commit 23ad7609bcf1d16788a15a8e2ac1d242673ef004 parent de1e1f670e34594a7f1e4cc9012deb36d79c511b Author: Davide P. Cervone <dpvc@union.edu> Date: Wed, 11 May 2011 20:13:25 -0400 Add ability to load extra stretchy characters on demand, and add data for more stretchable characters. Diffstat:
14 files changed, 858 insertions(+), 21 deletions(-)
diff --git a/config/Accessible-full.js b/config/Accessible-full.js @@ -88,7 +88,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1";var a=Ma (function(b,e,d){var a,c=e.Browser.isMSIE;b.Augment({LEFTBUTTON:(c?1:0),MENUKEY:"altKey",noContextMenuBug:e.Browser.isKonequeror,msieQuirks:(c&&!(document.compatMode==="BackCompat")),msieEventBug:e.Browser.isIE9,config:{styles:{}},settings:e.config.menuSettings,Startup:function(){return MathJax.Ajax.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(e.config.displayAlign!=="center"){var h=e.config.displayAlign,f=e.config.displayIndent;var g={"text-align":h+"!important"};g["margin-"+h]=f+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":g,"div.MathJax_MathML math":{"text-align":h},"div.MathJax_MathContainer > span":{"text-align":h+"!important"}})}},Translate:function(g){if(!g.parentNode){return}var k=g.previousSibling;if(k&&String(k.className).match(/^MathJax(_MathML|_Display)?$/)){k.parentNode.removeChild(k)}var j=g.MathJax.elementJax.root;var i=(j.Get("display")==="block"?"div":"span");var h=document.createElement(i),f=h;h.className="MathJax_MathML";h.style.fontSize=this.config.scale+"%";if(c&&this.config.showMathMenuMSIE){f=MathJax.HTML.addElement(h,"span",{className:"MathJax_MathContainer",style:{display:"inline-block",position:"relative"}})}j.toNativeMML(f);g.parentNode.insertBefore(h,g);if(c){if(this.config.showMathMenuMSIE){this.MSIEoverlay(h)}}else{j=h.firstChild;j.oncontextmenu=this.ContextMenu;j.onmouseover=this.Mouseover;j.onmousedown=this.Mousedown;j.onclick=this.Click;j.ondblclick=this.DblClick}},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/MathJax_MathML/)){g.parentNode.removeChild(g)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(m){var l=m.firstChild;m.style.position="absolute";var n=m.scrollHeight,h=m.offsetWidth;var j=MathJax.HTML.addElement(m,"img",{src:"about:blank",style:{width:0,height:n+"px"}});var f=m.scrollHeight-n;m.removeChild(j);m.style.position="";var k,i,g=(m.parentNode.nodeName.toLowerCase()==="div");if(g&&this.quirks){k=-n;i=Math.floor(-h/2)}else{k=f-n,i=-h}MathJax.HTML.addElement(m,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{style:{display:"inline-block",position:"absolute",left:i+"px",top:k+"px",width:l.offsetWidth+"px",height:n+"px",cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"},onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent}]])},MSIEmath:function(f){var g=f.parentNode.previousSibling.firstChild;return(g.nodeName.toLowerCase()==="span"?g.firstChild:g)},MSIEevent:function(){var 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f=(c?this.parentNode.parentNode.nextSibling:this.parentNode.nextSibling);g.jax=e.getJaxFor(f);g.menu.items[1].menu.items[1].name=(g.jax.inputJax.id==="MathML"?"Original":g.jax.inputJax.id);delete b.trapClick;delete b.trapUp;return g.menu.Post(i)}else{if(!d.loadingMathMenu){d.loadingMathMenu=true;var h={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(d.Require("[MathJax]/extensions/MathMenu.js"),function(){delete d.loadingMathMenu},[this,arguments.callee,h,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(b.config.showMathMenu){if(!f){f=window.event}if(b.settings.context==="MathJax"){if(!b.noContextMenuBug||f.button!==2){return}}else{if(!f[b.MENUKEY]||f.button!==b.LEFTBUTTON){return}}return 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o=this.NativeMMLcopyAttributes,k=this.NativeMMLskipAttributes;if(this.type==="mstyle"){l=a.math.prototype.defaults}for(var n in l){if(!k[n]&&l.hasOwnProperty(n)){if(this[n]!=null){h.setAttribute(n,this.NativeMMLattribute(n,this[n]))}}}for(var j=0,g=o.length;j<g;j++){if(this[o[j]]!=null){h.setAttribute(o[j],this.NativeMMLattribute(o[j],this[o[j]]))}}},NativeMMLcopyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],NativeMMLskipAttributes:{texClass:1,useHeight:1,texprimestyle:1},NativeMMLattribute:function(h,g){g=String(g);if(b.NAMEDSPACE[g]){g=b.NAMEDSPACE[g]}else{if(g.match(/^\s*([-+]?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){g=((1/18)*RegExp.$1)+"em"}else{if(g==="-tex-caligraphic"){g="script"}else{if(g==="-tex-oldstyle"){g="normal"}}}}return g},NativeMMLelement:(c?function(g){return document.createElement("mjx:"+g)}:function(g){return 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j=0,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}}l.appendChild(h)}});if(MathJax.Hub.Browser.isFirefox){a.mtable.Augment({toNativeMML:function(g){if(this.width){var h=(this.style||"").replace(/;\s*$/,"").split(";");h.push("width:"+this.width);this.style=h.join(";")}this.SUPER(arguments).toNativeMML.call(this,g)}});a.mlabeledtr.Augment({toNativeMML:function(k){var h=this.NativeMMLelement("mtr");this.NativeMMLattributes(h);for(var j=1,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}else{h.appendChild(this.NativeMMLelement("mrow"))}}k.appendChild(h)}});var f=MathJax.Hub.config.root+"/fonts/HTML-CSS/TeX/otf";b.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS"},'[mathvariant="script"]':{"font-family":"MathJax_Script"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur"},'[mathvariant="-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic"},'[mathvariant="-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic","font-weight":"bold"},'[mathvariant="-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic"},'[mathvariant="-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic","font-weight":"bold"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sansserif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sansserif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sansserif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sansserif","font-style":"italic","font-weight":"bold"},"@font-face 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g=this.NativeMMLelement("mrow");this.data[0].toNativeMML(g);h.appendChild(g)}});a.chars.Augment({toNativeMML:function(g){g.appendChild(document.createTextNode(this.toString()))}});a.entity.Augment({toNativeMML:function(g){g.appendChild(document.createTextNode(this.toString()))}});e.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toNativeMML:function(g){this.Core().toNativeMML(g)}})});setTimeout(MathJax.Callback(["loadComplete",b,"jax.js"]),0)});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){d.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax); -(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} 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g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var 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i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var 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f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid 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k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var 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m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var 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g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.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}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");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=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieCharPaddingWidthBug:(h&&!g),msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));if(!y.fillExtenders){i=(g-o)/(s*r)}var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(k[4]){h*=k[4]}if(h!==1||k[3]){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(k[3]){o.firstChild.style.verticalAlign=this.Em(k[3]);o.bbox.h+=k[3];if(o.bbox.h<0){o.bbox.h=0}}if(k[5]){o.bbox.h+=k[5]}if(k[6]){o.bbox.d+=k[6]}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var 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b.ContextMenu.call(this,f,true)}},Mouseover:function(f){b.HandleEvent(f,"Mouseover",this)},Click:function(f){b.HandleEvent(f,"Click",this)},DblClick:function(f){b.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});e.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toNativeMML:function(k){var h=this.NativeMMLelement(this.type);this.NativeMMLattributes(h);for(var j=0,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}else{h.appendChild(this.NativeMMLelement("mrow"))}}k.appendChild(h)},NativeMMLattributes:function(h){var l=this.defaults;var o=this.NativeMMLcopyAttributes,k=this.NativeMMLskipAttributes;if(this.type==="mstyle"){l=a.math.prototype.defaults}for(var n in l){if(!k[n]&&l.hasOwnProperty(n)){if(this[n]!=null){h.setAttribute(n,this.NativeMMLattribute(n,this[n]))}}}for(var j=0,g=o.length;j<g;j++){if(this[o[j]]!=null){h.setAttribute(o[j],this.NativeMMLattribute(o[j],this[o[j]]))}}},NativeMMLcopyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],NativeMMLskipAttributes:{texClass:1,useHeight:1,texprimestyle:1},NativeMMLattribute:function(h,g){g=String(g);if(b.NAMEDSPACE[g]){g=b.NAMEDSPACE[g]}else{if(g.match(/^\s*([-+]?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){g=((1/18)*RegExp.$1)+"em"}else{if(g==="-tex-caligraphic"){g="script"}else{if(g==="-tex-oldstyle"){g="normal"}}}}return g},NativeMMLelement:(c?function(g){return document.createElement("mjx:"+g)}:function(g){return document.createElementNS(b.MMLnamespace,g)})});a.mrow.Augment({toNativeMML:function(j){if(this.inferred&&this.parent.inferRow){for(var h=0,g=this.data.length;h<g;h++){if(this.data[h]){this.data[h].toNativeMML(j)}else{j.appendChild(this.NativeMMLelement("mrow"))}}}else{this.SUPER(arguments).toNativeMML.call(this,j)}}});a.msubsup.Augment({toNativeMML:function(l){var k=this.type;if(this.data[this.sup]==null){k="msub"}if(this.data[this.sub]==null){k="msup"}var h=this.NativeMMLelement(k);this.NativeMMLattributes(h);delete this.data[0].inferred;for(var j=0,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}}l.appendChild(h)}});a.munderover.Augment({toNativeMML:function(l){var k=this.type;if(this.data[this.under]==null){k="mover"}if(this.data[this.over]==null){k="munder"}var h=this.NativeMMLelement(k);this.NativeMMLattributes(h);delete this.data[0].inferred;for(var j=0,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}}l.appendChild(h)}});if(MathJax.Hub.Browser.isFirefox){a.mtable.Augment({toNativeMML:function(g){if(this.width){var h=(this.style||"").replace(/;\s*$/,"").split(";");h.push("width:"+this.width);this.style=h.join(";")}this.SUPER(arguments).toNativeMML.call(this,g)}});a.mlabeledtr.Augment({toNativeMML:function(k){var h=this.NativeMMLelement("mtr");this.NativeMMLattributes(h);for(var j=1,g=this.data.length;j<g;j++){if(this.data[j]){this.data[j].toNativeMML(h)}else{h.appendChild(this.NativeMMLelement("mrow"))}}k.appendChild(h)}});var f=MathJax.Hub.config.root+"/fonts/HTML-CSS/TeX/otf";b.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS"},'[mathvariant="script"]':{"font-family":"MathJax_Script"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur"},'[mathvariant="-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic"},'[mathvariant="-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic","font-weight":"bold"},'[mathvariant="-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic"},'[mathvariant="-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic","font-weight":"bold"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sansserif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sansserif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sansserif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sansserif","font-style":"italic","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_AMS",src:"local('MathJax_AMS'), url('"+f+"/MathJax_AMS-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Script",src:"local('MathJax_Script'), url('"+f+"/MathJax_Script-Regular.otf')"},"@font-face /*3*/":{"font-family":"MathJax_Fraktur",src:"local('MathJax_Fraktur'), url('"+f+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Caligraphic",src:"local('MathJax_Caligraphic'), url('"+f+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur","font-weight":"bold",src:"local('MathJax_Fraktur-Bold'), url('"+f+"/MathJax_Fraktur-Bold.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Caligraphic","font-weight":"bold",src:"local('MathJax_Caligraphic-Bold'), url('"+f+"/MathJax_Caligraphic-Bold.otf')"}}}})}a.TeXAtom.Augment({toNativeMML:function(h){var g=this.NativeMMLelement("mrow");this.data[0].toNativeMML(g);h.appendChild(g)}});a.chars.Augment({toNativeMML:function(g){g.appendChild(document.createTextNode(this.toString()))}});a.entity.Augment({toNativeMML:function(g){g.appendChild(document.createTextNode(this.toString()))}});e.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toNativeMML:function(g){this.Core().toNativeMML(g)}})});setTimeout(MathJax.Callback(["loadComplete",b,"jax.js"]),0)});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){d.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax); -(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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l=this.data[1].toHTML(i);l.style.paddingRight=l.style.paddingLeft="";e.Measured(l,i)}else{i.bbox=this.HTMLzeroBBox()}var j=this.HTMLrootHeight(g.bbox.h+g.bbox.d,f,i)-k;var n=Math.min(i.bbox.w,i.bbox.rw);m=Math.max(n,g.offset);e.placeBox(i,m-n,j);return m-g.offset},HTMLrootHeight:function(h,g,f){return 0.45*(h-0.9*g)+0.6*g+Math.max(0,f.bbox.d-0.075)}});a.mfenced.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data.open){this.data.open.toHTML(k)}if(this.data[0]!=null){this.data[0].toHTML(k)}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){if(this.data["sep"+g]){this.data["sep"+g].toHTML(k)}this.data[g].toHTML(k)}}if(this.data.close){this.data.close.toHTML(k)}var n=this.HTMLcomputeBBox(k);var j=k.bbox.h,l=k.bbox.d;for(g=0,f=n.length;g<f;g++){n[g].HTMLstretchV(k,j,l)}if(n.length){this.HTMLcomputeBBox(k,true)}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcomputeBBox:function(k,j){var g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.munderover.Augment({toHTML:function(G,B,z){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,G)}G=this.HTMLcreateSpan(G);var K=this.HTMLgetScale();var j=e.createStack(G);var l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(g==-e.BIGDIMEN){g=F}if(z==null&&B!=null){g=F=B}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}o=e.TeX.big_op_spacing5*K;var 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete 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o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax 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g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} 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g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));if(!y.fillExtenders){i=(g-o)/(s*r)}var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(k[4]){h*=k[4]}if(h!==1||k[3]){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(k[3]){o.firstChild.style.verticalAlign=this.Em(k[3]);o.bbox.h+=k[3];if(o.bbox.h<0){o.bbox.h=0}}if(k[5]){o.bbox.h+=k[5]}if(k[6]){o.bbox.d+=k[6]}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=f.HTMLspanElement();if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" 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g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var 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o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete 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f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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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:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax 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h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=f.HTMLspanElement();if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.munderover.Augment({toHTML:function(G,B,z){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,G)}G=this.HTMLcreateSpan(G);var K=this.HTMLgetScale();var j=e.createStack(G);var l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(g==-e.BIGDIMEN){g=F}if(z==null&&B!=null){g=F=B}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}o=e.TeX.big_op_spacing5*K;var u=(H!=this.base&&f[this.ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q.insertBefore(e.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild)}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(g-q.bbox.w)/2,right:g-q.bbox.w}[f.align];p=v;n=0;if(H==this.over){if(u){E=Math.max(w*K*A,2.5/this.em);o=0;if(h.bbox.skew){p+=h.bbox.skew}}else{s=e.TeX.big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E=Math.max(s,r-Math.max(0,q.bbox.d))}E=Math.max(E,1.5/this.em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==this.under){if(u){E=3*w*K*A;o=0}else{s=e.TeX.big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E=Math.max(s,r-q.bbox.h)}E=Math.max(E,1.5/this.em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}e.placeBox(q,p,n)}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(C,A,w){C=this.HTMLcreateSpan(C);var G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var m=i.bbox.h-y,l=i.bbox.d+x,F=0,z;if(i.bbox.ic){F=i.bbox.ic}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&&i.bbox.scale===1&&!this.data[this.base].Get("largeop")){m=l=0}}var B=this.getValues("subscriptshift","superscriptshift");B.subscriptshift=(B.subscriptshift===""?0:e.length2em(B.subscriptshift));B.superscriptshift=(B.superscriptshift===""?0:e.length2em(B.superscriptshift));if(!f){if(k){l=Math.max(l,e.TeX.sub1*G,k.bbox.h-(4/5)*E,B.subscriptshift);e.placeBox(k,i.bbox.w+o-F,-l,k.bbox)}}else{if(!k){g=this.getValues("displaystyle","texprimestyle");z=e.TeX[(g.displaystyle?"sup1":(g.texprimestyle?"sup3":"sup2"))];m=Math.max(m,z*G,f.bbox.d+(1/4)*E,B.superscriptshift);e.placeBox(f,i.bbox.w+o,m,f.bbox)}else{l=Math.max(l,e.TeX.sub2*G);var n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.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}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");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=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieCharPaddingWidthBug:(h&&!g),msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));if(!y.fillExtenders){i=(g-o)/(s*r)}var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var 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u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete 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f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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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:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax 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f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" 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m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var g=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:m.mathbackground,width:e.Em(h),height:e.Em(l),verticalAlign:e.Em(f),marginLeft:e.Em(j),marginRight:e.Em(i)}});if(e.msieInlineBlockAlignBug){g.style.position="relative";g.style.width=g.style.height=0;g.style.verticalAlign=g.style.marginLeft=g.style.marginRight="";e.placeBox(e.addElement(g,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",width:e.Em(h),height:e.Em(l),background:m.mathbackground}}),j,k.bbox.h+n)}k.parentNode.insertBefore(g,k);if(e.msieColorPositionBug){k.style.position="relative"}return g}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(g==-e.BIGDIMEN){g=F}if(z==null&&B!=null){g=F=B}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}o=e.TeX.big_op_spacing5*K;var u=(H!=this.base&&f[this.ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q.insertBefore(e.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild)}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(g-q.bbox.w)/2,right:g-q.bbox.w}[f.align];p=v;n=0;if(H==this.over){if(u){E=Math.max(w*K*A,2.5/this.em);o=0;if(h.bbox.skew){p+=h.bbox.skew}}else{s=e.TeX.big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E=Math.max(s,r-Math.max(0,q.bbox.d))}E=Math.max(E,1.5/this.em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==this.under){if(u){E=3*w*K*A;o=0}else{s=e.TeX.big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E=Math.max(s,r-q.bbox.h)}E=Math.max(E,1.5/this.em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}e.placeBox(q,p,n)}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(C,A,w){C=this.HTMLcreateSpan(C);var 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c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});if(MathJax.Hub.Browser.isMSIE){MathJax.InputJax.TeX.Definitions.mathchar0mi.digamma=["03DC",{variantForm:true}];MathJax.InputJax.TeX.Definitions.mathchar0mi.varkappa=["03F0",{variantForm:true}]}});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=MathJax.InputJax.TeX.Definitions;var c=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){c["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(c["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){b.mathchar0mi.varnothing="2205";b.mathchar0mi.hslash="210F";b.mathchar0mi.blacktriangle="25B4";b.mathchar0mi.blacktriangledown="25BE";b.mathchar0mi.square="25FB";b.mathchar0mi.blacksquare="25FC";b.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];b.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];b.mathchar0mo.blacktriangleleft="25C2";b.mathchar0mo.blacktriangleright="25B8";b.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(c["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); -(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return 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k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var 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m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var 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g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.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}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");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=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieCharPaddingWidthBug:(h&&!g),msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));if(!y.fillExtenders){i=(g-o)/(s*r)}var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(k[4]){h*=k[4]}if(h!==1||k[3]){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(k[3]){o.firstChild.style.verticalAlign=this.Em(k[3]);o.bbox.h+=k[3];if(o.bbox.h<0){o.bbox.h=0}}if(k[5]){o.bbox.h+=k[5]}if(k[6]){o.bbox.d+=k[6]}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var 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u="MathJax_WinIE6";g.FONTDATA.FONTS[u]="WinIE6/Regular/Main.js";g.FONTDATA.RANGES.push({name:"arrows",low:8592,high:8601,offset:"AR"});var t={variant:"-WinIE6",8658:57866,8660:57867,8704:57868,8706:57869,8707:57870,8711:57871,8712:57872,8715:57873,8725:57874,8730:57875,8733:57876,8734:57877,8736:57878,8739:57879,8741:57880,8743:57881,8744:57882,8745:57883,8746:57884,8747:57885,8764:57886,8776:57887,8800:57888,8801:57889,8804:57890,8805:57891,8810:57892,8811:57893,8834:57894,8835:57895,8838:57896,8839:57897,8853:57898,8857:57899,8869:57900,9651:57901,9661:57902,9711:57903,9824:57904,9825:57905,9826:57906,9827:57907,9837:57908,9838:57909,9839:57910,8806:58053,8807:58054,8814:58055,8815:58056,9484:58058,9488:58059,9492:58060,9496:58061,9585:58062,9586:58063,9632:58064,9633:58065,9650:58066,9654:58068,9660:58069,9661:58070,9664:58071,9674:58072,8756:58073,8757:58074,8786:58075,9733:58076,8765:58077};var w={variant:"-WinIE6",8658:57930,8660:57931,8704:57932,8706:57933,8707:57934,8711:57935,8712:57936,8715:57937,8725:57938,8730:57939,8733:57940,8734:57941,8736:57942,8739:57943,8741:57944,8743:57945,8744:57946,8745:57947,8746:57948,8747:57949,8764:57950,8776:57951,8800:57952,8801:57953,8804:57954,8805:57955,8810:57956,8811:57957,8834:57958,8835:57959,8838:57960,8839:57961,8853:57962,8857:57963,8869:57964,9651:57965,9661:57966,9711:57967,9824:57968,9825:57969,9826:57970,9827:57971,9837:57972,9838:57973,9839:57974,8806:58053,8807:58054,8814:58055,8815:58056,9484:58058,9488:58059,9492:58060,9496:58061,9585:58062,9586:58063,9632:58064,9633:58065,9650:58066,9654:58068,9660:58069,9661:58070,9664:58071,9674:58072,8756:58073,8757:58074,8786:58075,9733:58076,8765:58077};var q={offsetAR:57856,variantAR:"-WinIE6",remap:t};var v={offsetAR:57920,variantAR:"-WinIE6",remap:w};g.Augment({FONTDATA:{VARIANT:{normal:q,bold:v,italic:q,"bold-italic":v,"-largeOp":{fonts:[u,c,d,f],remap:{8719:58000,8721:58001,8747:58005,8750:58006}},"-smallOp":{fonts:[u,d,f],remap:{8719:57984,8721:57985,8747:57989,8750:57990}},"-WinIE6":{fonts:[u]}},DELIMITERS:{8730:{HW:{0:[1,u,null,57875],1:[1.2,u,null,57986],2:[1.8,u,null,58002],3:[2.4,u,null,58018],4:[3,u,null,58034]}},124:{stretch:{ext:[57879,u]}},8739:{HW:{0:[1,u,null,57879]},stretch:{ext:[57879,u]}},9168:{HW:{1:[1,u,null,57879]},stretch:{ext:[57879,u]}},8741:{HW:{0:[1,u,null,57880]},stretch:{ext:[57880,u]}},8592:{HW:{0:[0.889,u,null,57856]},stretch:{left:[57856,u]}},8593:{HW:{0:[0.888,u,null,57857]},stretch:{top:[57991,u],ext:[57993,u]}},8594:{HW:{0:[0.889,u,null,57858]},stretch:{right:[57858,u]}},8595:{HW:{0:[0.888,u,null,57859]},stretch:{bot:[57992,u],ext:[57993,u]}},8596:{HW:{0:[1,u,null,57860]},stretch:{left:[57856,u],right:[57858,u]}},8597:{HW:{0:[1.044,u,null,57859]},stretch:{top:[57991,u],bot:[57992,u],ext:[57993,u]}}}}})}},Chrome:function(r){if(r.isPC&&!MathJax.Hub.Browser.versionAtLeast("5.0")){var q="-WinChrome";g.Augment({FONTDATA:{VARIANT:{normal:{remap:{62:[62,q]}},bold:{remap:{58097:[62,q]}},italic:{remap:{100:[100,q]}},"-tex-caligraphic":{remap:{84:[84,q]}},"-largeOp":{remap:{10752:[10752,q]}},"-smallOp":{remap:{8899:[8899,q]}},"-WinChrome":{fonts:["MathJax_WinChrome"]}},DELIMITERS:{93:{stretch:{bot:[9126,"MathJax_WinChrome"]}},8971:{stretch:{bot:[9126,"MathJax_WinChrome"]}}}}});g.FONTDATA.FONTS.MathJax_WinChrome={directory:"WinChrome/Regular",family:"MathJax_WinChrome",testString:"> T d "+String.fromCharCode(9126)+" "+String.fromCharCode(10752),skew:{84:0.0278,58096:0.0319},32:[0,0,250,0,0],62:[540,40,778,82,694],84:[717,69,545,34,834],100:[694,11,511,100,567],160:[0,0,250,0,0],8899:[750,250,833,55,777],9126:[1155,644,667,0,347],10752:[949,449,1511,56,1454],58096:[720,69,644,38,947],58097:[587,85,894,95,797]}}}})}(function(){var t=g.FONTDATA.FONTS,s=g.config.availableFonts;var r,q=[];if(g.allowWebFonts){for(r in t){if(t[r].family){if(s&&s.length&&g.Font.testFont(t[r])){t[r].available=true;g.Font.loadComplete(t[r])}else{t[r].isWebFont=true;if(g.FontFaceBug){t[r].family=r}q.push(g.Font.fontFace(r))}}}if(!g.config.preloadWebFonts){g.config.preloadWebFonts=[]}g.config.preloadWebFonts.push(f,h,d);if(q.length){g.config.styles["@font-face"]=q}}else{if(s&&s.length){for(r in t){if(t[r].family&&g.Font.testFont(t[r])){t[r].available=true;g.Font.loadComplete(t[r])}}}}})();l.loadComplete(g.fontDir+"/fontdata.js")})(MathJax.OutputJax["HTML-CSS"],MathJax.ElementJax.mml,MathJax.Ajax); diff --git a/jax/output/HTML-CSS/jax.js b/jax/output/HTML-CSS/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} 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f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font 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i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},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:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(l)}}var o=this.HTMLcomputeBBox(l);var k=l.bbox.h,n=l.bbox.d;for(g=0,f=o.length;g<f;g++){o[g].HTMLstretchV(l,k,n)}if(o.length){this.HTMLcomputeBBox(l,true)}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLlineBreaks:function(){var k=[[0,this]];for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){var l=this.data[h].lineBreak();if(l!=="none"){var g=(l==="after"?h+1:h);if(k.length===0||k[k.length-1]!==g){k.push([g,this.data[h]])}else{k[k.length-1]=[g,this.data[h]]}}}}k.push([this.data.length,k[k.length-1][1]]);return k},toHTMLmultiline:function(f){a.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(l,k,j,f){if(j==null){j=0}if(f==null){f=this.data.length}var h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=f.HTMLspanElement();if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(k){var m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var g=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:m.mathbackground,width:e.Em(h),height:e.Em(l),verticalAlign:e.Em(f),marginLeft:e.Em(j),marginRight:e.Em(i)}});if(e.msieInlineBlockAlignBug){g.style.position="relative";g.style.width=g.style.height=0;g.style.verticalAlign=g.style.marginLeft=g.style.marginRight="";e.placeBox(e.addElement(g,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",width:e.Em(h),height:e.Em(l),background:m.mathbackground}}),j,k.bbox.h+n)}k.parentNode.insertBefore(g,k);if(e.msieColorPositionBug){k.style.position="relative"}return g}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var 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u=(H!=this.base&&f[this.ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q.insertBefore(e.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild)}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(g-q.bbox.w)/2,right:g-q.bbox.w}[f.align];p=v;n=0;if(H==this.over){if(u){E=Math.max(w*K*A,2.5/this.em);o=0;if(h.bbox.skew){p+=h.bbox.skew}}else{s=e.TeX.big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E=Math.max(s,r-Math.max(0,q.bbox.d))}E=Math.max(E,1.5/this.em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==this.under){if(u){E=3*w*K*A;o=0}else{s=e.TeX.big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E=Math.max(s,r-q.bbox.h)}E=Math.max(E,1.5/this.em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}e.placeBox(q,p,n)}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(C,A,w){C=this.HTMLcreateSpan(C);var G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var m=i.bbox.h-y,l=i.bbox.d+x,F=0,z;if(i.bbox.ic){F=i.bbox.ic}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&&i.bbox.scale===1&&!this.data[this.base].Get("largeop")){m=l=0}}var B=this.getValues("subscriptshift","superscriptshift");B.subscriptshift=(B.subscriptshift===""?0:e.length2em(B.subscriptshift));B.superscriptshift=(B.superscriptshift===""?0:e.length2em(B.superscriptshift));if(!f){if(k){l=Math.max(l,e.TeX.sub1*G,k.bbox.h-(4/5)*E,B.subscriptshift);e.placeBox(k,i.bbox.w+o-F,-l,k.bbox)}}else{if(!k){g=this.getValues("displaystyle","texprimestyle");z=e.TeX[(g.displaystyle?"sup1":(g.texprimestyle?"sup3":"sup2"))];m=Math.max(m,z*G,f.bbox.d+(1/4)*E,B.superscriptshift);e.placeBox(f,i.bbox.w+o,m,f.bbox)}else{l=Math.max(l,e.TeX.sub2*G);var n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.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}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");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=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieCharPaddingWidthBug:(h&&!g),msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_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",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",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"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));if(!y.fillExtenders){i=(g-o)/(s*r)}var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(k[4]){h*=k[4]}if(h!==1||k[3]){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(k[3]){o.firstChild.style.verticalAlign=this.Em(k[3]);o.bbox.h+=k[3];if(o.bbox.h<0){o.bbox.h=0}}if(k[5]){o.bbox.h+=k[5]}if(k[6]){o.bbox.d+=k[6]}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var 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m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var 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g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); diff --git a/unpacked/jax/output/HTML-CSS/fonts/STIX/fontdata-extra.js b/unpacked/jax/output/HTML-CSS/fonts/STIX/fontdata-extra.js @@ -0,0 +1,408 @@ +/************************************************************* + * + * MathJax/jax/output/HTML-CSS/fonts/TeX/fontdata-extra.js + * + * Initializes the HTML-CSS OutputJax to use the MathJax TeX fonts + * for displaying mathematics. + * + * --------------------------------------------------------------------- + * + * Copyright (c) 2011 Design Science, Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function (HTMLCSS) { + + var DELIMITERS = HTMLCSS.FONTDATA.DELIMITERS; + + var GENERAL = "STIXGeneral", + BOLD = "STIXGeneral-bold", + VARIANT = "STIXVariants", + NONUNI = "STIXNonUnicode", + SIZE1 = "STIXSizeOneSym", + SIZE2 = "STIXSizeTwoSym", + SIZE3 = "STIXSizeThreeSym", + SIZE4 = "STIXSizeFourSym", + SIZE5 = "STIXSizeFiveSym"; + var H = "H", V = "V"; + + var delim = { + 0x219E: // left two-headed arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x219E,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21A0: // right two-headed arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x221A0,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21A4: // left arrow from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x2190,VARIANT], rep:[0x2212,GENERAL], right:[0x22A3,BOLD,0,.1,.6]} + }, + 0x21A5: // up arrow from bar + { + dir: V, HW: [[.816,GENERAL]], + stretch: {bot:[0x5F,GENERAL,.05,-.01,.8], ext:[0x23D0,GENERAL], top:[0x2191,GENERAL]} + }, + 0x21A6: // right arrow from bar + { + dir: H, HW: [[1,GENERAL]], + stretch: {left:[0x22A2,BOLD,0,0.1,.6], rep:[0x2212,GENERAL], right:[0x2192,GENERAL]} + }, + 0x21A7: // down arrow from bar + { + dir: V, HW: [[.816,GENERAL]], + stretch: {top:[0x22A4,BOLD,0.04,0,.6], ext:[0x23D0,GENERAL], bot:[0x2193,GENERAL]} + }, + 0x21B0: // up arrow with top leftwards + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x21B0,GENERAL], ext:[0x23D0,GENERAL,.152]} + }, + 0x21B1: // up arrow with top right + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x21B1,GENERAL], ext:[0x23D0,GENERAL,-.195]} + }, + 0x21BC: // left harpoon with barb up + { + dir: H, HW: [[.955,GENERAL]], stretch: {left:[0x21BC,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21BD: // left harpoon with barb down + { + dir: H, HW: [[.955,GENERAL]], stretch: {left:[0x21BD,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21BE: // up harpoon with barb right + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x21BE,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x21BF: // up harpoon with barb left + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x21BF,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x21C0: // right harpoon with barb up + { + dir: H, HW: [[.955,GENERAL]], stretch: {right:[0x21C0,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21C1: // right harpoon with barb down + { + dir: H, HW: [[.955,GENERAL]], stretch: {right:[0x21C1,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21C2: // down harpoon with barb right + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x21C2,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x21C3: // down harpoon with barb left + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x21C3,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x21DA: // left triple arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x21DA,GENERAL], rep:[0x2261,GENERAL]} + }, + 0x21DB: // right triple arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x21DB,GENERAL], rep:[0x2261,GENERAL]} + }, + 0x23B4: // top square bracket + { + dir: H, HW: [[.926,GENERAL],[1.063,SIZE1],[1.606,SIZE2],[2.147,SIZE3],[2.692,SIZE4],[3.237,SIZE5]], + stretch: {left:[0x2310,GENERAL], rep:[0x2212,GENERAL,0,.12], right:[0xAC,GENERAL]} + }, + 0x23B5: // bottom square bracket + { + dir: H, HW: [[.926,GENERAL],[1.063,SIZE1],[1.606,SIZE2],[2.147,SIZE3],[2.692,SIZE4],[3.237,SIZE5]], + stretch: {left:[0x2A3D,GENERAL,0,.12], rep:[0x2212,GENERAL,0,0,0,.12], right:[0x2A3C,GENERAL,0,.12]} + }, + 0x23DC: // top paren + { + dir: H, HW: [[.556,GENERAL],[.926,SIZE1],[1.460,SIZE2],[1.886,SIZE3],[2.328,SIZE4],[3.237,SIZE5]], + stretch: {left:[0xE13B,NONUNI], right:[0xE13C,NONUNI], rep:[0xE14A,NONUNI]} + }, + 0x23DD: // bottom paren + { + dir: H, HW: [[.556,GENERAL],[.926,SIZE1],[1.460,SIZE2],[1.886,SIZE3],[2.328,SIZE4],[3.237,SIZE5]], + stretch: {left:[0xE13D,NONUNI], right:[0xE13E,NONUNI], rep:[0xE14B,NONUNI]} + }, + 0x23E0: // top tortoise shell + { + dir: H, HW: [[.926,GENERAL],[1.460,SIZE1],[1.886,SIZE2],[2.312,SIZE3],[2.738,SIZE4],[3.164,SIZE5]], + stretch: {left:[0xE10D,NONUNI,-.1,-.1], rep:[0x2212,GENERAL,0,.05], right:[0xE10C,NONUNI,0,-.1], fullExtenders:true} + }, + 0x23E1: // bottom tortoise shell + { + dir: H, HW: [[.926,GENERAL],[1.460,SIZE1],[1.886,SIZE2],[2.312,SIZE3],[2.738,SIZE4],[3.164,SIZE5]], + stretch: {left:[0xE10C,NONUNI,-.1,.1], rep:[0x2212,GENERAL,0,-.1,0,.1], right:[0xE10D,NONUNI,0,.1], fullExtenders:true} + }, + 0x2906: // leftwards double arrow from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21D0,GENERAL], rep:[0x3D,GENERAL], right:[0x2AE4,GENERAL,0,-.09]} + }, + 0x2907: // rightwards double arrow from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x22A8,GENERAL,0,-.09], rep:[0x3D,GENERAL], right:[0x21D2,GENERAL]} + }, + 0x294E: // left barb up right barb up harpoon + { + dir: H, HW: [], + stretch: {left:[0x21BC,GENERAL], rep:[0x2212,GENERAL], right:[0x21C0,GENERAL]} + }, + 0x294F: // up barb right down barb right harpoon + { + dir: V, HW: [[.818,GENERAL]], + stretch: {top:[0x21BE,GENERAL], ext:[0x23D0,GENERAL], bot:[0x21C2,GENERAL]} + }, + 0x2950: // left barb dow right barb down harpoon + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21BD,GENERAL], rep:[0x2212,GENERAL], right:[0x21C1,GENERAL]} + }, + 0x2951: // up barb left down barb left harpoon + { + dir: V, HW: [[.818,GENERAL]], + stretch: {top:[0x21BF,GENERAL], ext:[0x23D0,GENERAL], bot:[0x21C3,GENERAL]} + }, + 0x295A: // leftwards harpoon with barb up from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21BC,GENERAL], rep:[0x2212,GENERAL], right:[0x22A3,BOLD,0,.1,.6]} + }, + 0x295B: // rightwards harpoon with barb up from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x22A2,BOLD,0,0.1,.6], rep:[0x2212,GENERAL], right:[0x21C0,GENERAL]} + }, + 0x295C: // up harpoon with barb right from bar + { + dir: V, HW: [[.818,GENERAL]], + stretch: {bot:[0x5F,GENERAL,.05,-.01,.8], ext:[0x23D0,GENERAL], top:[0x21BE,GENERAL]} + }, + 0x295D: // down harpoon with barb right from bar + { + dir: V, HW: [[.818,GENERAL]], + stretch: {top:[0x22A4,BOLD,0.04,0,.6], ext:[0x23D0,GENERAL], bot:[0x21C2,GENERAL]} + }, + 0x295E: // leftwards harpoon with barb down from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21BD,GENERAL], rep:[0x2212,GENERAL], right:[0x22A3,BOLD,0,.1,.6]} + }, + 0x295F: // rightwards harpoon with barb down from bar + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x22A2,BOLD,0,0.1,.6], rep:[0x2212,GENERAL], right:[0x21C1,GENERAL]} + }, + 0x2960: // up harpoon with barb left from bar + { + dir: V, HW: [[.818,GENERAL]], + stretch: {bot:[0x5F,GENERAL,.05,-.01,.8], ext:[0x23D0,GENERAL], top:[0x21BF,GENERAL]} + }, + 0x2961: // down harpoon with barb left from bar + { + dir: V, HW: [[.818,GENERAL]], + stretch: {top:[0x22A4,BOLD,0.04,0,.6], ext:[0x23D0,GENERAL], bot:[0x21C3,GENERAL]} + }, + + 0x02C7: // caron + { + dir: H, HW: [[.333,GENERAL],[.56,SIZE1],[.979,SIZE2],[1.458,SIZE3],[1.886,SIZE4],[2.328,SIZE5]] + }, + 0x02CD: // low macron + { + dir: H, HW: [[.334,GENERAL]], stretch: {rep:[0x2CD,GENERAL]} + }, + 0x02F7: // low tilde + { + dir: H, HW: [[.558,SIZE1],[.977,SIZE2],[1.458,SIZE3],[1.886,SIZE4],[2.328,SIZE5]] + }, + 0x219F: // upwards two headed arrow + { + dir: V, HW: [[.816,GENERAL]], stretch: {ext:[0x23D0,GENERAL], top:[0x219F,GENERAL]} + }, + 0x21A1: // downwards two headed arrow + { + dir: V, HW: [[.816,GENERAL]], stretch: {ext:[0x23D0,GENERAL], bot:[0x21A1,GENERAL]} + }, + 0x21A8: // up down arrow with base + { + dir: V, HW: [[.816,GENERAL]], + stretch: {top:[0x2191,GENERAL], ext:[0x23D0,GENERAL], bot:[0x2913,GENERAL]} + }, + 0x21A9: // left hook arrow + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x2190,GENERAL], rep:[0x2212,GENERAL], right:[0xE0B5,NONUNI]} + }, + 0x21AA: // right hook arrow + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0xE0B4,NONUNI], rep:[0x2212,GENERAL], right:[0x2192,GENERAL]} + }, + 0x21B2: // down arrow with tip left + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x21B2,GENERAL], ext:[0x23D0,GENERAL,.152]} + }, + 0x21B3: // down arrow with tip right + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x21B3,GENERAL], ext:[0x23D0,GENERAL,-.195]} + }, + 0x21B4: // right arrow with corner down + { + dir: H, HW: [[.926,GENERAL]], stretch: {rep:[0x2212,GENERAL,0,.4], right:[0x21B4,GENERAL]} + }, + 0x21B5: // down arrow with corner left + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x21B5,GENERAL], ext:[0x23D0,GENERAL,.57]} + }, + 0x21CB: // left harpoon over right harpoon + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x296A,GENERAL], rep:[0x3D,GENERAL], right:[0x296D,GENERAL]} + }, + 0x21CC: // right harpoon over left harpoon + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x296B,GENERAL], rep:[0x3D,GENERAL], right:[0x296C,GENERAL]} + }, + 0x21E0: // left dashed arrow + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21E0,GENERAL], rep:[0xE121,NONUNI,0,0,0,0,.1], fullExtenders:true} + }, + 0x21E1: // up dashed arrow + { + dir: V, HW: [[.818,GENERAL]], + stretch: {ext:[0xE12D,NONUNI], top:[0x21E1,GENERAL], fullExtenders: true} + }, + 0x21E2: // right dashed arrow + { + dir: H, HW: [[.926,GENERAL]], + stretch: {right:[0x21E2,VARIANT], rep:[0xE12E,NONUNI,0,0,0,0,.1], fullExtenders:true} + }, + 0x21E3: // down dashed arrow + { + dir: V, HW: [[.818,GENERAL]], + stretch: {ext:[0xE12C,NONUNI], bot:[0x21E3,GENERAL], fullExtenders: true} + }, + 0x21E4: // left arrow to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x21E4,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21E5: // right arrow to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x21E5,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21FD: // left open-headed arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x21FD,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21FE: // right open-headed arrow + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x21FE,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x21FF: // left right open-headed arrow + { + dir: H, HW: [[.926,GENERAL]], + stretch: {left:[0x21FD,GENERAL], rep:[0x2212,GENERAL], right:[0x21FE,GENERAL]} + }, + 0x27E6: // left white square bracket + { + dir: V, HW: [[.93,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.46,SIZE3],[3.075,SIZE4]], + stretch: {top:[0x2553,GENERAL], ext:[0x2551,GENERAL], bot:[0x2559,GENERAL]} + }, + 0x27E7: // right white square bracket + { + dir: V, HW: [[.93,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.46,SIZE3],[3.075,SIZE4]], + stretch: {top:[0x2556,GENERAL], ext:[0x2551,GENERAL], bot:[0x255C,GENERAL]} + }, + 0x27EA: // left double angle bracket + { + dir: V, HW: [[.931,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.461,SIZE3],[3.075,SIZE4]], + }, + 0x27EB: // right double angle bracket + { + dir: V, HW: [[.931,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.461,SIZE3],[3.075,SIZE4]], + }, + 0x290A: // up triple arrow + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x290A,GENERAL], ext:[0xE135,NONUNI]} + }, + 0x290B: // down triple arrow + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x290B,GENERAL], ext:[0xE135,NONUNI]} + }, + 0x2912: // up arrow to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x2912,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2913: // down arrow to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x2913,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2952: // left harpoon with barb up to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x2952,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x2953: // right harpoon with barb up to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x2953,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x2954: // up harpoon with barb right to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x2954,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2955: // down harpoon with barb right to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x2955,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2956: // left harpoon with barb down to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {left:[0x2956,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x2957: // right harpoon with barb down to bar + { + dir: H, HW: [[.926,GENERAL]], stretch: {right:[0x2957,GENERAL], rep:[0x2212,GENERAL]} + }, + 0x2958: // up harpoon with barb left to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {top:[0x2958,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2959: // down harpoon with barb left to bar + { + dir: V, HW: [[.818,GENERAL]], stretch: {bot:[0x2959,GENERAL], ext:[0x23D0,GENERAL]} + }, + 0x2980: // triple vertical bar + { + dir: V, HW: [[.874,GENERAL]], stretch: {ext:[0x2980,GENERAL]} + }, + 0x2997: // left black tortoise shell + { + dir: V, HW: [[.932,GENERAL]], + stretch: {top:[0xE10D,NONUNI,.1,.05], ext:[0x23D0,GENERAL,-.1], bot:[0xE10C,NONUNI,.1]} + }, + 0x2998: // right black tortoise shell + { + dir: V, HW: [[.932,GENERAL]], + stretch: {top:[0xE10C,NONUNI,-.1,.05], ext:[0x23D0,GENERAL], bot:[0xE10D,NONUNI,-.1]} + }, + + }; + + for (var id in delim) {if (delim.hasOwnProperty(id)) {DELIMITERS[id] = delim[id]}}; + + MathJax.Ajax.loadComplete(HTMLCSS.fontDir + "/fontdata-extra.js"); + +})(MathJax.OutputJax["HTML-CSS"]); + diff --git a/unpacked/jax/output/HTML-CSS/fonts/STIX/fontdata.js b/unpacked/jax/output/HTML-CSS/fonts/STIX/fontdata.js @@ -7,7 +7,7 @@ * * --------------------------------------------------------------------- * - * Copyright (c) 2009-2010 Design Science, Inc. + * Copyright (c) 2009-2011 Design Science, Inc. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. @@ -23,7 +23,7 @@ */ (function (HTMLCSS) { - var VERSION = "1.0"; + var VERSION = "1.1.1"; HTMLCSS.allowWebFonts = false; @@ -36,7 +36,7 @@ SIZE3 = "STIXSizeThreeSym", SIZE4 = "STIXSizeFourSym", SIZE5 = "STIXSizeFiveSym"; - var H = "H", V = "V"; + var H = "H", V = "V", EXTRAH = {load:"extra", dir:H}, EXTRAV = {load:"extra", dir:V}; HTMLCSS.Augment({ FONTDATA: { @@ -331,22 +331,117 @@ 0x005E: {alias: 0x02D6, dir:H}, // wide hat 0x005F: {alias: 0x23AF, dir:H}, // low line 0x007E: {alias: 0x02DC, dir:H}, // wide tilde - 0x00AF: {alias: 0x23AF, dir:H}, // over line + 0x00AF: {alias: 0x02C9, dir:H}, // macron 0x0302: {alias: 0x02C6, dir:H}, // wide hat 0x0303: {alias: 0x02DC, dir:H}, // wide tilde 0x030C: {alias: 0x02C7, dir:H}, // wide caron 0x0332: {alias: 0x23AF, dir:H}, // combining low line 0x2015: {alias: 0x23AF, dir:H}, // horizontal line 0x2017: {alias: 0x23AF, dir:H}, // horizontal line + 0x203E: {alias: 0x00AF, dir:H}, // overline 0x2212: {alias: 0x23AF, dir:H}, // minus + 0x2215: {alias: 0x002F, dir:V}, // division slash 0x2329: {alias: 0x27E8, dir:V}, // langle 0x232A: {alias: 0x27E9, dir:V}, // rangle + 0x23AF: {alias: 0x2212, dir:H}, // horizontal line extension 0x2500: {alias: 0x2212, dir:H}, // horizontal line 0x2758: {alias: 0x2223, dir:V}, // vertical separator 0x3008: {alias: 0x27E8, dir:V}, // langle 0x3009: {alias: 0x27E9, dir:V}, // rangle 0xFE37: {alias: 0x23DE, dir:H}, // horizontal brace down - 0xFE38: {alias: 0x23DF, dir:H} // horizontal brace up + 0xFE38: {alias: 0x23DF, dir:H}, // horizontal brace up + + 0x219E: EXTRAH, // left two-headed arrow + 0x21A0: EXTRAH, // right two-headed arrow + 0x21A4: EXTRAH, // left arrow from bar + 0x21A5: EXTRAV, // up arrow from bar + 0x21A6: EXTRAH, // right arrow from bar + 0x21A7: EXTRAV, // down arrow from bar + 0x21B0: EXTRAV, // up arrow with top leftwards + 0x21B1: EXTRAV, // up arrow with top right + 0x21BC: EXTRAH, // left harpoon with barb up + 0x21BD: EXTRAH, // left harpoon with barb down + 0x21BE: EXTRAV, // up harpoon with barb right + 0x21BF: EXTRAV, // up harpoon with barb left + 0x21C0: EXTRAH, // right harpoon with barb up + 0x21C1: EXTRAH, // right harpoon with barb down + 0x21C2: EXTRAV, // down harpoon with barb right + 0x21C3: EXTRAV, // down harpoon with barb left + 0x21DA: EXTRAH, // left triple arrow + 0x21DB: EXTRAH, // right triple arrow + 0x23B4: EXTRAH, // top square bracket + 0x23B5: EXTRAH, // bottom square bracket + 0x23DC: EXTRAH, // top paren + 0x23DD: EXTRAH, // bottom paren + 0x23E0: EXTRAH, // top tortoise shell + 0x23E1: EXTRAH, // bottom tortoise shell + 0x2906: EXTRAH, // leftwards double arrow from bar + 0x2907: EXTRAH, // rightwards double arrow from bar + 0x294E: EXTRAH, // left barb up right barb up harpoon + 0x294F: EXTRAV, // up barb right down barb right harpoon + 0x2950: EXTRAH, // left barb dow right barb down harpoon + 0x2951: EXTRAV, // up barb left down barb left harpoon + 0x295A: EXTRAH, // leftwards harpoon with barb up from bar + 0x295B: EXTRAH, // rightwards harpoon with barb up from bar + 0x295C: EXTRAV, // up harpoon with barb right from bar + 0x295D: EXTRAV, // down harpoon with barb right from bar + 0x295E: EXTRAH, // leftwards harpoon with barb down from bar + 0x295F: EXTRAH, // rightwards harpoon with barb down from bar + 0x2960: EXTRAV, // up harpoon with barb left from bar + 0x2961: EXTRAV, // down harpoon with barb left from bar + 0x27F5: {alias: 0x2190, dir:H}, // long left arrow + 0x27F6: {alias: 0x2192, dir:H}, // long right arrow + 0x27F7: {alias: 0x2194, dir:H}, // long left-right arrow + 0x27F8: {alias: 0x21D0, dir:H}, // long left double arrow + 0x27F9: {alias: 0x21D2, dir:H}, // long right double arrow + 0x27FA: {alias: 0x21D4, dir:H}, // long left-right double arrow + 0x27FB: {alias: 0x21A4, dir:H}, // long left arrow from bar + 0x27FC: {alias: 0x21A6, dir:H}, // long right arrow from bar + 0x27FD: {alias: 0x2906, dir:H}, // long left double arrow from bar + 0x27FE: {alias: 0x2907, dir:H}, // long right double arrow from bar + + 0x02C7: EXTRAH, // caron + 0x02CD: EXTRAH, // low macron + 0x02F7: EXTRAH, // low tilde + 0x219F: EXTRAV, // upwards two headed arrow + 0x21A1: EXTRAV, // downwards two headed arrow + 0x21A8: EXTRAV, // up down arrow with base + 0x21A9: EXTRAH, // left hook arrow + 0x21AA: EXTRAH, // right hook arrow + 0x21B2: EXTRAV, // down arrow with tip left + 0x21B3: EXTRAV, // down arrow with tip right + 0x21B4: EXTRAH, // right arrow with corner down + 0x21B5: EXTRAV, // down arrow with corner left + 0x21CB: EXTRAH, // left harpoon over right harpoon + 0x21CC: EXTRAH, // right harpoon over left harpoon + 0x21E0: EXTRAH, // left dashed arrow + 0x21E1: EXTRAV, // up dashed arrow + 0x21E2: EXTRAH, // right dashed arrow + 0x21E3: EXTRAV, // down dahsed arrow + 0x21E4: EXTRAH, // left arrow to bar + 0x21E5: EXTRAH, // right arrow to bar + 0x21FD: EXTRAH, // left open-headed arrow + 0x21FE: EXTRAH, // right open-headed arrow + 0x21FF: EXTRAH, // left right open-headed arrow + 0x27E6: EXTRAV, // left white square bracket + 0x27E7: EXTRAV, // right white square bracket + 0x27EA: EXTRAV, // left double angle bracket + 0x27EB: EXTRAV, // right double angle bracket + 0x290A: EXTRAV, // up triple arrow + 0x290B: EXTRAV, // down triple arrow + 0x2912: EXTRAV, // up arrow to bar + 0x2913: EXTRAV, // down arrow to bar + 0x2952: EXTRAH, // left harpoon with barb up to bar + 0x2953: EXTRAH, // right harpoon with barb up to bar + 0x2954: EXTRAV, // up harpoon with barb right to bar + 0x2955: EXTRAV, // down harpoon with barb right to bar + 0x2956: EXTRAH, // left harpoon with barb down to bar + 0x2957: EXTRAH, // right harpoon with barb down to bar + 0x2958: EXTRAV, // up harpoon with barb left to bar + 0x2959: EXTRAV, // down harpoon with barb left to bar + 0x2980: EXTRAV, // triple vertical bar + 0x2997: EXTRAV, // left balck tortoise shell + 0x2998: EXTRAV // right balck tortoise shell } } }); @@ -1383,6 +1478,8 @@ HTMLCSS.FONTDATA.FONTS['STIXGeneral'][0x22EE][0] += 400; // adjust height for \vdots HTMLCSS.FONTDATA.FONTS['STIXGeneral'][0x22F1][0] += 500; // adjust height for \ddots + HTMLCSS.FONTDATA.FONTS['STIXGeneral'][0x2212][1] += 100; // adjust depth for minus (arrow extender) + HTMLCSS.FONTDATA.FONTS['STIXGeneral'][0x003D][1] += 100; // adjust depth for = (double arrow extender) HTMLCSS.FONTDATA.FONTS['STIXNonUnicode'][0xE14A][0] += 200; // adjust height for brace extender HTMLCSS.FONTDATA.FONTS['STIXNonUnicode'][0xE14A][1] += 200; // adjust depth for brace extender HTMLCSS.FONTDATA.FONTS['STIXNonUnicode'][0xE14B][0] += 200; // adjust height for brace extender diff --git a/unpacked/jax/output/HTML-CSS/fonts/TeX/fontdata-extra.js b/unpacked/jax/output/HTML-CSS/fonts/TeX/fontdata-extra.js @@ -0,0 +1,232 @@ +/************************************************************* + * + * MathJax/jax/output/HTML-CSS/fonts/TeX/fontdata-extra.js + * + * Initializes the HTML-CSS OutputJax to use the MathJax TeX fonts + * for displaying mathematics. + * + * --------------------------------------------------------------------- + * + * Copyright (c) 2011 Design Science, Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function (HTMLCSS) { + + var DELIMITERS = HTMLCSS.FONTDATA.DELIMITERS; + + var MAIN = "MathJax_Main", + BOLD = "MathJax_Main-bold", + AMS = "MathJax_AMS", + SIZE1 = "MathJax_Size1", + SIZE4 = "MathJax_Size4"; + var H = "H", V = "V"; + + var delim = { + 0x219E: // left two-headed arrow + { + dir: H, HW: [[1,AMS]], stretch: {left:[0x219E,AMS], rep:[0x2212,MAIN]} + }, + 0x21A0: // right two-headed arrow + { + dir: H, HW: [[1,AMS]], stretch: {right:[0x221A0,AMS], rep:[0x2212,MAIN]} + }, + 0x21A4: // left arrow from bar + { + dir: H, HW: [], + stretch: {left:[0x2190,MAIN], rep:[0x2212,MAIN], right:[0x2223,SIZE1,0,-.05,.9]} + }, + 0x21A5: // up arrow from bar + { + dir: V, HW: [], + stretch: {bot:[0x22A5,BOLD,0,0,.75], ext:[0x23D0,SIZE1], top:[0x2191,SIZE1]} + }, + 0x21A6: // right arrow from bar + { + dir: H, HW: [[1,AMS]], + stretch: {left:[0x2223,SIZE1,-.09,-.05,.9], rep:[0x2212,MAIN], right:[0x2192,MAIN]} + }, + 0x21A7: // down arrow from bar + { + dir: V, HW: [], + stretch: {top:[0x22A4,BOLD,0,0,.75], ext:[0x23D0,SIZE1], bot:[0x2193,SIZE1]} + }, + 0x21B0: // up arrow with top leftwards + { + dir: V, HW: [[.722,AMS]], + stretch: {top:[0x21B0,AMS], ext:[0x23D0,SIZE1,.097]} + }, + 0x21B1: // up arrow with top right + { + dir: V, HW: [[.722,AMS]], + stretch: {top:[0x21B1,AMS,.27], ext:[0x23D0,SIZE1]} + }, + 0x21BC: // left harpoon with barb up + { + dir: H, HW: [[1,MAIN]], + stretch: {left:[0x21BC,MAIN], rep:[0x2212,MAIN]} + }, + 0x21BD: // left harpoon with barb down + { + dir: H, HW: [[1,MAIN]], + stretch: {left:[0x21BD,MAIN], rep:[0x2212,MAIN]} + }, + 0x21BE: // up harpoon with barb right + { + dir: V, HW: [[.888,AMS]], + stretch: {top:[0x21BE,AMS,.12,0,1.1], ext:[0x23D0,SIZE1]} + }, + 0x21BF: // up harpoon with barb left + { + dir: V, HW: [[.888,AMS]], + stretch: {top:[0x21BF,AMS,.12,0,1.1], ext:[0x23D0,SIZE1]} + }, + 0x21C0: // right harpoon with barb up + { + dir: H, HW: [[1,MAIN]], + stretch: {right:[0x21C0,MAIN], rep:[0x2212,MAIN]} + }, + 0x21C1: // right harpoon with barb down + { + dir: H, HW: [[1,MAIN]], + stretch: {right:[0x21C1,MAIN], rep:[0x2212,MAIN]} + }, + 0x21C2: // down harpoon with barb right + { + dir: V, HW: [[.888,AMS]], + stretch: {bot:[0x21C2,AMS,.12,0,1.1], ext:[0x23D0,SIZE1]} + }, + 0x21C3: // down harpoon with barb left + { + dir: V, HW: [[.888,AMS]], + stretch: {bot:[0x21C3,AMS,.12,0,1.1], ext:[0x23D0,SIZE1]} + }, + 0x21DA: // left triple arrow + { + dir: H, HW: [[1,AMS]], + stretch: {left:[0x21DA,AMS], rep:[0x2261,MAIN]} + }, + 0x21DB: // right triple arrow + { + dir: H, HW: [[1,AMS]], + stretch: {right:[0x21DB,AMS], rep:[0x2261,MAIN]} + }, + 0x23B4: // top square bracket + { + dir: H, HW: [], + stretch: {left:[0x250C,AMS,0,-.1], rep:[0x2212,MAIN,0,.35], right:[0x2510,AMS,0,-.1]} + }, + 0x23B5: // bottom square bracket + { + dir: H, HW: [], + stretch: {left:[0x2514,AMS,0,.26], rep:[0x2212,MAIN,0,0,0,.25], right:[0x2518,AMS,0,.26]} + }, + 0x23DC: // top paren + { + dir: H, HW: [[.778,AMS,0,0x2322],[1,MAIN,0,0x2322]], + stretch: {left:[0xE150,SIZE4], rep:[0xE154,SIZE4], right:[0xE151,SIZE4]} + }, + 0x23DD: // bottom paren + { + dir: H, HW: [[.778,AMS,0,0x2323],[1,MAIN,0,0x2323]], + stretch: {left:[0xE152,SIZE4], rep:[0xE154,SIZE4], right:[0xE153,SIZE4]} + }, + 0x23E0: // top tortoise shell + { + dir: H, HW: [], + stretch: {left:[0x2CA,MAIN,-.1], rep:[0x2C9,MAIN,0,.13], right:[0x2CB,MAIN], fullExtenders:true} + }, + 0x23E1: // bottom tortoise shell + { + dir: H, HW: [], + stretch: {left:[0x2CB,MAIN,-.1,.1], rep:[0x2C9,MAIN], right:[0x2CA,MAIN,-.1,.1], fullExtenders:true} + }, + 0x2906: // leftwards double arrow from bar + { + dir: H, HW: [], + stretch: {left:[0x21D0,MAIN], rep:[0x3D,MAIN], right:[0x2223,SIZE1,0,-.1]} + }, + 0x2907: // rightwards double arrow from bar + { + dir: H, HW: [], + stretch: {left:[0x22A8,AMS,0,-.12], rep:[0x3D,MAIN], right:[0x21D2,MAIN]} + }, + 0x294E: // left barb up right barb up harpoon + { + dir: H, HW: [], + stretch: {left:[0x21BC,MAIN], rep:[0x2212,MAIN], right:[0x21C0,MAIN]} + }, + 0x294F: // up barb right down barb right harpoon + { + dir: V, HW: [], + stretch: {top:[0x21BE,AMS,.12,0,1.1], ext:[0x23D0,SIZE1], bot:[0x21C2,AMS,.12,0,1.1]} + }, + 0x2950: // left barb dow right barb down harpoon + { + dir: H, HW: [], + stretch: {left:[0x21BD,MAIN], rep:[0x2212,MAIN], right:[0x21C1,MAIN]} + }, + 0x2951: // up barb left down barb left harpoon + { + dir: V, HW: [], + stretch: {top:[0x21BF,AMS,.12,0,1.1], ext:[0x23D0,SIZE1], bot:[0x21C3,AMS,.12,0,1.1]} + }, + 0x295A: // leftwards harpoon with barb up from bar + { + dir: H, HW: [], + stretch: {left:[0x21BC,MAIN], rep:[0x2212,MAIN], right:[0x2223,SIZE1,0,-.05,.9]} + }, + 0x295B: // rightwards harpoon with barb up from bar + { + dir: H, HW: [], + stretch: {left:[0x2223,SIZE1,-.09,-.05,.9], rep:[0x2212,MAIN], right:[0x21C0,MAIN]} + }, + 0x295C: // up harpoon with barb right from bar + { + dir: V, HW: [], + stretch: {bot:[0x22A5,BOLD,0,0,.75], ext:[0x23D0,SIZE1], top:[0x21BE,AMS,.12,0,1.1]} + }, + 0x295D: // down harpoon with barb right from bar + { + dir: V, HW: [], + stretch: {top:[0x22A4,BOLD,0,0,.75], ext:[0x23D0,SIZE1], bot:[0x21C2,AMS,.12,0,1.1]} + }, + 0x295E: // leftwards harpoon with barb down from bar + { + dir: H, HW: [], + stretch: {left:[0x21BD,MAIN], rep:[0x2212,MAIN], right:[0x2223,SIZE1,0,-.05,.9]} + }, + 0x295F: // rightwards harpoon with barb down from bar + { + dir: H, HW: [], + stretch: {left:[0x2223,SIZE1,-.09,-.05,.9], rep:[0x2212,MAIN], right:[0x21C1,MAIN]} + }, + 0x2960: // up harpoon with barb left from bar + { + dir: V, HW: [], + stretch: {bot:[0x22A5,BOLD,0,0,.75], ext:[0x23D0,SIZE1], top:[0x21BF,AMS,.12,0,1.1]} + }, + 0x2961: // down harpoon with barb left from bar + { + dir: V, HW: [], + stretch: {top:[0x22A4,BOLD,0,0,.75], ext:[0x23D0,SIZE1], bot:[0x21C3,AMS,.12,0,1.1]} + } + }; + + for (var id in delim) {if (delim.hasOwnProperty(id)) {DELIMITERS[id] = delim[id]}}; + + MathJax.Ajax.loadComplete(HTMLCSS.fontDir + "/fontdata-extra.js"); + +})(MathJax.OutputJax["HTML-CSS"]); + diff --git a/unpacked/jax/output/HTML-CSS/fonts/TeX/fontdata.js b/unpacked/jax/output/HTML-CSS/fonts/TeX/fontdata.js @@ -7,7 +7,7 @@ * * --------------------------------------------------------------------- * - * Copyright (c) 2009 Design Science, Inc. + * Copyright (c) 2009-2011 Design Science, Inc. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. @@ -23,7 +23,7 @@ */ (function (HTMLCSS,MML,AJAX) { - var VERSION = "1.0.1"; + var VERSION = "1.1.1"; var MAIN = "MathJax_Main", BOLD = "MathJax_Main-bold", @@ -33,7 +33,7 @@ SIZE2 = "MathJax_Size2", SIZE3 = "MathJax_Size3", SIZE4 = "MathJax_Size4"; - var H = "H", V = "V"; + var H = "H", V = "V", EXTRAH = {load:"extra", dir:H}, EXTRAV = {load:"extra", dir:V}; HTMLCSS.Augment({ FONTDATA: { @@ -244,6 +244,10 @@ dir: V, HW: [[1,MAIN],[1.2,SIZE1],[1.8,SIZE2],[2.4,SIZE3],[3.0,SIZE4]], stretch: {top: [0x23AB,SIZE4], mid:[0x23AC,SIZE4], bot: [0x23AD,SIZE4], ext: [0x23AA,SIZE4]} }, + 0x00AF: // macron + { + dir: H, HW: [[.59,MAIN]], stretch: {rep:[0xAF,MAIN]} + }, 0x02C6: // wide hat { dir: H, HW: [[.267+.05,MAIN],[.567+.05,SIZE1],[1.005+.05,SIZE2],[1.447+.1,SIZE3],[1.909+.1,SIZE4]] @@ -396,11 +400,15 @@ 0x005E: {alias: 0x02C6, dir:H}, // wide hat 0x005F: {alias: 0x2212, dir:H}, // low line 0x007E: {alias: 0x02DC, dir:H}, // wide tilde - 0x00AF: {alias: 0x2212, dir:H}, // over line + 0x02C9: {alias: 0x00AF, dir:H}, // macron + 0x0302: {alias: 0x02C6, dir:H}, // wide hat + 0x0303: {alias: 0x02DC, dir:H}, // wide tilde + 0x030C: {alias: 0x02C7, dir:H}, // wide caron 0x0332: {alias: 0x2212, dir:H}, // combining low line 0x2015: {alias: 0x2212, dir:H}, // horizontal line 0x2017: {alias: 0x2212, dir:H}, // horizontal line - 0x203E: {alias: 0x2212, dir:H}, // over line + 0x203E: {alias: 0x00AF, dir:H}, // overline + 0x2215: {alias: 0x002F, dir:V}, // division slash 0x2329: {alias: 0x27E8, dir:V}, // langle 0x232A: {alias: 0x27E9, dir:V}, // rangle 0x23AF: {alias: 0x2212, dir:H}, // horizontal line extension @@ -409,7 +417,56 @@ 0x3008: {alias: 0x27E8, dir:V}, // langle 0x3009: {alias: 0x27E9, dir:V}, // rangle 0xFE37: {alias: 0x23DE, dir:H}, // horizontal brace down - 0xFE38: {alias: 0x23DF, dir:H} // horizontal brace up + 0xFE38: {alias: 0x23DF, dir:H}, // horizontal brace up + + 0x219E: EXTRAH, // left two-headed arrow + 0x21A0: EXTRAH, // right two-headed arrow + 0x21A4: EXTRAH, // left arrow from bar + 0x21A5: EXTRAV, // up arrow from bar + 0x21A6: EXTRAH, // right arrow from bar + 0x21A7: EXTRAV, // down arrow from bar + 0x21B0: EXTRAV, // up arrow with top leftwards + 0x21B1: EXTRAV, // up arrow with top right + 0x21BC: EXTRAH, // left harpoon with barb up + 0x21BD: EXTRAH, // left harpoon with barb down + 0x21BE: EXTRAV, // up harpoon with barb right + 0x21BF: EXTRAV, // up harpoon with barb left + 0x21C0: EXTRAH, // right harpoon with barb up + 0x21C1: EXTRAH, // right harpoon with barb down + 0x21C2: EXTRAV, // down harpoon with barb right + 0x21C3: EXTRAV, // down harpoon with barb left + 0x21DA: EXTRAH, // left triple arrow + 0x21DB: EXTRAH, // right triple arrow + 0x23B4: EXTRAH, // top square bracket + 0x23B5: EXTRAH, // bottom square bracket + 0x23DC: EXTRAH, // top paren + 0x23DD: EXTRAH, // bottom paren + 0x23E0: EXTRAH, // top tortoise shell + 0x23E1: EXTRAH, // bottom tortoise shell + 0x2906: EXTRAH, // leftwards double arrow from bar + 0x2907: EXTRAH, // rightwards double arrow from bar + 0x294E: EXTRAH, // left barb up right barb up harpoon + 0x294F: EXTRAV, // up barb right down barb right harpoon + 0x2950: EXTRAH, // left barb dow right barb down harpoon + 0x2951: EXTRAV, // up barb left down barb left harpoon + 0x295A: EXTRAH, // leftwards harpoon with barb up from bar + 0x295B: EXTRAH, // rightwards harpoon with barb up from bar + 0x295C: EXTRAV, // up harpoon with barb right from bar + 0x295D: EXTRAV, // down harpoon with barb right from bar + 0x295E: EXTRAH, // leftwards harpoon with barb down from bar + 0x295F: EXTRAH, // rightwards harpoon with barb down from bar + 0x2960: EXTRAV, // up harpoon with barb left from bar + 0x2961: EXTRAV, // down harpoon with barb left from bar + 0x27F5: {alias: 0x2190, dir:H}, // long left arrow + 0x27F6: {alias: 0x2192, dir:H}, // long right arrow + 0x27F7: {alias: 0x2194, dir:H}, // long left-right arrow + 0x27F8: {alias: 0x21D0, dir:H}, // long left double arrow + 0x27F9: {alias: 0x21D2, dir:H}, // long right double arrow + 0x27FA: {alias: 0x21D4, dir:H}, // long left-right double arrow + 0x27FB: {alias: 0x21A4, dir:H}, // long left arrow from bar + 0x27FC: {alias: 0x21A6, dir:H}, // long right arrow from bar + 0x27FD: {alias: 0x2906, dir:H}, // long left double arrow from bar + 0x27FE: {alias: 0x2907, dir:H} // long right double arrow from bar } } }); @@ -1406,6 +1463,8 @@ HTMLCSS.FONTDATA.FONTS['MathJax_Main'][0x22F1][0] += 700; // adjust height for \ddots HTMLCSS.FONTDATA.FONTS['MathJax_Size4'][0xE154][0] += 200; // adjust height for brace extender HTMLCSS.FONTDATA.FONTS['MathJax_Size4'][0xE154][1] += 200; // adjust depth for brace extender + HTMLCSS.FONTDATA.FONTS['MathJax_Main'][0x2212][1] += 100; // adjust depth of minus (used as arrow extender) + HTMLCSS.FONTDATA.FONTS['MathJax_Main'][0x003D][1] += 100; // adjust depth of = (used as arrow extender) if (!HTMLCSS.imgFonts) { MathJax.Hub.Browser.Select({ diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js @@ -783,6 +783,7 @@ 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]} @@ -856,7 +857,8 @@ } if (W > w) { var rW = rep.bbox.rw-rep.bbox.lw, rw = rW - .05, n, N, k = (delim.mid ? 2 : 1); - N = n = Math.ceil((W-w)/(k*rw)); rw = (W-w)/(k*n); + N = n = Math.ceil((W-w)/(k*rw)); + if (!delim.fillExtenders) {rw = (W-w)/(k*n)} var dx = (n/(n+1))*(rW - rw); rw = rW - dx; x -= rep.bbox.lw + dx; while (k-- > 0) { while (n-- > 0) {this.placeBox(this.addBox(stack,rep.cloneNode(true)),x,0,true); x += rw} @@ -885,12 +887,19 @@ 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 (scale !== 1) { + if (data[4]) {scale *= data[4]} + if (scale !== 1 || data[3]) { SPAN = this.addElement(span,"span",{style:{fontSize: this.Percent(scale)}, scale:scale}); 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[2]) {span.style.marginLeft = this.Em(data[2])} // x offset + if (data[3]) { // y offset + 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]} // extra height + if (data[6]) {span.bbox.d += data[6]} // extra depth if (this.AccentBug && span.bbox.w === 0) { // Handle combining characters by adding a non-breaking space and removing that width SPAN.firstChild.nodeValue += this.NBSP;