/*

*  /MathJax/config/MML_HTMLorMML-full.js
*  
*  Copyright (c) 2010-2018 The MathJax Consortium
*
*  Part of the MathJax library.
*  See http://www.mathjax.org for details.
* 
*  Licensed under the Apache License, Version 2.0;
*  you may not use this file except in compliance with the License.
*
*      http://www.apache.org/licenses/LICENSE-2.0
*/

MathJax.Hub.Config({delayJaxRegistration: true});

MathJax.Ajax.Preloading(

"[MathJax]/jax/input/MathML/config.js",
"[MathJax]/jax/output/HTML-CSS/config.js",
"[MathJax]/jax/output/NativeMML/config.js",
"[MathJax]/jax/output/PreviewHTML/config.js",
"[MathJax]/config/MMLorHTML.js",
"[MathJax]/extensions/mml2jax.js",
"[MathJax]/extensions/MathEvents.js",
"[MathJax]/extensions/MathZoom.js",
"[MathJax]/extensions/MathMenu.js",
"[MathJax]/jax/element/mml/jax.js",
"[MathJax]/extensions/toMathML.js",
"[MathJax]/jax/input/MathML/jax.js",
"[MathJax]/jax/output/NativeMML/jax.js",
"[MathJax]/jax/output/HTML-CSS/jax.js",
"[MathJax]/jax/output/HTML-CSS/autoload/mtable.js",
"[MathJax]/jax/output/PreviewHTML/jax.js",
"[MathJax]/extensions/fast-preview.js",
"[MathJax]/extensions/AssistiveMML.js",
"[MathJax]/extensions/a11y/accessibility-menu.js"

);

MathJax.Hub.Config({

extensions: ['[a11y]/accessibility-menu.js']

});

MathJax.InputJax.MathML=MathJax.InputJax({id:“MathML”,version:“2.7.5”,directory:MathJax.InputJax.directory+“/MathML”,extensionDir:MathJax.InputJax.extensionDir+“/MathML”,entityDir:MathJax.InputJax.directory+“/MathML/entities”,config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register(“math/mml”);MathJax.InputJax.MathML.loadComplete(“config.js”); MathJax.OutputJax[“HTML-CSS”]=MathJax.OutputJax({id:“HTML-CSS”,version:“2.7.5”,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:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:[“STIX”,“TeX”],preferredFont:“TeX”,webFont:“TeX”,imageFont:“TeX”,undefinedFamily:“STIXGeneral,‘Arial Unicode MS’,serif”,mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,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 .MJX-monospace”:{“font-family”:“monospace”},“.MathJax .MJX-sans-serif”:{“font-family”:“sans-serif”},“#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=2, OffY=2, Color=‘gray’, Positive=‘true’)”,padding:“3px 4px”,“z-index”:401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax[“HTML-CSS”].config.styles[“#MathJax_Tooltip”].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax[“HTML-CSS”].Register(“jax/mml”)}MathJax.Hub.Register.StartupHook(“End Config”,[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:[“$”,“$”],displayMathDelimiters:[“$$”,“$$”],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=[“[Math]”],j;var h=document.createElement(“span”,{className:“MathJax_Preview”});if(e.inputJax===“TeX”){if(e.root.Get(“displaystyle”)){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^s+/,“”).replace(/s+$/,“”)+j[1]]}}for(var g=0,d=k.length;g/i,“”).replace(/<\?xml:namespace .*?\/>/i,“”);b=b.replace(/ /g,“ ”)}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element(“span”);c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!==“none”){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement(“script”);b.type=“math/mml”;d.insertBefore(b,f);var c=“”,e,a=f;while(f&&f.nodeName!==“/MATH”){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName===“/MATH”){f.parentNode.removeChild(f)}b.text=c+“”;if(this.config.preview!==“none”){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName===“#text”){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName===“#comment”){c=“”}});a.xml.Augment({toMathML:function(d){return(d||“”)+this.toString()}});MathJax.Hub.Register.StartupHook(“TeX mathchoice Ready”,function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post(“toMathML Ready”)});MathJax.Ajax.loadComplete(“[MathJax]/extensions/toMathML.js”); (function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[[“MathML”,e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!==“string”){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error([“ErrorParsingMathML”,“Error parsing MathML”])}}var g=j.getElementsByTagName(“parsererror”)[0];if(g){c.Error([“ParsingError”,“Error parsing MathML: %1”,g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,“”)])}if(j.childNodes.length!==1){c.Error([“MathMLSingleElement”,“MathML must be formed by a single element”])}if(j.firstChild.nodeName.toLowerCase()===“html”){var f=j.getElementsByTagName(“h1”)[0];if(f&&f.textContent===“XML parsing error”&&f.nextSibling){c.Error([“ParsingError”,“Error parsing MathML: %1”,String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,“”)])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,“”)!==“math”){c.Error([“MathMLRootElement”,“MathML must be formed by a element, not %1”,“<"j.firstChild.nodeName”>“])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute(”class“)||”“);var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,”“);var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]===”OP“&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post([”MathML Jax - unknown node type“,g]);return a.Error(b(”UnknownNodeType“,”Unknown node type: %1“,g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f[”class“]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||”“).split(/ /);var j=[];for(var g=0,e=h.length;ga.NOTATION.UPDIAGONALARROW”/“)){f.notation+=” “+a.NOTATION.UPDIAGONALARROW}}else{if(h[g]===”MJX-variant“){f.variantForm=true;if(!MathJax.Extension[”TeX/AMSsymbols“]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(”[MathJax]/extensions/TeX/AMSsymbols.js“))}}else{if(h[g].substr(0,11)!==”MJX-TeXAtom“){f.mathvariant=h[g].substr(3);if(f.mathvariant===”-tex-caligraphic-bold“||f.mathvariant===”-tex-oldstyle-bold“){if(!MathJax.Extension[”TeX/boldsymbol“]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(”[MathJax]/extensions/TeX/boldsymbol.js“))}}}}}}else{j.push(h[g])}}if(j.length){f[”class“]=j.join(” “)}else{delete f[”class“]}},AddAttributes:function(g,j){g.attr={};g.attrNames=[];for(var h=0,e=j.attributes.length;hf.nodeValue”’“])}}}else{if(e.type===”annotation-xml“){e.Append(a.xml(f))}else{var h=this.MakeMML(f);e.Append(h);if(h.mmlSelfClosing&&h.data.length){e.Append.apply(e,h.data);h.data=[]}}}}if(e.type===”mrow“&&e.data.length>=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type===”mo“&&l.Get(”fence“)&&n.type===”mo“&&n.Get(”fence“)){if(l.data[0]){e.open=l.data.join(”“)}if(n.data[0]){e.close=n.data.join(”“)}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+="http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=([‘”])http:.*?2)/ig,“ xmlns:$1 $1”)+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'s*$/,“$2”);return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[tnr]/g,“ ”).replace(/^ +/,“”).replace(/ +$/,“”).replace(/ +/g,“ ”)},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+“/”h“.js”))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:[“OriginalMathML”,“Original MathML”],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,“”)===“math”){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,“”)}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/n.*/,“”);MathJax.Hub.signal.Post([“MathML Jax - parse error”,f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,“text/xml”)},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML=“

”+e.replace(/<([a-z]+)([^>]*)/>/g,“<$1$2>”)+“
”;var f=this.div.firstChild;this.div.innerHTML=“”;return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=[“MSXML2.DOMDocument.6.0”,“MSXML2.DOMDocument.5.0”,“MSXML2.DOMDocument.4.0”,“MSXML2.DOMDocument.3.0”,“MSXML2.DOMDocument.2.0”,“Microsoft.XMLDOM”];for(var g=0,e=f.length;g span“:{”text-align“:o+”!important“}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+”/MathEvents.js“)},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element(”span“,{style:{position:”absolute“,”font-size-adjust“:”none“}},[[”div“,{className:”MathJax_mmlExBox“}],[”span“,{className:”MathJax_MathML“}]]);f.math(f.mspace().With({width:”60ex“})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement(”object“);m.id=”mathplayer“;m.classid=”clsid:32F66A20-7614-11D4-BD11-00104BD3F987“;document.getElementsByTagName(”head“)[0].appendChild(m);document.namespaces.add(”m“,”http://www.w3.org/1998/Math/MathML“);c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport(”#mathplayer“);c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._([”MathML“,”MathPlayer“],”MathJax was not able to set up MathPlayer.nnIf MathPlayer is not installed, you need to install it first.nOtherwise, your security settings may be preventing ActiveX ncontrols from running. Use the Internet Options item undernthe Tools menu and select the Security tab, then press thenCustom Level button. Check that the settings forn’Run ActiveX Controls’, and ‘Binary and script behaviors’nare enabled.nnCurrently you will see error messages rather thanntypeset mathematics.“))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+”%“;n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+”px“}}if(this.msieIE8HeightBug){u.style.position=”“}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:”-.0556em“,negativeverythinmathspace:”-.1111em“,negativethinmathspace:”-.1667em“,negativemediummathspace:”-.2222em“,negativethickmathspace:”-.2778em“,negativeverythickmathspace:”-.3333em“,negativeveryverythickmathspace:”-.3889em“,veryverythinmathspace:”.0556em“,verythinmathspace:”.1111em“,thinmathspace:”.1667em“,mediummathspace:”.2222em“,thickmathspace:”.2778em“,verythickmathspace:”.3333em“,veryverythickmathspace:”.3889em“}});c.Register.StartupHook(”mml Jax Ready“,function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function®{var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement(”mrow“);s.appendChild(q);s=q}for(;rB”%“)}if(z===”l“){t.insertBefore(A,t.firstChild)}}if(p||z!==”l“){j(”Right“,t.lastChild);if(x!==”r“){t.appendChild(this.NativeMMLelement(”mtd“)).setAttribute(”style“,”padding:0;width:“o”%“)}if(z===”r“){if(z!==x){r.setAttribute(”lspace“,”-1width“)}t.appendChild(A)}}}C.appendChild(t)}});f.mtd.Augment({toNativeMML:function®{var p=r.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(p);if(l.mtdWidthBug){l.adjustWidths.push(p);p=p.appendChild(this.NativeMMLelement(”mrow“))}for(var q=0,o=this.data.length;q1/”:{“font-family”:“MathJax_Caligraphic-WEB”,src:“url(‘”n“/MathJax_Caligraphic-Regular.otf’)”},“@font-face /2/”:{“font-family”:“MathJax_Caligraphic-WEB”,“font-weight”:“bold”,src:“url(‘”n“/MathJax_Caligraphic-Bold.otf’)”}}}});if(!this.handlesVariants){l.Augment({config:{styles:{‘[mathvariant=“double-struck”]’:{“font-family”:“MathJax_AMS, MathJax_AMS-WEB”},‘[mathvariant=“script”]’:{“font-family”:“MathJax_Script, MathJax_Script-WEB”},‘[mathvariant=“fraktur”]’:{“font-family”:“MathJax_Fraktur, MathJax_Fraktur-WEB”},‘[mathvariant=“bold-script”]’:{“font-family”:“MathJax_Script, MathJax_Caligraphic-WEB”,“font-weight”:“bold”},‘[mathvariant=“bold-fraktur”]’:{“font-family”:“MathJax_Fraktur, MathJax_Fraktur-WEB”,“font-weight”:“bold”},‘[mathvariant=“monospace”]’:{“font-family”:“monospace”},‘[mathvariant=“sans-serif”]’:{“font-family”:“sans-serif”},‘[mathvariant=“bold-sans-serif”]’:{“font-family”:“sans-serif”,“font-weight”:“bold”},‘[mathvariant=“sans-serif-italic”]’:{“font-family”:“sans-serif”,“font-style”:“italic”},‘[mathvariant=“sans-serif-bold-italic”]’:{“font-family”:“sans-serif”,“font-style”:“italic”,“font-weight”:“bold”},“@font-face /3/”:{“font-family”:“MathJax_AMS-WEB”,src:“url(‘”n“/MathJax_AMS-Regular.otf’)”},“@font-face /4/”:{“font-family”:“MathJax_Script-WEB”,src:“url(‘”n“/MathJax_Script-Regular.otf’)”},“@font-face /5/”:{“font-family”:“MathJax_Fraktur-WEB”,src:“url(‘”n“/MathJax_Fraktur-Regular.otf’)”},“@font-face /6/”:{“font-family”:“MathJax_Fraktur-WEB”,“font-weight”:“bold”,src:“url(‘”n“/MathJax_Fraktur-Bold.otf’)”}}}})}}f.math.Augment({toNativeMML:function(y,p){var A=this.NativeMMLelement(this.type),w=A;var u=(p?MathJax.InputJax[p.inputJax].annotationEncoding:null);var v,r;l.adjustWidths=[];A.setAttribute(“xmlns”,l.MMLnamespace);this.NativeMMLattributes(A);if(l.widthBug){A=A.appendChild(this.NativeMMLelement(“mrow”))}if(u){A=A.appendChild(this.NativeMMLelement(“semantics”));A.appendChild(this.NativeMMLelement(“mrow”));var s=A.appendChild(this.NativeMMLelement(“annotation”));s.appendChild(document.createTextNode(p.originalText));s.setAttribute(“encoding”,u);A=A.firstChild}for(v=0,r=this.data.length;v0;u–){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:“mrow”);this.NativeMMLattributes(o);o.removeAttribute(“separators”);if(t){o.setAttribute(“open”,q.open);o.setAttribute(“close”,q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement(“mrow”)}}else{o.removeAttribute(“open”);o.removeAttribute(“close”)}if(!t){r=this.NativeMMLelement(“mo”);r.setAttribute(“fence”,“true”);r.textContent=q.open;o.appendChild®}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement(“mo”);r.setAttribute(“separator”,“true”);r.textContent=q.separators[u-1];o.appendChild®}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement(“mrow”))}}if(!t){r=this.NativeMMLelement(“mo”);r.setAttribute(“fence”,“true”);r.textContent=q.close;o.appendChild®}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement(“mrow”);this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(p,o){var q=this.toString();if(o){q=o(q)}p.appendChild(document.createTextNode(q))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;pr“‘,’”r“-”;if(p.weight){r+=“Bold”}if(p.style){r+=“Italic”}if(!p.weight&&!p.style){r+=“Regular”}p.familyFixed=r=“‘”r“’”}var o=this.getComparisonWidths(p.testString,p.noStyleChar);var s=null;if(o){this.div.style.fontFamily=r+“,”+this.comparisonFont[0];if(this.div.offsetWidth==o[0]){this.div.style.fontFamily=r+“,”+this.comparisonFont[o[2]];if(this.div.offsetWidth==o[1]){s=false}}if(s===null&&(this.div.offsetWidth!=o[3]||this.div.offsetHeight!=o[4])){if(!p.noStyleChar&&d.FONTDATA&&d.FONTDATA.hasStyleChar){for(var q=0,n=this.testSize.length;qd.fontInUse“/”+o.directory);var q=e([“LoadWebFont”,“Loading web-font %1”,d.fontInUse+“/”+o.directory]);var m=MathJax.Callback({});var p=MathJax.Callback([“loadComplete”,this,o,q,m]);j.timer.start(j,[this.checkWebFont,o,p],0,this.timeout);return m},loadComplete:function(p,r,o,m){MathJax.Message.Clear®;if(m===j.STATUS.OK){this.webFontLoaded=true;o();return}this.loadError(p);if(b.Browser.isFirefox&&d.allowWebFonts){var q=document.location.protocol+“//”+document.location.hostname;if(document.location.port!=“”){q+=“:”+document.location.port}q+=“/”;if(j.fileURL(d.webfontDir).substr(0,q.length)!==q){this.firefoxFontError(p)}}if(!this.webFontLoaded){d.loadWebFontError(p,o)}else{o()}},loadError:function(m){e([“CantLoadWebFont”,“Can’t load web font %1”,d.fontInUse+“/”+m.directory],null,2000);b.Startup.signal.Post(“HTML-CSS Jax - web font error for ”d.fontInUse“/”+m.directory)},firefoxFontError:function(m){e([“FirefoxCantLoadWebFont”,“Firefox can’t load web fonts from a remote host”],null,3000);b.Startup.signal.Post(“HTML-CSS Jax - Firefox web fonts on remote host error”)},checkWebFont:function(m,n,o){if(m.time(o)){return}if(d.Font.testFont(n)){o(m.STATUS.OK)}else{setTimeout(m,m.delay)}},fontFace:function(q){var r=d.allowWebFonts;var t=d.FONTDATA.FONTS[q];if(d.msieFontCSSBug&&!t.family.match(/-Web$/)){t.family+=“-Web”}if(t.isWebFont){delete t.familyFixed}var m=d.webfontDir+“/”+r;var p=j.fileURL(m);var o=q.replace(/-b/,“-B”).replace(/-i/,“-I”).replace(/-Bold-/,“-Bold”);if(!o.match(/-/)){o+=“-Regular”}if(r===“svg”){o+=“.svg#”+o}else{o+=“.”+r}var n=j.fileRev(m+“/”+o.replace(/#.*/,“”));var s={“font-family”:t.family,src:“url(‘”p“/”+o+n+“’)”};if(r===“otf”){o=o.replace(/otf$/,“woff”);n=j.fileRev(m+“/”+o);s.src+=“ format(‘opentype’)”;p=j.fileURL(d.webfontDir+“/woff”);s.src=“url(‘”p“/”+o+n+“’) format(‘woff’), ”+s.src}else{if(r!==“eot”){s.src+=“ format(‘”r“’)”}}if(!(d.FontFaceBug&&t.isWebFont)){if(q.match(/-bold/)){s[“font-weight”]=“bold”}if(q.match(/-italic/)){s[“font-style”]=“italic”}}return s}});var l,a,c;var g=MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<8;d.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","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax:focus, body :focus .MathJax":{display:"inline-table"},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax.MathJax_FullWidth":{"text-align":"center",display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"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","box-sizing":"content-box"},".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_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_test.mjx-test-display":{display:(g?"block":"table")+"!important"},".MathJax_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".MathJax_em_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60em"},".mjx-test-inline .MathJax_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_right_box":{display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:b.config.menuSettings,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var o=this.settings,n=this.config,m=o.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(n.availableFonts)}if(o.scale){n.scale=o.scale}if(m&&m!=="Auto"&&this.fontName[m]){n.availableFonts=[];delete n.fonts;if(h(this.fontName[m])){n.preferredFont=this.fontName[m][0];n.webFont=this.fontName[m][1]}else{n.preferredFont=n.webFont=this.fontName[m]}if(n.preferredFont){n.availableFonts[0]=n.preferredFont}}if(n.fonts){n.availableFonts=n.fonts;n.preferredFont=n.webFont=n.fonts[0];if(n.webFont==="STIX"){n.webFont+="-Web"}}m=this.Font.findFont(n.availableFonts,n.preferredFont);if(!m&&this.allowWebFonts){m=n.webFont;if(m){this.webFonts=true}}if(!m&&this.config.imageFont){m=n.imageFont;this.imgFonts=true}if(m){this.fontInUse=m;this.fontDir+="/"+m;this.webfontDir+="/"+m;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{e(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){l=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=l.ContextMenu;this.Mousedown=l.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var n=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(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(m){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.TestSpan=this.Element("span",{className:"MathJax_test"},[["span",{className:"MathJax_left_box"}],["span",{className:"MathJax_ex_box"}],["span",{className:"MathJax_em_box"}],["span",{className:"MathJax_right_box"}]]);return j.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(p){for(var o=0,n=p.length;o=r.HTMLCSSlast+r.HTMLCSSchunk){this.postTranslate(r,true);r.HTMLCSSchunk=Math.floor(r.HTMLCSSchunk*this.config.EqnChunkFactor);r.HTMLCSSdelay=true}return false},savePreview:function(m){var n=m.MathJax.preview;if(n){m.MathJax.tmpPreview=document.createElement(“span”);n.parentNode.replaceChild(m.MathJax.tmpPreview,n)}},restorePreview:function(m){var n=m.MathJax.tmpPreview;if(n){n.parentNode.replaceChild(m.MathJax.preview,n);delete m.MathJax.tmpPreview}},getMetrics:function(m){var n=m.HTMLCSS;this.em=i.mbase.prototype.em=n.em*n.scale;this.outerEm=n.em;this.scale=n.scale;this.cwidth=n.cwidth;this.linebreakWidth=n.lineWidth},postTranslate:function(o,u){var r=o.jax[this.id],v,p,s,q;for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;sn.root.spanID)“-zoom”;var r=document.getElementById(o).firstChild;while(r&&r.style.width!==p){r=r.nextSibling}if®{var u=r.offsetWidth;r.style.width=“100%”;if(u>m){y.style.width=(u+100)+“px”}}}r=y.firstChild.firstChild.style;if(z.H!=null&&z.H>z.h){r.marginTop=d.Em(z.H-Math.max(z.h,d.FONTDATA.lineH))}if(z.D!=null&&z.D>z.d){r.marginBottom=d.Em(z.D-Math.max(z.d,d.FONTDATA.lineD))}if(z.lw<0){r.paddingLeft=d.Em(-z.lw)}if(z.rw>z.w){r.marginRight=d.Em(z.rw-z.w)}y.style.position=“absolute”;if(!p){x.style.position=“absolute”}var w=y.offsetWidth,t=y.offsetHeight,A=x.offsetHeight,s=x.offsetWidth;y.style.position=x.style.position=“”;return{Y:-l.getBBox(y).h,mW:s,mH:A,zW:w,zH:t}},initImg:function(m){},initHTML:function(n,m){},initFont:function(m){var o=d.FONTDATA.FONTS,n=d.config.availableFonts;if(n&&n.length&&d.Font.testFont(o[m])){o[m].available=true;if(o[m].familyFixed){o[m].family=o[m].familyFixed;delete o[m].familyFixed}return null}if(!this.allowWebFonts){return null}o[m].isWebFont=true;if(d.FontFaceBug){o[m].family=m;if(d.msieFontCSSBug){o[m].family+=“-Web”}}return j.Styles({“@font-face”:this.Font.fontFace(m)})},Remove:function(m){var n=document.getElementById(m.inputID+“-Frame”);if(n){if(m.HTMLCSS.display){n=n.parentNode}n.parentNode.removeChild(n)}delete m.HTMLCSS},getHD:function(n,o){if(n.bbox&&this.config.noReflows&&!o){return{h:n.bbox.h,d:n.bbox.d}}var m=n.style.position;n.style.position=“absolute”;this.HDimg.style.height=“0px”;n.appendChild(this.HDspan);var p={h:n.offsetHeight};this.HDimg.style.height=p.h+“px”;p.d=n.offsetHeight-p.h;p.h-=p.d;p.h/=this.em;p.d/=this.em;n.removeChild(this.HDspan);n.style.position=m;return p},getW:function(q){var n,p,o=(q.bbox||{}).w,r=q;if(q.bbox&&this.config.noReflows&&q.bbox.exactW!==false){if(!q.bbox.exactW){if(q.style.paddingLeft){o+=this.unEm(q.style.paddingLeft)*(q.scale||1)}if(q.style.paddingRight){o+=this.unEm(q.style.paddingRight)*(q.scale||1)}}return o}if(q.bbox&&q.bbox.exactW){return o}if((q.bbox&&o>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!q.firstChild){n=q.offsetWidth;p=q.parentNode.offsetHeight}else{if(q.bbox&&o<0&&this.msieNegativeBBoxBug){n=-q.offsetWidth,p=q.parentNode.offsetHeight}else{var m=q.style.position;q.style.position="absolute";r=this.startMarker;q.insertBefore(r,q.firstChild);q.appendChild(this.endMarker);n=this.endMarker.offsetLeft-r.offsetLeft;q.removeChild(this.endMarker);q.removeChild(r);q.style.position=m}}if(p!=null){q.parentNode.HH=p/this.em}return n/this.em},Measured:function(o,n){var p=o.bbox;if(p.width==null&&p.w&&!p.isMultiline){var m=this.getW(o);p.rw+=m-p.w;p.w=m;p.exactW=true}if(!n){n=o.parentNode}if(!n.bbox){n.bbox=p}return o},Remeasured:function(n,m){m.bbox=this.Measured(n,m).bbox},MeasureSpans:function(q){var t=[],v,s,p,w,n,r,o,u;for(s=0,p=q.length;s=0&&!this.initialSkipBug)||(w.w<0&&this.msieNegativeBBoxBug)){t.push([v])}else{if(this.initialSkipBug){n=this.startMarker.cloneNode(true);r=this.endMarker.cloneNode(true);v.insertBefore(n,v.firstChild);v.appendChild(r);t.push([v,n,r,v.style.position]);v.style.position="absolute"}else{r=this.endMarker.cloneNode(true);v.appendChild(r);t.push([v,null,r])}}}for(s=0,p=t.length;s=0&&!this.initialSkipBug)||this.negativeBBoxes||!v.firstChild){o=v.offsetWidth;u.HH=u.offsetHeight/this.em}else{if(w.w<0&&this.msieNegativeBBoxBug){o=-v.offsetWidth,u.HH=u.offsetHeight/this.em}else{o=t[s][2].offsetLeft-((t[s][1]||{}).offsetLeft||0)}}o/=this.em;w.rw+=o-w.w;w.w=o;w.exactW=true;if(!u.bbox){u.bbox=w}}for(s=0,p=t.length;s=0){r.style.width=this.Em(s);r.style.display=“inline-block”;r.style.overflow=“hidden”}else{if(this.msieNegativeSpaceBug){r.style.height=“”}r.style.marginLeft=this.Em(s);if(d.safariNegativeSpaceBug&&r.parentNode.firstChild==r){this.createBlank(r,0,true)}}if(o&&o!==i.COLOR.TRANSPARENT){r.style.backgroundColor=o;r.style.position=“relative”}return r},createRule:function(t,p,r,u,n){if(p<-r){r=-p}var o=d.TeX.min_rule_thickness,q=1;if(u>0&&u*this.em0&&(p+r)*this.emp+r){m.borderTop=this.Px(p+r)+“ ”+n;m.width=this.Em(u);m.height=(this.msieRuleBug&&p+r>0?this.Em(p+r):0)}else{m.borderLeft=this.Px(u)+“ ”+n;m.width=(this.msieRuleBug&&u>0?this.Em(u):0);m.height=this.Em(p+r)}var s=this.addElement(t,“span”,{style:m,noAdjust:true,HH:p+r,isMathJax:true,bbox:{h:p,d:r,w:u,rw:u,lw:0,exactW:true}});if(t.isBox||t.className==“mspace”){t.bbox=s.bbox,t.HH=p+r}return s},createFrame:function(v,s,u,x,z,n){if(s<-u){u=-s}var r=2*z;if(this.msieFrameSizeBug){if(xF.w){d.createBlank(w,F.rw-F.w+0.1)}}if(!this.msieClipRectBug&&!F.noclip&&!q){var E=3/this.em;var C=(F.H==null?F.h:F.H),n=(F.D==null?F.d:F.D);var G=A-C-E,s=A+n+E,p=-1000,m=F.rw+1000;w.style.clip=“rect(”+this.Em(G)+“ ”+this.Em(m)+“ ”+this.Em(s)+“ ”+this.Em(p)+“)”}}w.style.top=this.Em(-u-A);w.style.left=this.Em(v+I);if(F&&B){if(F.H!=null&&(B.H==null||F.H+u>B.H)){B.H=F.H+u}if(F.D!=null&&(B.D==null||F.D-u>B.D)){B.D=F.D-u}if(F.h+u>B.h){B.h=F.h+u}if(F.d-u>B.d){B.d=F.d-u}if(B.H!=null&&B.H<=B.h){delete B.H}if(B.D!=null&&B.D<=B.d){delete B.D}if(F.w+v>B.w){B.w=F.w+v;if(B.width==null){z.style.width=this.Em(B.w)}}if(F.rw+v>B.rw){B.rw=F.rw+v}if(F.lw+vo.load“.js”))}for(var u=0,r=o.HW.length;u=p-0.01||(u==r-1&&!o.stretch)){if(o.HW[u][2]){s*=o.HW[u][2]}if(o.HW[u][3]){n=o.HW[u][3]}var t=this.addElement(w,“span”);this.createChar(t,[n,o.HW[u][1]],s,q);w.bbox=t.bbox;w.offset=0.65*w.bbox.w;w.scale=s;return}}if(o.stretch){this[“extendDelimiter”+o.dir](w,v,o.stretch,s,q)}},extendDelimiterV:function(B,u,F,G,x){var p=this.createStack(B,true);var w=this.createBox(p),v=this.createBox(p);this.createChar(w,(F.top||F.ext),G,x);this.createChar(v,(F.bot||F.ext),G,x);var o={bbox:{w:0,lw:0,rw:0}},E=o,q;var C=w.bbox.h+w.bbox.d+v.bbox.h+v.bbox.d;var s=-w.bbox.h;this.placeBox(w,0,s,true);s-=w.bbox.d;if(F.mid){E=this.createBox(p);this.createChar(E,F.mid,G,x);C+=E.bbox.h+E.bbox.d}if(F.min&&uC){o=this.Element(“span”);this.createChar(o,F.ext,G,x);var D=o.bbox.h+o.bbox.d,m=D-0.05,z,r,A=(F.mid?2:1);r=z=Math.min(Math.ceil((u-C)/(A*m)),this.maxStretchyParts);if(!F.fullExtenders){m=(u-C)/(A*z)}var t=(z/(z+1))*(D-m);m=D-t;s+=t+m-o.bbox.h;while(A–>0){while(z–>0){if(!this.msieCloneNodeBug){q=o.cloneNode(true)}else{q=this.Element(“span”);this.createChar(q,F.ext,G,x)}q.bbox=o.bbox;s-=m;this.placeBox(this.addBox(p,q),0,s,true)}s+=t-o.bbox.d;if(F.mid&&A){this.placeBox(E,0,s-E.bbox.h,true);z=r;s+=-(E.bbox.h+E.bbox.d)+t+m-o.bbox.h}}}else{s+=(C-u)/2;if(F.mid){this.placeBox(E,0,s-E.bbox.h,true);s+=-(E.bbox.h+E.bbox.d)}s+=(C-u)/2}this.placeBox(v,0,s-v.bbox.h,true);s-=v.bbox.h+v.bbox.d;B.bbox={w:Math.max(w.bbox.w,o.bbox.w,v.bbox.w,E.bbox.w),lw:Math.min(w.bbox.lw,o.bbox.lw,v.bbox.lw,E.bbox.lw),rw:Math.max(w.bbox.rw,o.bbox.rw,v.bbox.rw,E.bbox.rw),h:0,d:-s,exactW:true};B.scale=G;B.offset=0.55*B.bbox.w;B.isMultiChar=true;this.setStackWidth(p,B.bbox.w)},extendDelimiterH:function(C,p,F,H,z){var s=this.createStack(C,true);var q=this.createBox(s),D=this.createBox(s);this.createChar(q,(F.left||F.rep),H,z);this.createChar(D,(F.right||F.rep),H,z);var m=this.Element(“span”);this.createChar(m,F.rep,H,z);var E={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},o;this.placeBox(q,-q.bbox.lw,0,true);var v=(q.bbox.rw-q.bbox.lw)+(D.bbox.rw-D.bbox.lw)-0.05,u=q.bbox.rw-q.bbox.lw-0.025,y;if(F.mid){E=this.createBox(s);this.createChar(E,F.mid,H,z);v+=E.bbox.w}if(F.min&&pv){var 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o=0,n=u.length;o0){q+=2*B;w-=B}if(z>0){z+=2*B;m-=B}u=-q-w;if(v){u-=v.right;m-=v.bottom;t+=v.left;r+=v.right;C.h+=v.top;C.d+=v.bottom;C.w+=v.left+v.right;C.lw-=v.left;C.rw+=v.right}if(x){z+=x.top+x.bottom;q+=x.left+x.right;u-=x.right;m-=x.bottom;t+=x.left;r+=x.right;C.h+=x.top;C.d+=x.bottom;C.w+=x.left+x.right;C.lw-=x.left;C.rw+=x.right}if®{y.style.paddingRight=d.Em®}var p=d.Element(“span”,{id:“MathJax-Color-”+this.spanID+d.idPostfix,isMathJax:true,style:{display:“inline-block”,backgroundColor:A.mathbackground,width:d.Em(q),height:d.Em(z),verticalAlign:d.Em(m),marginLeft:d.Em(w),marginRight:d.Em(u)}});d.setBorders(p,v);if(C.width){p.style.width=C.width;p.style.marginRight=“-”+C.width}if(d.msieInlineBlockAlignBug){p.style.position=“relative”;p.style.width=p.style.height=0;p.style.verticalAlign=p.style.marginLeft=p.style.marginRight=“”;p.style.border=p.style.padding=“”;if(v&&d.msieBorderWidthBug){z+=v.top+v.bottom;q+=v.left+v.right}p.style.width=d.Em(t+B);d.placeBox(d.addElement(p,“span”,{noAdjust:true,isMathJax:true,style:{display:“inline-block”,position:“absolute”,overflow:“hidden”,background:(A.mathbackground||“transparent”),width:d.Em(q),height:d.Em(z)}}),w,C.h+B);d.setBorders(p.firstChild,v)}y.parentNode.insertBefore(p,y);if(d.msieColorPositionBug){y.style.position=“relative”}return p}return null},HTMLremoveColor:function(){var m=document.getElementById(“MathJax-Color-”+this.spanID+d.idPostfix);if(m){m.parentNode.removeChild(m)}},HTMLhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!==“mo”){return}var o=this.getValues(“scriptlevel”,“lspace”,“rspace”);if(o.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var n=this.HTMLgetMu(q);o.lspace=Math.max(0,d.length2em(o.lspace,n));o.rspace=Math.max(0,d.length2em(o.rspace,n));var m=this,p=this.Parent();while(p&&p.isEmbellished()&&p.Core()===m){m=p;p=p.Parent();q=m.HTMLspanElement()}if(o.lspace){q.style.paddingLeft=d.Em(o.lspace)}if(o.rspace){q.style.paddingRight=d.Em(o.rspace)}}}else{var r=this.texSpacing();if(r!==""){this.HTMLgetScale();r=d.length2em(r,this.scale)/(q.scale||1)*this.mscale;if(q.style.paddingLeft){r+=d.unEm(q.style.paddingLeft)}q.style.paddingLeft=d.Em(r)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var o=1,m=this.getValues("scriptlevel","fontsize");m.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var n=this.HTMLspanElement();if(n.style.fontSize!=""){m.fontsize=n.style.fontSize}}if(m.fontsize&&!this.mathsize){m.mathsize=m.fontsize}if(m.scriptlevel!==0){if(m.scriptlevel>2){m.scriptlevel=2}o=Math.pow(this.Get(“scriptsizemultiplier”),m.scriptlevel);m.scriptminsize=d.length2em(this.Get(“scriptminsize”));if(o2){n.scriptlevel=2}m=Math.sqrt(Math.pow(n.scriptsizemultiplier,n.scriptlevel))}return m},HTMLgetVariant:function(){var m=this.getValues(“mathvariant”,“fontfamily”,“fontweight”,“fontstyle”);m.hasVariant=this.Get(“mathvariant”,true);if(!m.hasVariant){m.family=m.fontfamily;m.weight=m.fontweight;m.style=m.fontstyle}if(this.style){var o=this.HTMLspanElement();if(!m.family&&o.style.fontFamily){m.family=o.style.fontFamily}if(!m.weight&&o.style.fontWeight){m.weight=o.style.fontWeight}if(!m.style&&o.style.fontStyle){m.style=o.style.fontStyle}}if(m.weight&&m.weight.match(/^d+$/)){m.weight=(parseInt(m.weight)>600?“bold”:“normal”)}var 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r=e.Element(“span”,{className:“MJXp-script-box”,style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),“vertical-align”:g.Em(-u-p.PHTML.d*0.8)}},[[“span”,{},[[“span”,{},[[“span”,{style:{“margin-bottom”:g.Em(-(n.PHTML.d-0.05))}}]]]]],[“span”,{},[[“span”,{},[[“span”,{style:{“margin-top”:g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild®;t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function®{r=this.PHTMLdefaultSpan(r,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});var o=this.getValues(“linethickness”,“displaystyle”);if(!o.displaystyle){if(this.data){this.data.PHTMLhandleScriptlevel(r.firstChild)}if(this.data){this.data.PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element(“span”,{className:“MJXp-box”},[[“span”,{className:“MJXp-denom”},[[“span”,{},[[“span”,{className:“MJXp-rule”,style:{height:“1em”}}]]],[“span”]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||“0”,0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=“none”;u.style.borderBottom=(o.linethickness<0.15?“1px”:q)+“ solid”;u.style.margin=q+“ 0”;q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop=“-.7em”}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element(“span”,{className:“MJXp-surd”},[[“span”,{style:{“font-size”:q+“%”,“margin-top”:w}},[“u221A”]]]);var s=e.Element(“span”,{className:“MJXp-root”},[[“span”,{className:“MJXp-rule”,style:{“border-top”:“.08em solid”}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className=“MJXp-right MJXp-scale”+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild®;u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element(“span”),q.firstChild);n.className=“MJXp-script”;var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,“open”,{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,“sep”+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,“close”,{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild(“open”,o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild(“sep”+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild(“close”,o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className=“MJXp-mrow”;return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues(“columnalign”,“rowalign”,“columnspacing”,“rowspacing”,“columnwidth”,“equalcolumns”,“equalrows”,“columnlines”,“rowlines”,“frame”,“framespacing”,“align”,“width”);var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N=g.length2em(N)}for(F=0,A=w.length;F<A;F++){w=g.length2em(w)}var K=e.Element(“span”);while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data;if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.PHTML,q=v.PHTMLspanElement();q.style.verticalAlign=C;var B=(v.type===“mlabeledtr”?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data;if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.PHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data){this.data.toPreviewHTML(n);MathJax.Hub.Insert(this.data.PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h.Augment({toPreviewHTML:function(n){}});MathJax.Hub.Register.StartupHook(“onLoad”,function(){setTimeout(MathJax.Callback(),0)})});MathJax.Hub.Register.StartupHook(“End 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Output”,function(){if(!h&&d.Active()){m=b.processUpdateTime;j=b.processUpdateDelay;k=b.config.messageStyle;b.processUpdateTime=i.updateTime;b.processUpdateDelay=i.updateDelay;b.Config({messageStyle:i.messageStyle});MathJax.Message.Clear(0,0);l=true}});b.Register.MessageHook(“End Math Output”,function(){if(!h&&l){b.processUpdateTime=m;b.processUpdateDelay=j;b.Config({messageStyle:k});h=true}})},Disable:function(){this.enabled=false},Enable:function(){this.enabled=true},Active:function(){return c.FastPreview&&this.enabled&&!(e||{}).noFastPreview},Preview:function(h){if(!this.Active()||!h.script.parentNode){return}var i=h.script.MathJax.preview||h.script.previousSibling;if(!i||i.className!==MathJax.Hub.config.preRemoveClass){i=g.Element(“span”,{className:MathJax.Hub.config.preRemoveClass});h.script.parentNode.insertBefore(i,h.script);h.script.MathJax.preview=i}i.innerHTML=“”;i.style.color=(a?“black”:“inherit”);return this.postFilter(i,h)},postFilter:function(j,i){if(!i.math.root.toPreviewHTML){var h=MathJax.Callback.Queue();h.Push([“Require”,MathJax.Ajax,“/jax/output/PreviewHTML/config.js”],[“Require”,MathJax.Ajax,“/jax/output/PreviewHTML/jax.js”]);b.RestartAfter(h.Push({}))}i.math.root.toPreviewHTML(j)},Register:function(h){b.Register.StartupHook(h+“ Jax Require”,function(){var i=MathJax.InputJax;i.postfilterHooks.Add([“Preview”,MathJax.Extension],50)})}};d.Register(“TeX”);d.Register(“MathML”);d.Register(“AsciiMath”);b.Register.StartupHook(“End Config”,);b.Startup.signal.Post(“fast-preview Ready”)})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete(“/extensions/fast-preview.js”); (function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:“2.7.5”,config:b.CombineConfig(“AssistiveMML”,{disabled:false,styles:{“.MJX_Assistive_MathML”:{position:“absolute!important”,top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?“rect(1px 1px 1px 1px)”:“rect(1px, 1px, 1px, 1px)”),padding:“1px 0 0 0!important”,border:“0!important”,height:“1px!important”,width:“1px!important”,overflow:“hidden!important”,display:“block!important”,“-webkit-touch-callout”:“none”,“-webkit-user-select”:“none”,“-khtml-user-select”:“none”,“-moz-user-select”:“none”,“-ms-user-select”:“none”,“user-select”:“none”},“.MJX_Assistive_MathML.MJX_Assistive_MathML_Block”:{width:“100%!important”}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook(“End Math”,function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g)}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j<g;j++){l=document.getElementById(h.inputID+“-Frame”);if(l&&l.getAttribute(“data-mathml”)){l.removeAttribute(“data-mathml”);if(l.lastChild&&l.lastChild.className.match(/MJX_Assistive_MathML/)){l.removeChild(l.lastChild)}}}},HandleMML:function(l){var g=l.jax.length,h,i,n,j;while(l.i<g){h=l.jax;n=document.getElementById(h.inputID+“-Frame”);if(h.outputJax!==“NativeMML”&&h.outputJax!==“PlainSource”&&n&&!n.getAttribute(“data-mathml”)){try{i=h.root.toMathML(“”).replace(/n */g,“”).replace(/<!–.*?–>/g,“”)}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(,k.restart)}n.setAttribute(“data-mathml”,i);j=f.addElement(n,“span”,{isMathJax:true,unselectable:“on”,className:“MJX_Assistive_MathML”+(h.root.Get(“display”)===“block”?“ MJX_Assistive_MathML_Block”:“”)});try{j.innerHTML=i}catch(k){}n.style.position=“relative”;n.setAttribute(“role”,“presentation”);n.firstChild.setAttribute(“aria-hidden”,“true”);j.setAttribute(“role”,“presentation”)}l.i++}l.callback()}};b.Startup.signal.Post(“AssistiveMML Ready”)})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue([“Require”,MathJax.Ajax,“/extensions/toMathML.js”],[“loadComplete”,MathJax.Ajax,“/extensions/AssistiveMML.js”],function(){MathJax.Hub.Register.StartupHook(“End Config”,)}); !function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty©&&b.push©;return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+“/extensions/a11y”);var i=b={version:“1.5.0”,prefix:“”,defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b;c++){var d=i.MakeOption(a);void 0===e&&(e=i.defaults)}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules;e++)b=a.placeHolder;var f=d.FindId(“Accessibility”);if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId(“Settings”,“Renderer”)||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift(“Accessibility”);var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId(“Locale”);h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules;b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules;d++)e&&c.push(b.module);return c.length?a.Startup.loadArray©:null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:“”,name:,module:“”,placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,“”),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(,i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND([“OptionsWhenActive”,“(Options when Active)”],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue([“Require”,MathJax.Ajax,this.module,])},Enable:function(a){var b=MathJax.Extension;b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j(“collapsible”,“Collapsible Math”,“/collapsible.js”,“collapsible”)),i.Register(j(“autocollapse”,“Auto 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