mw.loader.implement("ext.math.mathjax.jax.output.HTML-CSS",function($,jQuery){(function(AJAX,HUB,HTMLCSS){var MML,isMobile=HUB.Browser.isMobile;var MESSAGE=function(){var data=[].slice.call(arguments,0);data[0][0]=["HTML-CSS",data[0][0]];return MathJax.Message.Set.apply(MathJax.Message,data);};var FONTTEST=MathJax.Object.Subclass({timeout:(isMobile?15:8)*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"},"STIX-Web":{family:"STIXWeb_Size1",testString:"() {} []"},"Asana-Math":{family:"AsanaMath_Size1",testString:"() {} []"},"Gyre-Pagella":{family:"GyrePagella_Size1",testString:"() {} []"},"Gyre-Termes":{family:"GyreTermes_Size1",testString:"() {} []"},"Latin-Modern":{family:"LatinModern_Size1",testString:"() {} []"},"Neo-Euler":{family:"NeoEuler_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],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(fonts,pref){if(pref&&this.testCollection(pref)){return pref}for(var i=0,m=fonts.length;i<m;i++){if(fonts[i]===pref)continue;if(this.testCollection(fonts[i])){return fonts[i]}}return null;},testCollection:function(name){return this.testFont(this.FontInfo[name])},testFont:function(font){if(font.isWebFont&&HTMLCSS.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal";}else{this.div.style.fontWeight=(font.weight||"normal");this.div.style.fontStyle=(font.style||"normal");}var W=this.getComparisonWidths(font.
testString,font.noStyleChar);if(W){this.div.style.fontFamily="'"+font.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==W[0]){this.div.style.fontFamily="'"+font.family+"',"+this.comparisonFont[W[2]];if(this.div.offsetWidth==W[1]){return false}}if(this.div.offsetWidth!=W[3]||this.div.offsetHeight!=W[4]){if(font.noStyleChar||!HTMLCSS.FONTDATA||!HTMLCSS.FONTDATA.hasStyleChar){return true}for(var i=0,m=this.testSize.length;i<m;i++){if(this.testStyleChar(font,this.testSize[i])){return true}}}}return false;},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(font,size){var n=3+(font.weight?2:0)+(font.style?4:0);var extra="",dw=0;var SIZE=this.div.style.fontSize;this.div.style.fontSize=size;if(HTMLCSS.msieItalicWidthBug&&font.style==="italic"){this.text.nodeValue=extra=this.compChar;dw=this.div.offsetWidth;}if(HTMLCSS.safariTextNodeBug){this.div.innerHTML=this.compChar+extra}else{this.text.nodeValue=this.compChar+extra}var W=this.div.offsetWidth-dw;if(
HTMLCSS.safariTextNodeBug){this.div.innerHTML=this.styleChar+extra}else{this.text.nodeValue=this.styleChar+extra}var N=Math.floor((this.div.offsetWidth-dw)/W+.5);if(N===n){if(HTMLCSS.safariTextNodeBug){this.div.innerHTML=this.versionChar+extra}else{this.text.nodeValue=this.versionChar+extra}font.version=Math.floor((this.div.offsetWidth-dw)/W+1.5)/2;}this.div.style.fontSize=SIZE;return(N===n);},getComparisonWidths:function(string,noStyleChar){if(HTMLCSS.FONTDATA&&HTMLCSS.FONTDATA.hasStyleChar&&!noStyleChar){string+=this.styleChar+" "+this.compChar}if(HTMLCSS.safariTextNodeBug){this.div.innerHTML=string}else{this.text.nodeValue=string}this.div.style.fontFamily=this.comparisonFont[0];var W=this.div.offsetWidth;this.div.style.fontFamily=HTMLCSS.webFontDefault;var sW=this.div.offsetWidth,sH=this.div.offsetHeight;for(var i=1,m=this.comparisonFont.length;i<m;i++){this.div.style.fontFamily=this.comparisonFont[i];if(this.div.offsetWidth!=W){return[W,this.div.offsetWidth,i,sW,sH]}}return null;},
loadWebFont:function(font){HUB.Startup.signal.Post("HTML-CSS Jax - Web-Font "+HTMLCSS.fontInUse+"/"+font.directory);var n=MESSAGE(["LoadWebFont","Loading web-font %1",HTMLCSS.fontInUse+"/"+font.directory]);var done=MathJax.Callback({});var callback=MathJax.Callback(["loadComplete",this,font,n,done]);AJAX.timer.start(AJAX,[this.checkWebFont,font,callback],0,this.timeout);return done;},loadComplete:function(font,n,done,status){MathJax.Message.Clear(n);if(status===AJAX.STATUS.OK){this.webFontLoaded=true;done();return}this.loadError(font);if(HUB.Browser.isFirefox&&HTMLCSS.allowWebFonts){var host=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){host+=":"+document.location.port}host+="/";if(AJAX.fileURL(HTMLCSS.webfontDir).substr(0,host.length)!==host){this.firefoxFontError(font)}}if(!this.webFontLoaded){HTMLCSS.loadWebFontError(font,done)}else{done()}},loadError:function(font){MESSAGE(["CantLoadWebFont","Can't load web font %1",HTMLCSS.fontInUse+"/"+
font.directory],null,2000);HUB.Startup.signal.Post(["HTML-CSS Jax - web font error",HTMLCSS.fontInUse+"/"+font.directory,font]);},firefoxFontError:function(font){MESSAGE(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3000);HUB.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error");},checkWebFont:function(check,font,callback){if(check.time(callback))return;if(HTMLCSS.Font.testFont(font)){callback(check.STATUS.OK)}else{setTimeout(check,check.delay)}},fontFace:function(name){var type=HTMLCSS.allowWebFonts;var FONT=HTMLCSS.FONTDATA.FONTS[name];if(HTMLCSS.msieFontCSSBug&&!FONT.family.match(/-Web$/)){FONT.family+="-Web"}var dir=AJAX.fileURL(HTMLCSS.webfontDir+"/"+type);var fullname=name.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!fullname.match(/-/)){fullname+="-Regular"}if(type==="svg"){fullname+=".svg#"+fullname}else{fullname+="."+type}var def={"font-family":FONT.family,src:"url('"+dir+"/"+fullname+"')"};if(
type==="otf"){def.src+=" format('opentype')";dir=AJAX.fileURL(HTMLCSS.webfontDir+"/woff");def.src="url('"+dir+"/"+fullname.replace(/otf$/,"woff")+"') format('woff'), "+def.src;}else if(type!=="eot"){def.src+=" format('"+type+"')"}if(!(HTMLCSS.FontFaceBug&&FONT.isWebFont)){if(name.match(/-bold/)){def["font-weight"]="bold"}if(name.match(/-italic/)){def["font-style"]="italic"}}return def;}});var EVENT,TOUCH,HOVER;HTMLCSS.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=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:HUB.config.menuSettings,hideProcessedMath:true,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.Font=FONTTEST();this.SUPER(arguments).Config.call(this);var settings=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(settings.scale){this.config.scale=settings.scale}if(settings.font&&settings.font!=="Auto"){if(settings.font==="TeXLocal"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else if(settings.font==="TeXWeb"){this.config.availableFonts=[];this.config.
preferredFont="";this.config.webFont="TeX"}else if(settings.font==="TeXimage"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}else if(settings.font==="STIXlocal"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="STIX-Web"}else if(settings.font==="STIXWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="STIX-Web"}else if(settings.font==="AsanaMathWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Asana-Math"}else if(settings.font==="GyrePagellaWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Pagella"}else if(settings.font==="GyreTermesWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Termes"}else if(settings.font==="LatinModernWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Latin-Modern"}else if(settings.font==="NeoEulerWeb"){
this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Neo-Euler"}}var font=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!font&&this.allowWebFonts){font=this.config.webFont;if(font){this.webFonts=true}}if(!font&&this.config.imageFont){font=this.config.imageFont;this.imgFonts=true}if(font){this.fontInUse=font;this.fontDir+="/"+font;this.webfontDir+="/"+font;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");HUB.Startup.signal.Post("HTML-CSS Jax - using image fonts");}}else{MESSAGE(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);this.fontInUse="generic";this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:.8,lineD:.2,ffLineH:.8,FONTS:{},VARIANT:{"normal":{fonts:[]},"-generic-variant":{fonts:[]},"-largeOp":{fonts:[]},"-smallOp":{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:0x2D,REMAP:{}};HUB.Startup.signal.
Post("HTML-CSS Jax - no valid font");}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");},Startup:function(){EVENT=MathJax.Extension.MathEvents.Event;TOUCH=MathJax.Extension.MathEvents.Touch;HOVER=MathJax.Extension.MathEvents.Hover;this.ContextMenu=EVENT.ContextMenu;this.Mousedown=EVENT.AltContextMenu;this.Mouseover=HOVER.Mouseover;this.Mouseout=HOVER.Mouseout;this.Mousemove=HOVER.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 div=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=div.
offsetWidth/5;this.hiddenDiv.removeChild(div);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(err){}}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 AJAX.Styles(this.config.styles,["InitializeHTML",this]);},removeSTIXfonts:function(fonts){for(var i=0,m=fonts.length;i<m;i++){if(fonts[i]==="STIX"){fonts.splice(i,1);m--;i--;}}if(this.config.preferredFont===
"STIX"){this.config.preferredFont=fonts[0]}},PreloadWebFonts:function(){if(!HTMLCSS.allowWebFonts||!HTMLCSS.config.preloadWebFonts)return;for(var i=0,m=HTMLCSS.config.preloadWebFonts.length;i<m;i++){var FONT=HTMLCSS.FONTDATA.FONTS[HTMLCSS.config.preloadWebFonts[i]];if(!FONT.available){HTMLCSS.Font.testFont(FONT)}}},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(state){var scripts=state.jax[this.id],i,m=scripts.length,script,prev,span,div,test,jax,ex,em,scale,maxwidth,relwidth=false,linebreak=this.config.linebreaks.automatic,width=this.config.linebreaks.width;if(linebreak){relwidth=(width.match(
/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(relwidth){width=width.replace(/\s*container\s*/,"")}else{maxwidth=this.defaultWidth}if(width===""){width="100%"}}else{maxwidth=100000}for(i=0;i<m;i++){script=scripts[i];if(!script.parentNode)continue;prev=script.previousSibling;if(prev&&String(prev.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){prev.parentNode.removeChild(prev)}jax=script.MathJax.elementJax;if(!jax)continue;jax.HTMLCSS={display:(jax.root.Get("display")==="block")}
span=div=this.Element("span",{className:"MathJax",id:jax.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:EVENT.Menu,onmousedown:EVENT.Mousedown,onmouseover:EVENT.Mouseover,onmouseout:EVENT.Mouseout,onmousemove:EVENT.Mousemove,onclick:EVENT.Click,ondblclick:EVENT.DblClick});if(HUB.Browser.noContextMenu){span.ontouchstart=TOUCH.start;span.ontouchend=TOUCH.end;}if(jax.HTMLCSS.display){div=this.Element("div",{className:"MathJax_Display"});div.appendChild(span);}else if(this.msieDisappearingBug){span.style.display="inline-block"}div.setAttribute("role","textbox");div.setAttribute("aria-readonly","true");div.className+=" MathJax_Processing";script.parentNode.insertBefore(div,script);script.parentNode.insertBefore(this.EmExSpan.cloneNode(true),script);if(relwidth){div.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),div)}}for(i=0;i<m;i++){script=scripts[i];if(!script.parentNode)continue;test=script.previousSibling;div=test.previousSibling;jax=script.MathJax.elementJax;if
(!jax)continue;ex=test.firstChild.offsetHeight/60;em=test.lastChild.firstChild.offsetHeight/60;if(relwidth){maxwidth=div.previousSibling.firstChild.offsetWidth}if(ex===0||ex==="NaN"){this.hiddenDiv.appendChild(div);jax.HTMLCSS.isHidden=true;ex=this.defaultEx;em=this.defaultEm;if(relwidth){maxwidth=this.defaultWidth}}scale=(this.config.matchFontHeight?ex/this.TeX.x_height/em:1);scale=Math.floor(Math.max(this.config.minScaleAdjust/100,scale)*this.config.scale);jax.HTMLCSS.scale=scale/100;jax.HTMLCSS.fontSize=scale+"%";jax.HTMLCSS.em=jax.HTMLCSS.outerEm=em;this.em=em*scale/100;jax.HTMLCSS.ex=ex;jax.HTMLCSS.lineWidth=(linebreak?this.length2em(width,1,maxwidth/this.em):1000000);}for(i=0;i<m;i++){script=scripts[i];if(!script.parentNode)continue;test=scripts[i].previousSibling;jax=scripts[i].MathJax.elementJax;if(!jax)continue;if(relwidth){span=test.previousSibling;if(!jax.HTMLCSS.isHidden){span=span.previousSibling}span.parentNode.removeChild(span);}test.parentNode.removeChild(test);}state.
HTMLCSSeqn=state.HTMLCSSlast=0;state.HTMLCSSi=-1;state.HTMLCSSchunk=this.config.EqnChunk;state.HTMLCSSdelay=false;},Translate:function(script,state){if(!script.parentNode)return;if(state.HTMLCSSdelay){state.HTMLCSSdelay=false;HUB.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay));}var jax=script.MathJax.elementJax,math=jax.root,span=document.getElementById(jax.inputID+"-Frame"),div=(jax.HTMLCSS.display?span.parentNode:span);this.em=MML.mbase.prototype.em=jax.HTMLCSS.em*jax.HTMLCSS.scale;this.outerEm=jax.HTMLCSS.em;this.scale=jax.HTMLCSS.scale;this.linebreakWidth=jax.HTMLCSS.lineWidth;if(this.scale!==1){span.style.fontSize=jax.HTMLCSS.fontSize}this.initImg(span);this.initHTML(math,span);math.setTeXclass();try{math.toHTML(span,div)}catch(err){if(err.restart){while(span.firstChild){span.removeChild(span.firstChild)}}throw err;}if(jax.HTMLCSS.isHidden){script.parentNode.insertBefore(div,script)}div.className=div.className.split(/ /)[0];if(this.hideProcessedMath){div.className
+=" MathJax_Processed";if(script.MathJax.preview){jax.HTMLCSS.preview=script.MathJax.preview;delete script.MathJax.preview;}state.HTMLCSSeqn+=(state.i-state.HTMLCSSi);state.HTMLCSSi=state.i;if(state.HTMLCSSeqn>=state.HTMLCSSlast+state.HTMLCSSchunk){this.postTranslate(state,true);state.HTMLCSSchunk=Math.floor(state.HTMLCSSchunk*this.config.EqnChunkFactor);state.HTMLCSSdelay=true;}}},postTranslate:function(state,partial){var scripts=state.jax[this.id];if(!this.hideProcessedMath)return;for(var i=state.HTMLCSSlast,m=state.HTMLCSSeqn;i<m;i++){var script=scripts[i];if(script&&script.MathJax.elementJax){script.previousSibling.className=script.previousSibling.className.split(/ /)[0];var data=script.MathJax.elementJax.HTMLCSS;if(data.preview){data.preview.innerHTML="";script.MathJax.preview=data.preview;delete data.preview;}}}if(this.forceReflow){var sheet=(document.styleSheets||[])[0]||{};sheet.disabled=true;sheet.disabled=false;}state.HTMLCSSlast=state.HTMLCSSeqn;},getJaxFromMath:function(
math){if(math.parentNode.className==="MathJax_Display"){math=math.parentNode}do{math=math.nextSibling}while(math&&math.nodeName.toLowerCase()!=="script");return HUB.getJaxFor(math);},getHoverSpan:function(jax,math){return jax.root.HTMLspanElement()},getHoverBBox:function(jax,span,math){var bbox=span.bbox,em=jax.HTMLCSS.outerEm;var BBOX={w:bbox.w*em,h:bbox.h*em,d:bbox.d*em};if(bbox.width){BBOX.width=bbox.width}return BBOX;},Zoom:function(jax,span,math,Mw,Mh){span.className="MathJax";span.style.fontSize=jax.HTMLCSS.fontSize;var emex=span.appendChild(this.EmExSpan.cloneNode(true));var em=emex.lastChild.firstChild.offsetHeight/60;this.em=MML.mbase.prototype.em=em;this.outerEm=em/jax.HTMLCSS.scale;emex.parentNode.removeChild(emex);this.idPostfix="-zoom";jax.root.toHTML(span,span);this.idPostfix="";var width=jax.root.HTMLspanElement().bbox.width;if(width){span.style.width=Math.floor(Mw-1.5*HTMLCSS.em)+"px";span.style.display="inline-block";var id=(jax.root.id||"MathJax-Span-"+jax.root.spanID
)+"-zoom";var child=document.getElementById(id).firstChild;while(child&&child.style.width!==width){child=child.nextSibling}if(child){child.style.width="100%"}}span.style.position="absolute";if(!width){math.style.position="absolute"}var zW=span.offsetWidth,zH=span.offsetHeight,mH=math.offsetHeight,mW=math.offsetWidth;if(mW===0){mW=math.parentNode.offsetWidth};span.style.position=math.style.position="";return{Y:-EVENT.getBBox(span).h,mW:mW,mH:mH,zW:zW,zH:zH};},initImg:function(span){},initHTML:function(math,span){},initFont:function(name){var FONTS=HTMLCSS.FONTDATA.FONTS,AVAIL=HTMLCSS.config.availableFonts;if(AVAIL&&AVAIL.length&&HTMLCSS.Font.testFont(FONTS[name])){FONTS[name].available=true;return null}if(!this.allowWebFonts){return null}FONTS[name].isWebFont=true;if(HTMLCSS.FontFaceBug){FONTS[name].family=name;if(HTMLCSS.msieFontCSSBug){FONTS[name].family+="-Web"}}return AJAX.Styles({"@font-face":this.Font.fontFace(name)});},Remove:function(jax){var span=document.getElementById(jax.
inputID+"-Frame");if(span){if(jax.HTMLCSS.display){span=span.parentNode}span.parentNode.removeChild(span);}delete jax.HTMLCSS;},getHD:function(span){var position=span.style.position;span.style.position="absolute";this.HDimg.style.height="0px";span.appendChild(this.HDspan);var HD={h:span.offsetHeight};this.HDimg.style.height=HD.h+"px";HD.d=span.offsetHeight-HD.h;HD.h-=HD.d;HD.h/=this.em;HD.d/=this.em;span.removeChild(this.HDspan);span.style.position=position;return HD;},getW:function(span){var W,H,w=(span.bbox||{}).w,start=span;if(span.bbox&&span.bbox.exactW){return w}if((span.bbox&&w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!span.firstChild){W=span.offsetWidth;H=span.parentNode.offsetHeight;}else if(span.bbox&&w<0&&this.msieNegativeBBoxBug){W=-span.offsetWidth,H=span.parentNode.offsetHeight;}else{if(this.initialSkipBug){var position=span.style.position;span.style.position="absolute";start=this.startMarker;span.insertBefore(start,span.firstChild)}span.appendChild(this.endMarker);
W=this.endMarker.offsetLeft-start.offsetLeft;span.removeChild(this.endMarker);if(this.initialSkipBug){span.removeChild(start);span.style.position=position}}if(H!=null){span.parentNode.HH=H/this.em}return W/this.em;},Measured:function(span,parent){var bbox=span.bbox;if(bbox.width==null&&bbox.w&&!bbox.isMultiline){var w=this.getW(span);bbox.rw+=w-bbox.w;bbox.w=w;bbox.exactW=true;}if(!parent){parent=span.parentNode}if(!parent.bbox){parent.bbox=bbox}return span;},Remeasured:function(span,parent){parent.bbox=this.Measured(span,parent).bbox;},MeasureSpans:function(SPANS){var spans=[],span,i,m,bbox,start,end,W,parent;for(i=0,m=SPANS.length;i<m;i++){span=SPANS[i];if(!span)continue;bbox=span.bbox;parent=this.parentNode(span);if(bbox.exactW||bbox.width||bbox.w===0||bbox.isMultiline){if(!parent.bbox){parent.bbox=bbox}continue;}if(this.negativeBBoxes||!span.firstChild||(bbox.w>=0&&!this.initialSkipBug)||(bbox.w<0&&this.msieNegativeBBoxBug)){spans.push([span]);}else if(this.initialSkipBug){start=
this.startMarker.cloneNode(true);end=this.endMarker.cloneNode(true);span.insertBefore(start,span.firstChild);span.appendChild(end);spans.push([span,start,end,span.style.position]);span.style.position="absolute";}else{end=this.endMarker.cloneNode(true);span.appendChild(end);spans.push([span,null,end]);}}for(i=0,m=spans.length;i<m;i++){span=spans[i][0];bbox=span.bbox;parent=this.parentNode(span);if((bbox.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!span.firstChild){W=span.offsetWidth;parent.HH=parent.offsetHeight/this.em;}else if(bbox.w<0&&this.msieNegativeBBoxBug){W=-span.offsetWidth,parent.HH=parent.offsetHeight/this.em;}else{W=spans[i][2].offsetLeft-((spans[i][1]||{}).offsetLeft||0);}W/=this.em;bbox.rw+=W-bbox.w;bbox.w=W;bbox.exactW=true;if(!parent.bbox){parent.bbox=bbox}}for(i=0,m=spans.length;i<m;i++){span=spans[i];if(span[1]){span[1].parentNode.removeChild(span[1]),span[0].style.position=span[3]}if(span[2]){span[2].parentNode.removeChild(span[2])}}},Em:function(m){if(Math.abs
(m)<.0006){return"0em"}return m.toFixed(3).replace(/\.?0+$/,"")+"em";},EmRounded:function(m){m=(Math.round(m*HTMLCSS.em)+.05)/HTMLCSS.em;if(Math.abs(m)<.0006){return"0em"}return m.toFixed(3).replace(/\.?0+$/,"")+"em";},unEm:function(m){return parseFloat(m);},Px:function(m){m*=this.em;var s=(m<0?"-":"");return s+Math.abs(m).toFixed(1).replace(/\.?0+$/,"")+"px";},unPx:function(m){return parseFloat(m)/this.em;},Percent:function(m){return(100*m).toFixed(1).replace(/\.?0+$/,"")+"%";},length2em:function(length,mu,size){if(typeof(length)!=="string"){length=length.toString()}if(length===""){return""}if(length===MML.SIZE.NORMAL){return 1}if(length===MML.SIZE.BIG){return 2}if(length===MML.SIZE.SMALL){return.71}if(length==="infinity"){return HTMLCSS.BIGDIMEN}var factor=this.FONTDATA.TeX_factor;if(length.match(/mathspace$/)){return HTMLCSS.MATHSPACE[length]*factor}var match=length.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var m=parseFloat(match[1]||"1"),unit=match
[2];if(size==null){size=1};if(mu==null){mu=1}if(unit==="em"){return m*factor}if(unit==="ex"){return m*HTMLCSS.TeX.x_height*factor}if(unit==="%"){return m/100*size}if(unit==="px"){return m/HTMLCSS.em}if(unit==="pt"){return m/10*factor}if(unit==="pc"){return m*1.2*factor}if(unit==="in"){return m*this.pxPerInch/HTMLCSS.em}if(unit==="cm"){return m*this.pxPerInch/HTMLCSS.em/2.54}if(unit==="mm"){return m*this.pxPerInch/HTMLCSS.em/25.4}if(unit==="mu"){return m/18*factor*mu}return m*factor*size;},thickness2em:function(length,mu){var thick=HTMLCSS.TeX.rule_thickness;if(length===MML.LINETHICKNESS.MEDIUM){return thick}if(length===MML.LINETHICKNESS.THIN){return.67*thick}if(length===MML.LINETHICKNESS.THICK){return 1.67*thick}return this.length2em(length,mu,thick);},getPadding:function(span){var padding={top:0,right:0,bottom:0,left:0},has=false;for(var id in padding){if(padding.hasOwnProperty(id)){var pad=span.style["padding"+id.charAt(0).toUpperCase()+id.substr(1)];if(pad){padding[id]=this.
length2em(pad);has=true;}}}return(has?padding:false);},getBorders:function(span){var border={top:0,right:0,bottom:0,left:0},css={},has=false;for(var id in border){if(border.hasOwnProperty(id)){var ID="border"+id.charAt(0).toUpperCase()+id.substr(1);var style=span.style[ID+"Style"];if(style){has=true;border[id]=this.length2em(span.style[ID+"Width"]);css[ID]=[span.style[ID+"Width"],span.style[ID+"Style"],span.style[ID+"Color"]].join(" ");}}}border.css=css;return(has?border:false);},setBorders:function(span,borders){if(borders){for(var id in borders.css){if(borders.css.hasOwnProperty(id)){span.style[id]=borders.css[id];}}}},createStrut:function(span,h,before){var strut=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:h+"px",width:"1px",marginRight:"-1px"}});if(before){span.insertBefore(strut,span.firstChild)}else{span.appendChild(strut)}return strut;},createBlank:function(span,w,before){var blank=this.Element("span",{isMathJax:true,style:{display:
"inline-block",overflow:"hidden",height:"1px",width:this.Em(w)}});if(before){span.insertBefore(blank,span.firstChild)}else{span.appendChild(blank)}return blank;},createShift:function(span,w,before){var space=this.Element("span",{style:{marginLeft:this.Em(w)},isMathJax:true});if(before){span.insertBefore(space,span.firstChild)}else{span.appendChild(space)}return space;},createSpace:function(span,h,d,w,color,isSpace){if(h<-d){d=-h}var H=this.Em(h+d),D=this.Em(-d);if(this.msieInlineBlockAlignBug){D=this.Em(HTMLCSS.getHD(span.parentNode).d-d)}if(span.isBox||isSpace){var scale=(span.scale==null?1:span.scale);span.bbox={exactW:true,h:h*scale,d:d*scale,w:w*scale,rw:w*scale,lw:0};span.style.height=H;span.style.verticalAlign=D;span.HH=(h+d)*scale;}else{span=this.addElement(span,"span",{style:{height:H,verticalAlign:D},isMathJax:true});}if(w>=0){span.style.width=this.Em(w);span.style.display="inline-block";span.style.overflow="hidden";}else{if(this.msieNegativeSpaceBug){span.style.height=""}span
.style.marginLeft=this.Em(w);if(HTMLCSS.safariNegativeSpaceBug&&span.parentNode.firstChild==span){this.createBlank(span,0,true)}}if(color&&color!==MML.COLOR.TRANSPARENT){span.style.backgroundColor=color;span.style.position="relative";}return span;},createRule:function(span,h,d,w,color){if(h<-d){d=-h}var min=HTMLCSS.TeX.min_rule_thickness,f=1;if(w>0&&w*this.em<min){w=min/this.em}if(h+d>0&&(h+d)*this.em<min){f=1/(h+d)*(min/this.em);h*=f;d*=f}if(!color){color="solid"}else{color="solid "+color}color=this.Em(w)+" "+color;var H=(f===1?this.Em(h+d):min+"px"),D=this.Em(-d);var rule=this.addElement(span,"span",{style:{borderLeft:color,display:"inline-block",overflow:"hidden",width:0,height:H,verticalAlign:D},bbox:{h:h,d:d,w:w,rw:w,lw:0,exactW:true},noAdjust:true,HH:h+d,isMathJax:true});if(w>0&&rule.offsetWidth==0){rule.style.width=this.Em(w)}if(span.isBox||span.className=="mspace"){span.bbox=rule.bbox,span.HH=h+d}return rule;},createFrame:function(span,h,d,w,t,style){if(h<-d){d=-h}var T=2*t;if(
this.msieFrameSizeBug){if(w<T){w=T};if(h+d<T){h=T-d}}if(this.msieBorderWidthBug){T=0}var H=this.Em(h+d-T),D=this.Em(-d-t),W=this.Em(w-T);var B=this.Em(t)+" "+style;var frame=this.addElement(span,"span",{style:{border:B,display:"inline-block",overflow:"hidden",width:W,height:H},bbox:{h:h,d:d,w:w,rw:w,lw:0,exactW:true},noAdjust:true,HH:h+d,isMathJax:true});if(D){frame.style.verticalAlign=D}return frame;},parentNode:function(span){var parent=span.parentNode;if(parent.nodeName.toLowerCase()==="a"){parent=parent.parentNode}return parent;},createStack:function(span,nobbox,w){if(this.msiePaddingWidthBug){this.createStrut(span,0)}var relativeW=String(w).match(/%$/);var W=(!relativeW&&w!=null?w:0);span=this.addElement(span,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(relativeW?"100%":this.Em(W)),height:0}});if(!nobbox){span.parentNode.bbox=span.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:W,lw:this.BIGDIMEN,rw:(!relativeW&&w!=null?w
:-this.BIGDIMEN)};if(relativeW){span.bbox.width=w}}return span;},createBox:function(span,w){var box=this.addElement(span,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(w!=null){box.style.width=w}return box;},addBox:function(span,box){box.style.position="absolute";box.isBox=box.isMathJax=true;return span.appendChild(box);},placeBox:function(span,x,y,noclip){span.isMathJax=true;var parent=HTMLCSS.parentNode(span),bbox=span.bbox,BBOX=parent.bbox;if(this.msiePlaceBoxBug){this.addText(span,this.NBSP)}if(this.imgSpaceBug){this.addText(span,this.imgSpace)}var HH,dx=0;if(span.HH!=null){HH=span.HH}else if(bbox){HH=Math.max(3,bbox.h+bbox.d)}else{HH=span.offsetHeight/this.em}if(!span.noAdjust){HH+=1;HH=Math.round(HH*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(span,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(HH)}});}else{this.addElement(span,"span",{isMathJax:true,style:{display:"inline-block",
width:0,height:this.Em(HH)}});if(HTMLCSS.chromeHeightBug){HH-=(span.lastChild.offsetHeight-Math.round(HH*this.em))/this.em}}}if(bbox){if(this.initialSkipBug){if(bbox.lw<0){dx=bbox.lw;HTMLCSS.createBlank(span,-dx,true)}if(bbox.rw>bbox.w){HTMLCSS.createBlank(span,bbox.rw-bbox.w+.1)}}if(!this.msieClipRectBug&&!bbox.noclip&&!noclip){var dd=3/this.em;var H=(bbox.H==null?bbox.h:bbox.H),D=(bbox.D==null?bbox.d:bbox.D);var t=HH-H-dd,b=HH+D+dd,l=bbox.lw-3*dd,r=1000;if(this.initialSkipBug&&bbox.lw<0){l=-3*dd}if(bbox.isFixed){r=bbox.width-l}span.style.clip="rect("+this.Em(t)+" "+this.Em(r)+" "+this.Em(b)+" "+this.Em(l)+")";}}span.style.top=this.Em(-y-HH);span.style.left=this.Em(x+dx);if(bbox&&BBOX){if(bbox.H!=null&&(BBOX.H==null||bbox.H+y>BBOX.H)){BBOX.H=bbox.H+y}if(bbox.D!=null&&(BBOX.D==null||bbox.D-y>BBOX.D)){BBOX.D=bbox.D-y}if(bbox.h+y>BBOX.h){BBOX.h=bbox.h+y}if(bbox.d-y>BBOX.d){BBOX.d=bbox.d-y}if(BBOX.H!=null&&BBOX.H<=BBOX.h){delete BBOX.H}if(BBOX.D!=null&&BBOX.D<=BBOX.d){delete BBOX.D}if(
bbox.w+x>BBOX.w){BBOX.w=bbox.w+x;if(BBOX.width==null){parent.style.width=this.Em(BBOX.w)}}if(bbox.rw+x>BBOX.rw){BBOX.rw=bbox.rw+x}if(bbox.lw+x<BBOX.lw){BBOX.lw=bbox.lw+x}if(bbox.width!=null&&!bbox.isFixed){if(BBOX.width==null){parent.style.width=BBOX.width="100%";if(bbox.minWidth){parent.style.minWidth=BBOX.minWidth=bbox.minWidth}}span.style.width=bbox.width;}}},alignBox:function(span,align,y){this.placeBox(span,0,y);var bbox=span.bbox;if(bbox.isMultiline)return;var isRelative=bbox.width!=null&&!bbox.isFixed;var r=0,c=-bbox.w/2,l="50%";if(this.initialSkipBug){r=bbox.w-bbox.rw-.1;c+=bbox.lw}if(this.msieMarginScaleBug){c=(c*this.em)+"px"}else{c=this.Em(c)}if(isRelative){c="";l=(50-parseFloat(bbox.width)/2)+"%"}HUB.Insert(span.style,({right:{left:"",right:this.Em(r)},center:{left:l,marginLeft:c}})[align]);},setStackWidth:function(span,w){if(typeof(w)==="number"){span.style.width=this.Em(Math.max(0,w));var bbox=span.bbox;if(bbox){bbox.w=w;bbox.exactW=true};bbox=span.parentNode.bbox;if(bbox
){bbox.w=w;bbox.exactW=true};}else{span.style.width=span.parentNode.style.width="100%";if(span.bbox){span.bbox.width=w}if(span.parentNode.bbox){span.parentNode.bbox.width=w}}},createDelimiter:function(span,code,HW,scale,font){if(!code){span.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};span.bbox.rw=span.bbox.w;this.createSpace(span,span.bbox.h,span.bbox.d,span.bbox.w);return;}if(!scale){scale=1};if(!(HW instanceof Array)){HW=[HW,HW]}var hw=HW[1];HW=HW[0];var delim={alias:code};while(delim.alias){code=delim.alias;delim=this.FONTDATA.DELIMITERS[code];if(!delim){delim={HW:[0,this.FONTDATA.VARIANT[MML.VARIANT.NORMAL]]}}}if(delim.load){HUB.RestartAfter(AJAX.Require(this.fontDir+"/fontdata-"+delim.load+".js"))}for(var i=0,m=delim.HW.length;i<m;i++){if(delim.HW[i][0]*scale>=HW-.01||(i==m-1&&!delim.stretch)){if(delim.HW[i][2]){scale*=delim.HW[i][2]}if(delim.HW[i][3]){code=delim.HW[i][3]}var chr=this.addElement(span,"span");this.createChar(chr,[code,delim.HW[i][1]],scale,font);span.bbox=chr
.bbox;span.offset=.65*span.bbox.w;span.scale=scale;return;}}if(delim.stretch){this["extendDelimiter"+delim.dir](span,hw,delim.stretch,scale,font)}},extendDelimiterV:function(span,H,delim,scale,font){var stack=this.createStack(span,true);var top=this.createBox(stack),bot=this.createBox(stack);this.createChar(top,(delim.top||delim.ext),scale,font);this.createChar(bot,(delim.bot||delim.ext),scale,font);var ext={bbox:{w:0,lw:0,rw:0}},mid=ext,EXT;var h=top.bbox.h+top.bbox.d+bot.bbox.h+bot.bbox.d;var y=-top.bbox.h;this.placeBox(top,0,y,true);y-=top.bbox.d;if(delim.mid){mid=this.createBox(stack);this.createChar(mid,delim.mid,scale,font);h+=mid.bbox.h+mid.bbox.d;}if(delim.min&&H<h*delim.min){H=h*delim.min}if(H>h){ext=this.Element("span");this.createChar(ext,delim.ext,scale,font);var eH=ext.bbox.h+ext.bbox.d,eh=eH-.05,n,N,k=(delim.mid?2:1);N=n=Math.min(Math.ceil((H-h)/(k*eh)),this.maxStretchyParts);if(!delim.fullExtenders){eh=(H-h)/(k*n)}var dy=(n/(n+1))*(eH-eh);eh=eH-dy;y+=dy+eh-ext.bbox.h;
while(k-->0){while(n-->0){if(!this.msieCloneNodeBug){EXT=ext.cloneNode(true)}else{EXT=this.Element("span");this.createChar(EXT,delim.ext,scale,font)}EXT.bbox=ext.bbox;y-=eh;this.placeBox(this.addBox(stack,EXT),0,y,true);}y+=dy-ext.bbox.d;if(delim.mid&&k){this.placeBox(mid,0,y-mid.bbox.h,true);n=N;y+=-(mid.bbox.h+mid.bbox.d)+dy+eh-ext.bbox.h;}}}else{y+=(h-H)/2;if(delim.mid){this.placeBox(mid,0,y-mid.bbox.h,true);y+=-(mid.bbox.h+mid.bbox.d)}y+=(h-H)/2;}this.placeBox(bot,0,y-bot.bbox.h,true);y-=bot.bbox.h+bot.bbox.d;span.bbox={w:Math.max(top.bbox.w,ext.bbox.w,bot.bbox.w,mid.bbox.w),lw:Math.min(top.bbox.lw,ext.bbox.lw,bot.bbox.lw,mid.bbox.lw),rw:Math.max(top.bbox.rw,ext.bbox.rw,bot.bbox.rw,mid.bbox.rw),h:0,d:-y,exactW:true}
span.scale=scale;span.offset=.55*span.bbox.w;span.isMultiChar=true;this.setStackWidth(stack,span.bbox.w);},extendDelimiterH:function(span,W,delim,scale,font){var stack=this.createStack(span,true);var left=this.createBox(stack),right=this.createBox(stack);this.createChar(left,(delim.left||delim.rep),scale,font);this.createChar(right,(delim.right||delim.rep),scale,font);var rep=this.Element("span");this.createChar(rep,delim.rep,scale,font);var mid={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},REP;this.placeBox(left,-left.bbox.lw,0,true);var w=(left.bbox.rw-left.bbox.lw)+(right.bbox.rw-right.bbox.lw)-.05,x=left.bbox.rw-left.bbox.lw-.025,dx;if(delim.mid){mid=this.createBox(stack);this.createChar(mid,delim.mid,scale,font);w+=mid.bbox.w;}if(delim.min&&W<w*delim.min){W=w*delim.min}if(W>w){var rW=rep.bbox.rw-rep.bbox.lw,rw=rW-.05,n,N,k=(delim.mid?2:1);N=n=Math.min(Math.ceil((W-w)/(k*rw)),this.maxStretchyParts);if(!delim.fillExtenders){rw=(W-w)/(k*n)}dx=(n/(n+1))*(rW-rw);rw=rW-dx;x-=rep.bbox.lw+dx
;while(k-->0){while(n-->0){if(!this.cloneNodeBug){REP=rep.cloneNode(true)}else{REP=this.Element("span");this.createChar(REP,delim.rep,scale,font)}REP.bbox=rep.bbox;this.placeBox(this.addBox(stack,REP),x,0,true);x+=rw;}if(delim.mid&&k){this.placeBox(mid,x,0,true);x+=mid.bbox.w-dx;n=N}}}else{x-=(w-W)/2;if(delim.mid){this.placeBox(mid,x,0,true);x+=mid.bbox.w};x-=(w-W)/2;}this.placeBox(right,x,0,true);span.bbox={w:x+right.bbox.rw,lw:0,rw:x+right.bbox.rw,H:Math.max(left.bbox.h,rep.bbox.h,right.bbox.h,mid.bbox.h),D:Math.max(left.bbox.d,rep.bbox.d,right.bbox.d,mid.bbox.d),h:rep.bbox.h,d:rep.bbox.d,exactW:true}
span.scale=scale;span.isMultiChar=true;this.setStackWidth(stack,span.bbox.w);},createChar:function(span,data,scale,font){span.isMathJax=true;var SPAN=span,text="",variant={fonts:[data[1]],noRemap:true};if(font&&font===MML.VARIANT.BOLD){variant.fonts=[data[1]+"-bold",data[1]]}if(typeof(data[1])!=="string"){variant=data[1]}if(data[0]instanceof Array){for(var i=0,m=data[0].length;i<m;i++){text+=String.fromCharCode(data[0][i])}}else{text=String.fromCharCode(data[0])}if(data[4]){scale*=data[4]}if(scale!==1||data[3]){SPAN=this.addElement(span,"span",{style:{fontSize:this.Percent(scale)},scale:scale,isMathJax:true});this.handleVariant(SPAN,variant,text);span.bbox=SPAN.bbox;}else{this.handleVariant(span,variant,text)}if(data[2]){span.style.marginLeft=this.Em(data[2])}if(data[3]){span.firstChild.style.verticalAlign=this.Em(data[3]);span.bbox.h+=data[3];if(span.bbox.h<0){span.bbox.h=0}}if(data[5]){span.bbox.h+=data[5]}if(data[6]){span.bbox.d+=data[6]}if(this.AccentBug&&span.bbox.w===0){SPAN.
firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(span,h){h-=span.bbox.h;span.bbox.d-=h;span.bbox.h+=h;if(h){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&span.isMultiChar)){if(span.firstChild.style.display===""&&span.style.top!==""){span=span.firstChild;h-=HTMLCSS.unEm(span.style.top)}span.style.position="relative";span.style.top=this.Em(-h);}else{span.style.verticalAlign=this.Em(h);if(HTMLCSS.ffVerticalAlignBug){HTMLCSS.createRule(span.parentNode,span.bbox.h,0,0)}}}},handleVariant:function(span,variant,text){var newtext="",n,c,font,VARIANT,SPAN=span,force=!!span.style.fontFamily;if(text.length===0)return;if(!span.bbox){span.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN};}if(!variant){variant=this.FONTDATA.VARIANT[MML.VARIANT.NORMAL]}VARIANT=variant;for(var i=0,m=text.length;i<m;i++){variant=VARIANT;n=text.charCodeAt(i);c=text.charAt(i);if(n>=0xD800&&n<0xDBFF){i++;n=(((n-0xD800)<<10)+(text.
charCodeAt(i)-0xDC00))+0x10000;if(this.FONTDATA.RemapPlane1){var nv=this.FONTDATA.RemapPlane1(n,variant);n=nv.n;variant=nv.variant;}}else{var id,M,RANGES=this.FONTDATA.RANGES;for(id=0,M=RANGES.length;id<M;id++){if(RANGES[id].name==="alpha"&&variant.noLowerCase)continue;var N=variant["offset"+RANGES[id].offset];if(N&&n>=RANGES[id].low&&n<=RANGES[id].high){if(RANGES[id].remap&&RANGES[id].remap[n]){n=N+RANGES[id].remap[n];}else{n=n-RANGES[id].low+N;if(RANGES[id].add){n+=RANGES[id].add}}if(variant["variant"+RANGES[id].offset]){variant=this.FONTDATA.VARIANT[variant["variant"+RANGES[id].offset]]}break;}}}if(variant.remap&&variant.remap[n]){if(variant.remap[n]instanceof Array){var remap=variant.remap[n];n=remap[0];variant=this.FONTDATA.VARIANT[remap[1]];}else if(typeof(variant.remap[n])==="string"){text=variant.remap[n]+text.substr(i+1);i=0;m=text.length;n=text.charCodeAt(0);}else{n=variant.remap[n];if(variant.remap.variant){variant=this.FONTDATA.VARIANT[variant.remap.variant]}}}if(this.
FONTDATA.REMAP[n]&&!variant.noRemap){n=this.FONTDATA.REMAP[n];if(n instanceof Array){variant=this.FONTDATA.VARIANT[n[1]];n=n[0]}if(typeof(n)==="string"){text=n+text.substr(i+1);i=0;m=text.length;n=n.charCodeAt(0);}}font=this.lookupChar(variant,n);c=font[n];if(force||(!this.checkFont(font,SPAN.style)&&!c[5].img)){if(newtext.length){this.addText(SPAN,newtext);newtext=""};var addSpan=!!SPAN.style.fontFamily||!!span.style.fontStyle||!!span.style.fontWeight||!font.directory||force;force=false;if(SPAN!==span){addSpan=!this.checkFont(font,span.style);SPAN=span}if(addSpan){SPAN=this.addElement(span,"span",{isMathJax:true,subSpan:true})}this.handleFont(SPAN,font,SPAN!==span);}newtext=this.handleChar(SPAN,font,c,n,newtext);if(!(c[5]||{}).space){if(c[0]/1000>span.bbox.h){span.bbox.h=c[0]/1000}if(c[1]/1000>span.bbox.d){span.bbox.d=c[1]/1000}}if(span.bbox.w+c[3]/1000<span.bbox.lw){span.bbox.lw=span.bbox.w+c[3]/1000}if(span.bbox.w+c[4]/1000>span.bbox.rw){span.bbox.rw=span.bbox.w+c[4]/1000}span.bbox.
w+=c[2]/1000;}if(newtext.length){this.addText(SPAN,newtext)}if(span.scale&&span.scale!==1){span.bbox.h*=span.scale;span.bbox.d*=span.scale;span.bbox.w*=span.scale;span.bbox.lw*=span.scale;span.bbox.rw*=span.scale;}if(text.length==1&&font.skew&&font.skew[n]){span.bbox.skew=font.skew[n]}},checkFont:function(font,style){var weight=(style.fontWeight||"normal");if(weight.match(/^\d+$/)){weight=(parseInt(weight)>=600?"bold":"normal")}return(font.family.replace(/'/g,"")===style.fontFamily.replace(/'/g,"")&&(font.style||"normal")===(style.fontStyle||"normal")&&(font.weight||"normal")===weight);},handleFont:function(span,font,force){span.style.fontFamily=font.family;if(!font.directory){span.style.fontSize=Math.floor(100/HTMLCSS.scale+.5)+"%"}if(!(HTMLCSS.FontFaceBug&&font.isWebFont)){var style=font.style||"normal",weight=font.weight||"normal";if(style!=="normal"||force){span.style.fontStyle=style}if(weight!=="normal"||force){span.style.fontWeight=weight}}},handleChar:function(span,font,c,n,text
){var C=c[5];if(C.space){if(text.length){this.addText(span,text)}HTMLCSS.createShift(span,c[2]/1000);return"";}if(C.img){return this.handleImg(span,font,c,n,text)}if(C.isUnknown&&this.FONTDATA.DELIMITERS[n]){if(text.length){this.addText(span,text)}var scale=span.scale;HTMLCSS.createDelimiter(span,n,0,1,font);if(this.FONTDATA.DELIMITERS[n].dir==="V"){span.style.verticalAlign=this.Em(span.bbox.d);span.bbox.h+=span.bbox.d;span.bbox.d=0;}span.scale=scale;c[0]=span.bbox.h*1000;c[1]=span.bbox.d*1000;c[2]=span.bbox.w*1000;c[3]=span.bbox.lw*1000;c[4]=span.bbox.rw*1000;return"";}if(C.c==null){if(n<=0xFFFF){C.c=String.fromCharCode(n)}else{var N=n-0x10000;C.c=String.fromCharCode((N>>10)+0xD800)+String.fromCharCode((N&0x3FF)+0xDC00);}}if(C.rfix){this.addText(span,text+C.c);HTMLCSS.createShift(span,C.rfix/1000);return""}if(c[2]||!this.msieAccentBug||text.length){return text+C.c}HTMLCSS.createShift(span,c[3]/1000);HTMLCSS.createShift(span,(c[4]-c[3])/1000);this.addText(span,C.c);HTMLCSS.createShift(
span,-c[4]/1000);return"";},handleImg:function(span,font,c,n,text){return text},lookupChar:function(variant,n){var i,m;if(!variant.FONTS){var FONTS=this.FONTDATA.FONTS;var fonts=(variant.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(fonts instanceof Array)){fonts=[fonts]}if(variant.fonts!=fonts){variant.fonts=fonts}variant.FONTS=[];for(i=0,m=fonts.length;i<m;i++){if(FONTS[fonts[i]]){variant.FONTS.push(FONTS[fonts[i]]);FONTS[fonts[i]].name=fonts[i];}}}for(i=0,m=variant.FONTS.length;i<m;i++){var font=variant.FONTS[i];if(typeof(font)==="string"){delete variant.FONTS;this.loadFont(font);}if(font[n]){if(font[n].length===5){font[n][5]={}}if(HTMLCSS.allowWebFonts&&!font.available){this.loadWebFont(font)}else{return font}}else{this.findBlock(font,n)}}return this.unknownChar(variant,n);},unknownChar:function(variant,n){var unknown=(variant.defaultFont||{family:HTMLCSS.config.undefinedFamily});if(variant.bold){unknown.weight="bold"};if(variant.italic){unknown.style="italic"}if(!unknown[n]){
unknown[n]=[800,200,500,0,500,{isUnknown:true}]}HUB.signal.Post(["HTML-CSS Jax - unknown char",n,variant]);return unknown;},findBlock:function(font,c){if(font.Ranges){for(var i=0,m=font.Ranges.length;i<m;i++){if(c<font.Ranges[i][0])return;if(c<=font.Ranges[i][1]){var file=font.Ranges[i][2];for(var j=font.Ranges.length-1;j>=0;j--){if(font.Ranges[j][2]==file){font.Ranges.splice(j,1)}}this.loadFont(font.directory+"/"+file+".js");}}}},loadFont:function(file){var queue=MathJax.Callback.Queue();queue.Push(["Require",AJAX,this.fontDir+"/"+file]);if(this.imgFonts){if(!MathJax.isPacked){file=file.replace(/\/([^\/]*)$/,HTMLCSS.imgPacked+"/$1")}queue.Push(["Require",AJAX,this.webfontDir+"/png/"+file]);}HUB.RestartAfter(queue.Push({}));},loadWebFont:function(font){font.available=font.isWebFont=true;if(HTMLCSS.FontFaceBug){font.family=font.name;if(HTMLCSS.msieFontCSSBug){font.family+="-Web"}}HUB.RestartAfter(this.Font.loadWebFont(font));},loadWebFontError:function(font,done){HUB.Startup.signal.Post
("HTML-CSS Jax - disable web fonts");font.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;HUB.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");HUB.Startup.signal.Post("HTML-CSS Jax - using image fonts");MESSAGE(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);AJAX.Require(this.directory+"/imageFonts.js",done);}else{this.allowWebFonts=false;done();}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,
negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:.430554,quad:1,num1:.676508,num2:.393732,num3:.44373,denom1:.685951,denom2:.344841,sup1:.412892,sup2:.362892,sup3:.288888,sub1:.15,sub2:.247217,sup_drop:.386108,sub_drop:.05,delim1:2.39,delim2:1.0,axis_height:.25,rule_thickness:.06,big_op_spacing1:.111111,big_op_spacing2:.166666,big_op_spacing3:.2,big_op_spacing4:.6,big_op_spacing5:.1,scriptspace:.1,nulldelimiterspace:.12,delimiterfactor:901,delimitershortfall:.1,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){MML=MathJax.ElementJax.mml;MML.mbase.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);if(this.type!="mrow"){span=this.HTMLhandleSize(span)}for(var i=0,m=this.data.length;i<m;i++){if(this.data[i]){this.data[i].toHTML(span)}}var stretchy=this.HTMLcomputeBBox(span);var h=span.bbox.h,d=span.bbox.d;for(i=0,m=stretchy.length;i<m;i++){stretchy[i].
HTMLstretchV(span,h,d)}if(stretchy.length){this.HTMLcomputeBBox(span,true)}if(this.HTMLlineBreaks(span)){span=this.HTMLmultiline(span)}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLlineBreaks:function(){return false},HTMLmultiline:function(){MML.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(span,full,i,m){if(i==null){i=0};if(m==null){m=this.data.length}var BBOX=span.bbox={exactW:true},stretchy=[];while(i<m){var core=this.data[i];if(!core)continue;if(!full&&core.HTMLcanStretch("Vertical")){stretchy.push(core);core=(core.CoreMO()||core)}this.HTMLcombineBBoxes(core,BBOX);i++;}this.HTMLcleanBBox(BBOX);return stretchy;},HTMLcombineBBoxes:function(core,BBOX){if(BBOX.w==null){this.HTMLemptyBBox(BBOX)}var child=(core.bbox?core:core.HTMLspanElement());if(!child||!child.bbox)return;var bbox=child.bbox;if(bbox.d>BBOX.d){BBOX.d=bbox.d}if(bbox.h>BBOX.h){BBOX.h=bbox.h}if(bbox.D!=null&&bbox.D>BBOX.D){BBOX.D=bbox.D}if(bbox.H!=null&&bbox.H>BBOX.H){BBOX.H=bbox.H
}if(child.style.paddingLeft){BBOX.w+=HTMLCSS.unEm(child.style.paddingLeft)*(child.scale||1)}if(BBOX.w+bbox.lw<BBOX.lw){BBOX.lw=BBOX.w+bbox.lw}if(BBOX.w+bbox.rw>BBOX.rw){BBOX.rw=BBOX.w+bbox.rw}BBOX.w+=bbox.w;if(child.style.paddingRight){BBOX.w+=HTMLCSS.unEm(child.style.paddingRight)*(child.scale||1)}if(bbox.width){BBOX.width=bbox.width;BBOX.minWidth=bbox.minWidth}if(bbox.ic){BBOX.ic=bbox.ic}else{delete BBOX.ic}if(BBOX.exactW&&!bbox.exactW){delete BBOX.exactW}},HTMLemptyBBox:function(BBOX){BBOX.h=BBOX.d=BBOX.H=BBOX.D=BBOX.rw=-HTMLCSS.BIGDIMEN;BBOX.w=0;BBOX.lw=HTMLCSS.BIGDIMEN;return BBOX;},HTMLcleanBBox:function(BBOX){if(BBOX.h===this.BIGDIMEN){BBOX.h=BBOX.d=BBOX.H=BBOX.D=BBOX.w=BBOX.rw=BBOX.lw=0}if(BBOX.D<=BBOX.d){delete BBOX.D};if(BBOX.H<=BBOX.h){delete BBOX.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(direction){if(this.isEmbellished()){var core=this.Core();if(core&&core!==this){return core.HTMLcanStretch(direction)}}return false;},HTMLstretchH:
function(box,W){return this.HTMLspanElement()},HTMLstretchV:function(box,h,d){return this.HTMLspanElement()},HTMLnotEmpty:function(data){while(data){if((data.type!=="mrow"&&data.type!=="texatom")||data.data.length>1){return true}data=data.data[0];}return false;},HTMLmeasureChild:function(n,box){if(this.data[n]){HTMLCSS.Measured(this.data[n].toHTML(box),box)}else{box.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(n,box){if(!this.data[n]){this.SetData(n,MML.mrow())}return this.data[n].toHTML(box);},HTMLcreateSpan:function(span){if(this.spanID){var SPAN=this.HTMLspanElement();if(SPAN&&(SPAN.parentNode===span||(SPAN.parentNode||{}).parentNode===span)){while(SPAN.firstChild){SPAN.removeChild(SPAN.firstChild)}SPAN.bbox=this.HTMLzeroBBox();SPAN.scale=1;SPAN.isMultChar=SPAN.HH=null;SPAN.style.cssText="";return SPAN;}}if(this.href){span=HTMLCSS.addElement(span,"a",{href:this.href,isMathJax:true})}span=HTMLCSS.addElement(span,"span",{className:this.type,isMathJax:true});if(HTMLCSS.imgHeightBug
){span.style.display="inline-block"}if(this["class"]){span.className+=" "+this["class"]}if(!this.spanID){this.spanID=HTMLCSS.GetID()}span.id=(this.id||"MathJax-Span-"+this.spanID)+HTMLCSS.idPostfix;span.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){span.style.cssText=this.style;if(span.style.fontSize){this.mathsize=span.style.fontSize;span.style.fontSize=""}this.styles={border:HTMLCSS.getBorders(span),padding:HTMLCSS.getPadding(span)}
if(this.styles.border){span.style.border=""}if(this.styles.padding){span.style.padding=""}}if(this.href){span.parentNode.bbox=span.bbox}return span;},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+HTMLCSS.idPostfix);},HTMLhandleVariant:function(span,variant,text){HTMLCSS.handleVariant(span,variant,text)},HTMLhandleSize:function(span){if(!span.scale){span.scale=this.HTMLgetScale();if(span.scale!==1){span.style.fontSize=HTMLCSS.Percent(span.scale)}}return span;},HTMLhandleDir:function(span){var dir=this.Get("dir",true);if(dir){span.dir=dir}return span;},HTMLhandleColor:function(span){var values=this.getValues("mathcolor","color");if(this.mathbackground){values.mathbackground=this.mathbackground}if(this.background){values.background=this.background}if(this.style&&span.style.backgroundColor){values.mathbackground=span.style.backgroundColor;span.style.backgroundColor="transparent";}var borders=(this.styles||{}).
border,padding=(this.styles||{}).padding;if(values.color&&!this.mathcolor){values.mathcolor=values.color}if(values.background&&!this.mathbackground){values.mathbackground=values.background}if(values.mathcolor){span.style.color=values.mathcolor}if((values.mathbackground&&values.mathbackground!==MML.COLOR.TRANSPARENT)||borders||padding){var bbox=span.bbox,dd=(bbox.exact?0:1/HTMLCSS.em),lW=0,rW=0,lpad=span.style.paddingLeft,rpad=span.style.paddingRight;if(this.isToken){lW=bbox.lw;rW=bbox.rw-bbox.w}if(lpad!==""){lW+=HTMLCSS.unEm(lpad)*(span.scale||1)}if(rpad!==""){rW-=HTMLCSS.unEm(rpad)*(span.scale||1)}var dw=(HTMLCSS.PaddingWidthBug||bbox.keepPadding||bbox.exactW?0:rW-lW);var W=Math.max(0,HTMLCSS.getW(span)+dw);var H=bbox.h+bbox.d,D=-bbox.d,lp=0,rp=0;if(W>0){W+=2*dd;lW-=dd};if(H>0){H+=2*dd;D-=dd};rW=-W-lW;if(borders){rW-=borders.right;D-=borders.bottom;lp+=borders.left;rp+=borders.right;bbox.h+=borders.top;bbox.d+=borders.bottom;bbox.w+=borders.left+borders.right;bbox.lw-=borders.left;
bbox.rw+=borders.right;}if(padding){H+=padding.top+padding.bottom;W+=padding.left+padding.right;rW-=padding.right;D-=padding.bottom;lp+=padding.left;rp+=padding.right;bbox.h+=padding.top;bbox.d+=padding.bottom;bbox.w+=padding.left+padding.right;bbox.lw-=padding.left;bbox.rw+=padding.right;}if(rp){span.style.paddingRight=HTMLCSS.Em(rp)}var frame=HTMLCSS.Element("span",{id:"MathJax-Color-"+this.spanID+HTMLCSS.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:values.mathbackground,width:HTMLCSS.Em(W),height:HTMLCSS.Em(H),verticalAlign:HTMLCSS.Em(D),marginLeft:HTMLCSS.Em(lW),marginRight:HTMLCSS.Em(rW)}});HTMLCSS.setBorders(frame,borders);if(bbox.width){frame.style.width=bbox.width;frame.style.marginRight="-"+bbox.width}if(HTMLCSS.msieInlineBlockAlignBug){frame.style.position="relative";frame.style.width=frame.style.height=0;frame.style.verticalAlign=frame.style.marginLeft=frame.style.marginRight="";frame.style.border=frame.style.padding="";if(borders&&HTMLCSS.
msieBorderWidthBug){H+=borders.top+borders.bottom;W+=borders.left+borders.right}frame.style.width=HTMLCSS.Em(lp+dd);HTMLCSS.placeBox(HTMLCSS.addElement(frame,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(values.mathbackground||"transparent"),width:HTMLCSS.Em(W),height:HTMLCSS.Em(H)}}),lW,bbox.h+dd);HTMLCSS.setBorders(frame.firstChild,borders);}span.parentNode.insertBefore(frame,span);if(HTMLCSS.msieColorPositionBug){span.style.position="relative"}return frame;}return null;},HTMLremoveColor:function(){var color=document.getElementById("MathJax-Color-"+this.spanID+HTMLCSS.idPostfix);if(color){color.parentNode.removeChild(color)}},HTMLhandleSpace:function(span){if(this.useMMLspacing){if(this.type!=="mo")return;var values=this.getValues("scriptlevel","lspace","rspace");if(values.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var mu=this.HTMLgetMu(span);values.lspace=Math.max(0,HTMLCSS.length2em(values
.lspace,mu));values.rspace=Math.max(0,HTMLCSS.length2em(values.rspace,mu));var core=this,parent=this.Parent();while(parent&&parent.isEmbellished()&&parent.Core()===core){core=parent;parent=parent.Parent();span=core.HTMLspanElement()}if(values.lspace){span.style.paddingLeft=HTMLCSS.Em(values.lspace)}if(values.rspace){span.style.paddingRight=HTMLCSS.Em(values.rspace)}}}else{var space=this.texSpacing();if(space!==""){space=HTMLCSS.length2em(space,this.HTMLgetScale())/(span.scale||1);if(span.style.paddingLeft){space+=HTMLCSS.unEm(span.style.paddingLeft)}span.style.paddingLeft=HTMLCSS.Em(space);}}},HTMLgetScale:function(){var scale=1,values=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var span=this.HTMLspanElement();if(span.style.fontSize!=""){values.fontsize=span.style.fontSize}}if(values.fontsize&&!this.mathsize){values.mathsize=values.fontsize}if(values.scriptlevel!==0){if(values.scriptlevel>2){values.scriptlevel=2}scale=Math.pow(this.Get("scriptsizemultiplier"),
values.scriptlevel);values.scriptminsize=HTMLCSS.length2em(this.Get("scriptminsize"));if(scale<values.scriptminsize){scale=values.scriptminsize}}if(this.isToken){scale*=HTMLCSS.length2em(values.mathsize)}return scale;},HTMLgetMu:function(span){var mu=1,values=this.getValues("scriptlevel","scriptsizemultiplier");if(span.scale&&span.scale!==1){mu=1/span.scale}if(values.scriptlevel!==0){if(values.scriptlevel>2){values.scriptlevel=2}mu=Math.sqrt(Math.pow(values.scriptsizemultiplier,values.scriptlevel));}return mu;},HTMLgetVariant:function(){var values=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");values.hasVariant=this.Get("mathvariant",true);if(!values.hasVariant){values.family=values.fontfamily;values.weight=values.fontweight;values.style=values.fontstyle;}if(this.style){var span=this.HTMLspanElement();if(!values.family&&span.style.fontFamily){values.family=span.style.fontFamily}if(!values.weight&&span.style.fontWeight){values.weight=span.style.fontWeight}if(!values
.style&&span.style.fontStyle){values.style=span.style.fontStyle}}if(values.weight&&values.weight.match(/^\d+$/)){values.weight=(parseInt(values.weight)>600?"bold":"normal")}var variant=values.mathvariant;if(this.variantForm){variant="-"+HTMLCSS.fontInUse+"-variant"}if(values.family&&!values.hasVariant){if(!values.weight&&values.mathvariant.match(/bold/)){values.weight="bold"}if(!values.style&&values.mathvariant.match(/italic/)){values.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:values.family,style:values.style,weight:values.weight}};}if(values.weight==="bold"){variant={normal:MML.VARIANT.BOLD,italic:MML.VARIANT.BOLDITALIC,fraktur:MML.VARIANT.BOLDFRAKTUR,script:MML.VARIANT.BOLDSCRIPT,"sans-serif":MML.VARIANT.BOLDSANSSERIF,"sans-serif-italic":MML.VARIANT.SANSSERIFBOLDITALIC}[variant]||variant;}else if(values.weight==="normal"){variant={bold:MML.VARIANT.normal,"bold-italic":MML.VARIANT.ITALIC,"bold-fraktur":MML.VARIANT.FRAKTUR,"bold-script":MML.VARIANT.SCRIPT,
"bold-sans-serif":MML.VARIANT.SANSSERIF,"sans-serif-bold-italic":MML.VARIANT.SANSSERIFITALIC}[variant]||variant;}if(values.style==="italic"){variant={normal:MML.VARIANT.ITALIC,bold:MML.VARIANT.BOLDITALIC,"sans-serif":MML.VARIANT.SANSSERIFITALIC,"bold-sans-serif":MML.VARIANT.SANSSERIFBOLDITALIC}[variant]||variant;}else if(values.style==="normal"){variant={italic:MML.VARIANT.NORMAL,"bold-italic":MML.VARIANT.BOLD,"sans-serif-italic":MML.VARIANT.SANSSERIF,"sans-serif-bold-italic":MML.VARIANT.BOLDSANSSERIF}[variant]||variant;}if(!(variant in HTMLCSS.FONTDATA.VARIANT)){variant="normal";}return HTMLCSS.FONTDATA.VARIANT[variant];}},{HTMLautoload:function(){var file=HTMLCSS.autoloadDir+"/"+this.type+".js";HUB.RestartAfter(AJAX.Require(file));},HTMLautoloadFile:function(name){var file=HTMLCSS.autoloadDir+"/"+name+".js";HUB.RestartAfter(AJAX.Require(file));},HTMLstretchH:function(box,w){this.HTMLremoveColor();return this.toHTML(box,w);},HTMLstretchV:function(box,h,d){this.HTMLremoveColor();return this
.toHTML(box,h,d);}});MML.chars.Augment({toHTML:function(span,variant,remap,chars){var text=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(remap){text=remap(text,chars)}if(variant.fontInherit){var scale=Math.floor(100/HTMLCSS.scale+.5)+"%";HTMLCSS.addElement(span,"span",{style:{"font-size":scale}},[text]);if(variant.bold){span.lastChild.style.fontWeight="bold"}if(variant.italic){span.lastChild.style.fontStyle="italic"}var HD=HTMLCSS.getHD(span),W=HTMLCSS.getW(span);span.bbox={h:HD.h,d:HD.d,w:W,lw:0,rw:W,exactW:true};}else{this.HTMLhandleVariant(span,variant,text);}}});MML.entity.Augment({toHTML:function(span,variant,remap,chars){var text=this.toString().replace(/[\u2061-\u2064]/g,"");if(remap){text=remap(text,chars)}if(variant.fontInherit){var scale=Math.floor(100/HTMLCSS.scale+.5)+"%";HTMLCSS.addElement(span,"span",{style:{"font-size":scale}},[text]);if(variant.bold){span.lastChild.style.fontWeight="bold"}if(variant.italic){span.lastChild.style.fontStyle="italic"}var HD=HTMLCSS.
getHD(span),W=HTMLCSS.getW(span);span.bbox={h:HD.h,d:HD.d,w:W,lw:0,rw:W,exactW:true};}else{this.HTMLhandleVariant(span,variant,text);}}});MML.mi.Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));span.bbox=null;var variant=this.HTMLgetVariant();for(var i=0,m=this.data.length;i<m;i++){if(this.data[i]){this.data[i].toHTML(span,variant)}}if(!span.bbox){span.bbox=this.HTMLzeroBBox()}var text=this.data.join(""),bbox=span.bbox;if(bbox.skew&&text.length!==1){delete bbox.skew}if(bbox.rw>bbox.w&&text.length===1&&!variant.noIC){bbox.ic=bbox.rw-bbox.w;HTMLCSS.createBlank(span,bbox.ic);bbox.w=bbox.rw;}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);this.HTMLhandleDir(span);return span;}});MML.mn.Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));span.bbox=null;var variant=this.HTMLgetVariant();for(var i=0,m=this.data.length;i<m;i++){if(this.data[i]){this.data[i].toHTML(span,variant)}}if(!span.bbox){span.bbox=this.HTMLzeroBBox()}
if(this.data.join("").length!==1){delete span.bbox.skew}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);this.HTMLhandleDir(span);return span;}});MML.mo.Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));if(this.data.length==0){return span}else{span.bbox=null}var text=this.data.join("");var variant=this.HTMLgetVariant();var values=this.getValues("largeop","displaystyle");if(values.largeop){variant=HTMLCSS.FONTDATA.VARIANT[values.displaystyle?"-largeOp":"-smallOp"]}var parent=this.CoreParent(),isScript=(parent&&parent.isa(MML.msubsup)&&this!==parent.data[parent.base]),mapchars=(isScript?this.HTMLremapChars:null);if(text.length===1&&parent&&parent.isa(MML.munderover)&&this.CoreText(parent.data[parent.base]).length===1){var over=parent.data[parent.over],under=parent.data[parent.under];if(over&&this===over.CoreMO()&&parent.Get("accent")){mapchars=HTMLCSS.FONTDATA.REMAPACCENT}else if(under&&this===under.CoreMO()&&parent.Get("accentunder")){mapchars=
HTMLCSS.FONTDATA.REMAPACCENTUNDER}}if(isScript&&text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){variant=HTMLCSS.FONTDATA.VARIANT["-"+HTMLCSS.fontInUse+"-variant"]}for(var i=0,m=this.data.length;i<m;i++){if(this.data[i]){this.data[i].toHTML(span,variant,this.HTMLremap,mapchars)}}if(!span.bbox){span.bbox=this.HTMLzeroBBox()}if(text.length!==1){delete span.bbox.skew}if(HTMLCSS.AccentBug&&span.bbox.w===0&&text.length===1&&span.firstChild){span.firstChild.nodeValue+=HTMLCSS.NBSP;HTMLCSS.createSpace(span,0,0,-span.offsetWidth/HTMLCSS.em);}if(values.largeop){var p=(span.bbox.h-span.bbox.d)/2-HTMLCSS.TeX.axis_height*span.scale;if(HTMLCSS.safariVerticalAlignBug&&span.lastChild.nodeName==="IMG"){span.lastChild.style.verticalAlign=HTMLCSS.Em(HTMLCSS.unEm(span.lastChild.style.verticalAlign||0)/HTMLCSS.em-p/span.scale);}else if(HTMLCSS.konquerorVerticalAlignBug&&span.lastChild.nodeName==="IMG"){span.style.position="relative";span.lastChild.style.position="relative";span.lastChild.style.top=HTMLCSS.Em
(p/span.scale);}else{span.style.verticalAlign=HTMLCSS.Em(-p/span.scale);}span.bbox.h-=p;span.bbox.d+=p;if(span.bbox.rw>span.bbox.w){span.bbox.ic=span.bbox.rw-span.bbox.w;HTMLCSS.createBlank(span,span.bbox.ic);span.bbox.w=span.bbox.rw;}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);this.HTMLhandleDir(span);return span;},CoreParent:function(){var parent=this;while(parent&&parent.isEmbellished()&&parent.CoreMO()===this&&!parent.isa(MML.math)){parent=parent.Parent()}return parent;},CoreText:function(parent){if(!parent){return""}if(parent.isEmbellished()){return parent.CoreMO().data.join("")}while((parent.isa(MML.mrow)||parent.isa(MML.TeXAtom)||parent.isa(MML.mstyle)||parent.isa(MML.mphantom))&&parent.data.length===1&&parent.data[0]){parent=parent.data[0]}if(!parent.isToken){return""}else{return parent.data.join("")}},HTMLremapChars:{'*':"\u2217",'"':"\u2033","\u00B0":"\u2218","\u00B2":"2","\u00B3":"3","\u00B4":"\u2032","\u00B9":"1"},HTMLremap:function(text,map){text=text.replace(
/-/g,"\u2212");if(map){text=text.replace(/'/g,"\u2032").replace(/`/g,"\u2035");if(text.length===1){text=map[text]||text}}return text;},HTMLcanStretch:function(direction){if(!this.Get("stretchy")){return false}var c=this.data.join("");if(c.length>1){return false}var parent=this.CoreParent();if(parent&&parent.isa(MML.munderover)&&this.CoreText(parent.data[parent.base]).length===1){var over=parent.data[parent.over],under=parent.data[parent.under];if(over&&this===over.CoreMO()&&parent.Get("accent")){c=HTMLCSS.FONTDATA.REMAPACCENT[c]||c}else if(under&&this===under.CoreMO()&&parent.Get("accentunder")){c=HTMLCSS.FONTDATA.REMAPACCENTUNDER[c]||c}}c=HTMLCSS.FONTDATA.DELIMITERS[c.charCodeAt(0)];return(c&&c.dir==direction.substr(0,1));},HTMLstretchV:function(box,h,d){this.HTMLremoveColor();var values=this.getValues("symmetric","maxsize","minsize");var span=this.HTMLspanElement(),mu=this.HTMLgetMu(span),H;var axis=HTMLCSS.TeX.axis_height,scale=span.scale;if(values.symmetric){H=2*Math.max(h-axis,d+
axis)}else{H=h+d}values.maxsize=HTMLCSS.length2em(values.maxsize,mu,span.bbox.h+span.bbox.d);values.minsize=HTMLCSS.length2em(values.minsize,mu,span.bbox.h+span.bbox.d);H=Math.max(values.minsize,Math.min(values.maxsize,H));span=this.HTMLcreateSpan(box);HTMLCSS.createDelimiter(span,this.data.join("").charCodeAt(0),H,scale);if(values.symmetric){H=(span.bbox.h+span.bbox.d)/2+axis}else{H=(span.bbox.h+span.bbox.d)*h/(h+d)}HTMLCSS.positionDelimiter(span,H);this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:function(box,W){this.HTMLremoveColor();var values=this.getValues("maxsize","minsize","mathvariant","fontweight");if((values.fontweight==="bold"||parseInt(values.fontweight)>=600)&&!this.Get("mathvariant",true)){values.mathvariant=MML.VARIANT.BOLD}var span=this.HTMLspanElement(),mu=this.HTMLgetMu(span),scale=span.scale;values.maxsize=HTMLCSS.length2em(values.maxsize,mu,span.bbox.w);values.minsize=HTMLCSS.length2em(values.minsize,mu,span.bbox.w);W=Math.max(
values.minsize,Math.min(values.maxsize,W));span=this.HTMLcreateSpan(box);HTMLCSS.createDelimiter(span,this.data.join("").charCodeAt(0),W,scale,values.mathvariant);this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;}});MML.mtext.Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));var variant=this.HTMLgetVariant();if(HTMLCSS.config.mtextFontInherit||this.Parent().type==="merror"){variant={bold:variant.bold,italic:variant.italic,fontInherit:true}}for(var i=0,m=this.data.length;i<m;i++){if(this.data[i]){this.data[i].toHTML(span,variant)}}if(!span.bbox){span.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete span.bbox.skew}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);this.HTMLhandleDir(span);return span;}});MML.merror.Augment({toHTML:function(span){var SPAN=MathJax.HTML.addElement(span,"span",{style:{display:"inline-block"}});span=this.SUPER(arguments).toHTML.call(this,SPAN);var HD=HTMLCSS.getHD(SPAN),W=HTMLCSS.getW(SPAN)
;SPAN.bbox={h:HD.h,d:HD.d,w:W,lw:0,rw:W,exactW:true};SPAN.id=span.id;span.id=null;return SPAN;}});MML.ms.Augment({toHTML:MML.mbase.HTMLautoload});MML.mglyph.Augment({toHTML:MML.mbase.HTMLautoload});MML.mspace.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);var values=this.getValues("height","depth","width");var mu=this.HTMLgetMu(span);values.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){values.mathbackground=this.background}var h=HTMLCSS.length2em(values.height,mu),d=HTMLCSS.length2em(values.depth,mu),w=HTMLCSS.length2em(values.width,mu);HTMLCSS.createSpace(span,h,d,w,values.mathbackground,true);return span;}});MML.mphantom.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);if(this.data[0]!=null){var box=this.data[0].toHTML(span);if(D!=null){HTMLCSS.Remeasured(this.data[0].HTMLstretchV(span,HW,D),span)}else if(HW!=null){HTMLCSS.Remeasured(this.data[0].HTMLstretchH(span,HW),span)}else{box=HTMLCSS.Measured(box,span)}span.bbox={
w:box.bbox.w,h:box.bbox.h,d:box.bbox.d,lw:0,rw:0,exactW:true};for(var i=0,m=span.childNodes.length;i<m;i++){span.childNodes[i].style.visibility="hidden"}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.mpadded.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);if(this.data[0]!=null){var stack=HTMLCSS.createStack(span,true);var box=HTMLCSS.createBox(stack);var child=this.data[0].toHTML(box);if(D!=null){HTMLCSS.Remeasured(this.data[0].HTMLstretchV(box,HW,D),box)}else if(HW!=null){HTMLCSS.Remeasured(this.data[0].HTMLstretchH(box,HW),box)}else{HTMLCSS.Measured(child,box)}var values=this.getValues("height","depth","width","lspace","voffset"),x=0,y=0,mu=this.HTMLgetMu(span);if(values.lspace){x=this.HTMLlength2em(box,values.lspace,mu)}if(values.voffset){y=this.HTMLlength2em(box,values.voffset,mu)}HTMLCSS.placeBox(box,x,y);span.bbox={h:box.bbox.h,d:box.bbox.d,w:box.bbox.w,exactW:
true,lw:Math.min(0,box.bbox.lw+x),rw:Math.max(box.bbox.w,box.bbox.rw+x),H:Math.max((box.bbox.H==null?-HTMLCSS.BIGDIMEN:box.bbox.H),box.bbox.h+y),D:Math.max((box.bbox.D==null?-HTMLCSS.BIGDIMEN:box.bbox.D),box.bbox.d-y)};if(values.height!==""){span.bbox.h=this.HTMLlength2em(box,values.height,mu,"h",0)}if(values.depth!==""){span.bbox.d=this.HTMLlength2em(box,values.depth,mu,"d",0)}if(values.width!==""){span.bbox.w=this.HTMLlength2em(box,values.width,mu,"w",0)}if(span.bbox.H<=span.bbox.h){delete span.bbox.H}if(span.bbox.D<=span.bbox.d){delete span.bbox.D}var dimen=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/
span.bbox.exact=!!((this.data[0]&&this.data[0].data.length==0)||dimen.exec(values.height)||dimen.exec(values.width)||dimen.exec(values.depth));HTMLCSS.setStackWidth(stack,span.bbox.w);}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLlength2em:function(span,length,mu,d,m){if(m==null){m=-HTMLCSS.BIGDIMEN}var match=String(length).match(/width|height|depth/);var size=(match?span.bbox[match[0].charAt(0)]:(d?span.bbox[d]:0));var v=HTMLCSS.length2em(length,mu,size);if(d&&String(length).match(/^\s*[-+]/)){return Math.max(m,span.bbox[d]+v)}else{return v}},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.mrow.Augment({HTMLlineBreaks:function(span){if(!this.parent.linebreakContainer){return false}return(HTMLCSS.config.linebreaks.automatic&&span.bbox.w>HTMLCSS.linebreakWidth)||this.hasNewline();},HTMLstretchH:function(box,w){this.HTMLremoveColor();var span=this.HTMLspanElement();this.data[this.core].HTMLstretchH(span,w);this.HTMLcomputeBBox(span
,true);this.HTMLhandleColor(span);return span;},HTMLstretchV:function(box,h,d){this.HTMLremoveColor();var span=this.HTMLspanElement();this.data[this.core].HTMLstretchV(span,h,d);this.HTMLcomputeBBox(span,true);this.HTMLhandleColor(span);return span;}});MML.mstyle.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);if(this.data[0]!=null){var SPAN=this.data[0].toHTML(span);if(D!=null){this.data[0].HTMLstretchV(span,HW,D)}else if(HW!=null){this.data[0].HTMLstretchH(span,HW)}span.bbox=SPAN.bbox;}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.mfrac.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);var frac=HTMLCSS.createStack(span);var num=HTMLCSS.createBox(frac),den=HTMLCSS.createBox(frac);HTMLCSS.MeasureSpans([this.HTMLboxChild(0,num),this.HTMLboxChild(1,den)]);var values=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var scale=
this.HTMLgetScale(),isDisplay=values.displaystyle;var a=HTMLCSS.TeX.axis_height*scale;if(values.bevelled){var delta=(isDisplay?.4:.15);var H=Math.max(num.bbox.h+num.bbox.d,den.bbox.h+den.bbox.d)+2*delta;var bevel=HTMLCSS.createBox(frac);HTMLCSS.createDelimiter(bevel,0x2F,H);HTMLCSS.placeBox(num,0,(num.bbox.d-num.bbox.h)/2+a+delta);HTMLCSS.placeBox(bevel,num.bbox.w-delta/2,(bevel.bbox.d-bevel.bbox.h)/2+a);HTMLCSS.placeBox(den,num.bbox.w+bevel.bbox.w-delta,(den.bbox.d-den.bbox.h)/2+a-delta);}else{var W=Math.max(num.bbox.w,den.bbox.w);var t=HTMLCSS.thickness2em(values.linethickness,scale),p,q,u,v;var mt=HTMLCSS.TeX.min_rule_thickness/this.em;if(isDisplay){u=HTMLCSS.TeX.num1;v=HTMLCSS.TeX.denom1}else{u=(t===0?HTMLCSS.TeX.num3:HTMLCSS.TeX.num2);v=HTMLCSS.TeX.denom2}u*=scale;v*=scale;if(t===0){p=Math.max((isDisplay?7:3)*HTMLCSS.TeX.rule_thickness,2*mt);q=(u-num.bbox.d)-(den.bbox.h-v);if(q<p){u+=(p-q)/2;v+=(p-q)/2}}else{p=Math.max((isDisplay?2:0)*mt+t,t/2+1.5*mt);q=(u-num.bbox.d)-(a+t/2);if(q
<p){u+=p-q}q=(a-t/2)-(den.bbox.h-v);if(q<p){v+=p-q}var rule=HTMLCSS.createBox(frac);HTMLCSS.createRule(rule,t,0,W+2*t);HTMLCSS.placeBox(rule,0,a-t/2);}HTMLCSS.alignBox(num,values.numalign,u);HTMLCSS.alignBox(den,values.denomalign,-v);}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLcanStretch:function(direction){return false},HTMLhandleSpace:function(span){if(!this.texWithDelims){var space=(this.useMMLspacing?0:HTMLCSS.length2em(this.texSpacing()||0))+.12;span.style.paddingLeft=HTMLCSS.Em(space);span.style.paddingRight=HTMLCSS.Em(.12);}}});MML.msqrt.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);var sqrt=HTMLCSS.createStack(span);var base=HTMLCSS.createBox(sqrt),rule=HTMLCSS.createBox(sqrt),surd=HTMLCSS.createBox(sqrt);var scale=this.HTMLgetScale();var t=HTMLCSS.TeX.rule_thickness*scale,p,q,H,W;if(this.Get("displaystyle")){p=HTMLCSS.TeX.x_height*scale}else{p=t}q=Math.max(t+p/4,1.5*HTMLCSS.TeX.min_rule_thickness/this.em);var BASE=this.HTMLboxChild(
0,base);H=BASE.bbox.h+BASE.bbox.d+q+t;HTMLCSS.createDelimiter(surd,0x221A,H,scale);HTMLCSS.MeasureSpans([BASE,surd]);W=BASE.bbox.w;var x=0;if(surd.isMultiChar||(HTMLCSS.AdjustSurd&&HTMLCSS.imgFonts)){surd.bbox.w*=.95}if(surd.bbox.h+surd.bbox.d>H){q=((surd.bbox.h+surd.bbox.d)-(H-t))/2}var ruleC=HTMLCSS.FONTDATA.DELIMITERS[HTMLCSS.FONTDATA.RULECHAR];if(!ruleC||W<ruleC.HW[0][0]*scale||scale<.75){HTMLCSS.createRule(rule,0,t,W);}else{HTMLCSS.createDelimiter(rule,HTMLCSS.FONTDATA.RULECHAR,W,scale);}H=BASE.bbox.h+q+t;q=H*HTMLCSS.rfuzz;if(surd.isMultiChar){q=HTMLCSS.rfuzz}x=this.HTMLaddRoot(sqrt,surd,x,surd.bbox.h+surd.bbox.d-H,scale);HTMLCSS.placeBox(surd,x,H-surd.bbox.h);HTMLCSS.placeBox(rule,x+surd.bbox.w,H-rule.bbox.h+q);HTMLCSS.placeBox(base,x+surd.bbox.w,0);this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLaddRoot:function(sqrt,surd,x,d,scale){return x}});MML.mroot.Augment({toHTML:MML.msqrt.prototype.toHTML,HTMLaddRoot:function(sqrt,surd,x,d,scale){var box=HTMLCSS.
createBox(sqrt);if(this.data[1]){var root=this.data[1].toHTML(box);root.style.paddingRight=root.style.paddingLeft="";HTMLCSS.Measured(root,box);}else{box.bbox=this.HTMLzeroBBox()}var h=this.HTMLrootHeight(surd.bbox.h+surd.bbox.d,scale,box)-d;var w=Math.min(box.bbox.w,box.bbox.rw);x=Math.max(w,surd.offset);HTMLCSS.placeBox(box,x-w,h);return x-surd.offset;},HTMLrootHeight:function(d,scale,root){return.45*(d-.9*scale)+.6*scale+Math.max(0,root.bbox.d-.075);}});MML.mfenced.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);if(this.data.open){this.data.open.toHTML(span)}if(this.data[0]!=null){this.data[0].toHTML(span)}for(var i=1,m=this.data.length;i<m;i++){if(this.data[i]){if(this.data["sep"+i]){this.data["sep"+i].toHTML(span)}this.data[i].toHTML(span);}}if(this.data.close){this.data.close.toHTML(span)}var stretchy=this.HTMLcomputeBBox(span);var h=span.bbox.h,d=span.bbox.d;for(i=0,m=stretchy.length;i<m;i++){stretchy[i].HTMLstretchV(span,h,d)}if(stretchy.length){this.
HTMLcomputeBBox(span,true)}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLcomputeBBox:function(span,full){var BBOX=span.bbox={},stretchy=[];this.HTMLcheckStretchy(this.data.open,BBOX,stretchy,full);this.HTMLcheckStretchy(this.data[0],BBOX,stretchy,full);for(var i=1,m=this.data.length;i<m;i++){if(this.data[i]){this.HTMLcheckStretchy(this.data["sep"+i],BBOX,stretchy,full);this.HTMLcheckStretchy(this.data[i],BBOX,stretchy,full);}}this.HTMLcheckStretchy(this.data.close,BBOX,stretchy,full);this.HTMLcleanBBox(BBOX);return stretchy;},HTMLcheckStretchy:function(core,BBOX,stretchy,full){if(core){if(!full&&core.HTMLcanStretch("Vertical")){stretchy.push(core);core=(core.CoreMO()||core)}this.HTMLcombineBBoxes(core,BBOX);}}});MML.menclose.Augment({toHTML:MML.mbase.HTMLautoload});MML.maction.Augment({toHTML:MML.mbase.HTMLautoload});MML.semantics.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);if(this.data[0]!=null){var SPAN=this.data[0].toHTML(span);if(D!=
null){this.data[0].HTMLstretchV(span,HW,D)}else if(HW!=null){this.data[0].HTMLstretchH(span,HW)}span.bbox=SPAN.bbox;}this.HTMLhandleSpace(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.munderover.Augment({toHTML:function(span,HW,D){var values=this.getValues("displaystyle","accent","accentunder","align");if(!values.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return MML.msubsup.prototype.toHTML.call(this,span)}span=this.HTMLcreateSpan(span);var scale=this.HTMLgetScale();var stack=HTMLCSS.createStack(span);var boxes=[],children=[],stretch=[],box,i,m;for(i=0,m=this.data.length;i<m;i++){if(this.data[i]!=null){box=boxes[i]=HTMLCSS.createBox(stack);children[i]=this.data[i].toHTML(box);if(i==this.base){if(D!=null){this.data[this.base].HTMLstretchV(box,HW,D)}else if(HW!=null){this.data[this.base].HTMLstretchH(box,HW)}stretch[i]=(D==null&&HW!=null?false:this.data[i].HTMLcanStretch("Horizontal"));
}else{stretch[i]=this.data[i].HTMLcanStretch("Horizontal");}}}HTMLCSS.MeasureSpans(children);var W=-HTMLCSS.BIGDIMEN,WW=W;for(i=0,m=this.data.length;i<m;i++){if(this.data[i]){if(boxes[i].bbox.w>WW){WW=boxes[i].bbox.w}if(!stretch[i]&&WW>W){W=WW}}}if(D==null&&HW!=null){W=HW}else if(W==-HTMLCSS.BIGDIMEN){W=WW}for(i=WW=0,m=this.data.length;i<m;i++){if(this.data[i]){box=boxes[i];if(stretch[i]){box.bbox=this.data[i].HTMLstretchH(box,W).bbox}if(box.bbox.w>WW){WW=box.bbox.w}}}var t=HTMLCSS.TeX.rule_thickness,factor=HTMLCSS.FONTDATA.TeX_factor;var base=boxes[this.base]||{bbox:this.HTMLzeroBBox()};var x,y,z1,z2,z3,dw,k,delta=0;if(base.bbox.ic){delta=1.3*base.bbox.ic+.05}for(i=0,m=this.data.length;i<m;i++){if(this.data[i]!=null){box=boxes[i];z3=HTMLCSS.TeX.big_op_spacing5*scale;var accent=(i!=this.base&&values[this.ACCENTS[i]]);if(accent&&box.bbox.w<=1/HTMLCSS.em+.0001){box.bbox.w=box.bbox.rw-box.bbox.lw;box.bbox.noclip=true;if(box.bbox.lw){box.insertBefore(HTMLCSS.createSpace(box.parentNode,0,0,
-box.bbox.lw),box.firstChild)}HTMLCSS.createBlank(box,0,0,box.bbox.rw+.1);}dw={left:0,center:(WW-box.bbox.w)/2,right:WW-box.bbox.w}[values.align];x=dw;y=0;if(i==this.over){if(accent){k=Math.max(t*scale*factor,2.5/this.em);z3=0;if(base.bbox.skew){x+=base.bbox.skew}}else{z1=HTMLCSS.TeX.big_op_spacing1*scale*factor;z2=HTMLCSS.TeX.big_op_spacing3*scale*factor;k=Math.max(z1,z2-Math.max(0,box.bbox.d));}k=Math.max(k,1.5/this.em);x+=delta/2;y=base.bbox.h+box.bbox.d+k;box.bbox.h+=z3;}else if(i==this.under){if(accent){k=3*t*scale*factor;z3=0;}else{z1=HTMLCSS.TeX.big_op_spacing2*scale*factor;z2=HTMLCSS.TeX.big_op_spacing4*scale*factor;k=Math.max(z1,z2-box.bbox.h);}k=Math.max(k,1.5/this.em);x-=delta/2;y=-(base.bbox.d+box.bbox.h+k);box.bbox.d+=z3;}HTMLCSS.placeBox(box,x,y);}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.msubsup.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);var
scale=this.HTMLgetScale(),mu=this.HTMLgetMu(span);var stack=HTMLCSS.createStack(span),values,children=[];var base=HTMLCSS.createBox(stack);if(this.data[this.base]){children.push(this.data[this.base].toHTML(base));if(D!=null){this.data[this.base].HTMLstretchV(base,HW,D)}else if(HW!=null){this.data[this.base].HTMLstretchH(base,HW)}}else{base.bbox=this.HTMLzeroBBox()}var x_height=HTMLCSS.TeX.x_height*scale,s=HTMLCSS.TeX.scriptspace*scale*.75;var sup,sub;if(this.HTMLnotEmpty(this.data[this.sup])){sup=HTMLCSS.createBox(stack);children.push(this.data[this.sup].toHTML(sup))}if(this.HTMLnotEmpty(this.data[this.sub])){sub=HTMLCSS.createBox(stack);children.push(this.data[this.sub].toHTML(sub))}HTMLCSS.MeasureSpans(children);if(sup){sup.bbox.w+=s;sup.bbox.rw=Math.max(sup.bbox.w,sup.bbox.rw)}if(sub){sub.bbox.w+=s;sub.bbox.rw=Math.max(sub.bbox.w,sub.bbox.rw)}HTMLCSS.placeBox(base,0,0);var sscale;if(sup){sscale=this.data[this.sup].HTMLgetScale();}else if(sub){sscale=this.data[this.sub].HTMLgetScale(
);}else{sscale=this.HTMLgetScale();}var q=HTMLCSS.TeX.sup_drop*sscale,r=HTMLCSS.TeX.sub_drop*sscale;var u=base.bbox.h-q,v=base.bbox.d+r,delta=0,p;if(base.bbox.ic){base.bbox.w-=base.bbox.ic;delta=1.3*base.bbox.ic+.05;}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&base.bbox.scale===1&&!this.data[this.base].Get("largeop")){u=v=0}}var min=this.getValues("subscriptshift","superscriptshift");min.subscriptshift=(min.subscriptshift===""?0:HTMLCSS.length2em(min.subscriptshift,mu));min.superscriptshift=(min.superscriptshift===""?0:HTMLCSS.length2em(min.superscriptshift,mu));if(!sup){if(sub){v=Math.max(v,HTMLCSS.TeX.sub1*scale,sub.bbox.h-(4/5)*x_height,min.subscriptshift);HTMLCSS.placeBox(sub,base.bbox.w,-v,sub.bbox);}}else{if(!sub){values=this.getValues("displaystyle","texprimestyle");p=HTMLCSS.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];u=Math.max(u,p*scale,sup.bbox.d+(1
/4)*x_height,min.superscriptshift);HTMLCSS.placeBox(sup,base.bbox.w+delta,u,sup.bbox);}else{v=Math.max(v,HTMLCSS.TeX.sub2*scale);var t=HTMLCSS.TeX.rule_thickness*scale;if((u-sup.bbox.d)-(sub.bbox.h-v)<3*t){v=3*t-u+sup.bbox.d+sub.bbox.h;q=(4/5)*x_height-(u-sup.bbox.d);if(q>0){u+=q;v-=q}}HTMLCSS.placeBox(sup,base.bbox.w+delta,Math.max(u,min.superscriptshift));HTMLCSS.placeBox(sub,base.bbox.w,-Math.max(v,min.subscriptshift));}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MML.mmultiscripts.Augment({toHTML:MML.mbase.HTMLautoload});MML.mtable.Augment({toHTML:MML.mbase.HTMLautoload});MML["annotation-xml"].Augment({toHTML:MML.mbase.HTMLautoload});MML.math.Augment({toHTML:function(span,node){var alttext=this.Get("alttext");if(alttext&&alttext!==""){node.setAttribute("aria-label",alttext)}var nobr=HTMLCSS.addElement(span,"nobr",{isMathJax:true});span=this.HTMLcreateSpan(nobr);var stack=HTMLCSS.
createStack(span),box=HTMLCSS.createBox(stack),math;stack.style.fontSize=nobr.parentNode.style.fontSize;nobr.parentNode.style.fontSize="";if(this.data[0]!=null){if(HTMLCSS.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}MML.mbase.prototype.displayAlign=HUB.config.displayAlign;MML.mbase.prototype.displayIndent=HUB.config.displayIndent;var html=this.data[0].toHTML(box);html.bbox.exactW=false;math=HTMLCSS.Measured(html,box);}HTMLCSS.placeBox(box,0,0);span.style.width=HTMLCSS.Em((Math.round(math.bbox.w*this.em)+.25)/HTMLCSS.outerEm);span.style.display="inline-block";var p=1/HTMLCSS.em,f=HTMLCSS.em/HTMLCSS.outerEm;HTMLCSS.em/=f;span.bbox.h*=f;span.bbox.d*=f;span.bbox.w*=f;span.bbox.lw*=f;span.bbox.rw*=f;if(math&&math.bbox.width!=null){span.style.minWidth=(math.bbox.minWidth||span.style.width);span.style.width=stack.style.width=math.bbox.width;
box.style.width="100%";}this.HTMLhandleColor(span);if(math){HTMLCSS.createRule(span,(math.bbox.h+p)*f,(math.bbox.d+p)*f,0)}if(!this.isMultiline&&this.Get("display")==="block"&&span.bbox.width==null){var values=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(values.indentalignfirst!==MML.INDENTALIGN.INDENTALIGN){values.indentalign=values.indentalignfirst}if(values.indentalign===MML.INDENTALIGN.AUTO){values.indentalign=this.displayAlign}node.style.textAlign=values.indentalign;if(values.indentshiftfirst!==MML.INDENTSHIFT.INDENTSHIFT){values.indentshift=values.indentshiftfirst}if(values.indentshift==="auto"){values.indentshift=this.displayIndent}if(values.indentshift&&values.indentalign!==MML.INDENTALIGN.CENTER){span.style[{left:"marginLeft",right:"marginRight"}[values.indentalign]]=HTMLCSS.Em(HTMLCSS.length2em(values.indentshift));}}return span;},HTMLspanElement:MML.mbase.prototype.HTMLspanElement});MML.TeXAtom.Augment({toHTML:function(span){span=this.
HTMLcreateSpan(span);if(this.data[0]!=null){if(this.texClass===MML.TEXCLASS.VCENTER){var stack=HTMLCSS.createStack(span);var box=HTMLCSS.createBox(stack);HTMLCSS.Measured(this.data[0].toHTML(box),box);HTMLCSS.placeBox(box,0,HTMLCSS.TeX.axis_height-(box.bbox.h+box.bbox.d)/2+box.bbox.d);}else{span.bbox=this.data[0].toHTML(span).bbox;}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",HTMLCSS,"jax.js"]),0);});});HUB.Register.StartupHook("End Config",function(){HUB.Browser.Select({MSIE:function(browser){var mode=(document.documentMode||0);var isIE7=browser.versionAtLeast("7.0");var isIE8=browser.versionAtLeast("8.0")&&mode>7;var quirks=(document.compatMode==="BackCompat");if(mode<9){HTMLCSS.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].opacity=0
HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";}HTMLCSS.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:quirks,msieDisappearingBug:(mode>=8),msieMarginScaleBug:(mode<8),msiePaddingWidthBug:true,msieBorderWidthBug:quirks,msieFrameSizeBug:(mode<=8),msieInlineBlockAlignBug:(!isIE8||quirks),msiePlaceBoxBug:(isIE8&&!quirks),msieClipRectBug:!isIE8,msieNegativeSpaceBug:quirks,cloneNodeBug:(isIE8&&browser.version==="8.0"),initialSkipBug:(mode<8),msieNegativeBBoxBug:(mode>=8),msieIE6:!isIE7,msieItalicWidthBug:true,FontFaceBug:true,msieFontCSSBug:browser.isIE9,allowWebFonts:(mode>=9?"woff":"eot")});},Firefox:function(browser){var webFonts=false;if(browser.versionAtLeast("3.5")){var root=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||HUB.config.root.match(/^https?:\/\//)||(HUB.config.root+"/").substr(0,root.length)===root){webFonts="otf"}}HTMLCSS.Augment({
ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:webFonts});},Safari:function(browser){var v3p0=browser.versionAtLeast("3.0");var v3p1=browser.versionAtLeast("3.1");var trueSafari=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var android=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var forceImages=(v3p1&&browser.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!browser.versionAtLeast("5.0"))||(android!=null&&(android[1]<2||(android[1]==2&&android[2]<2)))));HTMLCSS.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!v3p1,safariTextNodeBug:!v3p0,forceReflow:true,allowWebFonts:(v3p1&&!forceImages?"otf":false)});if(trueSafari){HTMLCSS.Augment({webFontDefault:(browser.isMobile?"sans-serif":"serif")});}if(browser.isPC){
HTMLCSS.Augment({adjustAvailableFonts:HTMLCSS.removeSTIXfonts,checkWebFontsTwice:true});}if(forceImages){var config=HUB.config["HTML-CSS"];if(config){config.availableFonts=[];config.preferredFont=null}else{HUB.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(browser){HTMLCSS.Augment({Em:HTMLCSS.EmRounded,cloneNodeBug:true,rfuzz:.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(browser.versionAtLeast("4.0")?"otf":"svg")});},Opera:function(browser){browser.isMini=(navigator.appVersion.match("Opera Mini")!=null);HTMLCSS.config.styles[".MathJax .merror"]["vertical-align"]=null;HTMLCSS.config.styles[".MathJax span"]["z-index"]=0;HTMLCSS.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:browser.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(browser.versionAtLeast("10.0")&&!browser.isMini?"otf":false),
adjustAvailableFonts:HTMLCSS.removeSTIXfonts});},Konqueror:function(browser){HTMLCSS.Augment({konquerorVerticalAlignBug:true});}});});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(HUB.config.menuSettings.zoom!=="None"){AJAX.Require("[MathJax]/extensions/MathZoom.js")}});})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);},{},{});
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