.d+m+l;c.createDelimiter(g,8730,n,h);c.MeasureSpans([q,g]);p=q.bbox.w;var u=0;if(g.isMultiChar||c.AdjustSurd&&c.imgFonts)g.bbox.w*=.95;g.bbox.h+g.bbox.d>n&&(m=(g.bbox.h+g.bbox.d-(n-l))/2);n=c.FONTDATA.DELIMITERS[c.FONTDATA.RULECHAR];!n||p<n.HW[0][0]*h||.75>h?c.createRule(e,0,l,p):c.createDelimiter(e,c.FONTDATA.RULECHAR,p,h);n=q.bbox.h+m+l;m=n*c.rfuzz;g.isMultiChar&&(m=c.rfuzz);u=this.HTMLaddRoot(a,g,u,g.bbox.h+g.bbox.d-n,h);c.placeBox(g,u,n-g.bbox.h);c.placeBox(e,u+g.bbox.w,n-e.bbox.h+m);c.placeBox(d,u+g.bbox.w,0);this.HTMLhandleSpace(b);this.HTMLhandleColor(b);return b},HTMLaddRoot:function(b,a,c,d,e){return c}});d.mroot.Augment({toHTML:d.msqrt.prototype.toHTML,HTMLaddRoot:function(b,a,d,e,g){b=c.createBox(b);this.data[1]?(d=this.data[1].toHTML(b),d.style.paddingRight=d.style.paddingLeft="",c.Measured(d,b)):b.bbox=this.HTMLzeroBBox();e=this.HTMLrootHeight(a.bbox.h+a.bbox.d,g,b)-e;g=Math.min(b.bbox.w,b.bbox.rw);d=Math.max(g,a.offset);c.placeBox(b,d-g,e);return d-a.offset},HTMLrootHeight:function(a,c,d){return.45*(a-.9*c)+.6*c+Math.max(0,d.bbox.d-.075)}});d.mfenced.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);this.data.open&&this.data.open.toHTML(a);null!=this.data[0]&&this.data[0].toHTML(a);for(var c=1,d=this.data.length;c<d;c++)this.data[c]&&(this.data["sep"+c]&&this.data["sep"+c].toHTML(a),this.data[c].toHTML(a));this.data.close&&this.data.close.toHTML(a);for(var e=this.HTMLcomputeBBox(a),g=a.bbox.h,h=a.bbox.d,c=0,d=e.length;c<d;c++)e[c].HTMLstretchV(a,g,h);e.length&&this.HTMLcomputeBBox(a,!0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcomputeBBox:function(a,c){var d=a.bbox={},e=[];this.HTMLcheckStretchy(this.data.open,d,e,c);this.HTMLcheckStretchy(this.data[0],d,e,c);for(var g=1,h=this.data.length;g<h;g++)this.data[g]&&(this.HTMLcheckStretchy(this.data["sep"+g],d,e,c),this.HTMLcheckStretchy(this.data[g],d,e,c));this.HTMLcheckStretchy(this.data.close,d,e,c);this.HTMLcleanBBox(d);return e},HTMLcheckStretchy:function(a,c,d,e){a&&(!e&&a.HTMLcanStretch("Vertical")&&(d.push(a),a=a.CoreMO()||a),this.HTMLcombineBBoxes(a,c))}});d.menclose.Augment({toHTML:d.mbase.HTMLautoload});d.maction.Augment({toHTML:d.mbase.HTMLautoload});d.semantics.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var e=this.data[0].toHTML(a);null!=d?this.data[0].HTMLstretchV(a,c,d):null!=c&&this.data[0].HTMLstretchH(a,c);a.bbox=e.bbox}this.HTMLhandleSpace(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.munderover.Augment({toHTML:function(a,f,e){var l=this.getValues("displaystyle","accent","accentunder","align");if(!l.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return d.msubsup.prototype.toHTML.call(this,a);a=this.HTMLcreateSpan(a);var g=this.HTMLgetScale(),h=c.createStack(a),m=[],n=[],p=[],q,w,u;w=0;for(u=this.data.length;w<u;w++)null!=this.data[w]&&(q=m[w]=c.createBox(h),n[w]=this.data[w].toHTML(q),w==this.base?(null!=e?this.data[this.base].HTMLstretchV(q,f,e):null!=f&&this.data[this.base].HTMLstretchH(q,f),p[w]=null==e&&null!=f?!1:this.data[w].HTMLcanStretch("Horizontal")):p[w]=this.data[w].HTMLcanStretch("Horizontal"));c.MeasureSpans(n);h=n=-c.BIGDIMEN;w=0;for(u=this.data.length;w<u;w++)this.data[w]&&(m[w].bbox.w>h&&(h=m[w].bbox.w),!p[w]&&h>n&&(n=h));null==e&&null!=f?n=f:n==-c.BIGDIMEN&&(n=h);w=h=0;for(u=this.data.length;w<u;w++)this.data[w]&&(q=m[w],p[w]&&(q.bbox=this.data[w].HTMLstretchH(q,n).bbox),q.bbox.w>h&&(h=q.bbox.w));f=c.TeX.rule_thickness;e=c.FONTDATA.TeX_factor;var p=m[this.base]||{bbox:this.HTMLzeroBBox()},v,A,D,B=0;p.bbox.ic&&(B=1.3*p.bbox.ic+.05);w=0;for(u=this.data.length;w<u;w++)null!=this.data[w]&&(q=m[w],n=c.TeX.big_op_spacing5*g,(D=w!=this.base&&l[this.ACCENTS[w]])&&q.bbox.w<=1/c.em+1E-4&&(q.bbox.w=q.bbox.rw-q.bbox.lw,q.bbox.noclip=!0,q.bbox.lw&&q.insertBefore(c.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild),c.createBlank(q,0,0,q.bbox.rw+.1)),v={left:0,center:(h-q.bbox.w)/2,right:h-q.bbox.w}[l.align],A=0,w==this.over?(D?(D=Math.max(f*g*e,2.5/this.em),n=0,p.bbox.skew&&(v+=p.bbox.skew)):(D=c.TeX.big_op_spacing1*g*e,A=c.TeX.big_op_spacing3*g*e,D=Math.max(D,A-Math.max(0,q.bbox.d))),D=Math.max(D,1.5/this.em),v+=B/2,A=p.bbox.h+q.bbox.d+D,q.bbox.h+=n):w==this.under&&(D?(D=3*f*g*e,n=0):(D=c.TeX.big_op_spacing2*g*e,A=c.TeX.big_op_spacing4*g*e,D=Math.max(D,A-q.bbox.h)),D=Math.max(D,1.5/this.em),v-=B/2,A=-(p.bbox.d+q.bbox.h+D),q.bbox.d+=n),c.placeBox(q,v,A));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.msubsup.Augment({toHTML:function(a,d,e){a=this.HTMLcreateSpan(a);var l=this.HTMLgetScale(),g=this.HTMLgetMu(a),h=c.createStack(a),m,n=[],p=c.createBox(h);this.data[this.base]?(n.push(this.data[this.base].toHTML(p)),null!=e?this.data[this.base].HTMLstretchV(p,d,e):null!=d&&this.data[this.base].HTMLstretchH(p,d)):p.bbox=this.HTMLzeroBBox();d=c.TeX.x_height*l;e=c.TeX.scriptspace*l*.75;var q;this.HTMLnotEmpty(this.data[this.sup])&&(q=c.createBox(h),n.push(this.data[this.sup].toHTML(q)));this.HTMLnotEmpty(this.data[this.sub])&&(m=c.createBox(h),n.push(this.data[this.sub].toHTML(m)));c.MeasureSpans(n);q&&(q.bbox.w+=e,q.bbox.rw=Math.max(q.bbox.w,q.bbox.rw));m&&(m.bbox.w+=e,m.bbox.rw=Math.max(m.bbox.w,m.bbox.rw));c.placeBox(p,0,0);var n=q?this.data[this.sup].HTMLgetScale():m?this.data[this.sub].HTMLgetScale():this.HTMLgetScale(),w=c.TeX.sup_drop*n,h=p.bbox.h-w,u=p.bbox.d+c.TeX.sub_drop*n,n=0;p.bbox.ic&&(p.bbox.w-=p.bbox.ic,n=1.3*p.bbox.ic+.05);!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||1!==this.data[this.base].data.join("").length||1!==p.bbox.scale||this.data[this.base].Get("largeop")||(h=u=0);e=this.getValues("subscriptshift","superscriptshift");e.subscriptshift=""===e.subscriptshift?0:c.length2em(e.subscriptshift,g);e.superscriptshift=""===e.superscriptshift?0:c.length2em(e.superscriptshift,g);q?m?(u=Math.max(u,c.TeX.sub2*l),l*=c.TeX.rule_thickness,h-q.bbox.d-(m.bbox.h-u)<3*l&&(u=3*l-h+q.bbox.d+m.bbox.h,w=.8*d-(h-q.bbox.d),0<w&&(h+=w,u-=w)),c.placeBox(q,p.bbox.w+n,Math.max(h,e.superscriptshift)),c.placeBox(m,p.bbox.w,-Math.max(u,e.subscriptshift))):(m=this.getValues("displaystyle","texprimestyle"),m=c.TeX[m.displaystyle?"sup1":m.texprimestyle?"sup3":"sup2"],h=Math.max(h,m*l,q.bbox.d+.25*d,e.superscriptshift),c.placeBox(q,p.bbox.w+n,h,q.bbox)):m&&(u=Math.max(u,c.TeX.sub1*l,m.bbox.h-.8*d,e.subscriptshift),c.placeBox(m,p.bbox.w,-u,m.bbox));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.mmultiscripts.Augment({toHTML:d.mbase.HTMLautoload});d.mtable.Augment({toHTML:d.mbase.HTMLautoload});d["annotation-xml"].Augment({toHTML:d.mbase.HTMLautoload});d.math.Augment({toHTML:function(a,f){var k=this.Get("alttext");k&&""!==k&&f.setAttribute("aria-label",k);var l=c.addElement(a,"nobr",{isMathJax:!0});a=this.HTMLcreateSpan(l);var k=c.createStack(a),g=c.createBox(k),h;k.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";null!=this.data[0]&&(c.msieColorBug&&(this.background&&(this.data[0].background=this.background,delete this.background),this.mathbackground&&(this.data[0].mathbackground=this.mathbackground,delete this.mathbackground)),d.mbase.prototype.displayAlign=e.config.displayAlign,d.mbase.prototype.displayIndent=e.config.displayIndent,h=this.data[0].toHTML(g),h.bbox.exactW=!1,h=c.Measured(h,g));c.placeBox(g,0,0);a.style.width=c.Em((Math.round(h.bbox.w*this.em)+.25)/c.outerEm);a.style.display="inline-block";var l=1/c.em,m=c.em/c.outerEm;c.em/=m;a.bbox.h*=m;a.bbox.d*=m;a.bbox.w*=m;a.bbox.lw*=m;a.bbox.rw*=m;h&&null!=h.bbox.width&&(a.style.minWidth=h.bbox.minWidth||a.style.width,a.style.width=k.style.width=h.bbox.width,g.style.width="100%");this.HTMLhandleColor(a);h&&c.createRule(a,(h.bbox.h+l)*m,(h.bbox.d+l)*m,0);this.isMultiline||"block"!==this.Get("display")||null!=a.bbox.width||(k=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift"),k.indentalignfirst!==d.INDENTALIGN.INDENTALIGN&&(k.indentalign=k.indentalignfirst),k.indentalign===d.INDENTALIGN.AUTO&&(k.indentalign=this.displayAlign),f.style.textAlign=k.indentalign,k.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT&&(k.indentshift=k.indentshiftfirst),"auto"===k.indentshift&&(k.indentshift=this.displayIndent),k.indentshift&&k.indentalign!==d.INDENTALIGN.CENTER&&(a.style[{left:"marginLeft",right:"marginRight"}[k.indentalign]]=c.Em(c.length2em(k.indentshift))));return a},HTMLspanElement:d.mbase.prototype.HTMLspanElement});d.TeXAtom.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);if(null!=this.data[0])if(this.texClass===d.TEXCLASS.VCENTER){var e=c.createStack(a),e=c.createBox(e);c.Measured(this.data[0].toHTML(e),e);c.placeBox(e,0,c.TeX.axis_height-(e.bbox.h+e.bbox.d)/2+e.bbox.d)}else a.bbox=this.data[0].toHTML(a).bbox;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",c,"jax.js"]),0)})});e.Register.StartupHook("End Config",function(){e.Browser.Select({MSIE:function(a){var d=document.documentMode||0,e=a.versionAtLeast("7.0"),l=a.versionAtLeast("8.0")&&7<d,g="BackCompat"===document.compatMode;9>d&&(c.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white",c.config.styles[".MathJax .MathJax_HitBox"].opacity=0,c.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity\x3d0)");c.Augment({PaddingWidthBug:!0,msieAccentBug:!0,msieColorBug:!0,msieColorPositionBug:!0,msieRelativeWidthBug:g,msieDisappearingBug:8<=d,msieMarginScaleBug:8>d,msiePaddingWidthBug:!0,msieBorderWidthBug:g,msieFrameSizeBug:8>=d,msieInlineBlockAlignBug:!l||g,msiePlaceBoxBug:l&&!g,msieClipRectBug:!l,msieNegativeSpaceBug:g,cloneNodeBug:l&&"8.0"===a.version,initialSkipBug:8>d,msieNegativeBBoxBug:8<=d,msieIE6:!e,msieItalicWidthBug:!0,FontFaceBug:!0,msieFontCSSBug:a.isIE9,allowWebFonts:9<=d?"woff":"eot"})},Firefox:function(a){var d=!1;a.versionAtLeast("3.5")&&(a=String(document.location).replace(/[^\/]*$/,""),"file:"!==document.location.protocol||e.config.root.match(/^https?:\/\//)||(e.config.root+"/").substr(0,a.length)===a)&&(d="otf");c.Augment({ffVerticalAlignBug:!0,AccentBug:!0,allowWebFonts:d})},Safari:function(a){var d=a.versionAtLeast("3.0"),k=a.versionAtLeast("3.1"),l=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ 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