commit d5f2ab74f391aadb89c6cb80f9a04390431f82cd parent b5d23c72fa5d151195a5594fc6235c2bac40c173 Author: Davide P. Cervone <dpvc@union.edu> Date: Sun, 11 Sep 2011 13:13:22 -0400 Merge branch 'performance' into v2.0-candidate (still need to optimize linebreak measurements) Diffstat:
20 files changed, 597 insertions(+), 296 deletions(-)
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)?/,"");c.Browser=c.Insert(c.Insert(new String("Unknown"),{version:"0.0"}),a);for(var t in a){if(a.hasOwnProperty(t)){if(a[t]&&t.substr(0,2)==="is"){t=t.slice(2);if(t==="Mac"||t==="PC"){continue}c.Browser=c.Insert(new String(t),a);var p=new RegExp(".*(Version)/((?:\\d+\\.)+\\d+)|.*("+t+")"+(t=="MSIE"?" 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diff --git a/config/Accessible-full.js b/config/Accessible-full.js @@ -56,7 +56,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.10",directory:MathJ MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -88,8 +88,8 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a= (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(k==="ContextMenu"){this.msieMath.fireEvent("on"+l.type,l)}}return g.False(l)},getJaxFromMath:function(k){return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){return l.firstChild},getHoverBBox:function(k,l,m){return g.getBBox(l.parentNode)},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)},NativeMMLattributes:function(n){var q=this.defaults;var s=this.NativeMMLcopyAttributes,p=this.NativeMMLskipAttributes;if(this.type==="mstyle"){q=e.math.prototype.defaults}for(var r in q){if(!p[r]&&q.hasOwnProperty(r)){if(this[r]!=null){n.setAttribute(r,this.NativeMMLattribute(r,this[r]))}}}for(var o=0,l=s.length;o<l;o++){if(this[s[o]]!=null){n.setAttribute(s[o],this.NativeMMLattribute(s[o],this[s[o]]))}}},NativeMMLcopyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],NativeMMLskipAttributes:{texClass:1,useHeight:1,texprimestyle:1},NativeMMLattribute:function(m,l){l=String(l);if(j.NAMEDSPACE[l]){l=j.NAMEDSPACE[l]}else{if(l.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){l=(RegExp.$2+(1/18)*RegExp.$1).replace(/(\.\d\d\d).*/,"$1")+"em"}else{if(l==="-tex-caligraphic"){l="script"}else{if(l==="-tex-oldstyle"){l="normal"}}}}return l},NativeMMLelement:function(l){var m=(h?document.createElement("mjx:"+l):document.createElementNS(j.MMLnamespace,l));m.isMathJax=true;return m}});e.mrow.Augment({toNativeMML:function(o){if(this.inferred&&this.parent.inferRow){for(var n=0,l=this.data.length;n<l;n++){if(this.data[n]){this.data[n].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}}else{this.SUPER(arguments).toNativeMML.call(this,o)}}});e.msubsup.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.sup]==null){p="msub"}if(this.data[this.sub]==null){p="msup"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});e.munderover.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.under]==null){p="mover"}if(this.data[this.over]==null){p="munder"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});if(b.Browser.isFirefox){e.mtable.Augment({toNativeMML:function(l){if(this.width){var m=(this.style||"").replace(/;\s*$/,"").split(";");m.push("width:"+this.width);this.style=m.join(";")}this.SUPER(arguments).toNativeMML.call(this,l)}});e.mlabeledtr.Augment({toNativeMML:function(p){var n=this.NativeMMLelement("mtr");this.NativeMMLattributes(n);for(var o=1,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)}});var k=MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf";j.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+k+"/MathJax_AMS-Regular.otf')*/"},"@font-face /*2*/":{"font-family":"MathJax_Script-WEB",src:"url('"+k+"/MathJax_Script-Regular.otf')"},"@font-face /*3*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+k+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+k+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Fraktur-Bold.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Caligraphic-Bold.otf')"}}}})}e.TeXAtom.Augment({toNativeMML:function(m){var l=this.NativeMMLelement("mrow");this.data[0].toNativeMML(l);m.appendChild(l)}});e.chars.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.entity.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.xml.Augment({toNativeMML:function(o){for(var n=0,l=this.data.length;n<l;n++){o.appendChild(this.data[n].cloneNode(true))}}});b.Register.StartupHook("TeX mathchoice Ready",function(){e.TeXmathchoice.Augment({toNativeMML:function(l){this.Core().toNativeMML(l)}})});setTimeout(MathJax.Callback(["loadComplete",j,"jax.js"]),0)});b.Browser.Select({MSIE:function(k){var l=(document.documentMode||0);j.msieIE8HeightBug=(l===8)},Opera:function(k){j.operaPositionBug=true}});b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); -(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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;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",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;var l=[],p=this.FONTDATA.VARIANT.normal.fonts;if(!(p instanceof Array)){p=[p]}for(var k=0,j=p.length;k<j;k++){l[k]=this.FONTDATA.FONTS[p[k]].family;if(!l[k]){l[k]=p[k]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":l.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 o=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=o.offsetWidth/5;this.hiddenDiv.removeChild(o);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(n){}}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(n){}}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"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},Translate:function(p){if(!p.parentNode){return}var n=p.previousSibling;if(n&&String(n.className).match(/^MathJax(_MathML|_Display)?$/)){n.parentNode.removeChild(n)}var j=p.MathJax.elementJax,q=j.root,r,i,l;r=i=l=this.Element("span",{className:"MathJax",isMathJax:true,jaxID:this.id,id:j.inputID+"-Span",oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(MathJax.Hub.Browser.noContextMenu){r.ontouchstart=h.start;r.ontouchend=h.end}var m=(q.Get("display")==="block");if(m){i=l=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});i.appendChild(r)}i.setAttribute("role","textbox");i.setAttribute("aria-readonly","true");if(this.useProcessingFrame){l=this.Element((m?"div":"span"),{className:"MathJax_Processing"});l.appendChild(i)}p.parentNode.insertBefore(l,p);var k;try{this.getScales(r);k=(this.em===0||String(this.em)==="NaN")}catch(o){k=true}if(k){this.hiddenDiv.appendChild(l);this.getScales(r)}j.em=this.em;j.outerEm=this.outerEm;j.scale=this.scale;this.getLinebreakWidth(l);this.initImg(r);this.initHTML(q,r);q.setTeXclass();try{q.toHTML(r,i)}catch(o){if(o.restart){l.parentNode.removeChild(l)}throw o}if(k){p.parentNode.insertBefore(l,p)}if(this.useProcessingFrame){l.parentNode.replaceChild(i,l)}},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=i.SourceElement();if(!j){return}j=j.previousSibling;if(!j){return}if(j.className.match(/^MathJax/)){j.parentNode.removeChild(j)}},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getScales:function(k){k.parentNode.insertBefore(this.HDMspan,k);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var j=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var i=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(j/this.TeX.x_height)/i)*this.config.scale);k.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&i===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=i*this.scale/100}k.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(k)},getMarginScale:function(i){return 1},getMSIEmarginScale:function(k){k.appendChild(this.marginCheck);var i=this.marginCheck.offsetWidth,j=this.marginMove.offsetWidth;var l=(2*j-i?j/(2*j-i):1);k.removeChild(this.marginCheck);return l},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(l){var j=l.offsetWidth,k=(l.bbox?l.bbox.w:-1),m=l;if((k<0||this.negativeSkipBug)&&j>=0&&!l.style.width){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.negativeSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));if(j.bbox){j.bbox.w=i}if(j.parentNode.bbox){j.parentNode.bbox.w=i}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var 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x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var 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k=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:v.mathbackground,width:e.Em(l),height:e.Em(u),verticalAlign:e.Em(i),marginLeft:e.Em(r),marginRight:e.Em(p)}});e.setBorders(k,q);if(t.bbox.width){k.style.width=t.bbox.width;k.style.marginRight="-"+t.bbox.width}if(e.msieInlineBlockAlignBug){k.style.position="relative";k.style.width=k.style.height=0;k.style.verticalAlign=k.style.marginLeft=k.style.marginRight="";k.style.border=k.style.padding="";if(q&&e.msieBorderWidthBug){u+=q.top+q.bottom;l+=q.left+q.right}k.style.width=e.Em(o+w);e.placeBox(e.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(v.mathbackground||"transparent"),width:e.Em(l),height:e.Em(u)}}),r,t.bbox.h+w);e.setBorders(k.firstChild,q)}t.parentNode.insertBefore(k,t);if(e.msieColorPositionBug){t.style.position="relative"}return k}return null},HTMLremoveColor:function(){var 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p=[],L=[],u,K,G,l=-e.BIGDIMEN,I=l;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K]=e.createBox(o);e.Measured(this.data[K].toHTML(u),u);if(K==this.base){if(C!=null){e.Remeasured(this.data[this.base].HTMLstretchV(u,F,C),u)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(u,F),u)}}L[K]=(C==null&&F!=null?false:this.data[K].HTMLcanStretch("Horizontal"))}else{L[K]=this.data[K].HTMLcanStretch("Horizontal")}if(u.bbox.w>I){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;K<G;K++){if(this.data[K]){u=p[K];if(L[K]){u.bbox=this.data[K].HTMLstretchH(u,l).bbox}if(u.bbox.w>I){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K];r=e.TeX.big_op_spacing5*N;var z=(K!=this.base&&j[this.ACCENTS[K]]);if(z&&u.bbox.w<=1/e.em+0.0001){u.bbox.w=u.bbox.rw-u.bbox.lw;u.bbox.noclip=true;if(u.bbox.lw&&!e.zeroWidthBug){u.insertBefore(e.createSpace(u.parentNode,0,0,-u.bbox.lw),u.firstChild)}e.createBlank(u,0,0,u.bbox.rw+0.1)}A={left:0,center:(I-u.bbox.w)/2,right:I-u.bbox.w}[j.align];s=A;q=0;if(K==this.over){if(z){H=Math.max(B*N*E,2.5/this.em);r=0;if(n.bbox.skew){s+=n.bbox.skew}}else{w=e.TeX.big_op_spacing1*N*E;v=e.TeX.big_op_spacing3*N*E;H=Math.max(w,v-Math.max(0,u.bbox.d))}H=Math.max(H,1.5/this.em);s+=M;q=n.bbox.h+u.bbox.d+H;u.bbox.h+=r}else{if(K==this.under){if(z){H=3*B*N*E;r=0}else{w=e.TeX.big_op_spacing2*N*E;v=e.TeX.big_op_spacing4*N*E;H=Math.max(w,v-u.bbox.h)}H=Math.max(H,1.5/this.em);s-=M;q=-(n.bbox.d+u.bbox.h+H);u.bbox.d+=r}}e.placeBox(u,s,q)}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(H,F,z){H=this.HTMLcreateSpan(H);var K=this.HTMLgetScale(),E=this.HTMLgetMu(H);var m=e.createStack(H),j;var l=e.createBox(m);this.HTMLmeasureChild(this.base,l);if(this.data[this.base]){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(l,F,z),l)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(l,F),l)}}}e.placeBox(l,0,0);var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var I=e.TeX.x_height*K,y=e.TeX.scriptspace*K*0.75;var i,n;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(m);e.Measured(this.data[this.sup].toHTML(i),i);i.bbox.w+=y;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){n=e.createBox(m);e.Measured(this.data[this.sub].toHTML(n),n);n.bbox.w+=y;n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw)}var B=e.TeX.sup_drop*k,A=e.TeX.sub_drop*k;var w=l.bbox.h-B,o=l.bbox.d+A,J=0,C;if(l.bbox.ic){J=l.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&&l.bbox.scale===1&&!this.data[this.base].Get("largeop")){w=o=0}}var G=this.getValues("subscriptshift","superscriptshift");G.subscriptshift=(G.subscriptshift===""?0:e.length2em(G.subscriptshift,E));G.superscriptshift=(G.superscriptshift===""?0:e.length2em(G.superscriptshift,E));if(!i){if(n){o=Math.max(o,e.TeX.sub1*K,n.bbox.h-(4/5)*I,G.subscriptshift);e.placeBox(n,l.bbox.w+y-J,-o,n.bbox)}}else{if(!n){j=this.getValues("displaystyle","texprimestyle");C=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];w=Math.max(w,C*K,i.bbox.d+(1/4)*I,G.superscriptshift);e.placeBox(i,l.bbox.w+y,w,i.bbox)}else{o=Math.max(o,e.TeX.sub2*K);var x=e.TeX.rule_thickness*K;if((w-i.bbox.d)-(n.bbox.h-o)<3*x){o=3*x-w+i.bbox.d+n.bbox.h;B=(4/5)*I-(w-i.bbox.d);if(B>0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,G.superscriptshift));e.placeBox(n,l.bbox.w+y-J,-Math.max(o,G.subscriptshift))}}this.HTMLhandleSpace(H);this.HTMLhandleColor(H);return H},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.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;q=e.Measured(this.data[0].toHTML(l),l)}e.placeBox(l,0,0);var i=1/e.em,m=e.em/e.outerEm;e.em/=m;r.bbox.h*=m;r.bbox.d*=m;r.bbox.w*=m;r.bbox.lw*=m;r.bbox.rw*=m;if(q&&q.bbox.width!=null){o.style.width=q.bbox.width;l.style.width="100%"}this.HTMLhandleColor(r);if(q){e.createRule(r,(q.bbox.h+i)*m,(q.bbox.d+i)*m,0)}if(!this.isMultiline&&this.Get("display")==="block"&&r.bbox.width==null){var s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(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,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:j,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:j,msieInlineBlockAlignBug:(!k||j),msieVerticalAlignBug:(k&&!j),msiePlaceBoxBug:(k&&!j),msieClipRectBug:!k,msieNegativeSpaceBug:j,msieCloneNodeBug:(k&&i.version==="8.0"),negativeSkipBug:true,msieIE6:!l,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:i.isIE9,allowWebFonts:"eot"})},Firefox:function(j){var k=false;if(j.versionAtLeast("3.5")){var i=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,i.length)===i){k="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:k})},Safari:function(m){var k=m.versionAtLeast("3.0");var j=m.versionAtLeast("3.1");var i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(i){e.Augment({konquerorVerticalAlignBug: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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;e.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",height:"1px",width:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,hideProcessedMath:true,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var j=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=j.offsetWidth/5;this.hiddenDiv.removeChild(j);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(i){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);if(this.msieMarginScaleBug){this.addElement(this.EmExSpan.lastChild,"span",null,[["span",{style:{display:"inline-block",width:"5em"}}],["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}]])}this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},preTranslate:function(l){var s=l.jax[this.id],t,p=s.length,x,r,z,k,v,j,u,n,q;for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}r=x.previousSibling;if(r&&String(r.className).match(/^MathJax(_Display)?$/)){r.parentNode.removeChild(r)}j=x.MathJax.elementJax;j.HTMLCSS={display:(j.root.Get("display")==="block")};z=k=this.Element("span",{className:"MathJax",id:j.inputID+"-Frame",isMathJax:true,oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(d.Browser.noContextMenu){z.ontouchstart=h.start;z.ontouchend=h.end}if(j.HTMLCSS.display){k=this.Element("div",{className:"MathJax_Display",style:{width:"100%"}});k.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}k.setAttribute("role","textbox");k.setAttribute("aria-readonly","true");k.className+=" MathJax_Processing";x.parentNode.insertBefore(k,x);x.parentNode.insertBefore(this.EmExSpan.cloneNode(true),x)}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=x.previousSibling;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60;if(u===0||u==="NaN"){this.hiddenDiv.appendChild(v.previousSibling);this.hiddenDiv.appendChild(v);j.HTMLCSS.isHidden=true;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60}n=j.HTMLCSS.em=v.lastChild.firstChild.offsetWidth/60;q=Math.floor(Math.max(this.config.minScaleAdjust/100,(u/this.TeX.x_height)/n)*this.config.scale);j.HTMLCSS.scale=q/100;j.HTMLCSS.fontSize=q+"%";j.HTMLCSS.marginScale=1}if(this.msieMarginScaleBug){for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=this.getTestSpan(x);v.lastChild.style.fontSize=j.HTMLCSS.fontSize}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);var o=v.lastChild.lastChild.offsetWidth,y=v.lastChild.lastChild.firstChild.offsetWidth;math.HTMLCSS.marginScale=(2*y-o?y/(2*y-o):1)}}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);v.parentNode.removeChild(v)}l.HTMLCSSeqn=l.HTMLCSSlast=0;l.HTMLCSSchunk=this.config.EqnChunk},getTestSpan:function(j){var i=j.MathJax.elementJax;var k=document.getElementById(i.inputID+"-Frame");if(i.HTMLCSS.display){k=k.parentNode}return k.nextSibling},Translate:function(j,n){if(!j.parentNode){return}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),o=(i.HTMLCSS.display?k.parentNode:k);this.em=a.mbase.prototype.em=i.HTMLCSS.em*i.HTMLCSS.scale;this.outerEm=i.HTMLCSS.em;this.msieMarginScale=i.HTMLCSS.marginScale;k.style.fontSize=i.HTMLCSS.fontSize;this.getLinebreakWidth(o);this.initImg(k);this.initHTML(m,k);m.setTeXclass();try{m.toHTML(k,o)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}throw l}if(i.HTMLCSS.isHidden){j.parentNode.insertBefore(o,j)}o.className=o.className.split(/ /)[0];if(this.hideProcessedMath){o.className+=" MathJax_Processed";if(j.MathJax.preview){i.HTMLCSS.preview=j.MathJax.preview;delete j.MathJax.preview}n.HTMLCSSeqn++;if(n.HTMLCSSeqn>=n.HTMLCSSlast+n.HTMLCSSchunk){this.postTranslate(n);n.HTMLCSSchunk=Math.floor(n.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(p){var k=p.jax[this.id];if(!this.hideProcessedMath){return}for(var n=p.HTMLCSSlast,j=p.HTMLCSSeqn;n<j;n++){var l=k[n];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var o=l.MathJax.elementJax.HTMLCSS;if(o.preview){o.preview.style.display="none";l.MathJax.preview=o.preview;delete o.preview}}}p.HTMLCSSlast=p.HTMLCSSeqn},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.HTMLCSS.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.HTMLCSS},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(m){var j,l,k=(m.bbox||{}).w,n=m;if(m.bbox&&m.bbox.exactW){return k}if((m.bbox&&k>=0&&!this.initialSkipBug)||this.negativeBBoxes||!m.firstChild){j=m.offsetWidth;l=m.parentNode.offsetHeight}else{if(m.bbox&&k<0&&this.msieNegativeBBoxBug){j=-m.offsetWidth,l=m.parentNode.offsetHeight}else{if(this.initialSkipBug){var i=m.style.position;m.style.position="absolute";n=this.startMarker;m.insertBefore(n,m.firstChild)}m.appendChild(this.endMarker);j=this.endMarker.offsetLeft-n.offsetLeft;m.removeChild(this.endMarker);if(this.initialSkipBug){m.removeChild(n);m.style.position=i}}}if(l!=null){m.parentNode.HH=l/this.em}return j/this.em},Measured:function(k,j){var l=k.bbox;if(l.width==null&&l.w&&!l.isMultiline){var i=this.getW(k);l.rw+=i-l.w;l.w=i;l.exactW=true}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=l}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={exactW:true,h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n;m.HH=(l+o)*m.scale}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0,exactW:true},noAdjust:true,HH:l+n,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox,p.HH=l+n}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0,exactW:true},noAdjust:true,HH:o+p,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u,C=0;if(q.HH!=null){u=q.HH}else{if(A){u=Math.max(3,A.h+A.d)}else{u=q.offsetHeight/this.em}}if(!q.noAdjust){u+=1;if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.initialSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.initialSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));var k=j.bbox;if(k){k.w=i;k.exactW=true}k=j.parentNode.bbox;if(k){k.w=i;k.exactW=true}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p,exactW:true};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d,exactW:true};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l<j;l++){if(r[q[l]]){o.FONTS.push(r[q[l]]);r[q[l]].name=q[l]}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[s]){if(k[s].length===5){k[s][5]={}}if(e.allowWebFonts&&!k.available){this.loadWebFont(k)}else{return k}}else{this.findBlock(k,s)}}var p=(o.defaultFont||{family:e.config.undefinedFamily});if(o.bold){p.weight="bold"}if(o.italic){p.style="italic"}p[s]=[800,200,500,0,500,{isUnknown:true}];return p},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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=(i.bbox?i:i.HTMLspanElement());if(!l||!l.bbox){return}var k=l.bbox;if(k.d>j.d){j.d=k.d}if(k.h>j.h){j.h=k.h}if(k.D!=null&&k.D>j.D){j.D=k.D}if(k.H!=null&&k.H>j.H){j.H=k.H}if(l.style.paddingLeft){j.w+=parseFloat(l.style.paddingLeft)*(l.scale||1)}if(j.w+k.lw<j.lw){j.lw=j.w+k.lw}if(j.w+k.rw>j.rw){j.rw=j.w+k.rw}j.w+=k.w;if(l.style.paddingRight){j.w+=parseFloat(l.style.paddingRight)*(l.scale||1)}if(k.width){j.width=k.width}if(j.exactW&&!k.exactW){delete j.exactW}},HTMLemptyBBox:function(i){i.h=i.d=i.H=i.D=i.rw=-e.BIGDIMEN;i.w=0;i.lw=e.BIGDIMEN;return i},HTMLcleanBBox:function(i){if(i.h===this.BIGDIMEN){i.h=i.d=i.H=i.D=i.w=i.rw=i.lw=0}if(i.D<=i.d){delete i.D}if(i.H<=i.h){delete i.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(i){if(this.isEmbellished()){return this.Core().HTMLcanStretch(i)}return false},HTMLstretchH:function(j,i){return this.HTMLspanElement()},HTMLstretchV:function(j,i,k){return 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S=aE;for(ac=0;ac<=an;ac++){if(!at[ac].bbox.width){b.setStackWidth(at[ac],ai[ac])}if(aH[ac]!=="auto"&&aH[ac]!=="fit"){at[ac].bbox.width=ai[ac];at[ac].bbox.isFixed=true}b.placeBox(at[ac].parentNode,S,0);S+=ai[ac]+aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createRule(av,g,0,1.25/b.em);b.addBox(av,q);q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(q,S-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}aP=av.bbox.w+aE;var ag;if(G.frame!=="none"){ag=b.createFrame(av,g,0,aP,1.25/b.em,G.frame);b.addBox(av,ag);b.placeBox(ag,0,aO,true);if(aF){ag.style.width="100%"}}R=ah;for(ad=0,ab=au.length-1;ad<ab;ad++){o=Math.max(aj,ar[ad]+ao[ad+1]+aL[ad]);if(v[ad]!=="none"){q=b.createRule(av,1.25/b.em,0,aP);b.addBox(av,q);q.bbox={h:1.25/b.em,d:0,w:aP,rw:aP,lw:0};b.placeBox(q,0,R-ar[ad]-(o-ar[ad]-ao[ad+1])/2,true);if(v[ad]==="dashed"||aF){q.style.borderTop=q.style.height+" "+v[ad];q.style.height=0;q.style.width=q.style.borderLeftWidth;q.style.borderLeft="";if(aF){q.style.width="100%"}}}R-=o}if(aF){r.bbox.width=G.width;av.style.width="100%"}if(at[ay]){var ap=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(ap.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){ap.indentalign=ap.indentalignfirst}if(ap.indentalign===a.INDENTALIGN.AUTO){ap.indentalign=this.displayAlign}if(ap.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){ap.indentshift=ap.indentshiftfirst}if(ap.indentshift==="auto"){ap.indentshift=this.displayIndent}var aI=b.createStack(r,false,"100%");b.addBox(aI,av);b.alignBox(av,ap.indentalign,0);if(ap.indentshift&&ap.indentalign!==a.INDENTALIGN.CENTER){av.style[{left:"Left",right:"Right"}[ap.indentalign]]=b.Em(b.length2em(ap.indentshift,ax))}at[ay].parentNode.parentNode.removeChild(at[ay].parentNode);b.addBox(aI,at[ay]);b.alignBox(at[ay],e[ay],0);if(b.msieRelativeWidthBug){av.style.top=at[ay].style.top=""}if(aF){av.style.width=G.width;r.bbox.width="100%"}at[ay].style.marginRight=at[ay].style.marginLeft=b.Em(b.length2em(G.minlabelspacing,ax))}if(!aF){this.HTMLhandleSpace(r)}var u=this.HTMLhandleColor(r);if(u&&aF){if(!ag){ag=b.createFrame(av,g,0,aP,0,"none");b.addBox(av,ag);b.placeBox(ag,0,aO,true);ag.style.width="100%"}ag.style.backgroundColor=u.style.backgroundColor;ag.parentNode.insertBefore(ag,ag.parentNode.firstChild);u.parentNode.removeChild(u)}return r},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")}); MathJax.Ajax.loadComplete("[MathJax]/config/Accessible-full.js"); diff --git a/config/Accessible.js b/config/Accessible.js @@ -53,7 +53,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.10",directory:MathJ MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); diff --git a/config/MML_HTMLorMML-full.js b/config/MML_HTMLorMML-full.js @@ -34,7 +34,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -54,8 +54,8 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(k==="ContextMenu"){this.msieMath.fireEvent("on"+l.type,l)}}return g.False(l)},getJaxFromMath:function(k){return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){return l.firstChild},getHoverBBox:function(k,l,m){return g.getBBox(l.parentNode)},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)},NativeMMLattributes:function(n){var q=this.defaults;var s=this.NativeMMLcopyAttributes,p=this.NativeMMLskipAttributes;if(this.type==="mstyle"){q=e.math.prototype.defaults}for(var r in q){if(!p[r]&&q.hasOwnProperty(r)){if(this[r]!=null){n.setAttribute(r,this.NativeMMLattribute(r,this[r]))}}}for(var o=0,l=s.length;o<l;o++){if(this[s[o]]!=null){n.setAttribute(s[o],this.NativeMMLattribute(s[o],this[s[o]]))}}},NativeMMLcopyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],NativeMMLskipAttributes:{texClass:1,useHeight:1,texprimestyle:1},NativeMMLattribute:function(m,l){l=String(l);if(j.NAMEDSPACE[l]){l=j.NAMEDSPACE[l]}else{if(l.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){l=(RegExp.$2+(1/18)*RegExp.$1).replace(/(\.\d\d\d).*/,"$1")+"em"}else{if(l==="-tex-caligraphic"){l="script"}else{if(l==="-tex-oldstyle"){l="normal"}}}}return l},NativeMMLelement:function(l){var m=(h?document.createElement("mjx:"+l):document.createElementNS(j.MMLnamespace,l));m.isMathJax=true;return m}});e.mrow.Augment({toNativeMML:function(o){if(this.inferred&&this.parent.inferRow){for(var n=0,l=this.data.length;n<l;n++){if(this.data[n]){this.data[n].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}}else{this.SUPER(arguments).toNativeMML.call(this,o)}}});e.msubsup.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.sup]==null){p="msub"}if(this.data[this.sub]==null){p="msup"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});e.munderover.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.under]==null){p="mover"}if(this.data[this.over]==null){p="munder"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});if(b.Browser.isFirefox){e.mtable.Augment({toNativeMML:function(l){if(this.width){var m=(this.style||"").replace(/;\s*$/,"").split(";");m.push("width:"+this.width);this.style=m.join(";")}this.SUPER(arguments).toNativeMML.call(this,l)}});e.mlabeledtr.Augment({toNativeMML:function(p){var n=this.NativeMMLelement("mtr");this.NativeMMLattributes(n);for(var o=1,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)}});var k=MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf";j.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+k+"/MathJax_AMS-Regular.otf')*/"},"@font-face /*2*/":{"font-family":"MathJax_Script-WEB",src:"url('"+k+"/MathJax_Script-Regular.otf')"},"@font-face /*3*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+k+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+k+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Fraktur-Bold.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Caligraphic-Bold.otf')"}}}})}e.TeXAtom.Augment({toNativeMML:function(m){var l=this.NativeMMLelement("mrow");this.data[0].toNativeMML(l);m.appendChild(l)}});e.chars.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.entity.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.xml.Augment({toNativeMML:function(o){for(var n=0,l=this.data.length;n<l;n++){o.appendChild(this.data[n].cloneNode(true))}}});b.Register.StartupHook("TeX mathchoice Ready",function(){e.TeXmathchoice.Augment({toNativeMML:function(l){this.Core().toNativeMML(l)}})});setTimeout(MathJax.Callback(["loadComplete",j,"jax.js"]),0)});b.Browser.Select({MSIE:function(k){var l=(document.documentMode||0);j.msieIE8HeightBug=(l===8)},Opera:function(k){j.operaPositionBug=true}});b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); -(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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;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",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;var l=[],p=this.FONTDATA.VARIANT.normal.fonts;if(!(p instanceof Array)){p=[p]}for(var k=0,j=p.length;k<j;k++){l[k]=this.FONTDATA.FONTS[p[k]].family;if(!l[k]){l[k]=p[k]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":l.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 o=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=o.offsetWidth/5;this.hiddenDiv.removeChild(o);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(n){}}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(n){}}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"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},Translate:function(p){if(!p.parentNode){return}var n=p.previousSibling;if(n&&String(n.className).match(/^MathJax(_MathML|_Display)?$/)){n.parentNode.removeChild(n)}var j=p.MathJax.elementJax,q=j.root,r,i,l;r=i=l=this.Element("span",{className:"MathJax",isMathJax:true,jaxID:this.id,id:j.inputID+"-Span",oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(MathJax.Hub.Browser.noContextMenu){r.ontouchstart=h.start;r.ontouchend=h.end}var m=(q.Get("display")==="block");if(m){i=l=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});i.appendChild(r)}i.setAttribute("role","textbox");i.setAttribute("aria-readonly","true");if(this.useProcessingFrame){l=this.Element((m?"div":"span"),{className:"MathJax_Processing"});l.appendChild(i)}p.parentNode.insertBefore(l,p);var k;try{this.getScales(r);k=(this.em===0||String(this.em)==="NaN")}catch(o){k=true}if(k){this.hiddenDiv.appendChild(l);this.getScales(r)}j.em=this.em;j.outerEm=this.outerEm;j.scale=this.scale;this.getLinebreakWidth(l);this.initImg(r);this.initHTML(q,r);q.setTeXclass();try{q.toHTML(r,i)}catch(o){if(o.restart){l.parentNode.removeChild(l)}throw o}if(k){p.parentNode.insertBefore(l,p)}if(this.useProcessingFrame){l.parentNode.replaceChild(i,l)}},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=i.SourceElement();if(!j){return}j=j.previousSibling;if(!j){return}if(j.className.match(/^MathJax/)){j.parentNode.removeChild(j)}},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getScales:function(k){k.parentNode.insertBefore(this.HDMspan,k);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var j=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var i=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(j/this.TeX.x_height)/i)*this.config.scale);k.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&i===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=i*this.scale/100}k.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(k)},getMarginScale:function(i){return 1},getMSIEmarginScale:function(k){k.appendChild(this.marginCheck);var i=this.marginCheck.offsetWidth,j=this.marginMove.offsetWidth;var l=(2*j-i?j/(2*j-i):1);k.removeChild(this.marginCheck);return l},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(l){var j=l.offsetWidth,k=(l.bbox?l.bbox.w:-1),m=l;if((k<0||this.negativeSkipBug)&&j>=0&&!l.style.width){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.negativeSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));if(j.bbox){j.bbox.w=i}if(j.parentNode.bbox){j.parentNode.bbox.w=i}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var 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x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var 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k=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:v.mathbackground,width:e.Em(l),height:e.Em(u),verticalAlign:e.Em(i),marginLeft:e.Em(r),marginRight:e.Em(p)}});e.setBorders(k,q);if(t.bbox.width){k.style.width=t.bbox.width;k.style.marginRight="-"+t.bbox.width}if(e.msieInlineBlockAlignBug){k.style.position="relative";k.style.width=k.style.height=0;k.style.verticalAlign=k.style.marginLeft=k.style.marginRight="";k.style.border=k.style.padding="";if(q&&e.msieBorderWidthBug){u+=q.top+q.bottom;l+=q.left+q.right}k.style.width=e.Em(o+w);e.placeBox(e.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(v.mathbackground||"transparent"),width:e.Em(l),height:e.Em(u)}}),r,t.bbox.h+w);e.setBorders(k.firstChild,q)}t.parentNode.insertBefore(k,t);if(e.msieColorPositionBug){t.style.position="relative"}return k}return null},HTMLremoveColor:function(){var 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p=[],L=[],u,K,G,l=-e.BIGDIMEN,I=l;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K]=e.createBox(o);e.Measured(this.data[K].toHTML(u),u);if(K==this.base){if(C!=null){e.Remeasured(this.data[this.base].HTMLstretchV(u,F,C),u)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(u,F),u)}}L[K]=(C==null&&F!=null?false:this.data[K].HTMLcanStretch("Horizontal"))}else{L[K]=this.data[K].HTMLcanStretch("Horizontal")}if(u.bbox.w>I){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;K<G;K++){if(this.data[K]){u=p[K];if(L[K]){u.bbox=this.data[K].HTMLstretchH(u,l).bbox}if(u.bbox.w>I){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K];r=e.TeX.big_op_spacing5*N;var z=(K!=this.base&&j[this.ACCENTS[K]]);if(z&&u.bbox.w<=1/e.em+0.0001){u.bbox.w=u.bbox.rw-u.bbox.lw;u.bbox.noclip=true;if(u.bbox.lw&&!e.zeroWidthBug){u.insertBefore(e.createSpace(u.parentNode,0,0,-u.bbox.lw),u.firstChild)}e.createBlank(u,0,0,u.bbox.rw+0.1)}A={left:0,center:(I-u.bbox.w)/2,right:I-u.bbox.w}[j.align];s=A;q=0;if(K==this.over){if(z){H=Math.max(B*N*E,2.5/this.em);r=0;if(n.bbox.skew){s+=n.bbox.skew}}else{w=e.TeX.big_op_spacing1*N*E;v=e.TeX.big_op_spacing3*N*E;H=Math.max(w,v-Math.max(0,u.bbox.d))}H=Math.max(H,1.5/this.em);s+=M;q=n.bbox.h+u.bbox.d+H;u.bbox.h+=r}else{if(K==this.under){if(z){H=3*B*N*E;r=0}else{w=e.TeX.big_op_spacing2*N*E;v=e.TeX.big_op_spacing4*N*E;H=Math.max(w,v-u.bbox.h)}H=Math.max(H,1.5/this.em);s-=M;q=-(n.bbox.d+u.bbox.h+H);u.bbox.d+=r}}e.placeBox(u,s,q)}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(H,F,z){H=this.HTMLcreateSpan(H);var K=this.HTMLgetScale(),E=this.HTMLgetMu(H);var m=e.createStack(H),j;var l=e.createBox(m);this.HTMLmeasureChild(this.base,l);if(this.data[this.base]){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(l,F,z),l)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(l,F),l)}}}e.placeBox(l,0,0);var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var I=e.TeX.x_height*K,y=e.TeX.scriptspace*K*0.75;var i,n;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(m);e.Measured(this.data[this.sup].toHTML(i),i);i.bbox.w+=y;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){n=e.createBox(m);e.Measured(this.data[this.sub].toHTML(n),n);n.bbox.w+=y;n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw)}var B=e.TeX.sup_drop*k,A=e.TeX.sub_drop*k;var w=l.bbox.h-B,o=l.bbox.d+A,J=0,C;if(l.bbox.ic){J=l.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&&l.bbox.scale===1&&!this.data[this.base].Get("largeop")){w=o=0}}var G=this.getValues("subscriptshift","superscriptshift");G.subscriptshift=(G.subscriptshift===""?0:e.length2em(G.subscriptshift,E));G.superscriptshift=(G.superscriptshift===""?0:e.length2em(G.superscriptshift,E));if(!i){if(n){o=Math.max(o,e.TeX.sub1*K,n.bbox.h-(4/5)*I,G.subscriptshift);e.placeBox(n,l.bbox.w+y-J,-o,n.bbox)}}else{if(!n){j=this.getValues("displaystyle","texprimestyle");C=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];w=Math.max(w,C*K,i.bbox.d+(1/4)*I,G.superscriptshift);e.placeBox(i,l.bbox.w+y,w,i.bbox)}else{o=Math.max(o,e.TeX.sub2*K);var x=e.TeX.rule_thickness*K;if((w-i.bbox.d)-(n.bbox.h-o)<3*x){o=3*x-w+i.bbox.d+n.bbox.h;B=(4/5)*I-(w-i.bbox.d);if(B>0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,G.superscriptshift));e.placeBox(n,l.bbox.w+y-J,-Math.max(o,G.subscriptshift))}}this.HTMLhandleSpace(H);this.HTMLhandleColor(H);return H},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.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;q=e.Measured(this.data[0].toHTML(l),l)}e.placeBox(l,0,0);var i=1/e.em,m=e.em/e.outerEm;e.em/=m;r.bbox.h*=m;r.bbox.d*=m;r.bbox.w*=m;r.bbox.lw*=m;r.bbox.rw*=m;if(q&&q.bbox.width!=null){o.style.width=q.bbox.width;l.style.width="100%"}this.HTMLhandleColor(r);if(q){e.createRule(r,(q.bbox.h+i)*m,(q.bbox.d+i)*m,0)}if(!this.isMultiline&&this.Get("display")==="block"&&r.bbox.width==null){var s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(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,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:j,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:j,msieInlineBlockAlignBug:(!k||j),msieVerticalAlignBug:(k&&!j),msiePlaceBoxBug:(k&&!j),msieClipRectBug:!k,msieNegativeSpaceBug:j,msieCloneNodeBug:(k&&i.version==="8.0"),negativeSkipBug:true,msieIE6:!l,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:i.isIE9,allowWebFonts:"eot"})},Firefox:function(j){var k=false;if(j.versionAtLeast("3.5")){var i=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,i.length)===i){k="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:k})},Safari:function(m){var k=m.versionAtLeast("3.0");var j=m.versionAtLeast("3.1");var i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(i){e.Augment({konquerorVerticalAlignBug: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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;e.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",height:"1px",width:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,hideProcessedMath:true,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var j=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=j.offsetWidth/5;this.hiddenDiv.removeChild(j);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(i){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);if(this.msieMarginScaleBug){this.addElement(this.EmExSpan.lastChild,"span",null,[["span",{style:{display:"inline-block",width:"5em"}}],["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}]])}this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},preTranslate:function(l){var s=l.jax[this.id],t,p=s.length,x,r,z,k,v,j,u,n,q;for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}r=x.previousSibling;if(r&&String(r.className).match(/^MathJax(_Display)?$/)){r.parentNode.removeChild(r)}j=x.MathJax.elementJax;j.HTMLCSS={display:(j.root.Get("display")==="block")};z=k=this.Element("span",{className:"MathJax",id:j.inputID+"-Frame",isMathJax:true,oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(d.Browser.noContextMenu){z.ontouchstart=h.start;z.ontouchend=h.end}if(j.HTMLCSS.display){k=this.Element("div",{className:"MathJax_Display",style:{width:"100%"}});k.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}k.setAttribute("role","textbox");k.setAttribute("aria-readonly","true");k.className+=" MathJax_Processing";x.parentNode.insertBefore(k,x);x.parentNode.insertBefore(this.EmExSpan.cloneNode(true),x)}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=x.previousSibling;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60;if(u===0||u==="NaN"){this.hiddenDiv.appendChild(v.previousSibling);this.hiddenDiv.appendChild(v);j.HTMLCSS.isHidden=true;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60}n=j.HTMLCSS.em=v.lastChild.firstChild.offsetWidth/60;q=Math.floor(Math.max(this.config.minScaleAdjust/100,(u/this.TeX.x_height)/n)*this.config.scale);j.HTMLCSS.scale=q/100;j.HTMLCSS.fontSize=q+"%";j.HTMLCSS.marginScale=1}if(this.msieMarginScaleBug){for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=this.getTestSpan(x);v.lastChild.style.fontSize=j.HTMLCSS.fontSize}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);var o=v.lastChild.lastChild.offsetWidth,y=v.lastChild.lastChild.firstChild.offsetWidth;math.HTMLCSS.marginScale=(2*y-o?y/(2*y-o):1)}}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);v.parentNode.removeChild(v)}l.HTMLCSSeqn=l.HTMLCSSlast=0;l.HTMLCSSchunk=this.config.EqnChunk},getTestSpan:function(j){var i=j.MathJax.elementJax;var k=document.getElementById(i.inputID+"-Frame");if(i.HTMLCSS.display){k=k.parentNode}return k.nextSibling},Translate:function(j,n){if(!j.parentNode){return}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),o=(i.HTMLCSS.display?k.parentNode:k);this.em=a.mbase.prototype.em=i.HTMLCSS.em*i.HTMLCSS.scale;this.outerEm=i.HTMLCSS.em;this.msieMarginScale=i.HTMLCSS.marginScale;k.style.fontSize=i.HTMLCSS.fontSize;this.getLinebreakWidth(o);this.initImg(k);this.initHTML(m,k);m.setTeXclass();try{m.toHTML(k,o)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}throw l}if(i.HTMLCSS.isHidden){j.parentNode.insertBefore(o,j)}o.className=o.className.split(/ /)[0];if(this.hideProcessedMath){o.className+=" MathJax_Processed";if(j.MathJax.preview){i.HTMLCSS.preview=j.MathJax.preview;delete j.MathJax.preview}n.HTMLCSSeqn++;if(n.HTMLCSSeqn>=n.HTMLCSSlast+n.HTMLCSSchunk){this.postTranslate(n);n.HTMLCSSchunk=Math.floor(n.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(p){var k=p.jax[this.id];if(!this.hideProcessedMath){return}for(var n=p.HTMLCSSlast,j=p.HTMLCSSeqn;n<j;n++){var l=k[n];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var o=l.MathJax.elementJax.HTMLCSS;if(o.preview){o.preview.style.display="none";l.MathJax.preview=o.preview;delete o.preview}}}p.HTMLCSSlast=p.HTMLCSSeqn},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.HTMLCSS.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.HTMLCSS},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(m){var j,l,k=(m.bbox||{}).w,n=m;if(m.bbox&&m.bbox.exactW){return k}if((m.bbox&&k>=0&&!this.initialSkipBug)||this.negativeBBoxes||!m.firstChild){j=m.offsetWidth;l=m.parentNode.offsetHeight}else{if(m.bbox&&k<0&&this.msieNegativeBBoxBug){j=-m.offsetWidth,l=m.parentNode.offsetHeight}else{if(this.initialSkipBug){var i=m.style.position;m.style.position="absolute";n=this.startMarker;m.insertBefore(n,m.firstChild)}m.appendChild(this.endMarker);j=this.endMarker.offsetLeft-n.offsetLeft;m.removeChild(this.endMarker);if(this.initialSkipBug){m.removeChild(n);m.style.position=i}}}if(l!=null){m.parentNode.HH=l/this.em}return j/this.em},Measured:function(k,j){var l=k.bbox;if(l.width==null&&l.w&&!l.isMultiline){var i=this.getW(k);l.rw+=i-l.w;l.w=i;l.exactW=true}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=l}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={exactW:true,h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n;m.HH=(l+o)*m.scale}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0,exactW:true},noAdjust:true,HH:l+n,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox,p.HH=l+n}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0,exactW:true},noAdjust:true,HH:o+p,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u,C=0;if(q.HH!=null){u=q.HH}else{if(A){u=Math.max(3,A.h+A.d)}else{u=q.offsetHeight/this.em}}if(!q.noAdjust){u+=1;if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.initialSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.initialSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));var k=j.bbox;if(k){k.w=i;k.exactW=true}k=j.parentNode.bbox;if(k){k.w=i;k.exactW=true}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p,exactW:true};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d,exactW:true};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l<j;l++){if(r[q[l]]){o.FONTS.push(r[q[l]]);r[q[l]].name=q[l]}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[s]){if(k[s].length===5){k[s][5]={}}if(e.allowWebFonts&&!k.available){this.loadWebFont(k)}else{return k}}else{this.findBlock(k,s)}}var p=(o.defaultFont||{family:e.config.undefinedFamily});if(o.bold){p.weight="bold"}if(o.italic){p.style="italic"}p[s]=[800,200,500,0,500,{isUnknown:true}];return p},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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=(i.bbox?i:i.HTMLspanElement());if(!l||!l.bbox){return}var k=l.bbox;if(k.d>j.d){j.d=k.d}if(k.h>j.h){j.h=k.h}if(k.D!=null&&k.D>j.D){j.D=k.D}if(k.H!=null&&k.H>j.H){j.H=k.H}if(l.style.paddingLeft){j.w+=parseFloat(l.style.paddingLeft)*(l.scale||1)}if(j.w+k.lw<j.lw){j.lw=j.w+k.lw}if(j.w+k.rw>j.rw){j.rw=j.w+k.rw}j.w+=k.w;if(l.style.paddingRight){j.w+=parseFloat(l.style.paddingRight)*(l.scale||1)}if(k.width){j.width=k.width}if(j.exactW&&!k.exactW){delete j.exactW}},HTMLemptyBBox:function(i){i.h=i.d=i.H=i.D=i.rw=-e.BIGDIMEN;i.w=0;i.lw=e.BIGDIMEN;return i},HTMLcleanBBox:function(i){if(i.h===this.BIGDIMEN){i.h=i.d=i.H=i.D=i.w=i.rw=i.lw=0}if(i.D<=i.d){delete i.D}if(i.H<=i.h){delete i.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(i){if(this.isEmbellished()){return this.Core().HTMLcanStretch(i)}return false},HTMLstretchH:function(j,i){return this.HTMLspanElement()},HTMLstretchV:function(j,i,k){return 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S=aE;for(ac=0;ac<=an;ac++){if(!at[ac].bbox.width){b.setStackWidth(at[ac],ai[ac])}if(aH[ac]!=="auto"&&aH[ac]!=="fit"){at[ac].bbox.width=ai[ac];at[ac].bbox.isFixed=true}b.placeBox(at[ac].parentNode,S,0);S+=ai[ac]+aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createRule(av,g,0,1.25/b.em);b.addBox(av,q);q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(q,S-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}aP=av.bbox.w+aE;var ag;if(G.frame!=="none"){ag=b.createFrame(av,g,0,aP,1.25/b.em,G.frame);b.addBox(av,ag);b.placeBox(ag,0,aO,true);if(aF){ag.style.width="100%"}}R=ah;for(ad=0,ab=au.length-1;ad<ab;ad++){o=Math.max(aj,ar[ad]+ao[ad+1]+aL[ad]);if(v[ad]!=="none"){q=b.createRule(av,1.25/b.em,0,aP);b.addBox(av,q);q.bbox={h:1.25/b.em,d:0,w:aP,rw:aP,lw:0};b.placeBox(q,0,R-ar[ad]-(o-ar[ad]-ao[ad+1])/2,true);if(v[ad]==="dashed"||aF){q.style.borderTop=q.style.height+" "+v[ad];q.style.height=0;q.style.width=q.style.borderLeftWidth;q.style.borderLeft="";if(aF){q.style.width="100%"}}}R-=o}if(aF){r.bbox.width=G.width;av.style.width="100%"}if(at[ay]){var ap=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(ap.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){ap.indentalign=ap.indentalignfirst}if(ap.indentalign===a.INDENTALIGN.AUTO){ap.indentalign=this.displayAlign}if(ap.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){ap.indentshift=ap.indentshiftfirst}if(ap.indentshift==="auto"){ap.indentshift=this.displayIndent}var aI=b.createStack(r,false,"100%");b.addBox(aI,av);b.alignBox(av,ap.indentalign,0);if(ap.indentshift&&ap.indentalign!==a.INDENTALIGN.CENTER){av.style[{left:"Left",right:"Right"}[ap.indentalign]]=b.Em(b.length2em(ap.indentshift,ax))}at[ay].parentNode.parentNode.removeChild(at[ay].parentNode);b.addBox(aI,at[ay]);b.alignBox(at[ay],e[ay],0);if(b.msieRelativeWidthBug){av.style.top=at[ay].style.top=""}if(aF){av.style.width=G.width;r.bbox.width="100%"}at[ay].style.marginRight=at[ay].style.marginLeft=b.Em(b.length2em(G.minlabelspacing,ax))}if(!aF){this.HTMLhandleSpace(r)}var u=this.HTMLhandleColor(r);if(u&&aF){if(!ag){ag=b.createFrame(av,g,0,aP,0,"none");b.addBox(av,ag);b.placeBox(ag,0,aO,true);ag.style.width="100%"}ag.style.backgroundColor=u.style.backgroundColor;ag.parentNode.insertBefore(ag,ag.parentNode.firstChild);u.parentNode.removeChild(u)}return r},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")}); MathJax.Ajax.loadComplete("[MathJax]/config/MML_HTMLorMML-full.js"); diff --git a/config/MML_HTMLorMML.js b/config/MML_HTMLorMML.js @@ -31,7 +31,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); diff --git a/config/TeX-AMS-MML_HTMLorMML-full.js b/config/TeX-AMS-MML_HTMLorMML-full.js @@ -43,7 +43,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.10",directory:MathJ MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -75,8 +75,8 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a= (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(k==="ContextMenu"){this.msieMath.fireEvent("on"+l.type,l)}}return g.False(l)},getJaxFromMath:function(k){return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){return l.firstChild},getHoverBBox:function(k,l,m){return g.getBBox(l.parentNode)},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)},NativeMMLattributes:function(n){var q=this.defaults;var s=this.NativeMMLcopyAttributes,p=this.NativeMMLskipAttributes;if(this.type==="mstyle"){q=e.math.prototype.defaults}for(var r in q){if(!p[r]&&q.hasOwnProperty(r)){if(this[r]!=null){n.setAttribute(r,this.NativeMMLattribute(r,this[r]))}}}for(var o=0,l=s.length;o<l;o++){if(this[s[o]]!=null){n.setAttribute(s[o],this.NativeMMLattribute(s[o],this[s[o]]))}}},NativeMMLcopyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],NativeMMLskipAttributes:{texClass:1,useHeight:1,texprimestyle:1},NativeMMLattribute:function(m,l){l=String(l);if(j.NAMEDSPACE[l]){l=j.NAMEDSPACE[l]}else{if(l.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){l=(RegExp.$2+(1/18)*RegExp.$1).replace(/(\.\d\d\d).*/,"$1")+"em"}else{if(l==="-tex-caligraphic"){l="script"}else{if(l==="-tex-oldstyle"){l="normal"}}}}return l},NativeMMLelement:function(l){var m=(h?document.createElement("mjx:"+l):document.createElementNS(j.MMLnamespace,l));m.isMathJax=true;return m}});e.mrow.Augment({toNativeMML:function(o){if(this.inferred&&this.parent.inferRow){for(var n=0,l=this.data.length;n<l;n++){if(this.data[n]){this.data[n].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}}else{this.SUPER(arguments).toNativeMML.call(this,o)}}});e.msubsup.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.sup]==null){p="msub"}if(this.data[this.sub]==null){p="msup"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});e.munderover.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.under]==null){p="mover"}if(this.data[this.over]==null){p="munder"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});if(b.Browser.isFirefox){e.mtable.Augment({toNativeMML:function(l){if(this.width){var m=(this.style||"").replace(/;\s*$/,"").split(";");m.push("width:"+this.width);this.style=m.join(";")}this.SUPER(arguments).toNativeMML.call(this,l)}});e.mlabeledtr.Augment({toNativeMML:function(p){var n=this.NativeMMLelement("mtr");this.NativeMMLattributes(n);for(var o=1,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)}});var k=MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf";j.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[mathvariant="-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+k+"/MathJax_AMS-Regular.otf')*/"},"@font-face /*2*/":{"font-family":"MathJax_Script-WEB",src:"url('"+k+"/MathJax_Script-Regular.otf')"},"@font-face /*3*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+k+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+k+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Fraktur-Bold.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+k+"/MathJax_Caligraphic-Bold.otf')"}}}})}e.TeXAtom.Augment({toNativeMML:function(m){var l=this.NativeMMLelement("mrow");this.data[0].toNativeMML(l);m.appendChild(l)}});e.chars.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.entity.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.xml.Augment({toNativeMML:function(o){for(var n=0,l=this.data.length;n<l;n++){o.appendChild(this.data[n].cloneNode(true))}}});b.Register.StartupHook("TeX mathchoice Ready",function(){e.TeXmathchoice.Augment({toNativeMML:function(l){this.Core().toNativeMML(l)}})});setTimeout(MathJax.Callback(["loadComplete",j,"jax.js"]),0)});b.Browser.Select({MSIE:function(k){var l=(document.documentMode||0);j.msieIE8HeightBug=(l===8)},Opera:function(k){j.operaPositionBug=true}});b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); -(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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;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",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;var l=[],p=this.FONTDATA.VARIANT.normal.fonts;if(!(p instanceof Array)){p=[p]}for(var k=0,j=p.length;k<j;k++){l[k]=this.FONTDATA.FONTS[p[k]].family;if(!l[k]){l[k]=p[k]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":l.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 o=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=o.offsetWidth/5;this.hiddenDiv.removeChild(o);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(n){}}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(n){}}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"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},Translate:function(p){if(!p.parentNode){return}var n=p.previousSibling;if(n&&String(n.className).match(/^MathJax(_MathML|_Display)?$/)){n.parentNode.removeChild(n)}var j=p.MathJax.elementJax,q=j.root,r,i,l;r=i=l=this.Element("span",{className:"MathJax",isMathJax:true,jaxID:this.id,id:j.inputID+"-Span",oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(MathJax.Hub.Browser.noContextMenu){r.ontouchstart=h.start;r.ontouchend=h.end}var m=(q.Get("display")==="block");if(m){i=l=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});i.appendChild(r)}i.setAttribute("role","textbox");i.setAttribute("aria-readonly","true");if(this.useProcessingFrame){l=this.Element((m?"div":"span"),{className:"MathJax_Processing"});l.appendChild(i)}p.parentNode.insertBefore(l,p);var k;try{this.getScales(r);k=(this.em===0||String(this.em)==="NaN")}catch(o){k=true}if(k){this.hiddenDiv.appendChild(l);this.getScales(r)}j.em=this.em;j.outerEm=this.outerEm;j.scale=this.scale;this.getLinebreakWidth(l);this.initImg(r);this.initHTML(q,r);q.setTeXclass();try{q.toHTML(r,i)}catch(o){if(o.restart){l.parentNode.removeChild(l)}throw o}if(k){p.parentNode.insertBefore(l,p)}if(this.useProcessingFrame){l.parentNode.replaceChild(i,l)}},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=i.SourceElement();if(!j){return}j=j.previousSibling;if(!j){return}if(j.className.match(/^MathJax/)){j.parentNode.removeChild(j)}},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getScales:function(k){k.parentNode.insertBefore(this.HDMspan,k);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var j=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var i=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(j/this.TeX.x_height)/i)*this.config.scale);k.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&i===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=i*this.scale/100}k.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(k)},getMarginScale:function(i){return 1},getMSIEmarginScale:function(k){k.appendChild(this.marginCheck);var i=this.marginCheck.offsetWidth,j=this.marginMove.offsetWidth;var l=(2*j-i?j/(2*j-i):1);k.removeChild(this.marginCheck);return l},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(l){var j=l.offsetWidth,k=(l.bbox?l.bbox.w:-1),m=l;if((k<0||this.negativeSkipBug)&&j>=0&&!l.style.width){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.negativeSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));if(j.bbox){j.bbox.w=i}if(j.parentNode.bbox){j.parentNode.bbox.w=i}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var 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x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var 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k=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:v.mathbackground,width:e.Em(l),height:e.Em(u),verticalAlign:e.Em(i),marginLeft:e.Em(r),marginRight:e.Em(p)}});e.setBorders(k,q);if(t.bbox.width){k.style.width=t.bbox.width;k.style.marginRight="-"+t.bbox.width}if(e.msieInlineBlockAlignBug){k.style.position="relative";k.style.width=k.style.height=0;k.style.verticalAlign=k.style.marginLeft=k.style.marginRight="";k.style.border=k.style.padding="";if(q&&e.msieBorderWidthBug){u+=q.top+q.bottom;l+=q.left+q.right}k.style.width=e.Em(o+w);e.placeBox(e.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(v.mathbackground||"transparent"),width:e.Em(l),height:e.Em(u)}}),r,t.bbox.h+w);e.setBorders(k.firstChild,q)}t.parentNode.insertBefore(k,t);if(e.msieColorPositionBug){t.style.position="relative"}return k}return null},HTMLremoveColor:function(){var 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p=[],L=[],u,K,G,l=-e.BIGDIMEN,I=l;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K]=e.createBox(o);e.Measured(this.data[K].toHTML(u),u);if(K==this.base){if(C!=null){e.Remeasured(this.data[this.base].HTMLstretchV(u,F,C),u)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(u,F),u)}}L[K]=(C==null&&F!=null?false:this.data[K].HTMLcanStretch("Horizontal"))}else{L[K]=this.data[K].HTMLcanStretch("Horizontal")}if(u.bbox.w>I){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;K<G;K++){if(this.data[K]){u=p[K];if(L[K]){u.bbox=this.data[K].HTMLstretchH(u,l).bbox}if(u.bbox.w>I){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K];r=e.TeX.big_op_spacing5*N;var z=(K!=this.base&&j[this.ACCENTS[K]]);if(z&&u.bbox.w<=1/e.em+0.0001){u.bbox.w=u.bbox.rw-u.bbox.lw;u.bbox.noclip=true;if(u.bbox.lw&&!e.zeroWidthBug){u.insertBefore(e.createSpace(u.parentNode,0,0,-u.bbox.lw),u.firstChild)}e.createBlank(u,0,0,u.bbox.rw+0.1)}A={left:0,center:(I-u.bbox.w)/2,right:I-u.bbox.w}[j.align];s=A;q=0;if(K==this.over){if(z){H=Math.max(B*N*E,2.5/this.em);r=0;if(n.bbox.skew){s+=n.bbox.skew}}else{w=e.TeX.big_op_spacing1*N*E;v=e.TeX.big_op_spacing3*N*E;H=Math.max(w,v-Math.max(0,u.bbox.d))}H=Math.max(H,1.5/this.em);s+=M;q=n.bbox.h+u.bbox.d+H;u.bbox.h+=r}else{if(K==this.under){if(z){H=3*B*N*E;r=0}else{w=e.TeX.big_op_spacing2*N*E;v=e.TeX.big_op_spacing4*N*E;H=Math.max(w,v-u.bbox.h)}H=Math.max(H,1.5/this.em);s-=M;q=-(n.bbox.d+u.bbox.h+H);u.bbox.d+=r}}e.placeBox(u,s,q)}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(H,F,z){H=this.HTMLcreateSpan(H);var K=this.HTMLgetScale(),E=this.HTMLgetMu(H);var m=e.createStack(H),j;var l=e.createBox(m);this.HTMLmeasureChild(this.base,l);if(this.data[this.base]){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(l,F,z),l)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(l,F),l)}}}e.placeBox(l,0,0);var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var I=e.TeX.x_height*K,y=e.TeX.scriptspace*K*0.75;var i,n;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(m);e.Measured(this.data[this.sup].toHTML(i),i);i.bbox.w+=y;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){n=e.createBox(m);e.Measured(this.data[this.sub].toHTML(n),n);n.bbox.w+=y;n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw)}var B=e.TeX.sup_drop*k,A=e.TeX.sub_drop*k;var w=l.bbox.h-B,o=l.bbox.d+A,J=0,C;if(l.bbox.ic){J=l.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&&l.bbox.scale===1&&!this.data[this.base].Get("largeop")){w=o=0}}var G=this.getValues("subscriptshift","superscriptshift");G.subscriptshift=(G.subscriptshift===""?0:e.length2em(G.subscriptshift,E));G.superscriptshift=(G.superscriptshift===""?0:e.length2em(G.superscriptshift,E));if(!i){if(n){o=Math.max(o,e.TeX.sub1*K,n.bbox.h-(4/5)*I,G.subscriptshift);e.placeBox(n,l.bbox.w+y-J,-o,n.bbox)}}else{if(!n){j=this.getValues("displaystyle","texprimestyle");C=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];w=Math.max(w,C*K,i.bbox.d+(1/4)*I,G.superscriptshift);e.placeBox(i,l.bbox.w+y,w,i.bbox)}else{o=Math.max(o,e.TeX.sub2*K);var x=e.TeX.rule_thickness*K;if((w-i.bbox.d)-(n.bbox.h-o)<3*x){o=3*x-w+i.bbox.d+n.bbox.h;B=(4/5)*I-(w-i.bbox.d);if(B>0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,G.superscriptshift));e.placeBox(n,l.bbox.w+y-J,-Math.max(o,G.subscriptshift))}}this.HTMLhandleSpace(H);this.HTMLhandleColor(H);return H},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.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;q=e.Measured(this.data[0].toHTML(l),l)}e.placeBox(l,0,0);var i=1/e.em,m=e.em/e.outerEm;e.em/=m;r.bbox.h*=m;r.bbox.d*=m;r.bbox.w*=m;r.bbox.lw*=m;r.bbox.rw*=m;if(q&&q.bbox.width!=null){o.style.width=q.bbox.width;l.style.width="100%"}this.HTMLhandleColor(r);if(q){e.createRule(r,(q.bbox.h+i)*m,(q.bbox.d+i)*m,0)}if(!this.isMultiline&&this.Get("display")==="block"&&r.bbox.width==null){var s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(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,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:j,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:j,msieInlineBlockAlignBug:(!k||j),msieVerticalAlignBug:(k&&!j),msiePlaceBoxBug:(k&&!j),msieClipRectBug:!k,msieNegativeSpaceBug:j,msieCloneNodeBug:(k&&i.version==="8.0"),negativeSkipBug:true,msieIE6:!l,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:i.isIE9,allowWebFonts:"eot"})},Firefox:function(j){var k=false;if(j.versionAtLeast("3.5")){var i=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,i.length)===i){k="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:k})},Safari:function(m){var k=m.versionAtLeast("3.0");var j=m.versionAtLeast("3.1");var i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(i){e.Augment({konquerorVerticalAlignBug: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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;e.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",height:"1px",width:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,hideProcessedMath:true,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var j=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=j.offsetWidth/5;this.hiddenDiv.removeChild(j);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(i){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);if(this.msieMarginScaleBug){this.addElement(this.EmExSpan.lastChild,"span",null,[["span",{style:{display:"inline-block",width:"5em"}}],["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}]])}this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},preTranslate:function(l){var s=l.jax[this.id],t,p=s.length,x,r,z,k,v,j,u,n,q;for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}r=x.previousSibling;if(r&&String(r.className).match(/^MathJax(_Display)?$/)){r.parentNode.removeChild(r)}j=x.MathJax.elementJax;j.HTMLCSS={display:(j.root.Get("display")==="block")};z=k=this.Element("span",{className:"MathJax",id:j.inputID+"-Frame",isMathJax:true,oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(d.Browser.noContextMenu){z.ontouchstart=h.start;z.ontouchend=h.end}if(j.HTMLCSS.display){k=this.Element("div",{className:"MathJax_Display",style:{width:"100%"}});k.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}k.setAttribute("role","textbox");k.setAttribute("aria-readonly","true");k.className+=" MathJax_Processing";x.parentNode.insertBefore(k,x);x.parentNode.insertBefore(this.EmExSpan.cloneNode(true),x)}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=x.previousSibling;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60;if(u===0||u==="NaN"){this.hiddenDiv.appendChild(v.previousSibling);this.hiddenDiv.appendChild(v);j.HTMLCSS.isHidden=true;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60}n=j.HTMLCSS.em=v.lastChild.firstChild.offsetWidth/60;q=Math.floor(Math.max(this.config.minScaleAdjust/100,(u/this.TeX.x_height)/n)*this.config.scale);j.HTMLCSS.scale=q/100;j.HTMLCSS.fontSize=q+"%";j.HTMLCSS.marginScale=1}if(this.msieMarginScaleBug){for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=this.getTestSpan(x);v.lastChild.style.fontSize=j.HTMLCSS.fontSize}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);var o=v.lastChild.lastChild.offsetWidth,y=v.lastChild.lastChild.firstChild.offsetWidth;math.HTMLCSS.marginScale=(2*y-o?y/(2*y-o):1)}}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);v.parentNode.removeChild(v)}l.HTMLCSSeqn=l.HTMLCSSlast=0;l.HTMLCSSchunk=this.config.EqnChunk},getTestSpan:function(j){var i=j.MathJax.elementJax;var k=document.getElementById(i.inputID+"-Frame");if(i.HTMLCSS.display){k=k.parentNode}return k.nextSibling},Translate:function(j,n){if(!j.parentNode){return}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),o=(i.HTMLCSS.display?k.parentNode:k);this.em=a.mbase.prototype.em=i.HTMLCSS.em*i.HTMLCSS.scale;this.outerEm=i.HTMLCSS.em;this.msieMarginScale=i.HTMLCSS.marginScale;k.style.fontSize=i.HTMLCSS.fontSize;this.getLinebreakWidth(o);this.initImg(k);this.initHTML(m,k);m.setTeXclass();try{m.toHTML(k,o)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}throw l}if(i.HTMLCSS.isHidden){j.parentNode.insertBefore(o,j)}o.className=o.className.split(/ /)[0];if(this.hideProcessedMath){o.className+=" MathJax_Processed";if(j.MathJax.preview){i.HTMLCSS.preview=j.MathJax.preview;delete j.MathJax.preview}n.HTMLCSSeqn++;if(n.HTMLCSSeqn>=n.HTMLCSSlast+n.HTMLCSSchunk){this.postTranslate(n);n.HTMLCSSchunk=Math.floor(n.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(p){var k=p.jax[this.id];if(!this.hideProcessedMath){return}for(var n=p.HTMLCSSlast,j=p.HTMLCSSeqn;n<j;n++){var l=k[n];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var o=l.MathJax.elementJax.HTMLCSS;if(o.preview){o.preview.style.display="none";l.MathJax.preview=o.preview;delete o.preview}}}p.HTMLCSSlast=p.HTMLCSSeqn},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.HTMLCSS.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.HTMLCSS},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(m){var j,l,k=(m.bbox||{}).w,n=m;if(m.bbox&&m.bbox.exactW){return k}if((m.bbox&&k>=0&&!this.initialSkipBug)||this.negativeBBoxes||!m.firstChild){j=m.offsetWidth;l=m.parentNode.offsetHeight}else{if(m.bbox&&k<0&&this.msieNegativeBBoxBug){j=-m.offsetWidth,l=m.parentNode.offsetHeight}else{if(this.initialSkipBug){var i=m.style.position;m.style.position="absolute";n=this.startMarker;m.insertBefore(n,m.firstChild)}m.appendChild(this.endMarker);j=this.endMarker.offsetLeft-n.offsetLeft;m.removeChild(this.endMarker);if(this.initialSkipBug){m.removeChild(n);m.style.position=i}}}if(l!=null){m.parentNode.HH=l/this.em}return j/this.em},Measured:function(k,j){var l=k.bbox;if(l.width==null&&l.w&&!l.isMultiline){var i=this.getW(k);l.rw+=i-l.w;l.w=i;l.exactW=true}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=l}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={exactW:true,h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n;m.HH=(l+o)*m.scale}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0,exactW:true},noAdjust:true,HH:l+n,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox,p.HH=l+n}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0,exactW:true},noAdjust:true,HH:o+p,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u,C=0;if(q.HH!=null){u=q.HH}else{if(A){u=Math.max(3,A.h+A.d)}else{u=q.offsetHeight/this.em}}if(!q.noAdjust){u+=1;if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.initialSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.initialSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));var k=j.bbox;if(k){k.w=i;k.exactW=true}k=j.parentNode.bbox;if(k){k.w=i;k.exactW=true}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p,exactW:true};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d,exactW:true};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l<j;l++){if(r[q[l]]){o.FONTS.push(r[q[l]]);r[q[l]].name=q[l]}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[s]){if(k[s].length===5){k[s][5]={}}if(e.allowWebFonts&&!k.available){this.loadWebFont(k)}else{return k}}else{this.findBlock(k,s)}}var p=(o.defaultFont||{family:e.config.undefinedFamily});if(o.bold){p.weight="bold"}if(o.italic){p.style="italic"}p[s]=[800,200,500,0,500,{isUnknown:true}];return p},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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=(i.bbox?i:i.HTMLspanElement());if(!l||!l.bbox){return}var k=l.bbox;if(k.d>j.d){j.d=k.d}if(k.h>j.h){j.h=k.h}if(k.D!=null&&k.D>j.D){j.D=k.D}if(k.H!=null&&k.H>j.H){j.H=k.H}if(l.style.paddingLeft){j.w+=parseFloat(l.style.paddingLeft)*(l.scale||1)}if(j.w+k.lw<j.lw){j.lw=j.w+k.lw}if(j.w+k.rw>j.rw){j.rw=j.w+k.rw}j.w+=k.w;if(l.style.paddingRight){j.w+=parseFloat(l.style.paddingRight)*(l.scale||1)}if(k.width){j.width=k.width}if(j.exactW&&!k.exactW){delete j.exactW}},HTMLemptyBBox:function(i){i.h=i.d=i.H=i.D=i.rw=-e.BIGDIMEN;i.w=0;i.lw=e.BIGDIMEN;return i},HTMLcleanBBox:function(i){if(i.h===this.BIGDIMEN){i.h=i.d=i.H=i.D=i.w=i.rw=i.lw=0}if(i.D<=i.d){delete i.D}if(i.H<=i.h){delete i.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(i){if(this.isEmbellished()){return this.Core().HTMLcanStretch(i)}return false},HTMLstretchH:function(j,i){return this.HTMLspanElement()},HTMLstretchV:function(j,i,k){return 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S=aE;for(ac=0;ac<=an;ac++){if(!at[ac].bbox.width){b.setStackWidth(at[ac],ai[ac])}if(aH[ac]!=="auto"&&aH[ac]!=="fit"){at[ac].bbox.width=ai[ac];at[ac].bbox.isFixed=true}b.placeBox(at[ac].parentNode,S,0);S+=ai[ac]+aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createRule(av,g,0,1.25/b.em);b.addBox(av,q);q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(q,S-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}aP=av.bbox.w+aE;var ag;if(G.frame!=="none"){ag=b.createFrame(av,g,0,aP,1.25/b.em,G.frame);b.addBox(av,ag);b.placeBox(ag,0,aO,true);if(aF){ag.style.width="100%"}}R=ah;for(ad=0,ab=au.length-1;ad<ab;ad++){o=Math.max(aj,ar[ad]+ao[ad+1]+aL[ad]);if(v[ad]!=="none"){q=b.createRule(av,1.25/b.em,0,aP);b.addBox(av,q);q.bbox={h:1.25/b.em,d:0,w:aP,rw:aP,lw:0};b.placeBox(q,0,R-ar[ad]-(o-ar[ad]-ao[ad+1])/2,true);if(v[ad]==="dashed"||aF){q.style.borderTop=q.style.height+" 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aI=b.createStack(r,false,"100%");b.addBox(aI,av);b.alignBox(av,ap.indentalign,0);if(ap.indentshift&&ap.indentalign!==a.INDENTALIGN.CENTER){av.style[{left:"Left",right:"Right"}[ap.indentalign]]=b.Em(b.length2em(ap.indentshift,ax))}at[ay].parentNode.parentNode.removeChild(at[ay].parentNode);b.addBox(aI,at[ay]);b.alignBox(at[ay],e[ay],0);if(b.msieRelativeWidthBug){av.style.top=at[ay].style.top=""}if(aF){av.style.width=G.width;r.bbox.width="100%"}at[ay].style.marginRight=at[ay].style.marginLeft=b.Em(b.length2em(G.minlabelspacing,ax))}if(!aF){this.HTMLhandleSpace(r)}var u=this.HTMLhandleColor(r);if(u&&aF){if(!ag){ag=b.createFrame(av,g,0,aP,0,"none");b.addBox(av,ag);b.placeBox(ag,0,aO,true);ag.style.width="100%"}ag.style.backgroundColor=u.style.backgroundColor;ag.parentNode.insertBefore(ag,ag.parentNode.firstChild);u.parentNode.removeChild(u)}return r},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")}); MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_HTMLorMML-full.js"); diff --git a/config/TeX-AMS-MML_HTMLorMML.js b/config/TeX-AMS-MML_HTMLorMML.js @@ -40,7 +40,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.10",directory:MathJ MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.8",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.10",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); diff --git a/config/TeX-AMS_HTML-full.js b/config/TeX-AMS_HTML-full.js @@ -33,7 +33,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.10",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+a},formatURL:function(a){return"#mjx-eqn-"+escape(a)}}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.Extension.tex2jax={version:"1.1.4",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":"")+(b.processRefs?"|\\\\(eq)?ref\\{[^}]*\\}":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"); @@ -55,8 +55,8 @@ MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels: MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:["2248",{variantForm:true}],subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"2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d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-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(b["-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"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-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:"() {} 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this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" 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(local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;var l=[],p=this.FONTDATA.VARIANT.normal.fonts;if(!(p instanceof Array)){p=[p]}for(var k=0,j=p.length;k<j;k++){l[k]=this.FONTDATA.FONTS[p[k]].family;if(!l[k]){l[k]=p[k]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":l.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 o=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=o.offsetWidth/5;this.hiddenDiv.removeChild(o);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(n){}}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(n){}}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"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},Translate:function(p){if(!p.parentNode){return}var n=p.previousSibling;if(n&&String(n.className).match(/^MathJax(_MathML|_Display)?$/)){n.parentNode.removeChild(n)}var j=p.MathJax.elementJax,q=j.root,r,i,l;r=i=l=this.Element("span",{className:"MathJax",isMathJax:true,jaxID:this.id,id:j.inputID+"-Span",oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(MathJax.Hub.Browser.noContextMenu){r.ontouchstart=h.start;r.ontouchend=h.end}var m=(q.Get("display")==="block");if(m){i=l=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});i.appendChild(r)}i.setAttribute("role","textbox");i.setAttribute("aria-readonly","true");if(this.useProcessingFrame){l=this.Element((m?"div":"span"),{className:"MathJax_Processing"});l.appendChild(i)}p.parentNode.insertBefore(l,p);var k;try{this.getScales(r);k=(this.em===0||String(this.em)==="NaN")}catch(o){k=true}if(k){this.hiddenDiv.appendChild(l);this.getScales(r)}j.em=this.em;j.outerEm=this.outerEm;j.scale=this.scale;this.getLinebreakWidth(l);this.initImg(r);this.initHTML(q,r);q.setTeXclass();try{q.toHTML(r,i)}catch(o){if(o.restart){l.parentNode.removeChild(l)}throw o}if(k){p.parentNode.insertBefore(l,p)}if(this.useProcessingFrame){l.parentNode.replaceChild(i,l)}},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=i.SourceElement();if(!j){return}j=j.previousSibling;if(!j){return}if(j.className.match(/^MathJax/)){j.parentNode.removeChild(j)}},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getScales:function(k){k.parentNode.insertBefore(this.HDMspan,k);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var j=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var i=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(j/this.TeX.x_height)/i)*this.config.scale);k.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&i===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=i*this.scale/100}k.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(k)},getMarginScale:function(i){return 1},getMSIEmarginScale:function(k){k.appendChild(this.marginCheck);var i=this.marginCheck.offsetWidth,j=this.marginMove.offsetWidth;var l=(2*j-i?j/(2*j-i):1);k.removeChild(this.marginCheck);return l},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(l){var j=l.offsetWidth,k=(l.bbox?l.bbox.w:-1),m=l;if((k<0||this.negativeSkipBug)&&j>=0&&!l.style.width){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.negativeSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));if(j.bbox){j.bbox.w=i}if(j.parentNode.bbox){j.parentNode.bbox.w=i}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l<j;l++){if(r[q[l]]){o.FONTS.push(r[q[l]]);r[q[l]].name=q[l]}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[s]){if(k[s].length===5){k[s][5]={}}if(e.allowWebFonts&&!k.available){this.loadWebFont(k)}else{return k}}else{this.findBlock(k,s)}}var p=(o.defaultFont||{family:e.config.undefinedFamily});if(o.bold){p.weight="bold"}if(o.italic){p.style="italic"}p[s]=[800,200,500,0,500,{isUnknown:true}];return p},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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=(i.bbox?i:i.HTMLspanElement());if(!l||!l.bbox){return}var k=l.bbox;if(k.d>j.d){j.d=k.d}if(k.h>j.h){j.h=k.h}if(k.D!=null&&k.D>j.D){j.D=k.D}if(k.H!=null&&k.H>j.H){j.H=k.H}if(l.style.paddingLeft){j.w+=parseFloat(l.style.paddingLeft)*(l.scale||1)}if(j.w+k.lw<j.lw){j.lw=j.w+k.lw}if(j.w+k.rw>j.rw){j.rw=j.w+k.rw}j.w+=k.w;if(l.style.paddingRight){j.w+=parseFloat(l.style.paddingRight)*(l.scale||1)}if(k.width){j.width=k.width}},HTMLemptyBBox:function(i){i.h=i.d=i.H=i.D=i.rw=-e.BIGDIMEN;i.w=0;i.lw=e.BIGDIMEN;return i},HTMLcleanBBox:function(i){if(i.h===this.BIGDIMEN){i.h=i.d=i.H=i.D=i.w=i.rw=i.lw=0}if(i.D<=i.d){delete i.D}if(i.H<=i.h){delete i.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(i){if(this.isEmbellished()){return this.Core().HTMLcanStretch(i)}return false},HTMLstretchH:function(j,i){return this.HTMLspanElement()},HTMLstretchV:function(j,i,k){return this.HTMLspanElement()},HTMLnotEmpty:function(i){while(i){if((i.type!=="mrow"&&i.type!=="texatom")||i.data.length>1){return true}i=i.data[0]}return false},HTMLmeasureChild:function(j,i){if(this.data[j]!=null){e.Measured(this.data[j].toHTML(i),i)}else{i.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(i){if(this.spanID){var j=this.HTMLspanElement();if(j){while(j.firstChild){j.removeChild(j.firstChild)}j.bbox={w:0,h:0,d:0,lw:0,rw:0};j.scale=1;j.isMultChar=null;j.style.cssText="";return j}}if(this.href){i=e.addElement(i,"a",{href:this.href,isMathJax:true})}i=e.addElement(i,"span",{className:this.type,isMathJax:true});if(e.imgHeightBug){i.style.display="inline-block"}if(this["class"]!=null){i.className+=" 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v=this.getValues("mathcolor","color");if(this.mathbackground){v.mathbackground=this.mathbackground}if(this.background){v.background=this.background}if(this.style&&t.style.backgroundColor){v.mathbackground=t.style.backgroundColor;t.style.backgroundColor="transparent"}var q=(this.styles||{}).border,s=(this.styles||{}).padding;if(v.color&&!this.mathcolor){v.mathcolor=v.color}if(v.background&&!this.mathbackground){v.mathbackground=v.background}if(v.mathcolor){t.style.color=v.mathcolor}if((v.mathbackground&&v.mathbackground!==a.COLOR.TRANSPARENT)||q||s){var w=(t.bbox.exact?0:1/e.em),r=0,p=0,j=t.style.paddingLeft,n=t.style.paddingRight;if(this.isToken){r=t.bbox.lw;p=t.bbox.rw-t.bbox.w}if(j!==""){r+=parseFloat(j)*(t.scale||1)}if(n!==""){p-=parseFloat(n)*(t.scale||1)}var l=Math.max(0,e.getW(t)+(e.PaddingWidthBug?0:p-r));var 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k=o.bbox={},p=[];this.HTMLcheckStretchy(this.data.open,k,p,n);this.HTMLcheckStretchy(this.data[0],k,p,n);for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){this.HTMLcheckStretchy(this.data["sep"+l],k,p,n);this.HTMLcheckStretchy(this.data[l],k,p,n)}}this.HTMLcheckStretchy(this.data.close,k,p,n);this.HTMLcleanBBox(k);return p},HTMLcheckStretchy:function(i,j,l,k){if(i){if(!k&&i.HTMLcanStretch("Vertical")){l.push(i);i=(i.CoreMO()||i)}this.HTMLcombineBBoxes(i,j)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(i){if(this.data[0]!=null){i=this.data[0].toHTML(i);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(i)}return i},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(j,i){return(this.data[0]!=null?this.data[0].HTMLstretchH(j,i):j)},HTMLstretchV:function(j,i,k){return(this.data[0]!=null?this.data[0].HTMLstretchV(j,i,k):j)}});a.munderover.Augment({toHTML:function(J,F,C){var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,J)}J=this.HTMLcreateSpan(J);var N=this.HTMLgetScale();var o=e.createStack(J);var p=[],L=[],u,K,G,l=-e.BIGDIMEN,I=l;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K]=e.createBox(o);e.Measured(this.data[K].toHTML(u),u);if(K==this.base){if(C!=null){e.Remeasured(this.data[this.base].HTMLstretchV(u,F,C),u)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(u,F),u)}}L[K]=(C==null&&F!=null?false:this.data[K].HTMLcanStretch("Horizontal"))}else{L[K]=this.data[K].HTMLcanStretch("Horizontal")}if(u.bbox.w>I){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;K<G;K++){if(this.data[K]){u=p[K];if(L[K]){u.bbox=this.data[K].HTMLstretchH(u,l).bbox}if(u.bbox.w>I){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K];r=e.TeX.big_op_spacing5*N;var z=(K!=this.base&&j[this.ACCENTS[K]]);if(z&&u.bbox.w<=1/e.em+0.0001){u.bbox.w=u.bbox.rw-u.bbox.lw;u.bbox.noclip=true;if(u.bbox.lw&&!e.zeroWidthBug){u.insertBefore(e.createSpace(u.parentNode,0,0,-u.bbox.lw),u.firstChild)}e.createBlank(u,0,0,u.bbox.rw+0.1)}A={left:0,center:(I-u.bbox.w)/2,right:I-u.bbox.w}[j.align];s=A;q=0;if(K==this.over){if(z){H=Math.max(B*N*E,2.5/this.em);r=0;if(n.bbox.skew){s+=n.bbox.skew}}else{w=e.TeX.big_op_spacing1*N*E;v=e.TeX.big_op_spacing3*N*E;H=Math.max(w,v-Math.max(0,u.bbox.d))}H=Math.max(H,1.5/this.em);s+=M;q=n.bbox.h+u.bbox.d+H;u.bbox.h+=r}else{if(K==this.under){if(z){H=3*B*N*E;r=0}else{w=e.TeX.big_op_spacing2*N*E;v=e.TeX.big_op_spacing4*N*E;H=Math.max(w,v-u.bbox.h)}H=Math.max(H,1.5/this.em);s-=M;q=-(n.bbox.d+u.bbox.h+H);u.bbox.d+=r}}e.placeBox(u,s,q)}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(H,F,z){H=this.HTMLcreateSpan(H);var K=this.HTMLgetScale(),E=this.HTMLgetMu(H);var m=e.createStack(H),j;var l=e.createBox(m);this.HTMLmeasureChild(this.base,l);if(this.data[this.base]){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(l,F,z),l)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(l,F),l)}}}e.placeBox(l,0,0);var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var I=e.TeX.x_height*K,y=e.TeX.scriptspace*K*0.75;var i,n;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(m);e.Measured(this.data[this.sup].toHTML(i),i);i.bbox.w+=y;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){n=e.createBox(m);e.Measured(this.data[this.sub].toHTML(n),n);n.bbox.w+=y;n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw)}var B=e.TeX.sup_drop*k,A=e.TeX.sub_drop*k;var w=l.bbox.h-B,o=l.bbox.d+A,J=0,C;if(l.bbox.ic){J=l.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&&l.bbox.scale===1&&!this.data[this.base].Get("largeop")){w=o=0}}var G=this.getValues("subscriptshift","superscriptshift");G.subscriptshift=(G.subscriptshift===""?0:e.length2em(G.subscriptshift,E));G.superscriptshift=(G.superscriptshift===""?0:e.length2em(G.superscriptshift,E));if(!i){if(n){o=Math.max(o,e.TeX.sub1*K,n.bbox.h-(4/5)*I,G.subscriptshift);e.placeBox(n,l.bbox.w+y-J,-o,n.bbox)}}else{if(!n){j=this.getValues("displaystyle","texprimestyle");C=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];w=Math.max(w,C*K,i.bbox.d+(1/4)*I,G.superscriptshift);e.placeBox(i,l.bbox.w+y,w,i.bbox)}else{o=Math.max(o,e.TeX.sub2*K);var x=e.TeX.rule_thickness*K;if((w-i.bbox.d)-(n.bbox.h-o)<3*x){o=3*x-w+i.bbox.d+n.bbox.h;B=(4/5)*I-(w-i.bbox.d);if(B>0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,G.superscriptshift));e.placeBox(n,l.bbox.w+y-J,-Math.max(o,G.subscriptshift))}}this.HTMLhandleSpace(H);this.HTMLhandleColor(H);return H},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.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;q=e.Measured(this.data[0].toHTML(l),l)}e.placeBox(l,0,0);var i=1/e.em,m=e.em/e.outerEm;e.em/=m;r.bbox.h*=m;r.bbox.d*=m;r.bbox.w*=m;r.bbox.lw*=m;r.bbox.rw*=m;if(q&&q.bbox.width!=null){o.style.width=q.bbox.width;l.style.width="100%"}this.HTMLhandleColor(r);if(q){e.createRule(r,(q.bbox.h+i)*m,(q.bbox.d+i)*m,0)}if(!this.isMultiline&&this.Get("display")==="block"&&r.bbox.width==null){var s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(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,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:j,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:j,msieInlineBlockAlignBug:(!k||j),msieVerticalAlignBug:(k&&!j),msiePlaceBoxBug:(k&&!j),msieClipRectBug:!k,msieNegativeSpaceBug:j,msieCloneNodeBug:(k&&i.version==="8.0"),negativeSkipBug:true,msieIE6:!l,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:i.isIE9,allowWebFonts:"eot"})},Firefox:function(j){var k=false;if(j.versionAtLeast("3.5")){var i=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,i.length)===i){k="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:k})},Safari:function(m){var k=m.versionAtLeast("3.0");var j=m.versionAtLeast("3.1");var i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(i){e.Augment({konquerorVerticalAlignBug: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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;e.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",height:"1px",width:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,hideProcessedMath:true,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var j=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=j.offsetWidth/5;this.hiddenDiv.removeChild(j);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(i){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);if(this.msieMarginScaleBug){this.addElement(this.EmExSpan.lastChild,"span",null,[["span",{style:{display:"inline-block",width:"5em"}}],["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}]])}this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},preTranslate:function(l){var s=l.jax[this.id],t,p=s.length,x,r,z,k,v,j,u,n,q;for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}r=x.previousSibling;if(r&&String(r.className).match(/^MathJax(_Display)?$/)){r.parentNode.removeChild(r)}j=x.MathJax.elementJax;j.HTMLCSS={display:(j.root.Get("display")==="block")};z=k=this.Element("span",{className:"MathJax",id:j.inputID+"-Frame",isMathJax:true,oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(d.Browser.noContextMenu){z.ontouchstart=h.start;z.ontouchend=h.end}if(j.HTMLCSS.display){k=this.Element("div",{className:"MathJax_Display",style:{width:"100%"}});k.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}k.setAttribute("role","textbox");k.setAttribute("aria-readonly","true");k.className+=" MathJax_Processing";x.parentNode.insertBefore(k,x);x.parentNode.insertBefore(this.EmExSpan.cloneNode(true),x)}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=x.previousSibling;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60;if(u===0||u==="NaN"){this.hiddenDiv.appendChild(v.previousSibling);this.hiddenDiv.appendChild(v);j.HTMLCSS.isHidden=true;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60}n=j.HTMLCSS.em=v.lastChild.firstChild.offsetWidth/60;q=Math.floor(Math.max(this.config.minScaleAdjust/100,(u/this.TeX.x_height)/n)*this.config.scale);j.HTMLCSS.scale=q/100;j.HTMLCSS.fontSize=q+"%";j.HTMLCSS.marginScale=1}if(this.msieMarginScaleBug){for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=this.getTestSpan(x);v.lastChild.style.fontSize=j.HTMLCSS.fontSize}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);var o=v.lastChild.lastChild.offsetWidth,y=v.lastChild.lastChild.firstChild.offsetWidth;math.HTMLCSS.marginScale=(2*y-o?y/(2*y-o):1)}}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);v.parentNode.removeChild(v)}l.HTMLCSSeqn=l.HTMLCSSlast=0;l.HTMLCSSchunk=this.config.EqnChunk},getTestSpan:function(j){var i=j.MathJax.elementJax;var k=document.getElementById(i.inputID+"-Frame");if(i.HTMLCSS.display){k=k.parentNode}return k.nextSibling},Translate:function(j,n){if(!j.parentNode){return}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),o=(i.HTMLCSS.display?k.parentNode:k);this.em=a.mbase.prototype.em=i.HTMLCSS.em*i.HTMLCSS.scale;this.outerEm=i.HTMLCSS.em;this.msieMarginScale=i.HTMLCSS.marginScale;k.style.fontSize=i.HTMLCSS.fontSize;this.getLinebreakWidth(o);this.initImg(k);this.initHTML(m,k);m.setTeXclass();try{m.toHTML(k,o)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}throw l}if(i.HTMLCSS.isHidden){j.parentNode.insertBefore(o,j)}o.className=o.className.split(/ /)[0];if(this.hideProcessedMath){o.className+=" MathJax_Processed";if(j.MathJax.preview){i.HTMLCSS.preview=j.MathJax.preview;delete j.MathJax.preview}n.HTMLCSSeqn++;if(n.HTMLCSSeqn>=n.HTMLCSSlast+n.HTMLCSSchunk){this.postTranslate(n);n.HTMLCSSchunk=Math.floor(n.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(p){var k=p.jax[this.id];if(!this.hideProcessedMath){return}for(var n=p.HTMLCSSlast,j=p.HTMLCSSeqn;n<j;n++){var l=k[n];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var o=l.MathJax.elementJax.HTMLCSS;if(o.preview){o.preview.style.display="none";l.MathJax.preview=o.preview;delete o.preview}}}p.HTMLCSSlast=p.HTMLCSSeqn},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.HTMLCSS.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.HTMLCSS},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(m){var j,l,k=(m.bbox||{}).w,n=m;if(m.bbox&&m.bbox.exactW){return k}if((m.bbox&&k>=0&&!this.initialSkipBug)||this.negativeBBoxes||!m.firstChild){j=m.offsetWidth;l=m.parentNode.offsetHeight}else{if(m.bbox&&k<0&&this.msieNegativeBBoxBug){j=-m.offsetWidth,l=m.parentNode.offsetHeight}else{if(this.initialSkipBug){var i=m.style.position;m.style.position="absolute";n=this.startMarker;m.insertBefore(n,m.firstChild)}m.appendChild(this.endMarker);j=this.endMarker.offsetLeft-n.offsetLeft;m.removeChild(this.endMarker);if(this.initialSkipBug){m.removeChild(n);m.style.position=i}}}if(l!=null){m.parentNode.HH=l/this.em}return j/this.em},Measured:function(k,j){var l=k.bbox;if(l.width==null&&l.w&&!l.isMultiline){var i=this.getW(k);l.rw+=i-l.w;l.w=i;l.exactW=true}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=l}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={exactW:true,h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n;m.HH=(l+o)*m.scale}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0,exactW:true},noAdjust:true,HH:l+n,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox,p.HH=l+n}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0,exactW:true},noAdjust:true,HH:o+p,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u,C=0;if(q.HH!=null){u=q.HH}else{if(A){u=Math.max(3,A.h+A.d)}else{u=q.offsetHeight/this.em}}if(!q.noAdjust){u+=1;if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.initialSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.initialSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));var 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B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d,exactW:true};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof 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i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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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S=aE;for(ac=0;ac<=an;ac++){if(!at[ac].bbox.width){b.setStackWidth(at[ac],ai[ac])}if(aH[ac]!=="auto"&&aH[ac]!=="fit"){at[ac].bbox.width=ai[ac];at[ac].bbox.isFixed=true}b.placeBox(at[ac].parentNode,S,0);S+=ai[ac]+aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createRule(av,g,0,1.25/b.em);b.addBox(av,q);q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(q,S-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}aP=av.bbox.w+aE;var ag;if(G.frame!=="none"){ag=b.createFrame(av,g,0,aP,1.25/b.em,G.frame);b.addBox(av,ag);b.placeBox(ag,0,aO,true);if(aF){ag.style.width="100%"}}R=ah;for(ad=0,ab=au.length-1;ad<ab;ad++){o=Math.max(aj,ar[ad]+ao[ad+1]+aL[ad]);if(v[ad]!=="none"){q=b.createRule(av,1.25/b.em,0,aP);b.addBox(av,q);q.bbox={h:1.25/b.em,d:0,w:aP,rw:aP,lw:0};b.placeBox(q,0,R-ar[ad]-(o-ar[ad]-ao[ad+1])/2,true);if(v[ad]==="dashed"||aF){q.style.borderTop=q.style.height+" 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aI=b.createStack(r,false,"100%");b.addBox(aI,av);b.alignBox(av,ap.indentalign,0);if(ap.indentshift&&ap.indentalign!==a.INDENTALIGN.CENTER){av.style[{left:"Left",right:"Right"}[ap.indentalign]]=b.Em(b.length2em(ap.indentshift,ax))}at[ay].parentNode.parentNode.removeChild(at[ay].parentNode);b.addBox(aI,at[ay]);b.alignBox(at[ay],e[ay],0);if(b.msieRelativeWidthBug){av.style.top=at[ay].style.top=""}if(aF){av.style.width=G.width;r.bbox.width="100%"}at[ay].style.marginRight=at[ay].style.marginLeft=b.Em(b.length2em(G.minlabelspacing,ax))}if(!aF){this.HTMLhandleSpace(r)}var u=this.HTMLhandleColor(r);if(u&&aF){if(!ag){ag=b.createFrame(av,g,0,aP,0,"none");b.addBox(av,ag);b.placeBox(ag,0,aO,true);ag.style.width="100%"}ag.style.backgroundColor=u.style.backgroundColor;ag.parentNode.insertBefore(ag,ag.parentNode.firstChild);u.parentNode.removeChild(u)}return r},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")}); MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML-full.js"); diff --git a/config/TeX-AMS_HTML.js b/config/TeX-AMS_HTML.js @@ -31,7 +31,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); 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#AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); 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h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.Extension.tex2jax={version:"1.1.4",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":"")+(b.processRefs?"|\\\\(eq)?ref\\{[^}]*\\}":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"); 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j=e.addElement(i,"span",{isMathJax:true});k=e.createFrame(j,i.bbox.h,i.bbox.d,i.bbox.w,0,"none");i.insertBefore(j,i.firstChild);j.style.marginRight=e.Em(-i.bbox.w);if(e.msieInlineBlockAlignBug){k.style.verticalAlign=e.Em(e.getHD(i).d-i.bbox.d)}}else{k=e.createFrame(i,i.bbox.h,i.bbox.d,i.bbox.w,0,"none");i.insertBefore(k,i.firstChild);k.style.marginRight=e.Em(-i.bbox.w)}k.className="MathJax_HitBox";k.id="MathJax-HitBox-"+this.spanID+(l||"")+e.idPostfix;var 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B=b.createBox(av);B.style.left=B.style.top=0;B.style.right=b.Em(aa+2*aE);B.style.display="inline-block";B.style.height="0px";if(b.msieRelativeWidthBug){B=b.createBox(B);B.style.position="relative";B.style.height="1em";B.style.width="100%";B.bbox=av.bbox}var aK=0,aQ=aE,k,l;if(af){k=100*(1-ae)/af,l=w/af}else{k=100*(1-ae)/(an+1);l=w/(an+1)}for(ac=0;ac<=an;ac++){b.placeBox(at[ac].parentNode,0,0);at[ac].style.position="relative";at[ac].style.left=b.Em(aQ);at[ac].style.width="100%";at[ac].parentNode.parentNode.removeChild(at[ac].parentNode);var ak=b.createBox(B);b.addBox(ak,at[ac]);at[ac]=ak;var h=ak.style;h.display="inline-block";h.left=aK+"%";if(aH[ac].match(/%$/)){var t=parseFloat(aH[ac])*Q;if(af===0){h.width=(k+t)+"%";aK+=k+t;ak=b.createBox(ak);b.addBox(ak,at[ac].firstChild);ak.style.left=0;ak.style.right=b.Em(l);aQ-=l}else{h.width=t+"%";aK+=t}}else{if(aH[ac]==="fit"||af===0){h.width=k+"%";ak=b.createBox(ak);b.addBox(ak,at[ac].firstChild);ak.style.left=0;ak.style.right=b.Em(l-ai[ac]);aQ+=ai[ac]-l;aK+=k}else{h.width=b.Em(ai[ac]);aQ+=ai[ac]}}if(b.msieRelativeWidthBug){b.addText(ak.firstChild,b.NBSP);ak.firstChild.style.position="relative"}aQ+=aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createBox(B);q.style.left=aK+"%";q=b.createRule(q,g,0,1.25/b.em);q.style.position="absolute";q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};q.parentNode.bbox=av.bbox;b.placeBox(q,aQ-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}else{var S=aE;for(ac=0;ac<=an;ac++){if(!at[ac].bbox.width){b.setStackWidth(at[ac],ai[ac])}if(aH[ac]!=="auto"&&aH[ac]!=="fit"){at[ac].bbox.width=ai[ac];at[ac].bbox.isFixed=true}b.placeBox(at[ac].parentNode,S,0);S+=ai[ac]+aw[ac];if(d[ac]!=="none"&&ac<an&&ac!==ay){q=b.createRule(av,g,0,1.25/b.em);b.addBox(av,q);q.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(q,S-aw[ac]/2,aO,true);q.style.borderStyle=d[ac]}}}aP=av.bbox.w+aE;var ag;if(G.frame!=="none"){ag=b.createFrame(av,g,0,aP,1.25/b.em,G.frame);b.addBox(av,ag);b.placeBox(ag,0,aO,true);if(aF){ag.style.width="100%"}}R=ah;for(ad=0,ab=au.length-1;ad<ab;ad++){o=Math.max(aj,ar[ad]+ao[ad+1]+aL[ad]);if(v[ad]!=="none"){q=b.createRule(av,1.25/b.em,0,aP);b.addBox(av,q);q.bbox={h:1.25/b.em,d:0,w:aP,rw:aP,lw:0};b.placeBox(q,0,R-ar[ad]-(o-ar[ad]-ao[ad+1])/2,true);if(v[ad]==="dashed"||aF){q.style.borderTop=q.style.height+" "+v[ad];q.style.height=0;q.style.width=q.style.borderLeftWidth;q.style.borderLeft="";if(aF){q.style.width="100%"}}}R-=o}if(aF){r.bbox.width=G.width;av.style.width="100%"}if(at[ay]){var ap=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(ap.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){ap.indentalign=ap.indentalignfirst}if(ap.indentalign===a.INDENTALIGN.AUTO){ap.indentalign=this.displayAlign}if(ap.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){ap.indentshift=ap.indentshiftfirst}if(ap.indentshift==="auto"){ap.indentshift=this.displayIndent}var aI=b.createStack(r,false,"100%");b.addBox(aI,av);b.alignBox(av,ap.indentalign,0);if(ap.indentshift&&ap.indentalign!==a.INDENTALIGN.CENTER){av.style[{left:"Left",right:"Right"}[ap.indentalign]]=b.Em(b.length2em(ap.indentshift,ax))}at[ay].parentNode.parentNode.removeChild(at[ay].parentNode);b.addBox(aI,at[ay]);b.alignBox(at[ay],e[ay],0);if(b.msieRelativeWidthBug){av.style.top=at[ay].style.top=""}if(aF){av.style.width=G.width;r.bbox.width="100%"}at[ay].style.marginRight=at[ay].style.marginLeft=b.Em(b.length2em(G.minlabelspacing,ax))}if(!aF){this.HTMLhandleSpace(r)}var u=this.HTMLhandleColor(r);if(u&&aF){if(!ag){ag=b.createFrame(av,g,0,aP,0,"none");b.addBox(av,ag);b.placeBox(ag,0,aO,true);ag.style.width="100%"}ag.style.backgroundColor=u.style.backgroundColor;ag.parentNode.insertBefore(ag,ag.parentNode.firstChild);u.parentNode.removeChild(u)}return r},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")}); diff --git a/jax/output/HTML-CSS/config.js b/jax/output/HTML-CSS/config.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.14",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",EqnChunk:50,EqnChunkFactor:1.5,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); 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:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(i){return this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" format('svg')"}if(!(e.FontFaceBug&&n.isWebFont)){if(k.match(/-bold/)){m["font-weight"]="bold"}if(k.match(/-italic/)){m["font-style"]="italic"}}return m}});var g,h,f;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",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;var l=[],p=this.FONTDATA.VARIANT.normal.fonts;if(!(p instanceof Array)){p=[p]}for(var k=0,j=p.length;k<j;k++){l[k]=this.FONTDATA.FONTS[p[k]].family;if(!l[k]){l[k]=p[k]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":l.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 o=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=o.offsetWidth/5;this.hiddenDiv.removeChild(o);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(n){}}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(n){}}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"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},Translate:function(p){if(!p.parentNode){return}var n=p.previousSibling;if(n&&String(n.className).match(/^MathJax(_MathML|_Display)?$/)){n.parentNode.removeChild(n)}var j=p.MathJax.elementJax,q=j.root,r,i,l;r=i=l=this.Element("span",{className:"MathJax",isMathJax:true,jaxID:this.id,id:j.inputID+"-Span",oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(MathJax.Hub.Browser.noContextMenu){r.ontouchstart=h.start;r.ontouchend=h.end}var m=(q.Get("display")==="block");if(m){i=l=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});i.appendChild(r)}i.setAttribute("role","textbox");i.setAttribute("aria-readonly","true");if(this.useProcessingFrame){l=this.Element((m?"div":"span"),{className:"MathJax_Processing"});l.appendChild(i)}p.parentNode.insertBefore(l,p);var k;try{this.getScales(r);k=(this.em===0||String(this.em)==="NaN")}catch(o){k=true}if(k){this.hiddenDiv.appendChild(l);this.getScales(r)}j.em=this.em;j.outerEm=this.outerEm;j.scale=this.scale;this.getLinebreakWidth(l);this.initImg(r);this.initHTML(q,r);q.setTeXclass();try{q.toHTML(r,i)}catch(o){if(o.restart){l.parentNode.removeChild(l)}throw o}if(k){p.parentNode.insertBefore(l,p)}if(this.useProcessingFrame){l.parentNode.replaceChild(i,l)}},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=i.SourceElement();if(!j){return}j=j.previousSibling;if(!j){return}if(j.className.match(/^MathJax/)){j.parentNode.removeChild(j)}},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getScales:function(k){k.parentNode.insertBefore(this.HDMspan,k);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var j=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var i=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(j/this.TeX.x_height)/i)*this.config.scale);k.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&i===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=i*this.scale/100}k.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(k)},getMarginScale:function(i){return 1},getMSIEmarginScale:function(k){k.appendChild(this.marginCheck);var i=this.marginCheck.offsetWidth,j=this.marginMove.offsetWidth;var l=(2*j-i?j/(2*j-i):1);k.removeChild(this.marginCheck);return l},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(l){var j=l.offsetWidth,k=(l.bbox?l.bbox.w:-1),m=l;if((k<0||this.negativeSkipBug)&&j>=0&&!l.style.width){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.negativeSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));if(j.bbox){j.bbox.w=i}if(j.parentNode.bbox){j.parentNode.bbox.w=i}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var 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q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof 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i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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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k=o.bbox={},p=[];this.HTMLcheckStretchy(this.data.open,k,p,n);this.HTMLcheckStretchy(this.data[0],k,p,n);for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){this.HTMLcheckStretchy(this.data["sep"+l],k,p,n);this.HTMLcheckStretchy(this.data[l],k,p,n)}}this.HTMLcheckStretchy(this.data.close,k,p,n);this.HTMLcleanBBox(k);return p},HTMLcheckStretchy:function(i,j,l,k){if(i){if(!k&&i.HTMLcanStretch("Vertical")){l.push(i);i=(i.CoreMO()||i)}this.HTMLcombineBBoxes(i,j)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(i){if(this.data[0]!=null){i=this.data[0].toHTML(i);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(i)}return i},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(j,i){return(this.data[0]!=null?this.data[0].HTMLstretchH(j,i):j)},HTMLstretchV:function(j,i,k){return(this.data[0]!=null?this.data[0].HTMLstretchV(j,i,k):j)}});a.munderover.Augment({toHTML:function(J,F,C){var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,J)}J=this.HTMLcreateSpan(J);var N=this.HTMLgetScale();var o=e.createStack(J);var p=[],L=[],u,K,G,l=-e.BIGDIMEN,I=l;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K]=e.createBox(o);e.Measured(this.data[K].toHTML(u),u);if(K==this.base){if(C!=null){e.Remeasured(this.data[this.base].HTMLstretchV(u,F,C),u)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(u,F),u)}}L[K]=(C==null&&F!=null?false:this.data[K].HTMLcanStretch("Horizontal"))}else{L[K]=this.data[K].HTMLcanStretch("Horizontal")}if(u.bbox.w>I){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;K<G;K++){if(this.data[K]){u=p[K];if(L[K]){u.bbox=this.data[K].HTMLstretchH(u,l).bbox}if(u.bbox.w>I){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K<G;K++){if(this.data[K]!=null){u=p[K];r=e.TeX.big_op_spacing5*N;var z=(K!=this.base&&j[this.ACCENTS[K]]);if(z&&u.bbox.w<=1/e.em+0.0001){u.bbox.w=u.bbox.rw-u.bbox.lw;u.bbox.noclip=true;if(u.bbox.lw&&!e.zeroWidthBug){u.insertBefore(e.createSpace(u.parentNode,0,0,-u.bbox.lw),u.firstChild)}e.createBlank(u,0,0,u.bbox.rw+0.1)}A={left:0,center:(I-u.bbox.w)/2,right:I-u.bbox.w}[j.align];s=A;q=0;if(K==this.over){if(z){H=Math.max(B*N*E,2.5/this.em);r=0;if(n.bbox.skew){s+=n.bbox.skew}}else{w=e.TeX.big_op_spacing1*N*E;v=e.TeX.big_op_spacing3*N*E;H=Math.max(w,v-Math.max(0,u.bbox.d))}H=Math.max(H,1.5/this.em);s+=M;q=n.bbox.h+u.bbox.d+H;u.bbox.h+=r}else{if(K==this.under){if(z){H=3*B*N*E;r=0}else{w=e.TeX.big_op_spacing2*N*E;v=e.TeX.big_op_spacing4*N*E;H=Math.max(w,v-u.bbox.h)}H=Math.max(H,1.5/this.em);s-=M;q=-(n.bbox.d+u.bbox.h+H);u.bbox.d+=r}}e.placeBox(u,s,q)}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(H,F,z){H=this.HTMLcreateSpan(H);var K=this.HTMLgetScale(),E=this.HTMLgetMu(H);var m=e.createStack(H),j;var l=e.createBox(m);this.HTMLmeasureChild(this.base,l);if(this.data[this.base]){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(l,F,z),l)}else{if(F!=null){e.Remeasured(this.data[this.base].HTMLstretchH(l,F),l)}}}e.placeBox(l,0,0);var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var I=e.TeX.x_height*K,y=e.TeX.scriptspace*K*0.75;var i,n;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(m);e.Measured(this.data[this.sup].toHTML(i),i);i.bbox.w+=y;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){n=e.createBox(m);e.Measured(this.data[this.sub].toHTML(n),n);n.bbox.w+=y;n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw)}var B=e.TeX.sup_drop*k,A=e.TeX.sub_drop*k;var w=l.bbox.h-B,o=l.bbox.d+A,J=0,C;if(l.bbox.ic){J=l.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&&l.bbox.scale===1&&!this.data[this.base].Get("largeop")){w=o=0}}var G=this.getValues("subscriptshift","superscriptshift");G.subscriptshift=(G.subscriptshift===""?0:e.length2em(G.subscriptshift,E));G.superscriptshift=(G.superscriptshift===""?0:e.length2em(G.superscriptshift,E));if(!i){if(n){o=Math.max(o,e.TeX.sub1*K,n.bbox.h-(4/5)*I,G.subscriptshift);e.placeBox(n,l.bbox.w+y-J,-o,n.bbox)}}else{if(!n){j=this.getValues("displaystyle","texprimestyle");C=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];w=Math.max(w,C*K,i.bbox.d+(1/4)*I,G.superscriptshift);e.placeBox(i,l.bbox.w+y,w,i.bbox)}else{o=Math.max(o,e.TeX.sub2*K);var x=e.TeX.rule_thickness*K;if((w-i.bbox.d)-(n.bbox.h-o)<3*x){o=3*x-w+i.bbox.d+n.bbox.h;B=(4/5)*I-(w-i.bbox.d);if(B>0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,G.superscriptshift));e.placeBox(n,l.bbox.w+y-J,-Math.max(o,G.subscriptshift))}}this.HTMLhandleSpace(H);this.HTMLhandleColor(H);return H},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete 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s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(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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(\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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this.testFont(this.FontInfo[i])},testFont:function(l){if(l.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]){if(l.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(k,m){var q=3+(k.weight?2:0)+(k.style?4:0);var j="",l=0;var p=this.div.style.fontSize;this.div.style.fontSize=m;if(e.msieItalicWidthBug&&k.style==="italic"){this.text.nodeValue=j=this.compChar;l=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+j}else{this.text.nodeValue=this.compChar+j}var i=this.div.offsetWidth-l;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+j}else{this.text.nodeValue=this.styleChar+j}var o=Math.floor((this.div.offsetWidth-l)/i+0.5);if(o===q){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+j}else{this.text.nodeValue=this.versionChar+j}k.version=Math.floor((this.div.offsetWidth-l)/i+1.5)/2}this.div.style.fontSize=p;return(o===q)},getComparisonWidths:function(n,l){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!l){n+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=n}else{this.text.nodeValue=n}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth,p=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];p=this.div.offsetWidth}for(var o=1,j=this.comparisonFont.length;o<j;o++){this.div.style.fontFamily=this.comparisonFont[o];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,o,p]}}return null},loadWebFont:function(j){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+j.directory);var l=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+j.directory);var i=MathJax.Callback({});var k=MathJax.Callback(["loadComplete",this,j,l,i]);c.timer.start(c,[this.checkWebFont,j,k],0,this.timeout);return i},loadComplete:function(k,m,j,i){MathJax.Message.Clear(m);if(i===c.STATUS.OK){j();return}this.loadError(k);if(d.Browser.isFirefox&&e.allowWebFonts){var l=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){l+=":"+document.location.port}l+="/";if(c.fileURL(e.webfontDir).substr(0,l.length)!==l){this.firefoxFontError(k)}}e.loadWebFontError(k,j)},loadError:function(i){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+i.directory,null,2000)},firefoxFontError:function(i){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(i,j,k){if(i.time(k)){return}if(e.Font.testFont(j)){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},fontFace:function(k){var l=e.allowWebFonts;var n=e.FONTDATA.FONTS[k];if(e.msieFontCSSBug&&!n.family.match(/-Web$/)){n.family+="-Web"}var j=c.fileURL(e.webfontDir+"/"+l);var i=k.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!i.match(/-/)){i+="-Regular"}if(l==="svg"){i+=".svg#"+i}else{i+="."+l}var m={"font-family":n.family,src:"url('"+j+"/"+i+"')"};if(l==="svg"){m.src+=" 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span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",height:"1px",width:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,hideProcessedMath:true,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var j=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(j.scale){this.config.scale=j.scale}if(j.font&&j.font!=="Auto"){if(j.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(j.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(j.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(j.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var i=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!i&&this.allowWebFonts){i=this.config.webFont;if(i){this.webFonts=true}}if(!i&&this.config.imageFont){i=this.config.imageFont;this.imgFonts=true}if(i){this.fontInUse=i;this.fontDir+="/"+i;this.webfontDir+="/"+i;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")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;h=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var j=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=j.offsetWidth/5;this.hiddenDiv.removeChild(j);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(i){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);if(this.msieMarginScaleBug){this.addElement(this.EmExSpan.lastChild,"span",null,[["span",{style:{display:"inline-block",width:"5em"}}],["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}]])}this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var k=0,j=e.config.preloadWebFonts.length;k<j;k++){var l=e.FONTDATA.FONTS[e.config.preloadWebFonts[k]];if(!l.available){e.Font.testFont(l)}}},preTranslate:function(l){var s=l.jax[this.id],t,p=s.length,x,r,z,k,v,j,u,n,q;for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}r=x.previousSibling;if(r&&String(r.className).match(/^MathJax(_Display)?$/)){r.parentNode.removeChild(r)}j=x.MathJax.elementJax;j.HTMLCSS={display:(j.root.Get("display")==="block")};z=k=this.Element("span",{className:"MathJax",id:j.inputID+"-Frame",isMathJax:true,oncontextmenu:g.Menu,onmousedown:g.Mousedown,onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousemove:g.Mousemove,onclick:g.Click,ondblclick:g.DblClick});if(d.Browser.noContextMenu){z.ontouchstart=h.start;z.ontouchend=h.end}if(j.HTMLCSS.display){k=this.Element("div",{className:"MathJax_Display",style:{width:"100%"}});k.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}k.setAttribute("role","textbox");k.setAttribute("aria-readonly","true");k.className+=" MathJax_Processing";x.parentNode.insertBefore(k,x);x.parentNode.insertBefore(this.EmExSpan.cloneNode(true),x)}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=x.previousSibling;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60;if(u===0||u==="NaN"){this.hiddenDiv.appendChild(v.previousSibling);this.hiddenDiv.appendChild(v);j.HTMLCSS.isHidden=true;u=j.HTMLCSS.ex=v.firstChild.offsetWidth/60}n=j.HTMLCSS.em=v.lastChild.firstChild.offsetWidth/60;q=Math.floor(Math.max(this.config.minScaleAdjust/100,(u/this.TeX.x_height)/n)*this.config.scale);j.HTMLCSS.scale=q/100;j.HTMLCSS.fontSize=q+"%";j.HTMLCSS.marginScale=1}if(this.msieMarginScaleBug){for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}j=x.MathJax.elementJax;v=this.getTestSpan(x);v.lastChild.style.fontSize=j.HTMLCSS.fontSize}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);var o=v.lastChild.lastChild.offsetWidth,y=v.lastChild.lastChild.firstChild.offsetWidth;math.HTMLCSS.marginScale=(2*y-o?y/(2*y-o):1)}}for(t=0;t<p;t++){x=s[t];if(!x.parentNode){continue}v=this.getTestSpan(x);v.parentNode.removeChild(v)}l.HTMLCSSeqn=l.HTMLCSSlast=0;l.HTMLCSSchunk=this.config.EqnChunk},getTestSpan:function(j){var i=j.MathJax.elementJax;var k=document.getElementById(i.inputID+"-Frame");if(i.HTMLCSS.display){k=k.parentNode}return k.nextSibling},Translate:function(j,n){if(!j.parentNode){return}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),o=(i.HTMLCSS.display?k.parentNode:k);this.em=a.mbase.prototype.em=i.HTMLCSS.em*i.HTMLCSS.scale;this.outerEm=i.HTMLCSS.em;this.msieMarginScale=i.HTMLCSS.marginScale;k.style.fontSize=i.HTMLCSS.fontSize;this.getLinebreakWidth(o);this.initImg(k);this.initHTML(m,k);m.setTeXclass();try{m.toHTML(k,o)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}throw l}if(i.HTMLCSS.isHidden){j.parentNode.insertBefore(o,j)}o.className=o.className.split(/ /)[0];if(this.hideProcessedMath){o.className+=" MathJax_Processed";if(j.MathJax.preview){i.HTMLCSS.preview=j.MathJax.preview;delete j.MathJax.preview}n.HTMLCSSeqn++;if(n.HTMLCSSeqn>=n.HTMLCSSlast+n.HTMLCSSchunk){this.postTranslate(n);n.HTMLCSSchunk=Math.floor(n.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(p){var k=p.jax[this.id];if(!this.hideProcessedMath){return}for(var n=p.HTMLCSSlast,j=p.HTMLCSSeqn;n<j;n++){var l=k[n];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var o=l.MathJax.elementJax.HTMLCSS;if(o.preview){o.preview.style.display="none";l.MathJax.preview=o.preview;delete o.preview}}}p.HTMLCSSlast=p.HTMLCSSeqn},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_Display"){i=i.parentNode}return d.getJaxFor(i.nextSibling)},getHoverSpan:function(i){return i.root.HTMLspanElement()},getHoverBBox:function(i,l){var m=l.bbox,k=i.outerEm;var j={w:m.w*k,h:m.h*k,d:m.d*k};if(m.width){j.width=m.width}return j},Zoom:function(p,s,r,i,o){s.className="MathJax";this.getScales(s,s);this.idPostfix="-zoom";p.toHTML(s,s);this.idPostfix="";var k=p.HTMLspanElement().bbox.width;if(k){s.style.width=Math.floor(i-1.5*e.em)+"px";s.style.display="inline-block";var j=(p.id||"MathJax-Span-"+p.spanID)+"-zoom";var l=document.getElementById(j).firstChild;while(l&&l.style.width!==k){l=l.nextSibling}if(l){l.style.width="100%"}}s.style.position=r.style.position="absolute";var q=s.offsetWidth,n=s.offsetHeight,t=r.offsetHeight,m=r.offsetWidth;if(m===0){m=r.parentNode.offsetWidth}s.style.position=r.style.position="";return{Y:-g.getBBox(s).h,mW:m,mH:t,zW:q,zH:n}},initImg:function(i){},initHTML:function(j,i){},initFont:function(i){var k=e.FONTDATA.FONTS,j=e.config.availableFonts;if(j&&j.length&&e.Font.testFont(k[i])){k[i].available=true;return null}if(!this.allowWebFonts){return null}k[i].isWebFont=true;if(e.FontFaceBug){k[i].family=i;if(e.msieFontCSSBug){k[i].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(i)})},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.HTMLCSS.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.HTMLCSS},getLinebreakWidth:function(k){if(this.config.linebreaks.automatic){var j=this.config.linebreaks.width,i;if(j.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){k.parentNode.insertBefore(this.linebreakSpan,k);i=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);j=j.replace(/\s*container\s*/,"")}else{i=document.body.offsetWidth/this.em}this.linebreakWidth=(j===""?i:this.length2em(j,i))}else{this.linebreakWidth=100000}},getHD:function(j){var i=j.style.position;j.style.position="absolute";this.HDimg.style.height="0px";j.appendChild(this.HDspan);var k={h:j.offsetHeight};this.HDimg.style.height=k.h+"px";k.d=j.offsetHeight-k.h;k.h-=k.d;k.h/=this.em;k.d/=this.em;j.removeChild(this.HDspan);j.style.position=i;return k},getW:function(m){var j,l,k=(m.bbox||{}).w,n=m;if(m.bbox&&m.bbox.exactW){return k}if((m.bbox&&k>=0&&!this.initialSkipBug)||this.negativeBBoxes||!m.firstChild){j=m.offsetWidth;l=m.parentNode.offsetHeight}else{if(m.bbox&&k<0&&this.msieNegativeBBoxBug){j=-m.offsetWidth,l=m.parentNode.offsetHeight}else{if(this.initialSkipBug){var i=m.style.position;m.style.position="absolute";n=this.startMarker;m.insertBefore(n,m.firstChild)}m.appendChild(this.endMarker);j=this.endMarker.offsetLeft-n.offsetLeft;m.removeChild(this.endMarker);if(this.initialSkipBug){m.removeChild(n);m.style.position=i}}}if(l!=null){m.parentNode.HH=l/this.em}return j/this.em},Measured:function(k,j){var l=k.bbox;if(l.width==null&&l.w&&!l.isMultiline){var i=this.getW(k);l.rw+=i-l.w;l.w=i;l.exactW=true}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=l}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(p,j,n){if(typeof(p)!=="string"){p=p.toString()}if(p===""){return""}if(p===a.SIZE.NORMAL){return 1}if(p===a.SIZE.BIG){return 2}if(p===a.SIZE.SMALL){return 0.71}if(p==="infinity"){return e.BIGDIMEN}var l=this.FONTDATA.TeX_factor;if(p.match(/mathspace$/)){return e.MATHSPACE[p]*l}var k=p.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1"),o=k[2];if(n==null){n=1}if(j==null){j=1}if(o==="em"){return i*l}if(o==="ex"){return i*e.TeX.x_height*l}if(o==="%"){return i/100*n}if(o==="px"){return i/e.em}if(o==="pt"){return i/10*l}if(o==="pc"){return i*1.2*l}if(o==="in"){return i*this.pxPerInch/e.em}if(o==="cm"){return i*this.pxPerInch/e.em/2.54}if(o==="mm"){return i*this.pxPerInch/e.em/25.4}if(o==="mu"){return i/18*l*j}return i*l*n},thickness2em:function(j,i){var k=e.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j.style["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(n){var k={top:0,right:0,bottom:0,left:0},l={},j=false;for(var o in k){if(k.hasOwnProperty(o)){var i="border"+o.charAt(0).toUpperCase()+o.substr(1);var m=n.style[i+"Style"];if(m){j=true;k[o]=this.length2em(n.style[i+"Width"]);l[i]=[n.style[i+"Width"],n.style[i+"Style"],n.style[i+"Color"]].join(" ")}}}k.css=l;return(j?k:false)},setBorders:function(i,j){if(j){for(var k in j.css){if(j.css.hasOwnProperty(k)){i.style[k]=j.css[k]}}}},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={exactW:true,h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n;m.HH=(l+o)*m.scale}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j;m.style.position="relative"}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness,m=1;if(q>0&&q*this.em<k){q=k/this.em}if(l+n>0&&(l+n)*this.em<k){m=1/(l+n)*(k/this.em);l*=m;n*=m}if(!j){j="solid"}else{j="solid "+j}j=this.Em(q)+" "+j;var r=(m===1?this.Em(l+n):k+"px"),i=this.Em(-n);var o=this.addElement(p,"span",{style:{borderLeft:j,display:"inline-block",overflow:"hidden",width:0,height:r,verticalAlign:i},bbox:{h:l,d:n,w:q,rw:q,lw:0,exactW:true},noAdjust:true,HH:l+n,isMathJax:true});if(q>0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox,p.HH=l+n}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0,exactW:true},noAdjust:true,HH:o+p,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u,C=0;if(q.HH!=null){u=q.HH}else{if(A){u=Math.max(3,A.h+A.d)}else{u=q.offsetHeight/this.em}}if(!q.noAdjust){u+=1;if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.initialSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p<v.lw){v.lw=A.lw+p}if(A.width!=null&&!A.isFixed){if(v.width==null){s.style.width=v.width="100%"}q.style.width=A.width}}},alignBox:function(k,q,p){this.placeBox(k,0,p);var n=k.bbox;if(n.isMultiline){return}var j=n.width!=null&&!n.isFixed;var m=0,o=-n.w/2,i="50%";if(this.initialSkipBug){m=n.w-n.rw-0.1;o+=n.lw}o=this.Em(o*this.msieMarginScale);if(j){o="";i=(50-parseFloat(n.width)/2)+"%"}d.Insert(k.style,({right:{left:"",right:this.Em(m)},center:{left:i,marginLeft:o}})[q])},setStackWidth:function(j,i){if(typeof(i)==="number"){j.style.width=this.Em(Math.max(0,i));var k=j.bbox;if(k){k.w=i;k.exactW=true}k=j.parentNode.bbox;if(k){k.w=i;k.exactW=true}}else{j.style.width=j.parentNode.style.width="100%";if(j.bbox){j.bbox.width=i}if(j.parentNode.bbox){j.parentNode.bbox.width=i}}},createDelimiter:function(t,j,l,p,n){if(!j){t.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};t.bbox.rw=t.bbox.w;this.createSpace(t,t.bbox.h,t.bbox.d,t.bbox.w);return}if(!p){p=1}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var r=0,o=k.HW.length;r<o;r++){if(k.HW[r][0]*p>=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var q=(v/(v+1))*(A-i);i=A-q;p+=q+i-j.bbox.h;while(w-->0){while(v-->0){if(!this.msieCloneNodeBug){m=j.cloneNode(true)}else{m=this.Element("span");this.createChar(m,C.ext,D,u)}p-=i;this.placeBox(this.addBox(l,m),0,p,true)}p+=q-j.bbox.d;if(C.mid&&w){this.placeBox(B,0,p-B.bbox.h,true);v=o;p+=-(B.bbox.h+B.bbox.d)+q+i-j.bbox.h}}}else{p+=(z-r)/2;if(C.mid){this.placeBox(B,0,p-B.bbox.h,true);p+=-(B.bbox.h+B.bbox.d)}p+=(z-r)/2}this.placeBox(s,0,p-s.bbox.h,true);p-=s.bbox.h+s.bbox.d;x.bbox={w:Math.max(t.bbox.w,j.bbox.w,s.bbox.w,B.bbox.w),lw:Math.min(t.bbox.lw,j.bbox.lw,s.bbox.lw,B.bbox.lw),rw:Math.max(t.bbox.rw,j.bbox.rw,s.bbox.rw,B.bbox.rw),h:0,d:-p,exactW:true};x.scale=D;x.offset=0.55*x.bbox.w;x.isMultiChar=true;this.setStackWidth(l,x.bbox.w)},extendDelimiterH:function(z,l,C,E,u){var p=this.createStack(z,true);var m=this.createBox(p),A=this.createBox(p);this.createChar(m,(C.left||C.rep),E,u);this.createChar(A,(C.right||C.rep),E,u);var i=this.Element("span");this.createChar(i,C.rep,E,u);var B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var D=i.bbox.rw-i.bbox.lw,o=D-0.05,v,q,y=(C.mid?2:1);q=v=Math.ceil((l-s)/(y*o));if(!C.fillExtenders){o=(l-s)/(y*v)}t=(v/(v+1))*(D-o);o=D-t;r-=i.bbox.lw+t;while(y-->0){while(v-->0){if(!this.msieCloneNodeBug){j=i.cloneNode(true)}else{j=this.Element("span");this.createChar(j,C.rep,E,u)}this.placeBox(this.addBox(p,j),r,0,true);r+=o}if(C.mid&&y){this.placeBox(B,r,0,true);r+=B.bbox.w-t;v=q}}}else{t=Math.min(s-l,m.bbox.w/2);r-=t/2;if(C.mid){this.placeBox(B,r,0,true);r+=B.bbox.w}r-=t/2}this.placeBox(A,r,0,true);z.bbox={w:r+A.bbox.rw,lw:0,rw:r+A.bbox.rw,H:Math.max(m.bbox.h,i.bbox.h,A.bbox.h,B.bbox.h),D:Math.max(m.bbox.d,i.bbox.d,A.bbox.d,B.bbox.d),h:i.bbox.h,d:i.bbox.d,exactW:true};z.scale=E;z.isMultiChar=true;this.setStackWidth(p,z.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===a.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p<k;p++){s+=String.fromCharCode(o[0][p])}}else{s=String.fromCharCode(o[0])}if(o[4]){l*=o[4]}if(l!==1||o[3]){q=this.addElement(r,"span",{style:{fontSize:this.Percent(l)},scale:l,isMathJax:true});this.handleVariant(q,n,s);r.bbox=q.bbox}else{this.handleVariant(r,n,s)}if(o[2]){r.style.marginLeft=this.Em(o[2])}if(o[3]){r.firstChild.style.verticalAlign=this.Em(o[3]);r.bbox.h+=o[3];if(r.bbox.h<0){r.bbox.h=0}}if(o[5]){r.bbox.h+=o[5]}if(o[6]){r.bbox.d+=o[6]}if(this.AccentBug&&r.bbox.w===0){q.firstChild.nodeValue+=this.NBSP;e.createSpace(r,0,0,-r.offsetWidth/e.em)}},positionDelimiter:function(j,i){i-=j.bbox.h;j.bbox.d-=i;j.bbox.h+=i;if(i){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&j.isMultiChar)){if(j.firstChild.style.display===""&&j.style.top!==""){j=j.firstChild;i-=parseFloat(j.style.top)}j.style.position="relative";j.style.top=this.Em(-i)}else{j.style.verticalAlign=this.Em(i);if(e.ffVerticalAlignBug){e.createRule(j.parentNode,j.bbox.h,0,0)}}}},handleVariant:function(y,o,r){var x="",v,B,s,k,A,C,j=y;if(r.length===0){return}if(!y.bbox){y.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}C=o;for(var z=0,w=r.length;z<w;z++){o=C;v=r.charCodeAt(z);B=r.charAt(z);if(B===this.PLANE1){z++;v=r.charCodeAt(z)+119808-56320;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&v>=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000<y.bbox.lw){y.bbox.lw=y.bbox.w+B[3]/1000}if(y.bbox.w+B[4]/1000>y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(k,i,m){k.style.fontFamily=i.family;if(!(e.FontFaceBug&&i.isWebFont)){var j=i.style||"normal",l=i.weight||"normal";if(j!=="normal"||m){k.style.fontStyle=j}if(l!=="normal"||m){k.style.fontWeight=l}}},handleChar:function(j,i,p,o,m){var l=p[5];if(l.img){return this.handleImg(j,i,p,o,m)}if(l.isUnknown&&this.FONTDATA.DELIMITERS[o]){if(m.length){this.addText(j,m)}var k=j.scale;e.createDelimiter(j,o,0,1,i);j.scale=k;p[0]=j.bbox.h*1000;p[1]=j.bbox.d*1000;p[2]=j.bbox.w*1000;p[3]=j.bbox.lw*1000;p[4]=j.bbox.rw*1000;return""}if(l.c==null){if(o<=65535){l.c=String.fromCharCode(o)}else{l.c=this.PLANE1+String.fromCharCode(o-119808+56320)}}if(p[2]||!this.msieAccentBug||m.length){return m+l.c}e.createShift(j,p[3]/1000);e.createShift(j,(p[4]-p[3])/1000);this.addText(j,l.c);e.createShift(j,-p[4]/1000);return""},handleImg:function(j,i,m,l,k){return k},lookupChar:function(o,s){var l,j;if(!o.FONTS){var r=this.FONTDATA.FONTS;var q=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l<j;l++){if(r[q[l]]){o.FONTS.push(r[q[l]]);r[q[l]].name=q[l]}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[s]){if(k[s].length===5){k[s][5]={}}if(e.allowWebFonts&&!k.available){this.loadWebFont(k)}else{return k}}else{this.findBlock(k,s)}}var p=(o.defaultFont||{family:e.config.undefinedFamily});if(o.bold){p.weight="bold"}if(o.italic){p.style="italic"}p[s]=[800,200,500,0,500,{isUnknown:true}];return p},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.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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n=this.data[1].toHTML(k);n.style.paddingRight=n.style.paddingLeft="";e.Measured(n,k)}else{k.bbox=this.HTMLzeroBBox()}var l=this.HTMLrootHeight(j.bbox.h+j.bbox.d,i,k)-m;var p=Math.min(k.bbox.w,k.bbox.rw);o=Math.max(p,j.offset);e.placeBox(k,o-p,l);return o-j.offset},HTMLrootHeight:function(k,j,i){return 0.45*(k-0.9*j)+0.6*j+Math.max(0,i.bbox.d-0.075)}});a.mfenced.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.data.open){this.data.open.toHTML(n)}if(this.data[0]!=null){this.data[0].toHTML(n)}for(var k=1,j=this.data.length;k<j;k++){if(this.data[k]){if(this.data["sep"+k]){this.data["sep"+k].toHTML(n)}this.data[k].toHTML(n)}}if(this.data.close){this.data.close.toHTML(n)}var p=this.HTMLcomputeBBox(n);var l=n.bbox.h,o=n.bbox.d;for(k=0,j=p.length;k<j;k++){p[k].HTMLstretchV(n,l,o)}if(p.length){this.HTMLcomputeBBox(n,true)}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n},HTMLcomputeBBox:function(o,n){var k=o.bbox={},p=[];this.HTMLcheckStretchy(this.data.open,k,p,n);this.HTMLcheckStretchy(this.data[0],k,p,n);for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){this.HTMLcheckStretchy(this.data["sep"+l],k,p,n);this.HTMLcheckStretchy(this.data[l],k,p,n)}}this.HTMLcheckStretchy(this.data.close,k,p,n);this.HTMLcleanBBox(k);return p},HTMLcheckStretchy:function(i,j,l,k){if(i){if(!k&&i.HTMLcanStretch("Vertical")){l.push(i);i=(i.CoreMO()||i)}this.HTMLcombineBBoxes(i,j)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(i){if(this.data[0]!=null){i=this.data[0].toHTML(i);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(i)}return i},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(j,i){return(this.data[0]!=null?this.data[0].HTMLstretchH(j,i):j)},HTMLstretchV:function(j,i,k){return(this.data[0]!=null?this.data[0].HTMLstretchV(j,i,k):j)}});a.munderover.Augment({toHTML:function(K,G,E){var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,K)}K=this.HTMLcreateSpan(K);var O=this.HTMLgetScale();var p=e.createStack(K);var 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L=this.HTMLgetScale(),F=this.HTMLgetMu(I);var n=e.createStack(I),j,l=[];var m=e.createBox(n);if(this.data[this.base]){l.push(this.data[this.base].toHTML(m));if(A!=null){this.data[this.base].HTMLstretchV(m,G,A)}else{if(G!=null){this.data[this.base].HTMLstretchH(m,G)}}}else{m.bbox=this.HTMLzeroBBox()}var k=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var J=e.TeX.x_height*L,z=e.TeX.scriptspace*L*0.75;var i,o;if(this.HTMLnotEmpty(this.data[this.sup])){i=e.createBox(n);l.push(this.data[this.sup].toHTML(i))}if(this.HTMLnotEmpty(this.data[this.sub])){o=e.createBox(n);l.push(this.data[this.sub].toHTML(o))}e.MeasureSpans(l);if(i){i.bbox.w+=z;i.bbox.rw=Math.max(i.bbox.w,i.bbox.rw)}if(o){o.bbox.w+=z;o.bbox.rw=Math.max(o.bbox.w,o.bbox.rw)}e.placeBox(m,0,0);var C=e.TeX.sup_drop*k,B=e.TeX.sub_drop*k;var x=m.bbox.h-C,w=m.bbox.d+B,K=0,E;if(m.bbox.ic){K=m.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&&m.bbox.scale===1&&!this.data[this.base].Get("largeop")){x=w=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:e.length2em(H.subscriptshift,F));H.superscriptshift=(H.superscriptshift===""?0:e.length2em(H.superscriptshift,F));if(!i){if(o){w=Math.max(w,e.TeX.sub1*L,o.bbox.h-(4/5)*J,H.subscriptshift);e.placeBox(o,m.bbox.w+z-K,-w,o.bbox)}}else{if(!o){j=this.getValues("displaystyle","texprimestyle");E=e.TeX[(j.displaystyle?"sup1":(j.texprimestyle?"sup3":"sup2"))];x=Math.max(x,E*L,i.bbox.d+(1/4)*J,H.superscriptshift);e.placeBox(i,m.bbox.w+z,x,i.bbox)}else{w=Math.max(w,e.TeX.sub2*L);var y=e.TeX.rule_thickness*L;if((x-i.bbox.d)-(o.bbox.h-w)<3*y){w=3*y-x+i.bbox.d+o.bbox.h;C=(4/5)*J-(x-i.bbox.d);if(C>0){x+=C;w-=C}}e.placeBox(i,m.bbox.w+z,Math.max(x,H.superscriptshift));e.placeBox(o,m.bbox.w+z-K,-Math.max(w,H.subscriptshift))}}this.HTMLhandleSpace(I);this.HTMLhandleColor(I);return I},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(r,j){var n=this.Get("alttext");if(n&&n!==""){j.setAttribute("aria-label",n)}var k=e.addElement(r,"nobr",{isMathJax:true});r=this.HTMLcreateSpan(k);var o=e.createStack(r),l=e.createBox(o),q;o.style.fontSize=k.parentNode.style.fontSize;k.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete 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s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(s.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){s.indentalign=s.indentalignfirst}if(s.indentalign===a.INDENTALIGN.AUTO){s.indentalign=this.displayAlign}j.style.textAlign=s.indentalign;if(s.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){s.indentshift=s.indentshiftfirst}if(s.indentshift==="auto"){s.indentshift=this.displayIndent}if(s.indentshift&&s.indentalign!==a.INDENTALIGN.CENTER){r.style[{left:"marginLeft",right:"marginRight"}[s.indentalign]]=e.Em(e.length2em(s.indentshift))}}return r},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});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(i){var m=(document.documentMode||0);var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&m>7;var j=(document.compatMode==="BackCompat");if(m<9){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({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:j,msieDisappearingBug:(m>=8),msieMarginScaleBug:(m<8),msiePaddingWidthBug:true,msieBorderWidthBug:j,msieInlineBlockAlignBug:(!k||j),msiePlaceBoxBug:(k&&!j),msieClipRectBug:!k,msieNegativeSpaceBug:j,msieCloneNodeBug:(k&&i.version==="8.0"),initialSkipBug:(m<8),msieNegativeBBoxBug:(m>=8),msieIE6:!l,msieItalicWidthBug:true,zeroWidthBug:(m<8),FontFaceBug:true,msieFontCSSBug:i.isIE9,allowWebFonts:"eot"})},Firefox:function(j){var k=false;if(j.versionAtLeast("3.5")){var i=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,i.length)===i){k="otf"}}e.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:k})},Safari:function(m){var k=m.versionAtLeast("3.0");var j=m.versionAtLeast("3.1");var i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(m.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(i){e.Augment({konquerorVerticalAlignBug: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/MathJax.js b/unpacked/MathJax.js @@ -1155,10 +1155,10 @@ MathJax.Message = { if (this.text) { if (this.div.parentNode == null) {this.Init()} // see ASCIIMathML comments above if (this.current == null) { - if (this.timer) {clearTimeout(this.timer)} + if (this.timer) {clearTimeout(this.timer); delete this.timer} if (delay == null) {delay = 600} if (delay === 0) {this.Remove()} - else {this.timer = setTimeout(MathJax.Callback(["Remove",this]),(delay||600))} + else {this.timer = setTimeout(MathJax.Callback(["Remove",this]),delay)} } else if (MathJax.Hub.config.messageStyle !== "none") { if (this.textNodeBug) {this.div.innerHTML = this.log[this.current].filteredText} else {this.text.nodeValue = this.log[this.current].filteredText} @@ -1358,18 +1358,26 @@ MathJax.Hub = { var queue = MathJax.Callback.Queue(["Clear",this.signal]); for (var i = 0, m = ec.elements.length; i < m; i++) { if (ec.elements[i]) { - var scripts = []; // filled in by prepareScripts + var state = { + scripts: [], // filled in by prepareScripts + start: new Date().getTime(), // timer for processing messages + i: 0, j: 0, // current script, current jax + jax: {}, // scripts grouped by output jax + jaxIDs: [] // id's of jax used + }; queue.Push( ["Post",this.signal,["Begin "+action,ec.elements[i]]], - ["Post",this.signal,["Begin Math",ec.elements[i]]], - ["prepareScripts",this,action,ec.elements[i],scripts], - ["Post",this.signal,["Begin Math Input",ec.elements[i]]], - ["processInput",this,scripts], - ["Post",this.signal,["End Math Input",ec.elements[i]]], - ["Post",this.signal,["Begin Math Output",ec.elements[i]]], - ["processOutput",this,scripts], - ["Post",this.signal,["End Math Output",ec.elements[i]]], - ["Post",this.signal,["End Math",ec.elements[i]]], + ["Post",this.signal,["Begin Math",ec.elements[i],action]], + ["prepareScripts",this,action,ec.elements[i],state], + ["Post",this.signal,["Begin Math Input",ec.elements[i],action]], + ["processInput",this,state], + ["Post",this.signal,["End Math Input",ec.elements[i],action]], + ["prepareOutput",this,state,"preProcess"], + ["Post",this.signal,["Begin Math Output",ec.elements[i],action]], + ["processOutput",this,state], + ["Post",this.signal,["End Math Output",ec.elements[i],action]], + ["prepareOutput",this,state,"postProcess"], + ["Post",this.signal,["End Math",ec.elements[i],action]], ["Post",this.signal,["End "+action,ec.elements[i]]] ); } @@ -1390,7 +1398,7 @@ MathJax.Hub = { } }, - prepareScripts: function (action,element,math) { + prepareScripts: function (action,element,state) { if (arguments.callee.disabled) return; var scripts = this.elementScripts(element); var STATE = MathJax.ElementJax.STATE; @@ -1404,19 +1412,17 @@ MathJax.Hub = { if (script.MathJax.state !== STATE.PENDING) {this.scriptAction[action](script)} } if (!script.MathJax) {script.MathJax = {state: STATE.PENDING}} - if (script.MathJax.state !== STATE.PROCESSED) {math.push(script)} + if (script.MathJax.state !== STATE.PROCESSED) {state.scripts.push(script)} } } }, checkScriptSiblings: function (script) { - if (script.MathJax && script.MathJax.checked) return; - var config = this.config; - var pre = script.previousSibling; - if (pre && pre.nodeName == "#text") { - var preJax,postJax; - var post = script.nextSibling; - if (post && post.nodeName != "#text") {post = null} + if (script.MathJax.checked) return; + var config = this.config, pre = script.previousSibling; + if (pre && pre.nodeName === "#text") { + var preJax,postJax, post = script.nextSibling; + if (post && post.nodeName !== "#text") {post = null} if (config.preJax) { if (typeof(config.preJax) === "string") {config.preJax = new RegExp(config.preJax+"$")} preJax = pre.nodeValue.match(config.preJax); @@ -1436,92 +1442,169 @@ MathJax.Hub = { } if (pre && !pre.nodeValue.match(/\S/)) {pre = pre.previousSibling} } - if (config.preRemoveClass && pre && pre.className == config.preRemoveClass) { - try {pre.innerHTML = ""} catch (err) {} - pre.style.display = "none"; - } - if (script.MathJax) {script.MathJax.checked = 1} + if (config.preRemoveClass && pre && pre.className === config.preRemoveClass) + {script.MathJax.preview = pre} + script.MathJax.checked = 1; }, - processInput: function (scripts,start,n) { - if (arguments.callee.disabled) {return null} - if (!start) {start = new Date().getTime()} - var result, STATE = MathJax.ElementJax.STATE; - var i = 0, script, prev; + processInput: function (state) { + var jax, STATE = MathJax.ElementJax.STATE; + var script, prev, m = state.scripts.length; try { - while (i < scripts.length) { - script = scripts[i]; if (!script) {i++; continue} + // + // Loop through the scripts + // + while (state.i < m) { + script = state.scripts[state.i]; if (!script) {state.i++; continue} + // + // Remove previous error marker, if any + // prev = script.previousSibling; if (prev && prev.className === "MathJax_Error") {prev.parentNode.removeChild(prev)} - var type = script.type.replace(/ *;(.|\s)*/,""); - if (!script.MathJax || script.MathJax.state === STATE.PROCESSED) {i++; continue}; + // + // Check if already processed or needs processing + // + if (!script.MathJax || script.MathJax.state === STATE.PROCESSED) {state.i++; continue}; if (!script.MathJax.elementJax || script.MathJax.state === STATE.UPDATE) { - this.checkScriptSiblings(script); - result = this.inputJax[type].Process(script); + this.checkScriptSiblings(script); // remove preJax/postJax etc. + var type = script.type.replace(/ *;(.|\s)*/,""); // the input jax type + jax = this.inputJax[type].Process(script,state); // run the input jax + if (typeof jax === 'function') { // if a callback was returned + if (jax.called) continue; // go back and call Process() again + this.RestartAfter(jax); // wait for the callback + } + jax.Attach(script,this.inputJax[type].id); // register the jax on the script + script.MathJax.state = STATE.OUTPUT; // mark it as needing output + // + if (!this.outputJax[jax.mimeType]) { // check for existing output jax + script.MathJax.state = STATE.UPDATE; + throw Error("No output jax registered for "+jax.mimeType); + } + // + // Record the output jax + // and put this script in the queue for that jax + // + jax.outputJax = this.outputJax[jax.mimeType][0].id; + if (!state.jax[jax.outputJax]) { + if (state.jaxIDs.length === 0) { + // use original array until we know there are more (rather than two copies) + state.jax[jax.outputJax] = state.scripts; + } else { + if (state.jaxIDs.length === 1) // get the script so far for the existing jax + {state.jax[state.jaxIDs[0]] = state.scripts.slice(0,state.i)} + state.jax[jax.outputJax] = []; // start a new array for the new jax + } + state.jaxIDs.push(jax.outputJax); // save the ID of the jax + } + if (state.jaxIDs.length > 1) {state.jax[jax.outputJax].push(script)} + } + // + // Go on to the next script, and check if we need to update the processing message + // + state.i++; var now = new Date().getTime(); + if (now - state.start > this.processUpdateTime && state.i < state.scripts.length) + {state.start = now; this.RestartAfter(MathJax.Callback.Delay(1))} + } + } catch (err) {return this.processError(err,state,"Input")} + // + // Put up final message, reset the state and return + // + if (state.scripts.length && this.config.showProcessingMessages) + {MathJax.Message.Set("Processing math: 100%",0)} + state.start = new Date().getTime(); state.i = state.j = 0; + return null; + }, + + // + // Pre- and post-process scripts by jax + // (to get scaling factors, hide/show output, and so on) + // Since this can cause the jax to load, we need to trap restarts + // + prepareOutput: function (state,method) { + while (state.j < state.jaxIDs.length) { + var id = state.jaxIDs[state.j], JAX = MathJax.OutputJax[id]; + if (JAX[method]) { + try { + var result = JAX[method](state); if (typeof result === 'function') { - if (result.called) continue; // go back and call Process() again + if (result.called) continue; // go back and try again this.RestartAfter(result); } - result.Attach(script,this.inputJax[type].id); - script.MathJax.state = STATE.OUTPUT; + } catch (err) { + if (!err.restart) { + MathJax.Message.Set("Error preparing "+id+" output ("+method+")",null,600); + MathJax.Hub.lastPrepError = err; + state.j++; + } + return MathJax.Callback.After(["prepareOutput",this,state,method],err.restart); } - i++; - if (new Date().getTime() - start > this.processUpdateTime && i < scripts.length) - {start = 0; this.RestartAfter(MathJax.Callback.Delay(1))} } - } catch (err) {return this.processError(err,scripts,i,n,start,"Input")} - if ((n || scripts.length) && this.config.showProcessingMessages) - {MathJax.Message.Set("Processing math: 100%",0)} + state.j++; + } return null; }, - processOutput: function (scripts,start,n) { - if (arguments.callee.disabled) {return null} - if (!start) {start = new Date().getTime()} - var result, STATE = MathJax.ElementJax.STATE; - var i = 0, script; + processOutput: function (state) { + var result, STATE = MathJax.ElementJax.STATE, script, m = state.scripts.length; try { - while (i < scripts.length) { - script = scripts[i]; if (!script || !script.MathJax) {i++; continue} - var jax = script.MathJax.elementJax; if (!jax) {i++; continue} - if (!this.outputJax[jax.mimeType]) { - script.MathJax.state = STATE.UPDATE; - throw Error("No output jax registered for "+jax.mimeType); - } - var outputJax = this.outputJax[jax.mimeType][0]; - jax.outputJax = outputJax.id; - result = outputJax.Process(script); - if (typeof result === 'function') { - if (result.called) continue; // go back and call Process() again - this.RestartAfter(result); - } - script.MathJax.state = STATE.PROCESSED; i++; + // + // Loop through the scripts + // + while (state.i < m) { + // + // Check that there is an element jax + // + script = state.scripts[state.i]; if (!script || !script.MathJax) {state.i++; continue} + var jax = script.MathJax.elementJax; if (!jax) {state.i++; continue} + // + // Call the output Jax's Process method (which will be its Translate() + // method once loaded). Mark it as complete and remove the preview. + // + result = MathJax.OutputJax[jax.outputJax].Process(script,state); + script.MathJax.state = STATE.PROCESSED; state.i++; + if (script.MathJax.preview) {script.MathJax.preview.style.display = "none"} + // + // Signal that new math is available + // this.signal.Post(["New Math",jax.inputID]); // FIXME: wait for this? (i.e., restart if returns uncalled callback) - if (new Date().getTime() - start > this.processUpdateTime && i < scripts.length) - {start = 0; this.RestartAfter(MathJax.Callback.Delay(1))} + // + // Update the processing message, if needed + // + var now = new Date().getTime(); + if (now - state.start > this.processUpdateTime && state.i < state.scripts.length) + {state.start = now; this.RestartAfter(MathJax.Callback.Delay(1))} } - } catch (err) {return this.processError(err,scripts,i,n,start,"Output")} - if ((n || scripts.length) && this.config.showProcessingMessages) { + } catch (err) {return this.processError(err,state,"Output")} + // + // Put up the typesetting-complete message + // + if (state.scripts.length && this.config.showProcessingMessages) { MathJax.Message.Set("Typesetting math: 100%",0); MathJax.Message.Clear(0); } + state.i = state.j = 0; return null; }, + + processMessage: function (state,type) { + var m = Math.floor(state.i/(state.scripts.length)*100); + var message = (type === "Output" ? "Typesetting" : "Processing"); + if (this.config.showProcessingMessages) {MathJax.Message.Set(message+" math: "+m+"%",0)} + }, - processError: function (err,scripts,i,n,start,type) { + processError: function (err,state,type) { if (!err.restart) { if (!this.config.errorSettings.message) {throw err} - this.formatError(scripts[i],err); i++; + this.formatError(state.scripts[state.i],err); state.i++; } - if (!n) {n = 0}; var m = Math.floor((n+i)/(n+scripts.length)*100); n += i; - var message = (type === "Output" ? "Typesetting" : "Processing"); - if (this.config.showProcessingMessages) {MathJax.Message.Set(message+" math: "+m+"%",0)} - return MathJax.Callback.After(["process"+type,this,scripts.slice(i),start,n],err.restart); + this.processMessage(state,type); + return MathJax.Callback.After(["process"+type,this,state],err.restart); }, formatError: function (script,err) { var error = MathJax.HTML.Element("span",{className:"MathJax_Error"},this.config.errorSettings.message); script.parentNode.insertBefore(error,script); + if (script.MathJax.preview) {script.MathJax.preview.style.display = "none"} this.lastError = err; }, @@ -1752,7 +1835,12 @@ MathJax.Hub.Startup = { onLoad: function (when) { var onload = this.onload = MathJax.Callback(function () {MathJax.Hub.Startup.signal.Post("onLoad")}); - if (window.addEventListener) {window.addEventListener("load",onload,false)} + if (document.readyState && document.readyState !== "loading") {return [onload]} + if (window.addEventListener) { + window.addEventListener("load",onload,false); + if (!this.params.noDOMContentEvent) + {window.addEventListener("DOMContentLoaded",onload,false)} + } else if (window.attachEvent) {window.attachEvent("onload",onload)} else {window.onload = onload} return onload; @@ -1839,12 +1927,12 @@ MathJax.Hub.Startup = { cObject.Augment(null,cdef); return this; }, - Process: function (element) { + preProcess: function (element) { var load, file = this.directory+"/"+this.JAXFILE; - this.constructor.prototype.Process = function (element) { - if (!load.called) {return load} + this.constructor.prototype.preProcess = function (element) { + if (!load.called) {return load} throw Error(file+" failed to load properly"); - }; + } load = AJAX.Require(file); return load; }, @@ -1874,7 +1962,11 @@ MathJax.Hub.Startup = { ["Post",HUB.Startup.signal,this.id+" Jax Startup"], ["Startup",this], ["Post",HUB.Startup.signal,this.id+" Jax Ready"], - [function (THIS) {THIS.Process = THIS.Translate},this.constructor.prototype], + [function (THIS) { + THIS.preProcess = THIS.preTranslate; + THIS.Process = THIS.Translate; + THIS.postProcess = THIS.postTranslate; + },this.constructor.prototype], ["loadComplete",AJAX,this.directory+"/"+file] ); } @@ -2016,7 +2108,7 @@ MathJax.Hub.Startup = { if (typeof(jax[id]) === 'undefined' && id !== 'newID') {delete this[id]} } for (id in jax) { - if (!this.hasOwnProperty(id)) continue; + if (!jax.hasOwnProperty(id)) continue; if (typeof(this[id]) === 'undefined' || (this[id] !== jax[id] && id !== 'inputID')) {this[id] = jax[id]} } diff --git a/unpacked/jax/output/HTML-CSS/autoload/maction.js b/unpacked/jax/output/HTML-CSS/autoload/maction.js @@ -44,9 +44,10 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { span = this.HTMLhandleSize(this.HTMLcreateSpan(span)); span.bbox = null; var selected = this.selected(); if (selected) { - HTMLCSS.Measured(selected.toHTML(span),span); + var box = selected.toHTML(span); if (D != null) {HTMLCSS.Remeasured(selected.HTMLstretchV(span,HW,D),span)} else if (HW != null) {HTMLCSS.Remeasured(selected.HTMLstretchH(span,HW),span)} + else {HTMLCSS.Measured(box,span)} this.HTMLhandleHitBox(span); } this.HTMLhandleSpace(span); @@ -162,7 +163,17 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { if (this === currentTip) return; tip.style.left = x+"px"; tip.style.top = y+"px"; tip.innerHTML = '<span class="MathJax"><nobr></nobr></span>'; - HTMLCSS.getScales(tip.firstChild,tip.firstChild); + // + // get em sizes (taken from HTMLCSS.preTranslate) + // + var emex = tip.insertBefore(HTMLCSS.EmExSpan.cloneNode(true),tip.firstChild); + var ex = emex.firstChild.offsetWidth/60; + HTMLCSS.em = MML.mbase.prototype.em = emex.lastChild.firstChild.offsetWidth/60; + var scale = Math.floor(Math.max(HTMLCSS.config.minScaleAdjust/100,(ex/HTMLCSS.TeX.x_height)/HTMLCSS.em) * HTMLCSS.config.scale); + HTMLCSS.msieMarginScale = (HTMLCSS.msieMarginScaleBug ? scale/100 : 1); + tip.firstChild.style.fontSize = scale+"%"; + emex.parentNode.removeChild(emex); + var stack = HTMLCSS.createStack(tip.firstChild.firstChild); var box = HTMLCSS.createBox(stack); try {HTMLCSS.Measured(this.data[1].toHTML(box),box)} catch(err) { diff --git a/unpacked/jax/output/HTML-CSS/autoload/mmultiscripts.js b/unpacked/jax/output/HTML-CSS/autoload/mmultiscripts.js @@ -31,11 +31,12 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { span = this.HTMLcreateSpan(span); var scale = this.HTMLgetScale(); var stack = HTMLCSS.createStack(span), values; var base = HTMLCSS.createBox(stack); - this.HTMLmeasureChild(this.base,base); if (this.data[this.base]) { - if (D != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchV(base,HW,D),base)} - else if (HW != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchH(base,HW),base)} - } + var child = this.data[this.base].toHTML(base); + if (D != null) {this.data[this.base].HTMLstretchV(base,HW,D)} + else if (HW != null) {this.data[this.base].HTMLstretchH(base,HW)} + HTMLCSS.Measured(child,base); + } else {base.bbox = this.HTMLzeroBBox()} var x_height = HTMLCSS.TeX.x_height * scale, s = HTMLCSS.TeX.scriptspace * scale * .75; // FIXME: .75 can be removed when IC is right? diff --git a/unpacked/jax/output/HTML-CSS/autoload/mtable.js b/unpacked/jax/output/HTML-CSS/autoload/mtable.js @@ -22,7 +22,7 @@ */ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { - var VERSION = "1.1.2"; + var VERSION = "1.1.3"; var MML = MathJax.ElementJax.mml, HTMLCSS = MathJax.OutputJax["HTML-CSS"]; @@ -38,7 +38,7 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { var stack = HTMLCSS.createStack(span); var scale = this.HTMLgetScale(), mu = this.HTMLgetMu(span), LABEL = -1; - var H = [], D = [], W = [], A = [], C = [], i, j, J = -1, m, M, s, row; + var H = [], D = [], W = [], A = [], C = [], i, j, J = -1, m, M, s, row, entries = []; var LHD = HTMLCSS.FONTDATA.baselineskip * scale * values.useHeight, LH = HTMLCSS.FONTDATA.lineH * scale, LD = HTMLCSS.FONTDATA.lineD * scale; @@ -55,7 +55,13 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { W[j] = -HTMLCSS.BIGDIMEN; } A[i][j] = HTMLCSS.createBox(C[j]); - HTMLCSS.Measured(row.data[j-s].toHTML(A[i][j]),A[i][j]); + entries.push(row.data[j-s].toHTML(A[i][j])); + } + } + HTMLCSS.MeasureSpans(entries); + for (i = 0, m = this.data.length; i < m; i++) { + row = this.data[i]; s = (row.type === "mlabeledtr" ? LABEL : 0); + for (j = s, M = row.data.length + s; j < M; j++) { if (row.data[j-s].isMultiline) {A[i][j].style.width = "100%"} if (A[i][j].bbox.h > H[i]) {H[i] = A[i][j].bbox.h} if (A[i][j].bbox.d > D[i]) {D[i] = A[i][j].bbox.d} @@ -431,9 +437,9 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { toHTML: function (span,HW,D) { span = this.HTMLcreateSpan(span); if (this.data[0]) { - var box = HTMLCSS.Measured(this.data[0].toHTML(span),span); - if (D != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchV(span,HW,D),span)} - else if (HW != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchH(span,HW),span)} + var box = this.data[0].toHTML(span); + if (D != null) {box = this.data[0].HTMLstretchV(span,HW,D)} + else if (HW != null) {box = this.data[0].HTMLstretchH(span,HW)} span.bbox = box.bbox; } this.HTMLhandleSpace(span); diff --git a/unpacked/jax/output/HTML-CSS/config.js b/unpacked/jax/output/HTML-CSS/config.js @@ -32,13 +32,16 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ webfontDir: MathJax.OutputJax.fontDir + "/HTML-CSS", // font name added later config: { - scale: 100, minScaleAdjust: 50, - availableFonts: ["STIX","TeX"], - preferredFont: "TeX", - webFont: "TeX", - imageFont: "TeX", - undefinedFamily: "STIXGeneral,'Arial Unicode MS',serif", - + scale: 100, minScaleAdjust: 50, // global math scaling factor, and minimum adjusted scale factor + availableFonts: ["STIX","TeX"], // list of local fonts to check for + preferredFont: "TeX", // preferred local font (TeX or STIX) + webFont: "TeX", // web-based font to use when no local fonts found (TeX is only choice) + imageFont: "TeX", // font to use for image fallback mode (TeX is only choice) + undefinedFamily: "STIXGeneral,'Arial Unicode MS',serif", // fonts to use for unknown unicode characters + + EqnChunk: 50, // number of equations to process before showing them + EqnChunkFactor: 1.5, // chunk size is multiplied by this after each chunk + linebreaks: { automatic: false, // when false, only process linebreak="newline", // when true, insert line breaks automatically in long expressions. diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js @@ -190,7 +190,6 @@ styles: { ".MathJax": { "display": "inline", - "font-family": "serif", "font-style": "normal", "font-weight": "normal", "line-height": "normal", @@ -243,6 +242,16 @@ visibility: "hidden", position:"fixed", width: 0, height: 0, overflow:"hidden" }, + ".MathJax_Processed": {display:"none!important"}, + + ".MathJax_ExBox": { + display:"block", overflow:"hidden", + height:"1px", width:"60ex" + }, + ".MathJax .MathJax_EmBox": { + display:"block", overflow:"hidden", + height:"1px", width:"60em" + }, ".MathJax .MathJax_HitBox": { cursor: "text", @@ -265,7 +274,9 @@ } }, settings: HUB.config.menuSettings, - + + hideProcessedMath: true, // use display:none until all math is processed + Font: null, // created by Config() below Config: function () { @@ -319,16 +330,6 @@ this.Mouseout = HOVER.Mouseout; this.Mousemove = HOVER.Mousemove; - // Set up default fonts - var family = [], fonts = this.FONTDATA.VARIANT.normal.fonts; - if (!(fonts instanceof Array)) {fonts = [fonts]} - for (var i = 0, m = fonts.length; i < m; i++) { - family[i] = this.FONTDATA.FONTS[fonts[i]].family; - if (!family[i]) {family[i] = fonts[i]} - } - this.config.styles[".MathJax .math span"] = - this.config.styles["#MathJax_getScales"] = {"font-family": family.join(',')}; - // Make hidden div for when math is in a display:none block this.hiddenDiv = this.Element("div",{ style:{visibility:"hidden", overflow:"hidden", position:"absolute", top:0, @@ -358,27 +359,23 @@ this.HDimg = HTMLCSS.createStrut(this.HDspan,0); } - // Used in getScales - 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(err) {} - } else { - this.HDMimg = HTMLCSS.createStrut(this.HDMspan,0); this.HDMimg.style.marginRight = ""; + // Used in preTranslate to get scaling factors + this.EmExSpan = this.Element("span", + {style:{position:"absolute","font-size-adjust":"none"}}, + [ + ["span",{className:"MathJax_ExBox"}], + ["span",{className:"MathJax"}, + [["span",{className:"MathJax_EmBox"}]] + ] + ] + ); + if (this.msieMarginScaleBug) { + this.addElement(this.EmExSpan.lastChild,"span",null,[ + ["span",{style:{display:"inline-block",width:"5em"}}], + ["span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}}] + ]); } - // Used for computing factor to fix margin width in MSIE - this.marginCheck = HTMLCSS.Element("span",null, - [["span",{style: {display:"inline-block", width:"5em"}}]]); - this.marginMove = HTMLCSS.addElement(this.marginCheck,"span", - {style: {display:"inline-block", width:"5em", marginLeft:"-5em"}}); - // Used in getLinebreakWidth this.linebreakSpan = HTMLCSS.Element("span",null, [["hr",{style: {width:"100%", size:1, padding:0, border:0, margin:0}}]]); @@ -405,48 +402,189 @@ if (!FONT.available) {HTMLCSS.Font.testFont(FONT)} } }, + + preTranslate: function (state) { + var scripts = state.jax[this.id], i, m = scripts.length, + script, prev, span, div, test, jax, ex, em, scale; + for (i = 0; i < m; i++) { + script = scripts[i]; if (!script.parentNode) continue; + // + // Remove any existing output + // + prev = script.previousSibling; + if (prev && String(prev.className).match(/^MathJax(_Display)?$/)) + {prev.parentNode.removeChild(prev)} + // + // Add the span, and a div if in display mode, + // then set the role and mark it as being processed + // + jax = script.MathJax.elementJax; + jax.HTMLCSS = {display: (jax.root.Get("display") === "block")} + span = div = this.Element("span",{ + className:"MathJax", id:jax.inputID+"-Frame", isMathJax:true, + oncontextmenu:EVENT.Menu, onmousedown: EVENT.Mousedown, + onmouseover:EVENT.Mouseover, onmouseout:EVENT.Mouseout, onmousemove:EVENT.Mousemove, + onclick:EVENT.Click, ondblclick:EVENT.DblClick + }); + if (HUB.Browser.noContextMenu) { + span.ontouchstart = TOUCH.start; + span.ontouchend = TOUCH.end; + } + if (jax.HTMLCSS.display) { + div = this.Element("div",{className:"MathJax_Display", style:{width:"100%"}}); + div.appendChild(span); + } else if (this.msieDisappearingBug) {span.style.display = "inline-block"} + // (screen readers don't know about role="math" yet, so use "textbox" instead) + div.setAttribute("role","textbox"); div.setAttribute("aria-readonly","true"); + div.className += " MathJax_Processing"; + script.parentNode.insertBefore(div,script); + // + // Add the test span for determining scales + // + script.parentNode.insertBefore(this.EmExSpan.cloneNode(true),script); + } + // + // Determine the scaling factors for each script + // (this only requires one reflow rather than a reflow for each equation) + // + for (i = 0; i < m; i++) { + script = scripts[i]; if (!script.parentNode) continue; + jax = script.MathJax.elementJax; test = script.previousSibling; + ex = jax.HTMLCSS.ex = test.firstChild.offsetWidth/60; + if (ex === 0 || ex === "NaN") { + // can't read width, so move to hidden div for processing + this.hiddenDiv.appendChild(test.previousSibling); + this.hiddenDiv.appendChild(test); + jax.HTMLCSS.isHidden = true; + ex = jax.HTMLCSS.ex = test.firstChild.offsetWidth/60; + } + em = jax.HTMLCSS.em = test.lastChild.firstChild.offsetWidth/60; + scale = Math.floor(Math.max(this.config.minScaleAdjust/100,(ex/this.TeX.x_height)/em) * this.config.scale); + jax.HTMLCSS.scale = scale/100; jax.HTMLCSS.fontSize = scale+"%"; + jax.HTMLCSS.marginScale = 1; + } + // + // If we need to determine MSIE margin scaling, + // set the font sizes (which is what causes the problem) + // and then read the scaling factor (again only one reflow needed) + // + if (this.msieMarginScaleBug) { + for (i = 0; i < m; i++) { + script = scripts[i]; if (!script.parentNode) continue; + jax = script.MathJax.elementJax; test = this.getTestSpan(script); + test.lastChild.style.fontSize = jax.HTMLCSS.fontSize; + } + for (i = 0; i < m; i++) { + script = scripts[i]; if (!script.parentNode) continue; + test = this.getTestSpan(script); + var W = test.lastChild.lastChild.offsetWidth, + w = test.lastChild.lastChild.firstChild.offsetWidth; + math.HTMLCSS.marginScale = (2*w - W ? w/(2*w - W) : 1); + } + } + // + // Remove the test spans used for determining scales + // + for (i = 0; i < m; i++) { + script = scripts[i]; if (!script.parentNode) continue; + test = this.getTestSpan(script); + test.parentNode.removeChild(test); + } + // + // Set state variables used for displaying equations in chunks + // + state.HTMLCSSeqn = state.HTMLCSSlast = 0; + state.HTMLCSSchunk = this.config.EqnChunk; + }, + getTestSpan: function (script) { + var jax = script.MathJax.elementJax; + var span = document.getElementById(jax.inputID+"-Frame"); + if (jax.HTMLCSS.display) {span = span.parentNode} + return span.nextSibling; + }, - Translate: function (script) { + Translate: function (script,state) { if (!script.parentNode) return; - var prev = script.previousSibling; - if (prev && String(prev.className).match(/^MathJax(_MathML|_Display)?$/)) - {prev.parentNode.removeChild(prev)} - var jax = script.MathJax.elementJax, math = jax.root, span, div, frame; - span = div = frame = this.Element("span",{ - className:"MathJax", isMathJax:true, jaxID:this.id, id:jax.inputID+"-Span", - oncontextmenu:EVENT.Menu, onmousedown: EVENT.Mousedown, - onmouseover:EVENT.Mouseover, onmouseout: EVENT.Mouseout, onmousemove: EVENT.Mousemove, - onclick:EVENT.Click, ondblclick:EVENT.DblClick - }); - if (MathJax.Hub.Browser.noContextMenu) { - span.ontouchstart = TOUCH.start; - span.ontouchend = TOUCH.end; - } - var blockMode = (math.Get("display") === "block"); - if (blockMode) { - div = frame = this.Element("div",{className:"MathJax_Display", style:{width:"100%", position:"relative"}}); - div.appendChild(span); - } - // (screen readers don't know about role="math" yet, so use "textbox" instead) - div.setAttribute("role","textbox"); div.setAttribute("aria-readonly","true"); - if (this.useProcessingFrame) { - frame = this.Element((blockMode ? "div" : "span"),{className:"MathJax_Processing"}); - frame.appendChild(div); - } - script.parentNode.insertBefore(frame,script); var isHidden; - try {this.getScales(span); isHidden = (this.em === 0 || String(this.em) === "NaN")} catch (err) {isHidden = true} - if (isHidden) {this.hiddenDiv.appendChild(frame); this.getScales(span)} - jax.em = this.em; jax.outerEm = this.outerEm; jax.scale = this.scale; - this.getLinebreakWidth(frame); + + // + // Get the data about the math + // + var jax = script.MathJax.elementJax, math = jax.root, + span = document.getElementById(jax.inputID+"-Frame"), + div = (jax.HTMLCSS.display ? span.parentNode : span); + // + // Set the font metrics + // + this.em = MML.mbase.prototype.em = jax.HTMLCSS.em * jax.HTMLCSS.scale; + this.outerEm = jax.HTMLCSS.em; this.msieMarginScale = jax.HTMLCSS.marginScale; + span.style.fontSize = jax.HTMLCSS.fontSize; + this.getLinebreakWidth(div); + // + // Typeset the math + // this.initImg(span); this.initHTML(math,span); math.setTeXclass(); try {math.toHTML(span,div)} catch (err) { - if (err.restart) {frame.parentNode.removeChild(frame)} + if (err.restart) {while (span.firstChild) {span.removeChild(span.firstChild)}} throw err; } - if (isHidden) {script.parentNode.insertBefore(frame,script)} - if (this.useProcessingFrame) frame.parentNode.replaceChild(div,frame); + // + // Put it in place, and remove the processing marker + // + if (jax.HTMLCSS.isHidden) {script.parentNode.insertBefore(div,script)} + div.className = div.className.split(/ /)[0]; + // + // Check if we are hiding the math until more is processed + // + if (this.hideProcessedMath) { + // + // Hide the math and don't let its preview be removed + // + div.className += " MathJax_Processed"; + if (script.MathJax.preview) { + jax.HTMLCSS.preview = script.MathJax.preview; + delete script.MathJax.preview; + } + // + // Check if we should show this chunk of equations + // + state.HTMLCSSeqn++; + if (state.HTMLCSSeqn >= state.HTMLCSSlast + state.HTMLCSSchunk) { + this.postTranslate(state); + state.HTMLCSSchunk = Math.floor(state.HTMLCSSchunk*this.config.EqnChunkFactor); + } + } + }, + + postTranslate: function (state) { + var scripts = state.jax[this.id]; + if (!this.hideProcessedMath) return; + // + // Reveal this chunk of math + // + for (var i = state.HTMLCSSlast, m = state.HTMLCSSeqn; i < m; i++) { + var script = scripts[i]; + if (script) { + // + // Remove the processed marker + // + script.previousSibling.className = script.previousSibling.className.split(/ /)[0]; + var data = script.MathJax.elementJax.HTMLCSS; + // + // Remove the preview, if any + // + if (data.preview) { + data.preview.style.display = "none"; + script.MathJax.preview = data.preview; + delete data.preview; + } + } + } + // + // Save our place so we know what is revealed + // + state.HTMLCSSlast = state.HTMLCSSeqn; }, getJaxFromMath: function (math) { @@ -505,9 +643,12 @@ }, Remove: function (jax) { - var span = jax.SourceElement(); if (!span) return; - span = span.previousSibling; if (!span) return; - if (span.className.match(/^MathJax/)) {span.parentNode.removeChild(span)} + var span = document.getElementById(jax.inputID+"-Frame"); + if (span) { + if (jax.HTMLCSS.display) {span = span.parentNode} + span.parentNode.removeChild(span); + } + delete jax.HTMLCSS; }, getLinebreakWidth: function (div) { @@ -525,32 +666,6 @@ } }, - getScales: function (span) { - span.parentNode.insertBefore(this.HDMspan,span); - this.HDMspan.className = ""; this.HDMspan.id = ""; this.HDMspan.style.fontSize = ""; - this.HDMimg.style.height = "1px"; this.HDMimg.style.width = "60ex"; - var ex = this.HDMspan.offsetWidth/60; - this.HDMspan.className = "MathJax"; this.HDMspan.id = "MathJax_getScales"; - this.HDMimg.style.width = "60em"; - var em = this.outerEm = this.HDMspan.offsetWidth/60; - this.scale = Math.floor(Math.max(this.config.minScaleAdjust/100,(ex/this.TeX.x_height)/em) * this.config.scale); - span.style.fontSize = this.HDMspan.style.fontSize = this.scale+"%"; - this.em = MML.mbase.prototype.em = this.HDMspan.offsetWidth/60; - if (this.operaFontSizeBug && em === this.em && this.scale !== 100) { - // Opera 10.61 doesn't seem to process the fontSize setting above, so adjust manually - this.em = MML.mbase.prototype.em = em * this.scale/100; - } - span.parentNode.removeChild(this.HDMspan); - this.msieMarginScale = this.getMarginScale(span); - }, - getMarginScale: function (span) {return 1}, - getMSIEmarginScale: function (span) { - span.appendChild(this.marginCheck); - var W = this.marginCheck.offsetWidth, w = this.marginMove.offsetWidth; - var scale = (2*w - W ? w/(2*w - W) : 1); - span.removeChild(this.marginCheck); - return scale; - }, getHD: function (span) { var position = span.style.position; span.style.position = "absolute"; @@ -565,39 +680,90 @@ return HD; }, getW: function (span) { - var W = span.offsetWidth, w = (span.bbox ? span.bbox.w: -1), start = span; - if ((w < 0 || this.negativeSkipBug) && W >= 0 && !span.style.width) { + var W, H, w = (span.bbox||{}).w, start = span; + if (span.bbox && span.bbox.exactW) {return w} + if ((span.bbox && w >= 0 && !this.initialSkipBug) || this.negativeBBoxes || !span.firstChild) { + W = span.offsetWidth; H = span.parentNode.offsetHeight; + } else if (span.bbox && w < 0 && this.msieNegativeBBoxBug) { + W = -span.offsetWidth, H = span.parentNode.offsetHeight; + } else { // IE can't deal with a space at the beginning, so put something else first - if (this.negativeSkipBug) { + if (this.initialSkipBug) { var position = span.style.position; span.style.position = "absolute"; - start = this.startMarker; - if (span.firstChild) {span.insertBefore(start,span.firstChild)} - else {span.appendChild(start)} - start = this.startMarker; + start = this.startMarker; span.insertBefore(start,span.firstChild) } span.appendChild(this.endMarker); W = this.endMarker.offsetLeft - start.offsetLeft; span.removeChild(this.endMarker); - if (this.negativeSkipBug) { - span.removeChild(start); - span.style.position = position; - } + if (this.initialSkipBug) {span.removeChild(start); span.style.position = position} } + if (H != null) {span.parentNode.HH = H/this.em} return W/this.em; }, Measured: function (span,parent) { - if (span.bbox.width == null && span.bbox.w && !span.bbox.isMultiline) { + var bbox = span.bbox; + if (bbox.width == null && bbox.w && !bbox.isMultiline) { var w = this.getW(span); - span.bbox.rw += w - span.bbox.w; - span.bbox.w = w; + bbox.rw += w - bbox.w; + bbox.w = w; bbox.exactW = true; } if (!parent) {parent = span.parentNode} - if (!parent.bbox) {parent.bbox = span.bbox} + if (!parent.bbox) {parent.bbox = bbox} return span; }, Remeasured: function (span,parent) { parent.bbox = this.Measured(span,parent).bbox; }, + MeasureSpans: function (SPANS) { + var spans = [], span, i, m, bbox, start, end, W; + // + // Insert the needed markers + // + for (i = 0, m = SPANS.length; i < m; i++) { + span = SPANS[i]; if (!span) continue; + bbox = span.bbox; + if (bbox.exactW || bbox.width || bbox.w === 0 || bbox.isMultiline) { + if (!span.parentNode.bbox) {span.parentNode.bbox = bbox} + continue; + } + if (this.negativeBBoxes || !span.firstChild || (bbox.w >= 0 && !this.initialSkipBug) || + (bbox.w < 0 && this.msieNegativeBBoxBug)) { + spans.push([span]); + } else if (this.initialSkipBug) { + start = this.startMarker.cloneNode(true); end = this.endMarker.cloneNode(true); + span.insertBefore(start,span.firstChild); span.appendChild(end); + spans.push([span,start,end,span.style.position]); span.style.position = "absolute"; + } else { + end = this.endMarker.cloneNode(true); + span.appendChild(end); spans.push([span,null,end]); + } + } + // + // Read the widths and heights + // + for (i = 0, m = spans.length; i < m; i++) { + span = spans[i][0]; bbox = span.bbox; var parent = span.parentNode; + if ((bbox.w >= 0 && !this.initialSkipBug) || this.negativeBBoxes || !span.firstChild) { + W = span.offsetWidth; parent.HH = span.parentNode.offsetHeight/this.em; + } else if (bbox.w < 0 && this.msieNegativeBBoxBug) { + W = -span.offsetWidth, parent.HH = span.parentNode.offsetHeight/this.em; + } else { + W = spans[i][2].offsetLeft - spans[i][1].offsetLeft; + } + W /= this.em; + bbox.rw += W - bbox.w; + bbox.w = W; bbox.exactW = true; + if (!parent.bbox) {parent.bbox = bbox} + } + // + // Remove markers + // + for (i = 0, m = spans.length; i < m; i++) { + span = spans[i]; + if (span[1]) {span[1].parentNode.removeChild(span[1]), span[0].style.position = span[3]} + if (span[2]) {span[2].parentNode.removeChild(span[2])} + } + }, Em: function (m) { if (Math.abs(m) < .0006) {return "0em"} @@ -695,10 +861,12 @@ if (this.msieInlineBlockAlignBug) {D = this.Em(HTMLCSS.getHD(span.parentNode).d-d)} if (span.isBox || span.className == "mspace") { span.bbox = { + exactW: true, h: h*span.scale, d: d*span.scale, w: w*span.scale, rw: w*span.scale, lw: 0 }; span.style.height = H; span.style.verticalAlign = D; + span.HH = (h+d)*span.scale; } else { span = this.addElement(span,"span",{style: {height:H, verticalAlign:D}, isMathJax:true}); } @@ -728,10 +896,10 @@ var rule = this.addElement(span,"span",{ style: {borderLeft: color, display: "inline-block", overflow:"hidden", width:0, height:H, verticalAlign:D}, - bbox: {h:h, d:d, w:w, rw:w, lw:0}, noAdjust: true, isMathJax: true + bbox: {h:h, d:d, w:w, rw:w, lw:0, exactW:true}, noAdjust:true, HH:h+d, isMathJax:true }); if (w > 0 && rule.offsetWidth == 0) {rule.style.width = this.Em(w)} - if (span.isBox || span.className == "mspace") {span.bbox = rule.bbox} + if (span.isBox || span.className == "mspace") {span.bbox = rule.bbox, span.HH = h+d} return rule; }, createFrame: function (span,h,d,w,t,style) { @@ -740,7 +908,7 @@ var B = this.Em(t)+" "+style; var frame = this.addElement(span,"span",{ style: {border: B, display:"inline-block", overflow:"hidden", width:W, height:H}, - bbox: {h:h, d:d, w:w, rw:w, lw:0}, noAdjust: true, isMathJax: true + bbox: {h:h, d:d, w:w, rw:w, lw:0, exactW:true}, noAdjust: true, HH:h+d, isMathJax:true }); if (D) {frame.style.verticalAlign = D} return frame; @@ -751,12 +919,13 @@ var relativeW = String(w).match(/%$/); var W = (!relativeW && w != null ? w : 0); span = this.addElement(span,"span",{ - noAdjust: true, isMathJax: true, + noAdjust: true, HH: 0, isMathJax: true, style: {display:"inline-block", position:"relative", width:(relativeW ? "100%" : this.Em(W)), height:0} }); if (!nobbox) { span.parentNode.bbox = span.bbox = { + exactW: true, h: -this.BIGDIMEN, d: -this.BIGDIMEN, w:W, lw: this.BIGDIMEN, rw: (!relativeW && w != null ? w : -this.BIGDIMEN) }; @@ -779,8 +948,12 @@ if (this.msiePlaceBoxBug) {this.addText(span,this.NBSP)} if (this.imgSpaceBug) {this.addText(span,this.imgSpace)} // Place the box - var HH = span.offsetHeight/this.em + 1, dx = 0; - if (span.noAdjust) {HH -= 1} else { + var HH, dx = 0; + if (span.HH != null) {HH = span.HH} + else if (bbox) {HH = Math.max(3,bbox.h+bbox.d)} + else {HH = span.offsetHeight/this.em} + if (!span.noAdjust) { + HH += 1; if (this.msieInlineBlockAlignBug) { this.addElement(span,"img",{ className:"MathJax_strut", border:0, src:"about:blank", isMathJax:true, @@ -796,7 +969,7 @@ span.style.left = this.Em(x+dx); // Clip so that bbox doesn't include extra height and depth if (bbox) { - if (this.negativeSkipBug) { + if (this.initialSkipBug) { if (bbox.lw < 0) {dx = bbox.lw; HTMLCSS.createBlank(span,-dx,true); l = 0} if (bbox.rw > bbox.w) {HTMLCSS.createBlank(span,bbox.rw-bbox.w+.1)} } @@ -833,7 +1006,7 @@ var bbox = span.bbox; if (bbox.isMultiline) return; var isRelative = bbox.width != null && !bbox.isFixed; var r = 0, c = -bbox.w/2, l = "50%"; - if (this.negativeSkipBug) {r = bbox.w-bbox.rw-.1; c += bbox.lw} + if (this.initialSkipBug) {r = bbox.w-bbox.rw-.1; c += bbox.lw} c = this.Em(c*this.msieMarginScale); if (isRelative) {c = ""; l = (50 - parseFloat(bbox.width)/2) + "%"} HUB.Insert(span.style,({ @@ -844,8 +1017,8 @@ setStackWidth: function (span,w) { if (typeof(w) === "number") { span.style.width = this.Em(Math.max(0,w)); - if (span.bbox) {span.bbox.w = w}; - if (span.parentNode.bbox) {span.parentNode.bbox.w = w} + var bbox = span.bbox; if (bbox) {bbox.w = w; bbox.exactW = true}; + bbox = span.parentNode.bbox; if (bbox) {bbox.w = w; bbox.exactW = true}; } else { span.style.width = span.parentNode.style.width = "100%"; if (span.bbox) {span.bbox.width = w} @@ -923,7 +1096,7 @@ w: Math.max(top.bbox.w,ext.bbox.w,bot.bbox.w,mid.bbox.w), lw: Math.min(top.bbox.lw,ext.bbox.lw,bot.bbox.lw,mid.bbox.lw), rw: Math.max(top.bbox.rw,ext.bbox.rw,bot.bbox.rw,mid.bbox.rw), - h: 0, d: -y + h: 0, d: -y, exactW: true } span.scale = scale; span.offset = .55 * span.bbox.w; @@ -966,7 +1139,7 @@ w: x+right.bbox.rw, lw: 0, rw: x+right.bbox.rw, H: Math.max(left.bbox.h,rep.bbox.h,right.bbox.h,mid.bbox.h), D: Math.max(left.bbox.d,rep.bbox.d,right.bbox.d,mid.bbox.d), - h: rep.bbox.h, d: rep.bbox.d + h: rep.bbox.h, d: rep.bbox.d, exactW: true } span.scale = scale; span.isMultiChar = true; @@ -1002,7 +1175,7 @@ positionDelimiter: function (span,h) { h -= span.bbox.h; span.bbox.d -= h; span.bbox.h += h; if (h) { - if (this.safariVerticalAlignBug || this.msieVerticalAlignBug || this.konquerorVerticalAlignBug || + if (this.safariVerticalAlignBug || this.konquerorVerticalAlignBug || (this.operaVerticalAlignBug && span.isMultiChar)) { if (span.firstChild.style.display === "" && span.style.top !== "") {span = span.firstChild; h -= parseFloat(span.style.top)} @@ -1294,7 +1467,7 @@ HTMLmultiline: function () {MML.mbase.HTMLautoloadFile("multiline")}, HTMLcomputeBBox: function (span,full,i,m) { if (i == null) {i = 0}; if (m == null) {m = this.data.length} - var BBOX = span.bbox = {}, stretchy = []; + var BBOX = span.bbox = {exactW: true}, stretchy = []; while (i < m) { var core = this.data[i]; if (!core) continue; if (!full && core.HTMLcanStretch("Vertical")) @@ -1319,6 +1492,7 @@ BBOX.w += bbox.w; if (child.style.paddingRight) {BBOX.w += parseFloat(child.style.paddingRight)*(child.scale||1)} if (bbox.width) {BBOX.width = bbox.width} + if (BBOX.exactW && !bbox.exactW) {delete BBOX.exactW} }, HTMLemptyBBox: function (BBOX) { BBOX.h = BBOX.d = BBOX.H = BBOX.D = BBOX.rw = -HTMLCSS.BIGDIMEN; @@ -1347,9 +1521,13 @@ }, HTMLmeasureChild: function (n,box) { - if (this.data[n] != null) {HTMLCSS.Measured(this.data[n].toHTML(box),box)} + if (this.data[n]) {HTMLCSS.Measured(this.data[n].toHTML(box),box)} else {box.bbox = this.HTMLzeroBBox()} }, + HTMLboxChild: function (n,box) { + if (this.data[n]) {return this.data[n].toHTML(box)} + return null; + }, HTMLcreateSpan: function (span) { if (this.spanID) { @@ -1746,10 +1924,11 @@ toHTML: function (span,HW,D) { span = this.HTMLcreateSpan(span); if (this.data[0] != null) { - var box = HTMLCSS.Measured(this.data[0].toHTML(span),span); + var box = this.data[0].toHTML(span); if (D != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchV(span,HW,D),span)} else if (HW != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchH(span,HW),span)} - span.bbox = {w: box.bbox.w, h: box.bbox.h, d: box.bbox.d, lw: 0, rw: 0}; + else {box = HTMLCSS.Measured(box,span)} + span.bbox = {w: box.bbox.w, h: box.bbox.h, d: box.bbox.d, lw: 0, rw: 0, exactW: true}; for (var i = 0, m = span.childNodes.length; i < m; i++) {span.childNodes[i].style.visibility = "hidden"} } @@ -1767,16 +1946,17 @@ if (this.data[0] != null) { var stack = HTMLCSS.createStack(span,true); var box = HTMLCSS.createBox(stack); - HTMLCSS.Measured(this.data[0].toHTML(box),box); + var child = this.data[0].toHTML(box); if (D != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchV(box,HW,D),box)} else if (HW != null) {HTMLCSS.Remeasured(this.data[0].HTMLstretchH(box,HW),box)} + else {HTMLCSS.Measured(child,box)} var values = this.getValues("height","depth","width","lspace","voffset"), x = 0, y = 0, mu = this.HTMLgetMu(span); if (values.lspace) {x = this.HTMLlength2em(box,values.lspace,mu)} if (values.voffset) {y = this.HTMLlength2em(box,values.voffset,mu)} HTMLCSS.placeBox(box,x,y); span.bbox = { - h: box.bbox.h, d: box.bbox.d, w: box.bbox.w, + h: box.bbox.h, d: box.bbox.d, w: box.bbox.w, exactW: true, lw: Math.min(0,box.bbox.lw+x), rw: Math.max(box.bbox.w,box.bbox.rw+x), H: Math.max((box.bbox.H == null ? -HTMLCSS.BIGDIMEN : box.bbox.H),box.bbox.h+y), D: Math.max((box.bbox.D == null ? -HTMLCSS.BIGDIMEN : box.bbox.D),box.bbox.d-y) @@ -1853,8 +2033,8 @@ span = this.HTMLcreateSpan(span); var frac = HTMLCSS.createStack(span); var num = HTMLCSS.createBox(frac), den = HTMLCSS.createBox(frac); - this.HTMLmeasureChild(0,num); this.HTMLmeasureChild(1,den); - var values = this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"); + HTMLCSS.MeasureSpans([this.HTMLboxChild(0,num),this.HTMLboxChild(1,den)]); + var values = this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"); var scale = this.HTMLgetScale(), isDisplay = values.displaystyle; var a = HTMLCSS.TeX.axis_height * scale; if (values.bevelled) { @@ -1908,14 +2088,15 @@ var base = HTMLCSS.createBox(sqrt), rule = HTMLCSS.createBox(sqrt), surd = HTMLCSS.createBox(sqrt); - this.HTMLmeasureChild(0,base); var scale = this.HTMLgetScale(); var t = HTMLCSS.TeX.rule_thickness * scale, p,q, H, W; if (this.Get("displaystyle")) {p = HTMLCSS.TeX.x_height * scale} else {p = t} q = Math.max(t + p/4,1.5*HTMLCSS.TeX.min_rule_thickness/this.em); // force to be at least 1px - H = base.bbox.h + base.bbox.d + q + t; - W = base.bbox.w; - HTMLCSS.createDelimiter(surd,0x221A,H,scale); HTMLCSS.Measured(surd); + var BASE = this.HTMLboxChild(0,base); + H = BASE.bbox.h + BASE.bbox.d + q + t; + HTMLCSS.createDelimiter(surd,0x221A,H,scale); + HTMLCSS.MeasureSpans([BASE,surd]); + W = BASE.bbox.w; var x = 0; if (surd.isMultiChar || (HTMLCSS.AdjustSurd && HTMLCSS.imgFonts)) {surd.bbox.w *= .95} if (surd.bbox.h + surd.bbox.d > H) {q = ((surd.bbox.h+surd.bbox.d) - (H-t))/2} @@ -1925,7 +2106,7 @@ } else { HTMLCSS.createDelimiter(rule,HTMLCSS.FONTDATA.RULECHAR,W,scale); } - H = base.bbox.h + q + t; + H = BASE.bbox.h + q + t; q = H*HTMLCSS.rfuzz; if (surd.isMultiChar) {q = HTMLCSS.rfuzz} x = this.HTMLaddRoot(sqrt,surd,x,surd.bbox.h+surd.bbox.d-H,scale); HTMLCSS.placeBox(surd,x,H-surd.bbox.h); @@ -2032,20 +2213,26 @@ {return MML.msubsup.prototype.toHTML.call(this,span)} span = this.HTMLcreateSpan(span); var scale = this.HTMLgetScale(); var stack = HTMLCSS.createStack(span); - var boxes = [], stretch = [], box, i, m, W = -HTMLCSS.BIGDIMEN, WW = W; + var boxes = [], children = [], stretch = [], box, i, m; for (i = 0, m = this.data.length; i < m; i++) { if (this.data[i] != null) { box = boxes[i] = HTMLCSS.createBox(stack); - HTMLCSS.Measured(this.data[i].toHTML(box),box); + children[i] = this.data[i].toHTML(box); if (i == this.base) { - if (D != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchV(box,HW,D),box)} - else if (HW != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchH(box,HW),box)} + if (D != null) {this.data[this.base].HTMLstretchV(box,HW,D)} + else if (HW != null) {this.data[this.base].HTMLstretchH(box,HW)} stretch[i] = (D == null && HW != null ? false : this.data[i].HTMLcanStretch("Horizontal")); } else { stretch[i] = this.data[i].HTMLcanStretch("Horizontal"); } - if (box.bbox.w > WW) {WW = box.bbox.w} + } + } + HTMLCSS.MeasureSpans(children); + var W = -HTMLCSS.BIGDIMEN, WW = W; + for (i = 0, m = this.data.length; i < m; i++) { + if (this.data[i]) { + if (boxes[i].bbox.w > WW) {WW = boxes[i].bbox.w} if (!stretch[i] && WW > W) {W = WW} } } @@ -2110,28 +2297,25 @@ toHTML: function (span,HW,D) { span = this.HTMLcreateSpan(span); var scale = this.HTMLgetScale(), mu = this.HTMLgetMu(span); - var stack = HTMLCSS.createStack(span), values; + var stack = HTMLCSS.createStack(span), values, children = []; var base = HTMLCSS.createBox(stack); - this.HTMLmeasureChild(this.base,base); if (this.data[this.base]) { - if (D != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchV(base,HW,D),base)} - else if (HW != null) {HTMLCSS.Remeasured(this.data[this.base].HTMLstretchH(base,HW),base)} - } - HTMLCSS.placeBox(base,0,0); + children.push(this.data[this.base].toHTML(base)); + if (D != null) {this.data[this.base].HTMLstretchV(base,HW,D)} + else if (HW != null) {this.data[this.base].HTMLstretchH(base,HW)} + } else {base.bbox = this.HTMLzeroBBox()} var sscale = (this.data[this.sup] || this.data[this.sub] || this).HTMLgetScale(); var x_height = HTMLCSS.TeX.x_height * scale, s = HTMLCSS.TeX.scriptspace * scale * .75; // FIXME: .75 can be removed when IC is right? var sup, sub; - if (this.HTMLnotEmpty(this.data[this.sup])) { - sup = HTMLCSS.createBox(stack); - HTMLCSS.Measured(this.data[this.sup].toHTML(sup),sup); - sup.bbox.w += s; sup.bbox.rw = Math.max(sup.bbox.w,sup.bbox.rw); - } - if (this.HTMLnotEmpty(this.data[this.sub])) { - sub = HTMLCSS.createBox(stack); - HTMLCSS.Measured(this.data[this.sub].toHTML(sub),sub); - sub.bbox.w += s; sub.bbox.rw = Math.max(sub.bbox.w,sub.bbox.rw); - } + if (this.HTMLnotEmpty(this.data[this.sup])) + {sup = HTMLCSS.createBox(stack); children.push(this.data[this.sup].toHTML(sup))} + if (this.HTMLnotEmpty(this.data[this.sub])) + {sub = HTMLCSS.createBox(stack); children.push(this.data[this.sub].toHTML(sub))} + HTMLCSS.MeasureSpans(children); + if (sup) {sup.bbox.w += s; sup.bbox.rw = Math.max(sup.bbox.w,sup.bbox.rw)} + if (sub) {sub.bbox.w += s; sub.bbox.rw = Math.max(sub.bbox.w,sub.bbox.rw)} + HTMLCSS.placeBox(base,0,0); var q = HTMLCSS.TeX.sup_drop * sscale, r = HTMLCSS.TeX.sub_drop * sscale; var u = base.bbox.h - q, v = base.bbox.d + r, delta = 0, p; if (base.bbox.ic) {delta = base.bbox.ic} @@ -2279,35 +2463,38 @@ // HUB.Browser.Select({ MSIE: function (browser) { + var mode = (document.documentMode || 0); var isIE7 = browser.versionAtLeast("7.0"); - var isIE8 = browser.versionAtLeast("8.0") && document.documentMode > 7; + var isIE8 = browser.versionAtLeast("8.0") && mode > 7; var quirks = (document.compatMode === "BackCompat"); - // IE doesn't do mouse events on trasparent objects, - // so give a background color, but opacity makes it transparent - HTMLCSS.config.styles[".MathJax .MathJax_HitBox"]["background-color"] = "white"; - HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].opacity = 0 - HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].filter = "alpha(opacity=0)"; + if (mode < 9) { + // IE doesn't do mouse events on trasparent objects, + // so give a background color, but opacity makes it transparent + HTMLCSS.config.styles[".MathJax .MathJax_HitBox"]["background-color"] = "white"; + HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].opacity = 0 + HTMLCSS.config.styles[".MathJax .MathJax_HitBox"].filter = "alpha(opacity=0)"; + } // FIXME: work out tests for these? HTMLCSS.Augment({ - getMarginScale: HTMLCSS.getMSIEmarginScale, PaddingWidthBug: true, msieAccentBug: true, msieColorBug: true, msieColorPositionBug: true, // needs position:relative to put color behind text msieRelativeWidthBug: quirks, - msieMarginWidthBug: true, + msieDisappearingBug: (mode >= 8), // inline math disappears + msieMarginScaleBug: (mode < 8), // margins are not scaled properly by font-size msiePaddingWidthBug: true, msieBorderWidthBug: quirks, msieInlineBlockAlignBug: (!isIE8 || quirks), - msieVerticalAlignBug: (isIE8 && !quirks), msiePlaceBoxBug: (isIE8 && !quirks), msieClipRectBug: !isIE8, msieNegativeSpaceBug: quirks, msieCloneNodeBug: (isIE8 && browser.version === "8.0"), - negativeSkipBug: true, + initialSkipBug: (mode < 8), // confused by initial left-margin values + msieNegativeBBoxBug: (mode >= 8), // negative bboxes have positive widths msieIE6: !isIE7, msieItalicWidthBug: true, - zeroWidthBug: true, + zeroWidthBug: (mode < 8), FontFaceBug: true, msieFontCSSBug: browser.isIE9, allowWebFonts: "eot" @@ -2322,7 +2509,6 @@ (HUB.config.root+"/").substr(0,root.length) === root) {webFonts = "otf"} } HTMLCSS.Augment({ - useProcessingFrame: true, ffVerticalAlignBug: true, AccentBug: true, allowWebFonts: webFonts @@ -2346,10 +2532,10 @@ } } }, - useProcessingFrame: true, rfuzz: .011, AccentBug: true, AdjustSurd: true, + negativeBBoxes: true, safariNegativeSpaceBug: true, safariVerticalAlignBug: !v3p1, safariTextNodeBug: !v3p0, @@ -2363,7 +2549,6 @@ } if (forceImages) { // Force image mode for iOS prior to 4.2 and Droid prior to 2.2 - // (iPhone should do SVG web fonts, but crashes with MathJax) var config = HUB.config["HTML-CSS"]; if (config) {config.availableFonts = []; config.preferredFont = null} else {HUB.config["HTML-CSS"] = {availableFonts: [], preferredFont: null}} @@ -2372,10 +2557,10 @@ Chrome: function (browser) { HTMLCSS.Augment({ - useProcessingFrame: true, rfuzz: .011, AccentBug: true, AdjustSurd: true, + negativeBBoxes: true, allowWebFonts: (browser.versionAtLeast("4.0") ? "otf" : "svg"), safariNegativeSpaceBug: true, safariWebFontSerif: [""] @@ -2386,11 +2571,10 @@ browser.isMini = (navigator.appVersion.match("Opera Mini") != null); HTMLCSS.config.styles[".MathJax .merror"]["vertical-align"] = null; HTMLCSS.Augment({ - useProcessingFrame: true, operaHeightBug: true, operaVerticalAlignBug: true, operaFontSizeBug: browser.versionAtLeast("10.61"), - negativeSkipBug: true, + initialSkipBug: true, zeroWidthBug: true, FontFaceBug: true, PaddingWidthBug: true,