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jax.js 68 KB
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  1. /*
    2. 

  2.  *  /MathJax/jax/output/HTML-CSS/jax.js
    3. 

  3.  *  
    4. 

  4.  *  Copyright (c) 2009-2013 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Part of the MathJax library.
    7. 

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

  8.  * 
    9. 

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

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

  11.  *
    12. 

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

  13.  */(function(v,t,e){var k,x=function(){var a=[].slice.call(arguments,0);a[0][0]=["HTML-CSS",a[0][0]];return MathJax.Message.Set.apply(MathJax.Message,a)},A=MathJax.Object.Subclass({timeout:1E3*(t.Browser.isMobile?15:8),FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:"sans-serif monospace script Times Courier Arial Helvetica".split(" "),testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]);this.text=this.div.firstChild},findFont:function(a,b){if(b&&this.testCollection(b))return b;for(var c=0,f=a.length;c<f;c++)if(a[c]!==b&&this.testCollection(a[c]))return a[c];return null},testCollection:function(a){return this.testFont(this.FontInfo[a])},testFont:function(a){a.isWebFont&&e.FontFaceBug?this.div.style.fontWeight=this.div.style.fontStyle="normal":(this.div.style.fontWeight=a.weight||"normal",this.div.style.fontStyle=a.style||"normal");var b=this.getComparisonWidths(a.testString,a.noStyleChar);if(b){this.div.style.fontFamily="'"+a.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==b[0]&&(this.div.style.fontFamily="'"+a.family+"',"+this.comparisonFont[b[2]],this.div.offsetWidth==b[1]))return!1;if(this.div.offsetWidth!=b[3]||this.div.offsetHeight!=b[4]){if(a.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar)return!0;for(var b=0,c=this.testSize.length;b<c;b++)if(this.testStyleChar(a,this.testSize[b]))return!0}}return!1},styleChar:"\ueffd",versionChar:"\ueffe",compChar:"\uefff",testStyleChar:function(a,b){var c=3+(a.weight?2:0)+(a.style?4:0),f="",d=0,g=this.div.style.fontSize;this.div.style.fontSize=b;e.msieItalicWidthBug&&"italic"===a.style&&(this.text.nodeValue=f=this.compChar,d=this.div.offsetWidth);e.safariTextNodeBug?this.div.innerHTML=this.compChar+f:this.text.nodeValue=this.compChar+f;var h=this.div.offsetWidth-d;e.safariTextNodeBug?this.div.innerHTML=this.styleChar+f:this.text.nodeValue=this.styleChar+f;var l=Math.floor((this.div.offsetWidth-d)/h+.5);l===c&&(e.safariTextNodeBug?this.div.innerHTML=this.versionChar+f:this.text.nodeValue=this.versionChar+f,a.version=Math.floor((this.div.offsetWidth-d)/h+1.5)/2);this.div.style.fontSize=g;return l===c},getComparisonWidths:function(a,b){e.FONTDATA&&e.FONTDATA.hasStyleChar&&!b&&(a+=this.styleChar+" "+this.compChar);e.safariTextNodeBug?this.div.innerHTML=a:this.text.nodeValue=a;this.div.style.fontFamily=this.comparisonFont[0];var c=this.div.offsetWidth;this.div.style.fontFamily=e.webFontDefault;for(var f=this.div.offsetWidth,d=this.div.offsetHeight,g=1,h=this.comparisonFont.length;g<h;g++)if(this.div.style.fontFamily=this.comparisonFont[g],this.div.offsetWidth!=c)return[c,this.div.offsetWidth,g,f,d];return null},loadWebFont:function(a){t.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+a.directory);var b=x(["LoadWebFont","Loading web-font %1",e.fontInUse+"/"+a.directory]),c=MathJax.Callback({}),b=MathJax.Callback(["loadComplete",this,a,b,c]);v.timer.start(v,[this.checkWebFont,a,b],0,this.timeout);return c},loadComplete:function(a,b,c,f){MathJax.Message.Clear(b);f===v.STATUS.OK?(this.webFontLoaded=!0,c()):(this.loadError(a),t.Browser.isFirefox&&e.allowWebFonts&&(b=document.location.protocol+"//"+document.location.hostname,""!=document.location.port&&(b+=":"+document.location.port),b+="/",v.fileURL(e.webfontDir).substr(0,b.length)!==b&&this.firefoxFontError(a)),this.webFontLoaded?c():e.loadWebFontError(a,c))},loadError:function(a){x(["CantLoadWebFont","Can't load web font %1",e.fontInUse+"/"+a.directory],null,2E3);t.Startup.signal.Post(["HTML-CSS Jax - web font error",e.fontInUse+"/"+a.directory,a])},firefoxFontError:function(a){x(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3E3);t.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(a,b,c){a.time(c)||(e.Font.testFont(b)?c(a.STATUS.OK):setTimeout(a,a.delay))},fontFace:function(a){var b=e.allowWebFonts,c=e.FONTDATA.FONTS[a];e.msieFontCSSBug&&!c.family.match(/-Web$/)&&(c.family+="-Web");var f=v.fileURL(e.webfontDir+"/"+b),d=a.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");d.match(/-/)||(d+="-Regular");var d="svg"===b?d+(".svg#"+d):d+("."+b),g={"font-family":c.family,src:"url('"+f+"/"+d+"')"};"otf"===b?(g.src+=" format('opentype')",f=v.fileURL(e.webfontDir+"/woff"),g.src="url('"+f+"/"+d.replace(/otf$/,"woff")+"') format('woff'), "+g.src):"eot"!==b&&(g.src+=" format('"+b+"')");e.FontFaceBug&&c.isWebFont||(a.match(/-bold/)&&(g["font-weight"]="bold"),a.match(/-italic/)&&(g["font-style"]="italic"));return g}}),w,z,y;e.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important","float":"none ! important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",width:"1px",height:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity\x3d0)"},".MathJax .MathJax_HitBox *":{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:t.config.menuSettings,hideProcessedMath:!0,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1E3,Config:function(){this.require||(this.require=[]);this.Font=A();this.SUPER(arguments).Config.call(this);var a=this.settings;this.adjustAvailableFonts&&this.adjustAvailableFonts(this.config.availableFonts);a.scale&&(this.config.scale=a.scale);a.font&&"Auto"!==a.font&&("TeX (local)"===a.font?(this.config.availableFonts=["TeX"],this.config.preferredFont=this.config.webFont="TeX"):"STIX (local)"===a.font?(this.config.availableFonts=["STIX"],this.config.preferredFont="STIX",this.config.webFont="TeX"):"TeX (web)"===a.font?(this.config.availableFonts=[],this.config.preferredFont="",this.config.webFont="TeX"):"TeX (image)"===a.font&&(this.config.availableFonts=[],this.config.preferredFont=this.config.webFont=""));a=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);!a&&this.allowWebFonts&&(a=this.config.webFont)&&(this.webFonts=!0);!a&&this.config.imageFont&&(a=this.config.imageFont,this.imgFonts=!0);a?(this.fontInUse=a,this.fontDir+="/"+a,this.webfontDir+="/"+a,this.require.push(this.fontDir+"/fontdata.js"),this.imgFonts&&(this.require.push(this.directory+"/imageFonts.js"),t.Startup.signal.Post("HTML-CSS Jax - using image fonts"))):(x(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3E3),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:45,REMAP:{}},t.Startup.signal.Post("HTML-CSS Jax - no valid font"));this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){w=MathJax.Extension.MathEvents.Event;z=MathJax.Extension.MathEvents.Touch;y=MathJax.Extension.MathEvents.Hover;this.ContextMenu=w.ContextMenu;this.Mousedown=w.AltContextMenu;this.Mouseover=y.Mouseover;this.Mouseout=y.Mouseout;this.Mousemove=y.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"}});document.body.firstChild?document.body.insertBefore(this.hiddenDiv,document.body.firstChild):document.body.appendChild(this.hiddenDiv);this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var a=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=a.offsetWidth/5;this.hiddenDiv.removeChild(a);this.startMarker=this.createStrut(this.Element("span"),10,!0);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");this.operaHeightBug&&this.createStrut(this.HDspan,0);if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(b){}}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 v.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(a){for(var b=0,c=a.length;b<c;b++)"STIX"===a[b]&&(a.splice(b,1),c--,b--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=a[0])},PreloadWebFonts:function(){if(e.allowWebFonts&&e.config.preloadWebFonts)for(var a=0,b=e.config.preloadWebFonts.length;a<b;a++){var c=e.FONTDATA.FONTS[e.config.preloadWebFonts[a]];c.available||e.Font.testFont(c)}},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(a){var b=a.jax[this.id],c,f=b.length,d,g,e,l,n,m,k=!1,q=this.config.linebreaks.automatic,r=this.config.linebreaks.width;q?((k=null!=r.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?r=r.replace(/\s*container\s*/,""):m=this.defaultWidth,""===r&&(r="100%")):m=1E5;for(c=0;c<f;c++)if(d=b[c],d.parentNode&&((g=d.previousSibling)&&String(g.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)&&g.parentNode.removeChild(g),g=d.MathJax.elementJax))g.HTMLCSS={display:"block"===g.root.Get("display")},e=l=this.Element("span",{className:"MathJax",id:g.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:w.Menu,onmousedown:w.Mousedown,onmouseover:w.Mouseover,onmouseout:w.Mouseout,onmousemove:w.Mousemove,onclick:w.Click,ondblclick:w.DblClick}),t.Browser.noContextMenu&&(e.ontouchstart=z.start,e.ontouchend=z.end),g.HTMLCSS.display?(l=this.Element("div",{className:"MathJax_Display"}),l.appendChild(e)):this.msieDisappearingBug&&(e.style.display="inline-block"),l.setAttribute("role","textbox"),l.setAttribute("aria-readonly","true"),l.className+=" MathJax_Processing",d.parentNode.insertBefore(l,d),d.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),d),k&&l.parentNode.insertBefore(this.linebreakSpan.cloneNode(!0),l);for(c=0;c<f;c++)if(d=b[c],d.parentNode&&(n=d.previousSibling,l=n.previousSibling,g=d.MathJax.elementJax)){d=n.firstChild.offsetHeight/60;n=n.lastChild.firstChild.offsetHeight/60;k&&(m=l.previousSibling.firstChild.offsetWidth);if(0===d||"NaN"===d)this.hiddenDiv.appendChild(l),g.HTMLCSS.isHidden=!0,d=this.defaultEx,n=this.defaultEm,k&&(m=this.defaultWidth);l=Math.floor(Math.max(this.config.minScaleAdjust/100,d/this.TeX.x_height/n)*this.config.scale);g.HTMLCSS.scale=l/100;g.HTMLCSS.fontSize=l+"%";g.HTMLCSS.em=g.HTMLCSS.outerEm=n;this.em=n*l/100;g.HTMLCSS.ex=d;g.HTMLCSS.lineWidth=q?this.length2em(r,1,m/this.em):1E6}for(c=0;c<f;c++)if(d=b[c],d.parentNode&&(n=b[c].previousSibling,g=b[c].MathJax.elementJax))k&&(e=n.previousSibling,g.HTMLCSS.isHidden||(e=e.previousSibling),e.parentNode.removeChild(e)),n.parentNode.removeChild(n);a.HTMLCSSeqn=a.HTMLCSSlast=0;a.HTMLCSSi=-1;a.HTMLCSSchunk=this.config.EqnChunk;a.HTMLCSSdelay=!1},Translate:function(a,b){if(a.parentNode){b.HTMLCSSdelay&&(b.HTMLCSSdelay=!1,t.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay)));var c=a.MathJax.elementJax,f=c.root,d=document.getElementById(c.inputID+"-Frame"),g=c.HTMLCSS.display?d.parentNode:d;this.em=k.mbase.prototype.em=c.HTMLCSS.em*c.HTMLCSS.scale;this.outerEm=c.HTMLCSS.em;this.scale=c.HTMLCSS.scale;this.linebreakWidth=c.HTMLCSS.lineWidth;d.style.fontSize=c.HTMLCSS.fontSize;this.initImg(d);this.initHTML(f,d);f.setTeXclass();try{f.toHTML(d,g)}catch(e){if(e.restart)for(;d.firstChild;)d.removeChild(d.firstChild);throw e;}c.HTMLCSS.isHidden&&a.parentNode.insertBefore(g,a);g.className=g.className.split(/ /)[0];this.hideProcessedMath&&(g.className+=" MathJax_Processed",a.MathJax.preview&&(c.HTMLCSS.preview=a.MathJax.preview,delete a.MathJax.preview),b.HTMLCSSeqn+=b.i-b.HTMLCSSi,b.HTMLCSSi=b.i,b.HTMLCSSeqn>=b.HTMLCSSlast+b.HTMLCSSchunk&&(this.postTranslate(b),b.HTMLCSSchunk=Math.floor(b.HTMLCSSchunk*this.config.EqnChunkFactor),b.HTMLCSSdelay=!0))}},postTranslate:function(a){var b=a.jax[this.id];if(this.hideProcessedMath){for(var c=a.HTMLCSSlast,f=a.HTMLCSSeqn;c<f;c++){var d=b[c];if(d&&d.MathJax.elementJax){d.previousSibling.className=d.previousSibling.className.split(/ /)[0];var g=d.MathJax.elementJax.HTMLCSS;g.preview&&(g.preview.innerHTML="",d.MathJax.preview=g.preview,delete g.preview)}}this.forceReflow&&(b=(document.styleSheets||[])[0]||{},b.disabled=!0,b.disabled=!1);a.HTMLCSSlast=a.HTMLCSSeqn}},getJaxFromMath:function(a){"MathJax_Display"===a.parentNode.className&&(a=a.parentNode);do a=a.nextSibling;while(a&&"script"!==a.nodeName.toLowerCase());return t.getJaxFor(a)},getHoverSpan:function(a,b){return a.root.HTMLspanElement()},getHoverBBox:function(a,b,c){b=b.bbox;a=a.HTMLCSS.outerEm;a={w:b.w*a,h:b.h*a,d:b.d*a};b.width&&(a.width=b.width);return a},Zoom:function(a,b,c,f,d){b.className="MathJax";b.style.fontSize=a.HTMLCSS.fontSize;d=b.appendChild(this.EmExSpan.cloneNode(!0));var g=d.lastChild.firstChild.offsetHeight/60;this.em=k.mbase.prototype.em=g;this.outerEm=g/a.HTMLCSS.scale;d.parentNode.removeChild(d);this.idPostfix="-zoom";a.root.toHTML(b,b);this.idPostfix="";if(d=a.root.HTMLspanElement().bbox.width){b.style.width=Math.floor(f-1.5*e.em)+"px";b.style.display="inline-block";for(a=document.getElementById((a.root.id||"MathJax-Span-"+a.root.spanID)+"-zoom").firstChild;a&&a.style.width!==d;)a=a.nextSibling;a&&(a.style.width="100%")}b.style.position="absolute";d||(c.style.position="absolute");a=b.offsetWidth;f=b.offsetHeight;d=c.offsetHeight;g=c.offsetWidth;0===g&&(g=c.parentNode.offsetWidth);b.style.position=c.style.position="";return{Y:-w.getBBox(b).h,mW:g,mH:d,zW:a,zH:f}},initImg:function(a){},initHTML:function(a,b){},initFont:function(a){var b=e.FONTDATA.FONTS,c=e.config.availableFonts;if(c&&c.length&&e.Font.testFont(b[a]))return b[a].available=!0,null;if(!this.allowWebFonts)return null;b[a].isWebFont=!0;e.FontFaceBug&&(b[a].family=a,e.msieFontCSSBug&&(b[a].family+="-Web"));return v.Styles({"@font-face":this.Font.fontFace(a)})},Remove:function(a){var b=document.getElementById(a.inputID+"-Frame");b&&(a.HTMLCSS.display&&(b=b.parentNode),b.parentNode.removeChild(b));delete a.HTMLCSS},getHD:function(a){var b=a.style.position;a.style.position="absolute";this.HDimg.style.height="0px";a.appendChild(this.HDspan);var c={h:a.offsetHeight};this.HDimg.style.height=c.h+"px";c.d=a.offsetHeight-c.h;c.h-=c.d;c.h/=this.em;c.d/=this.em;a.removeChild(this.HDspan);a.style.position=b;return c},getW:function(a){var b,c;b=(a.bbox||{}).w;var f=a;if(a.bbox&&a.bbox.exactW)return b;if(a.bbox&&0<=b&&!this.initialSkipBug||this.negativeBBoxes||!a.firstChild)b=a.offsetWidth,c=a.parentNode.offsetHeight;else if(a.bbox&&0>b&&this.msieNegativeBBoxBug)b=-a.offsetWidth,c=a.parentNode.offsetHeight;else{if(this.initialSkipBug){var d=a.style.position;a.style.position="absolute";f=this.startMarker;a.insertBefore(f,a.firstChild)}a.appendChild(this.endMarker);b=this.endMarker.offsetLeft-f.offsetLeft;a.removeChild(this.endMarker);this.initialSkipBug&&(a.removeChild(f),a.style.position=d)}null!=c&&(a.parentNode.HH=c/this.em);return b/this.em},Measured:function(a,b){var c=a.bbox;if(null==c.width&&c.w&&!c.isMultiline){var f=this.getW(a);c.rw+=f-c.w;c.w=f;c.exactW=!0}b||(b=a.parentNode);b.bbox||(b.bbox=c);return a},Remeasured:function(a,b){b.bbox=this.Measured(a,b).bbox},MeasureSpans:function(a){var b=[],c,f,d,g,e;f=0;for(d=a.length;f<d;f++)if(c=a[f])g=c.bbox,e=this.parentNode(c),g.exactW||g.width||0===g.w||g.isMultiline?e.bbox||(e.bbox=g):this.negativeBBoxes||!c.firstChild||0<=g.w&&!this.initialSkipBug||0>g.w&&this.msieNegativeBBoxBug?b.push([c]):this.initialSkipBug?(g=this.startMarker.cloneNode(!0),e=this.endMarker.cloneNode(!0),c.insertBefore(g,c.firstChild),c.appendChild(e),b.push([c,g,e,c.style.position]),c.style.position="absolute"):(e=this.endMarker.cloneNode(!0),c.appendChild(e),b.push([c,null,e]));f=0;for(d=b.length;f<d;f++)c=b[f][0],g=c.bbox,e=this.parentNode(c),0<=g.w&&!this.initialSkipBug||this.negativeBBoxes||!c.firstChild?(a=c.offsetWidth,e.HH=e.offsetHeight/this.em):0>g.w&&this.msieNegativeBBoxBug?(a=-c.offsetWidth,e.HH=e.offsetHeight/this.em):a=b[f][2].offsetLeft-((b[f][1]||{}).offsetLeft||0),a/=this.em,g.rw+=a-g.w,g.w=a,g.exactW=!0,e.bbox||(e.bbox=g);f=0;for(d=b.length;f<d;f++)c=b[f],c[1]&&(c[1].parentNode.removeChild(c[1]),c[0].style.position=c[3]),c[2]&&c[2].parentNode.removeChild(c[2])},Em:function(a){return 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f=String(c).match(/%$/),d=f||null==c?0:c;a=this.addElement(a,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:f?"100%":this.Em(d),height:0}});b||(a.parentNode.bbox=a.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:d,lw:this.BIGDIMEN,rw:f||null==c?-this.BIGDIMEN:c},f&&(a.bbox.width=c));return a},createBox:function(a,b){var c=this.addElement(a,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});null!=b&&(c.style.width=b);return c},addBox:function(a,b){b.style.position="absolute";b.isBox=b.isMathJax=!0;return a.appendChild(b)},placeBox:function(a,b,c,f){a.isMathJax=!0;var d=e.parentNode(a),g=a.bbox,h=d.bbox;this.msiePlaceBoxBug&&this.addText(a,this.NBSP);this.imgSpaceBug&&this.addText(a,this.imgSpace);var 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t=p-.05,u,v,w=c.mid?2:1;v=u=Math.min(Math.ceil((b-q)/(w*t)),this.maxStretchyParts);c.fillExtenders||(t=(b-q)/(w*u));b=u/(u+1)*(p-t);t=p-b;for(r-=k.bbox.lw+b;0<w--;){for(;0<u--;)this.cloneNodeBug?(p=this.Element("span"),this.createChar(p,c.rep,f,d)):p=k.cloneNode(!0),p.bbox=k.bbox,this.placeBox(this.addBox(e,p),r,0,!0),r+=t;c.mid&&w&&(this.placeBox(m,r,0,!0),r+=m.bbox.w-b,u=v)}}else r-=(q-b)/2,c.mid&&(this.placeBox(m,r,0,!0),r+=m.bbox.w),r-=(q-b)/2;this.placeBox(l,r,0,!0);a.bbox={w:r+l.bbox.rw,lw:0,rw:r+l.bbox.rw,H:Math.max(h.bbox.h,k.bbox.h,l.bbox.h,m.bbox.h),D:Math.max(h.bbox.d,k.bbox.d,l.bbox.d,m.bbox.d),h:k.bbox.h,d:k.bbox.d,exactW:!0};a.scale=f;a.isMultiChar=!0;this.setStackWidth(e,a.bbox.w)},createChar:function(a,b,c,e){a.isMathJax=!0;var d=a,g="",h={fonts:[b[1]],noRemap:!0};e&&e===k.VARIANT.BOLD&&(h.fonts=[b[1]+"-bold",b[1]]);"string"!==typeof b[1]&&(h=b[1]);if(b[0]instanceof Array){e=0;for(var l=b[0].length;e<l;e++)g+=String.fromCharCode(b[0][e])}else 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l=d.data[d.over],n=d.data[d.under];l&&this===l.CoreMO()&&d.Get("accent")?h=e.FONTDATA.REMAPACCENT:n&&this===n.CoreMO()&&d.Get("accentunder")&&(h=e.FONTDATA.REMAPACCENTUNDER)}g&&b.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(c=e.FONTDATA.VARIANT["-"+e.fontInUse+"-variant"]);d=0;for(g=this.data.length;d<g;d++)this.data[d]&&this.data[d].toHTML(a,c,this.HTMLremap,h);a.bbox||(a.bbox=this.HTMLzeroBBox());1!==b.length&&delete a.bbox.skew;e.AccentBug&&0===a.bbox.w&&1===b.length&&a.firstChild&&(a.firstChild.nodeValue+=e.NBSP,e.createSpace(a,0,0,-a.offsetWidth/e.em));f.largeop&&(b=(a.bbox.h-a.bbox.d)/2-e.TeX.axis_height*a.scale,e.safariVerticalAlignBug&&"IMG"===a.lastChild.nodeName?a.lastChild.style.verticalAlign=e.Em(e.unEm(a.lastChild.style.verticalAlign||0)/e.em-b/a.scale):e.konquerorVerticalAlignBug&&"IMG"===a.lastChild.nodeName?(a.style.position="relative",a.lastChild.style.position="relative",a.lastChild.style.top=e.Em(b/a.scale)):a.style.verticalAlign=e.Em(-b/a.scale),a.bbox.h-=b,a.bbox.d+=b,a.bbox.rw>a.bbox.w&&(a.bbox.ic=a.bbox.rw-a.bbox.w,e.createBlank(a,a.bbox.ic),a.bbox.w=a.bbox.rw));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},CoreParent:function(){for(var a=this;a&&a.isEmbellished()&&a.CoreMO()===this&&!a.isa(k.math);)a=a.Parent();return a},CoreText:function(a){if(!a)return"";if(a.isEmbellished())return a.CoreMO().data.join("");for(;(a.isa(k.mrow)||a.isa(k.TeXAtom)||a.isa(k.mstyle)||a.isa(k.mphantom))&&1===a.data.length&&a.data[0];)a=a.data[0];return a.isToken?a.data.join(""):""},HTMLremapChars:{"*":"\u2217",'"':"\u2033","\u00b0":"\u2218","\u00b2":"2","\u00b3":"3","\u00b4":"\u2032","\u00b9":"1"},HTMLremap:function(a,b){a=a.replace(/-/g,"\u2212");b&&(a=a.replace(/'/g,"\u2032").replace(/`/g,"\u2035"),1===a.length&&(a=b[a]||a));return a},HTMLcanStretch:function(a){if(!this.Get("stretchy"))return!1;var b=this.data.join("");if(1<b.length)return!1;var c=this.CoreParent();if(c&&c.isa(k.munderover)&&1===this.CoreText(c.data[c.base]).length){var f=c.data[c.over],d=c.data[c.under];f&&this===f.CoreMO()&&c.Get("accent")?b=e.FONTDATA.REMAPACCENT[b]||b:d&&this===d.CoreMO()&&c.Get("accentunder")&&(b=e.FONTDATA.REMAPACCENTUNDER[b]||b)}return(b=e.FONTDATA.DELIMITERS[b.charCodeAt(0)])&&b.dir==a.substr(0,1)},HTMLstretchV:function(a,b,c){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize"),d=this.HTMLspanElement(),g=this.HTMLgetMu(d),h,l=e.TeX.axis_height,k=d.scale;h=f.symmetric?2*Math.max(b-l,c+l):b+c;f.maxsize=e.length2em(f.maxsize,g,d.bbox.h+d.bbox.d);f.minsize=e.length2em(f.minsize,g,d.bbox.h+d.bbox.d);h=Math.max(f.minsize,Math.min(f.maxsize,h));d=this.HTMLcreateSpan(a);e.createDelimiter(d,this.data.join("").charCodeAt(0),h,k);h=f.symmetric?(d.bbox.h+d.bbox.d)/2+l:(d.bbox.h+d.bbox.d)*b/(b+c);e.positionDelimiter(d,h);this.HTMLhandleSpace(d);this.HTMLhandleColor(d);return d},HTMLstretchH:function(a,b){this.HTMLremoveColor();var c=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===c.fontweight||600<=parseInt(c.fontweight))&&!this.Get("mathvariant",!0)&&(c.mathvariant=k.VARIANT.BOLD);var f=this.HTMLspanElement(),d=this.HTMLgetMu(f),g=f.scale;c.maxsize=e.length2em(c.maxsize,d,f.bbox.w);c.minsize=e.length2em(c.minsize,d,f.bbox.w);b=Math.max(c.minsize,Math.min(c.maxsize,b));f=this.HTMLcreateSpan(a);e.createDelimiter(f,this.data.join("").charCodeAt(0),b,g,c.mathvariant);this.HTMLhandleSpace(f);this.HTMLhandleColor(f);return f}});k.mtext.Augment({toHTML:function(a){a=this.HTMLhandleSize(this.HTMLcreateSpan(a));var b=this.HTMLgetVariant();if(e.config.mtextFontInherit||"merror"===this.Parent().type)b={bold:b.bold,italic:b.italic,fontInherit:!0};for(var c=0,f=this.data.length;c<f;c++)this.data[c]&&this.data[c].toHTML(a,b);a.bbox||(a.bbox=this.HTMLzeroBBox());1!==this.data.join("").length&&delete a.bbox.skew;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});k.merror.Augment({toHTML:function(a){var b=MathJax.HTML.addElement(a,"span",{style:{display:"inline-block"}});a=this.SUPER(arguments).toHTML.call(this,b);var c=e.getHD(b),f=e.getW(b);b.bbox={h:c.h,d:c.d,w:f,lw:0,rw:f,exactW:!0};b.id=a.id;a.id=null;return b}});k.ms.Augment({toHTML:k.mbase.HTMLautoload});k.mglyph.Augment({toHTML:k.mbase.HTMLautoload});k.mspace.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var b=this.getValues("height","depth","width"),c=this.HTMLgetMu(a);b.mathbackground=this.mathbackground;this.background&&!this.mathbackground&&(b.mathbackground=this.background);var f=e.length2em(b.height,c),d=e.length2em(b.depth,c),c=e.length2em(b.width,c);e.createSpace(a,f,d,c,b.mathbackground,!0);return a}});k.mphantom.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var f=this.data[0].toHTML(a);null!=c?e.Remeasured(this.data[0].HTMLstretchV(a,b,c),a):null!=b?e.Remeasured(this.data[0].HTMLstretchH(a,b),a):f=e.Measured(f,a);a.bbox={w:f.bbox.w,h:f.bbox.h,d:f.bbox.d,lw:0,rw:0,exactW:!0};b=0;for(c=a.childNodes.length;b<c;b++)a.childNodes[b].style.visibility="hidden"}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mpadded.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var f=e.createStack(a,!0),d=e.createBox(f),g=this.data[0].toHTML(d);null!=c?e.Remeasured(this.data[0].HTMLstretchV(d,b,c),d):null!=b?e.Remeasured(this.data[0].HTMLstretchH(d,b),d):e.Measured(g,d);b=this.getValues("height","depth","width","lspace","voffset");var g=c=0,h=this.HTMLgetMu(a);b.lspace&&(c=this.HTMLlength2em(d,b.lspace,h));b.voffset&&(g=this.HTMLlength2em(d,b.voffset,h));e.placeBox(d,c,g);a.bbox={h:d.bbox.h,d:d.bbox.d,w:d.bbox.w,exactW:!0,lw:Math.min(0,d.bbox.lw+c),rw:Math.max(d.bbox.w,d.bbox.rw+c),H:Math.max(null==d.bbox.H?-e.BIGDIMEN:d.bbox.H,d.bbox.h+g),D:Math.max(null==d.bbox.D?-e.BIGDIMEN:d.bbox.D,d.bbox.d-g)};""!==b.height&&(a.bbox.h=this.HTMLlength2em(d,b.height,h,"h",0));""!==b.depth&&(a.bbox.d=this.HTMLlength2em(d,b.depth,h,"d",0));""!==b.width&&(a.bbox.w=this.HTMLlength2em(d,b.width,h,"w",0));a.bbox.H<=a.bbox.h&&delete a.bbox.H;a.bbox.D<=a.bbox.d&&delete a.bbox.D;d=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;a.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||d.exec(b.height)||d.exec(b.width)||d.exec(b.depth));e.setStackWidth(f,a.bbox.w)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLlength2em:function(a,b,c,f,d){null==d&&(d=-e.BIGDIMEN);var g=String(b).match(/width|height|depth/),g=g?a.bbox[g[0].charAt(0)]:f?a.bbox[f]:0;c=e.length2em(b,c,g);return f&&String(b).match(/^\s*[-+]/)?Math.max(d,a.bbox[f]+c):c},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mrow.Augment({HTMLlineBreaks:function(a){return this.parent.linebreakContainer?e.config.linebreaks.automatic&&a.bbox.w>e.linebreakWidth||this.hasNewline():!1},HTMLstretchH:function(a,b){this.HTMLremoveColor();var c=this.HTMLspanElement();this.data[this.core].HTMLstretchH(c,b);this.HTMLcomputeBBox(c,!0);this.HTMLhandleColor(c);return c},HTMLstretchV:function(a,b,c){this.HTMLremoveColor();a=this.HTMLspanElement();this.data[this.core].HTMLstretchV(a,b,c);this.HTMLcomputeBBox(a,!0);this.HTMLhandleColor(a);return a}});k.mstyle.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var e=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=e.bbox}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mfrac.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var b=e.createStack(a),c=e.createBox(b),f=e.createBox(b);e.MeasureSpans([this.HTMLboxChild(0,c),this.HTMLboxChild(1,f)]);var d=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),g=this.HTMLgetScale(),h=d.displaystyle,l=e.TeX.axis_height*g;if(d.bevelled){var d=h?.4:.15,k=Math.max(c.bbox.h+c.bbox.d,f.bbox.h+f.bbox.d)+2*d,b=e.createBox(b);e.createDelimiter(b,47,k);e.placeBox(c,0,(c.bbox.d-c.bbox.h)/2+l+d);e.placeBox(b,c.bbox.w-d/2,(b.bbox.d-b.bbox.h)/2+l);e.placeBox(f,c.bbox.w+b.bbox.w-d,(f.bbox.d-f.bbox.h)/2+l-d)}else{var k=Math.max(c.bbox.w,f.bbox.w),m=e.thickness2em(d.linethickness,g),p,q,r=e.TeX.min_rule_thickness/this.em;h?(p=e.TeX.num1,q=e.TeX.denom1):(p=0===m?e.TeX.num3:e.TeX.num2,q=e.TeX.denom2);p*=g;q*=g;0===m?(g=Math.max((h?7:3)*e.TeX.rule_thickness,2*r),h=p-c.bbox.d-(f.bbox.h-q),h<g&&(p+=(g-h)/2,q+=(g-h)/2)):(g=Math.max((h?2:0)*r+m,m/2+1.5*r),h=p-c.bbox.d-(l+m/2),h<g&&(p+=g-h),h=l-m/2-(f.bbox.h-q),h<g&&(q+=g-h),b=e.createBox(b),e.createRule(b,m,0,k+2*m),e.placeBox(b,0,l-m/2));e.alignBox(c,d.numalign,p);e.alignBox(f,d.denomalign,-q)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcanStretch:function(a){return!1},HTMLhandleSpace:function(a){if(!this.texWithDelims){var b=(this.useMMLspacing?0:e.length2em(this.texSpacing()||0))+.12;a.style.paddingLeft=e.Em(b);a.style.paddingRight=e.Em(.12)}}});k.msqrt.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var b=e.createStack(a),c=e.createBox(b),f=e.createBox(b),d=e.createBox(b),g=this.HTMLgetScale(),h=e.TeX.rule_thickness*g,l,k,m;l=this.Get("displaystyle")?e.TeX.x_height*g:h;l=Math.max(h+l/4,1.5*e.TeX.min_rule_thickness/this.em);var p=this.HTMLboxChild(0,c);k=p.bbox.h+p.bbox.d+l+h;e.createDelimiter(d,8730,k,g);e.MeasureSpans([p,d]);m=p.bbox.w;var q=0;if(d.isMultiChar||e.AdjustSurd&&e.imgFonts)d.bbox.w*=.95;d.bbox.h+d.bbox.d>k&&(l=(d.bbox.h+d.bbox.d-(k-h))/2);k=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];!k||m<k.HW[0][0]*g||.75>g?e.createRule(f,0,h,m):e.createDelimiter(f,e.FONTDATA.RULECHAR,m,g);k=p.bbox.h+l+h;l=k*e.rfuzz;d.isMultiChar&&(l=e.rfuzz);q=this.HTMLaddRoot(b,d,q,d.bbox.h+d.bbox.d-k,g);e.placeBox(d,q,k-d.bbox.h);e.placeBox(f,q+d.bbox.w,k-f.bbox.h+l);e.placeBox(c,q+d.bbox.w,0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLaddRoot:function(a,b,c,e,d){return c}});k.mroot.Augment({toHTML:k.msqrt.prototype.toHTML,HTMLaddRoot:function(a,b,c,f,d){a=e.createBox(a);this.data[1]?(c=this.data[1].toHTML(a),c.style.paddingRight=c.style.paddingLeft="",e.Measured(c,a)):a.bbox=this.HTMLzeroBBox();f=this.HTMLrootHeight(b.bbox.h+b.bbox.d,d,a)-f;d=Math.min(a.bbox.w,a.bbox.rw);c=Math.max(d,b.offset);e.placeBox(a,c-d,f);return c-b.offset},HTMLrootHeight:function(a,b,c){return.45*(a-.9*b)+.6*b+Math.max(0,c.bbox.d-.075)}});k.mfenced.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);this.data.open&&this.data.open.toHTML(a);null!=this.data[0]&&this.data[0].toHTML(a);for(var b=1,c=this.data.length;b<c;b++)this.data[b]&&(this.data["sep"+b]&&this.data["sep"+b].toHTML(a),this.data[b].toHTML(a));this.data.close&&this.data.close.toHTML(a);for(var e=this.HTMLcomputeBBox(a),d=a.bbox.h,g=a.bbox.d,b=0,c=e.length;b<c;b++)e[b].HTMLstretchV(a,d,g);e.length&&this.HTMLcomputeBBox(a,!0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcomputeBBox:function(a,b){var c=a.bbox={},e=[];this.HTMLcheckStretchy(this.data.open,c,e,b);this.HTMLcheckStretchy(this.data[0],c,e,b);for(var d=1,g=this.data.length;d<g;d++)this.data[d]&&(this.HTMLcheckStretchy(this.data["sep"+d],c,e,b),this.HTMLcheckStretchy(this.data[d],c,e,b));this.HTMLcheckStretchy(this.data.close,c,e,b);this.HTMLcleanBBox(c);return e},HTMLcheckStretchy:function(a,b,c,e){a&&(!e&&a.HTMLcanStretch("Vertical")&&(c.push(a),a=a.CoreMO()||a),this.HTMLcombineBBoxes(a,b))}});k.menclose.Augment({toHTML:k.mbase.HTMLautoload});k.maction.Augment({toHTML:k.mbase.HTMLautoload});k.semantics.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var e=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=e.bbox}this.HTMLhandleSpace(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.munderover.Augment({toHTML:function(a,b,c){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return k.msubsup.prototype.toHTML.call(this,a);a=this.HTMLcreateSpan(a);var d=this.HTMLgetScale(),g=e.createStack(a),h=[],l=[],n=[],m,p,q;p=0;for(q=this.data.length;p<q;p++)null!=this.data[p]&&(m=h[p]=e.createBox(g),l[p]=this.data[p].toHTML(m),p==this.base?(null!=c?this.data[this.base].HTMLstretchV(m,b,c):null!=b&&this.data[this.base].HTMLstretchH(m,b),n[p]=null==c&&null!=b?!1:this.data[p].HTMLcanStretch("Horizontal")):n[p]=this.data[p].HTMLcanStretch("Horizontal"));e.MeasureSpans(l);g=l=-e.BIGDIMEN;p=0;for(q=this.data.length;p<q;p++)this.data[p]&&(h[p].bbox.w>g&&(g=h[p].bbox.w),!n[p]&&g>l&&(l=g));null==c&&null!=b?l=b:l==-e.BIGDIMEN&&(l=g);p=g=0;for(q=this.data.length;p<q;p++)this.data[p]&&(m=h[p],n[p]&&(m.bbox=this.data[p].HTMLstretchH(m,l).bbox),m.bbox.w>g&&(g=m.bbox.w));b=e.TeX.rule_thickness;c=e.FONTDATA.TeX_factor;var n=h[this.base]||{bbox:this.HTMLzeroBBox()},r,t,u,v=0;n.bbox.ic&&(v=1.3*n.bbox.ic+.05);p=0;for(q=this.data.length;p<q;p++)null!=this.data[p]&&(m=h[p],l=e.TeX.big_op_spacing5*d,(u=p!=this.base&&f[this.ACCENTS[p]])&&m.bbox.w<=1/e.em+1E-4&&(m.bbox.w=m.bbox.rw-m.bbox.lw,m.bbox.noclip=!0,m.bbox.lw&&m.insertBefore(e.createSpace(m.parentNode,0,0,-m.bbox.lw),m.firstChild),e.createBlank(m,0,0,m.bbox.rw+.1)),r={left:0,center:(g-m.bbox.w)/2,right:g-m.bbox.w}[f.align],t=0,p==this.over?(u?(u=Math.max(b*d*c,2.5/this.em),l=0,n.bbox.skew&&(r+=n.bbox.skew)):(u=e.TeX.big_op_spacing1*d*c,t=e.TeX.big_op_spacing3*d*c,u=Math.max(u,t-Math.max(0,m.bbox.d))),u=Math.max(u,1.5/this.em),r+=v/2,t=n.bbox.h+m.bbox.d+u,m.bbox.h+=l):p==this.under&&(u?(u=3*b*d*c,l=0):(u=e.TeX.big_op_spacing2*d*c,t=e.TeX.big_op_spacing4*d*c,u=Math.max(u,t-m.bbox.h)),u=Math.max(u,1.5/this.em),r-=v/2,t=-(n.bbox.d+m.bbox.h+u),m.bbox.d+=l),e.placeBox(m,r,t));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.msubsup.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);var f=this.HTMLgetScale(),d=this.HTMLgetMu(a),g=e.createStack(a),h,k=[],n=e.createBox(g);this.data[this.base]?(k.push(this.data[this.base].toHTML(n)),null!=c?this.data[this.base].HTMLstretchV(n,b,c):null!=b&&this.data[this.base].HTMLstretchH(n,b)):n.bbox=this.HTMLzeroBBox();b=e.TeX.x_height*f;c=e.TeX.scriptspace*f*.75;var m;this.HTMLnotEmpty(this.data[this.sup])&&(m=e.createBox(g),k.push(this.data[this.sup].toHTML(m)));this.HTMLnotEmpty(this.data[this.sub])&&(h=e.createBox(g),k.push(this.data[this.sub].toHTML(h)));e.MeasureSpans(k);m&&(m.bbox.w+=c,m.bbox.rw=Math.max(m.bbox.w,m.bbox.rw));h&&(h.bbox.w+=c,h.bbox.rw=Math.max(h.bbox.w,h.bbox.rw));e.placeBox(n,0,0);var k=m?this.data[this.sup].HTMLgetScale():h?this.data[this.sub].HTMLgetScale():this.HTMLgetScale(),p=e.TeX.sup_drop*k,g=n.bbox.h-p,q=n.bbox.d+e.TeX.sub_drop*k,k=0;n.bbox.ic&&(n.bbox.w-=n.bbox.ic,k=1.3*n.bbox.ic+.05);!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||1!==this.data[this.base].data.join("").length||1!==n.bbox.scale||this.data[this.base].Get("largeop")||(g=q=0);c=this.getValues("subscriptshift","superscriptshift");c.subscriptshift=""===c.subscriptshift?0:e.length2em(c.subscriptshift,d);c.superscriptshift=""===c.superscriptshift?0:e.length2em(c.superscriptshift,d);m?h?(q=Math.max(q,e.TeX.sub2*f),f*=e.TeX.rule_thickness,g-m.bbox.d-(h.bbox.h-q)<3*f&&(q=3*f-g+m.bbox.d+h.bbox.h,p=.8*b-(g-m.bbox.d),0<p&&(g+=p,q-=p)),e.placeBox(m,n.bbox.w+k,Math.max(g,c.superscriptshift)),e.placeBox(h,n.bbox.w,-Math.max(q,c.subscriptshift))):(h=this.getValues("displaystyle","texprimestyle"),h=e.TeX[h.displaystyle?"sup1":h.texprimestyle?"sup3":"sup2"],g=Math.max(g,h*f,m.bbox.d+.25*b,c.superscriptshift),e.placeBox(m,n.bbox.w+k,g,m.bbox)):h&&(q=Math.max(q,e.TeX.sub1*f,h.bbox.h-.8*b,c.subscriptshift),e.placeBox(h,n.bbox.w,-q,h.bbox));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mmultiscripts.Augment({toHTML:k.mbase.HTMLautoload});k.mtable.Augment({toHTML:k.mbase.HTMLautoload});k["annotation-xml"].Augment({toHTML:k.mbase.HTMLautoload});k.math.Augment({toHTML:function(a,b){var c=this.Get("alttext");c&&""!==c&&b.setAttribute("aria-label",c);var f=e.addElement(a,"nobr",{isMathJax:!0});a=this.HTMLcreateSpan(f);var c=e.createStack(a),d=e.createBox(c),g;c.style.fontSize=f.parentNode.style.fontSize;f.parentNode.style.fontSize="";null!=this.data[0]&&(e.msieColorBug&&(this.background&&(this.data[0].background=this.background,delete this.background),this.mathbackground&&(this.data[0].mathbackground=this.mathbackground,delete this.mathbackground)),k.mbase.prototype.displayAlign=t.config.displayAlign,k.mbase.prototype.displayIndent=t.config.displayIndent,g=this.data[0].toHTML(d),g.bbox.exactW=!1,g=e.Measured(g,d));e.placeBox(d,0,0);a.style.width=e.Em((Math.round(g.bbox.w*this.em)+.25)/e.outerEm);a.style.display="inline-block";var f=1/e.em,h=e.em/e.outerEm;e.em/=h;a.bbox.h*=h;a.bbox.d*=h;a.bbox.w*=h;a.bbox.lw*=h;a.bbox.rw*=h;g&&null!=g.bbox.width&&(a.style.minWidth=g.bbox.minWidth||a.style.width,a.style.width=c.style.width=g.bbox.width,d.style.width="100%");this.HTMLhandleColor(a);g&&e.createRule(a,(g.bbox.h+f)*h,(g.bbox.d+f)*h,0);this.isMultiline||"block"!==this.Get("display")||null!=a.bbox.width||(c=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift"),c.indentalignfirst!==k.INDENTALIGN.INDENTALIGN&&(c.indentalign=c.indentalignfirst),c.indentalign===k.INDENTALIGN.AUTO&&(c.indentalign=this.displayAlign),b.style.textAlign=c.indentalign,c.indentshiftfirst!==k.INDENTSHIFT.INDENTSHIFT&&(c.indentshift=c.indentshiftfirst),"auto"===c.indentshift&&(c.indentshift=this.displayIndent),c.indentshift&&c.indentalign!==k.INDENTALIGN.CENTER&&(a.style[{left:"marginLeft",right:"marginRight"}[c.indentalign]]=e.Em(e.length2em(c.indentshift))));return a},HTMLspanElement:k.mbase.prototype.HTMLspanElement});k.TeXAtom.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);if(null!=this.data[0])if(this.texClass===k.TEXCLASS.VCENTER){var b=e.createStack(a),b=e.createBox(b);e.Measured(this.data[0].toHTML(b),b);e.placeBox(b,0,e.TeX.axis_height-(b.bbox.h+b.bbox.d)/2+b.bbox.d)}else a.bbox=this.data[0].toHTML(a).bbox;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});t.Register.StartupHook("End Config",function(){t.Browser.Select({MSIE:function(a){var b=document.documentMode||0,c=a.versionAtLeast("7.0"),f=a.versionAtLeast("8.0")&&7<b,d="BackCompat"===document.compatMode;9>b&&(e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white",e.config.styles[".MathJax .MathJax_HitBox"].opacity=0,e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity\x3d0)");e.Augment({PaddingWidthBug:!0,msieAccentBug:!0,msieColorBug:!0,msieColorPositionBug:!0,msieRelativeWidthBug:d,msieDisappearingBug:8<=b,msieMarginScaleBug:8>b,msiePaddingWidthBug:!0,msieBorderWidthBug:d,msieFrameSizeBug:8>=b,msieInlineBlockAlignBug:!f||d,msiePlaceBoxBug:f&&!d,msieClipRectBug:!f,msieNegativeSpaceBug:d,cloneNodeBug:f&&"8.0"===a.version,initialSkipBug:8>b,msieNegativeBBoxBug:8<=b,msieIE6:!c,msieItalicWidthBug:!0,FontFaceBug:!0,msieFontCSSBug:a.isIE9,allowWebFonts:9<=b?"woff":"eot"})},Firefox:function(a){var b=!1;a.versionAtLeast("3.5")&&(a=String(document.location).replace(/[^\/]*$/,""),"file:"!==document.location.protocol||t.config.root.match(/^https?:\/\//)||(t.config.root+"/").substr(0,a.length)===a)&&(b="otf");e.Augment({ffVerticalAlignBug:!0,AccentBug:!0,allowWebFonts:b})},Safari:function(a){var b=a.versionAtLeast("3.0"),c=a.versionAtLeast("3.1"),f=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/),d=navigator.appVersion.match(/ Android (\d+)\.(\d+)/),d=c&&a.isMobile&&(navigator.platform.match(/iPad|iPod|iPhone/)&&!a.versionAtLeast("5.0")||null!=d&&(2>d[1]||2==d[1]&&2>d[2]));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:.011,AccentBug:!0,AdjustSurd:!0,negativeBBoxes:!0,safariNegativeSpaceBug:!0,safariVerticalAlignBug:!c,safariTextNodeBug:!b,forceReflow:!0,allowWebFonts:c&&!d?"otf":!1});f&&e.Augment({webFontDefault:a.isMobile?"sans-serif":"serif"});a.isPC&&e.Augment({adjustAvailableFonts:e.removeSTIXfonts,checkWebFontsTwice:!0});d&&((a=t.config["HTML-CSS"])?(a.availableFonts=[],a.preferredFont=null):t.config["HTML-CSS"]={availableFonts:[],preferredFont:null})},Chrome:function(a){e.Augment({Em:e.EmRounded,cloneNodeBug:!0,rfuzz:.011,AccentBug:!0,AdjustSurd:!0,negativeBBoxes:!0,safariNegativeSpaceBug:!0,safariWebFontSerif:[""],forceReflow:!0,allowWebFonts:a.versionAtLeast("4.0")?"otf":"svg"})},Opera:function(a){a.isMini=null!=navigator.appVersion.match("Opera Mini");e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.config.styles[".MathJax span"]["z-index"]=0;e.Augment({operaHeightBug:!0,operaVerticalAlignBug:!0,operaFontSizeBug:a.versionAtLeast("10.61"),initialSkipBug:!0,FontFaceBug:!0,PaddingWidthBug:!0,allowWebFonts:a.versionAtLeast("10.0")&&!a.isMini?"otf":!1,adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(a){e.Augment({konquerorVerticalAlignBug:!0})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){"None"!==t.config.menuSettings.zoom&&v.Require("[MathJax]/extensions/MathZoom.js")})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);
    14.