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AM_HTMLorMML-full.js

AM_HTMLorMML-full.js 213 KB
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  1. /*
    2. 

  2.  *  /MathJax/config/AM_HTMLorMML-full.js
    3. 

  3.  *  
    4. 

  4.  *  Copyright (c) 2010-2013 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Part of the MathJax library.
    7. 

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

  8.  * 
    9. 

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

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

  11.  *
    12. 

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

  13.  */MathJax.Hub.Config({delayJaxRegistration:!0});MathJax.Ajax.Preloading("[MathJax]/jax/input/AsciiMath/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/jax/output/NativeMML/config.js","[MathJax]/config/MMLorHTML.js","[MathJax]/extensions/asciimath2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/jax/input/AsciiMath/jax.js","[MathJax]/jax/output/NativeMML/jax.js","[MathJax]/jax/output/HTML-CSS/jax.js","[MathJax]/jax/output/HTML-CSS/autoload/mtable.js");MathJax.Hub.Config({"v1.0-compatible":!1});MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.2",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{displaystyle:!0,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js");MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.2",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",mtextFontInherit:!1,EqnChunk:MathJax.Hub.Browser.isMobile?10:50,EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:!1,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},"#MathJax_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\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'true')",padding:"3px 4px","z-index":401}}}});MathJax.Hub.Browser.isMSIE&&9<=document.documentMode&&delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter;MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax["HTML-CSS"].Register("jax/mml");MathJax.Hub.Register.StartupHook("End Config",[function(c,g){var b=c.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(k){var g=c.getJaxFor(k),l=["[Math]"],m=document.createElement("span",{className:"MathJax_Preview"});"TeX"===g.inputJax&&(g.root.Get("displaystyle")?(l=b.displayMathDelimiters,l=[l[0]+g.originalText+l[1]],b.multilineDisplay&&(l=l[0].split(/\n/))):(l=b.inlineMathDelimiters,l=[l[0]+g.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+l[1]]));for(var g=0,t=l.length;g<t;g++)m.appendChild(document.createTextNode(l[g])),g<t-1&&m.appendChild(document.createElement("br"));k.parentNode.insertBefore(m,k)}},c.config["HTML-CSS"]||{});"0.0"===c.Browser.version||c.Browser.versionAtLeast(b.minBrowserVersion[c.Browser]||0)||(g.Translate=b.minBrowserTranslate,c.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),c.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:"2.2",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,minScaleAdjust:50,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.NativeMML.Register("jax/mml");MathJax.OutputJax.NativeMML.loadComplete("config.js");(function(c,g){var b=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}}),k={Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},n="0.0"===g.version||g.versionAtLeast(k[g]||0),l=g.isFirefox&&g.versionAtLeast("1.5")||g.isMSIE&&g.hasMathPlayer||g.isSafari&&g.versionAtLeast("5.0")||g.isOpera&&g.versionAtLeast("9.52");c.Register.StartupHook("End Config",function(){var k=b.prefer&&"object"===typeof b.prefer?b.prefer[MathJax.Hub.Browser]||b.prefer.other||"HTML":b.prefer;n||l?!l||"MML"!==k&&n?(MathJax.OutputJax["HTML-CSS"]?MathJax.OutputJax["HTML-CSS"].Register("jax/mml"):c.config.jax.unshift("output/HTML-CSS"),c.Startup.signal.Post("HTML-CSS output selected")):(MathJax.OutputJax.NativeMML?MathJax.OutputJax.NativeMML.Register("jax/mml"):c.config.jax.unshift("output/NativeMML"),c.Startup.signal.Post("NativeMML output selected")):(c.PreProcess.disabled=!0,c.prepareScripts.disabled=!0,MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),c.Startup.signal.Post("MathJax not supported"))})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");MathJax.Extension.asciimath2jax={version:"2.2",config:{delimiters:[["`","`"]],skipTags:"script noscript style textarea pre code".split(" "),ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},PreProcess:function(c){this.configured||(this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.configured=!0);"string"===typeof c&&(c=document.getElementById(c));c||(c=document.body);this.createPatterns()&&this.scanElement(c,c.nextSibling)},createPatterns:function(){var c=[],g,b,k=this.config;this.match={};if(0===k.delimiters.length)return!1;g=0;for(b=k.delimiters.length;g<b;g++)c.push(this.patternQuote(k.delimiters[g][0])),this.match[k.delimiters[g][0]]={mode:"",end:k.delimiters[g][1],pattern:this.endPattern(k.delimiters[g][1])};this.start=new RegExp(c.sort(this.sortLength).join("|"),"g");this.skipTags=new RegExp("^("+k.skipTags.join("|")+")$","i");c=[];MathJax.Hub.config.preRemoveClass&&c.push(MathJax.Hub.config.preRemoveClass);k.ignoreClass&&c.push(k.ignoreClass);this.ignoreClass=c.length?new RegExp("(^| )("+c.join("|")+")( |$)"):/^$/;this.processClass=new RegExp("(^| )("+k.processClass+")( |$)");return!0},patternQuote:function(c){return c.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(c){return new RegExp(this.patternQuote(c)+"|\\\\.","g")},sortLength:function(c,g){return c.length!==g.length?g.length-c.length:c==g?0:c<g?-1:1},scanElement:function(c,g,b){for(var k,n,l;c&&c!=g;)"#text"===c.nodeName.toLowerCase()?b||(c=this.scanText(c)):(k="undefined"===typeof c.className?"":c.className,n="undefined"===typeof c.tagName?"":c.tagName,"string"!==typeof k&&(k=String(k)),l=this.processClass.exec(k),!c.firstChild||k.match(/(^| )MathJax/)||!l&&this.skipTags.exec(n)||(k=(b||this.ignoreClass.exec(k))&&!l,this.scanElement(c.firstChild,g,k))),c&&(c=c.nextSibling)},scanText:function(c){if(""==c.nodeValue.replace(/\s+/,""))return c;var g,b;this.search={start:!0};for(this.pattern=this.start;c;){for(this.pattern.lastIndex=0;c&&"#text"===c.nodeName.toLowerCase()&&(g=this.pattern.exec(c.nodeValue));)c=this.search.start?this.startMatch(g,c):this.endMatch(g,c);this.search.matched&&(c=this.encloseMath(c));if(c){do b=c,c=c.nextSibling;while(c&&("br"===c.nodeName.toLowerCase()||"#comment"===c.nodeName.toLowerCase()));if(!c||"#text"!==c.nodeName)return b}}return c},startMatch:function(c,g){var b=this.match[c[0]];null!=b&&(this.search={end:b.end,mode:b.mode,open:g,olen:c[0].length,opos:this.pattern.lastIndex-c[0].length},this.switchPattern(b.pattern));return g},endMatch:function(c,g){c[0]==this.search.end&&(this.search.close=g,this.search.cpos=this.pattern.lastIndex,this.search.clen=this.search.isBeginEnd?0:c[0].length,this.search.matched=!0,g=this.encloseMath(g),this.switchPattern(this.start));return g},switchPattern:function(c){c.lastIndex=this.pattern.lastIndex;this.pattern=c;this.search.start=c===this.start},encloseMath:function(c){c=this.search;var g=c.close,b,k;(g=c.cpos===g.length?g.nextSibling:g.splitText(c.cpos))||(b=g=MathJax.HTML.addText(c.close.parentNode,""));c.close=g;for(k=c.opos?c.open.splitText(c.opos):c.open;k.nextSibling&&k.nextSibling!==g;)k.nodeValue=null!==k.nextSibling.nodeValue?"#comment"===k.nextSibling.nodeName?k.nodeValue+k.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):k.nodeValue+k.nextSibling.nodeValue:this.msieNewlineBug?k.nodeValue+("br"===k.nextSibling.nodeName.toLowerCase()?"\n":" "):k.nodeValue+" ",k.parentNode.removeChild(k.nextSibling);g=k.nodeValue.substr(c.olen,k.nodeValue.length-c.olen-c.clen);k.parentNode.removeChild(k);"none"!==this.config.preview&&this.createPreview(c.mode,g);k=this.createMathTag(c.mode,g);this.search={};this.pattern.lastIndex=0;b&&b.parentNode.removeChild(b);return k},insertNode:function(c){var g=this.search;g.close.parentNode.insertBefore(c,g.close)},createPreview:function(c,g){var b=this.config.preview;"none"!==b&&("AsciiMath"===b&&(b=[this.filterPreview(g)]),b&&(b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b),this.insertNode(b)))},createMathTag:function(c,g){var b=document.createElement("script");b.type="math/asciimath"+c;MathJax.HTML.setScript(b,g);this.insertNode(b);return b},filterPreview:function(c){return c},msieNewlineBug:MathJax.Hub.Browser.isMSIE&&9>(document.documentMode||0)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.asciimath2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/asciimath2jax.js");(function(c,g,b,k,n,l,m){var t=MathJax.Extension,p=t.MathEvents={version:"2.2"},a=c.config.menuSettings,h={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:b.fileURL(l.imageDir+"/MenuArrow-15.png")},fadeinInc:.2,fadeoutInc:.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15E3,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}},d=p.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(a){return d.Handler(a,"Mousedown",this)},Mouseup:function(a){return d.Handler(a,"Mouseup",this)},Mousemove:function(a){return d.Handler(a,"Mousemove",this)},Mouseover:function(a){return d.Handler(a,"Mouseover",this)},Mouseout:function(a){return d.Handler(a,"Mouseout",this)},Click:function(a){return d.Handler(a,"Click",this)},DblClick:function(a){return d.Handler(a,"DblClick",this)},Menu:function(a){return d.Handler(a,"ContextMenu",this)},Handler:function(a,h,f){if(b.loadingMathMenu)return d.False(a);var e=l[f.jaxID];a||(a=window.event);a.isContextMenu="ContextMenu"===h;if(e[h])return e[h](a,f);if(t.MathZoom)return t.MathZoom.HandleEvent(a,h,f)},False:function(a){a||(a=window.event);a&&(a.preventDefault&&a.preventDefault(),a.stopPropagation&&a.stopPropagation(),a.cancelBubble=!0,a.returnValue=!1);return!1},ContextMenu:function(h,f,e){var r=l[f.jaxID],g=r.getJaxFromMath(f);if((null!=r.config.showMathMenu?r:c).config.showMathMenu&&("MathJax"===a.context||e)){p.msieEventBug&&(h=window.event||h);d.ClearSelection();u.ClearHoverTimer();g.hover&&(g.hover.remove&&(clearTimeout(g.hover.remove),delete g.hover.remove),g.hover.nofade=!0);var w=MathJax.Menu;if(w){if(w.loadingDomain)return d.False(h);r=n.loadDomain("MathMenu");if(!r)return w.jax=g,f=w.menu.Find("Show Math As").menu,f.items[0].name=g.sourceMenuTitle,f.items[0].format=g.sourceMenuFormat||"MathML",f.items[1].name=m[g.inputJax].sourceMenuTitle,w.menu.Find("Math Settings","MathPlayer").hidden=!("NativeMML"===g.outputJax&&c.Browser.hasMathPlayer),w.menu.Post(h);w.loadingDomain=!0;g=function(){delete w.loadingDomain}}else{if(b.loadingMathMenu)return d.False(h);b.loadingMathMenu=!0;r=b.Require("[MathJax]/extensions/MathMenu.js");g=function(){delete b.loadingMathMenu;MathJax.Menu||(MathJax.Menu={})}}k.Queue(r,g,["ContextMenu",d,{pageX:h.pageX,pageY:h.pageY,clientX:h.clientX,clientY:h.clientY},f,e]);return d.False(h)}},AltContextMenu:function(h,f){var e=l[f.jaxID],b=(null!=e.config.showMathMenu?e:c).config.showMathMenu;if(b){b=(null!=e.config.showMathMenuMSIE?e:c).config.showMathMenuMSIE;if("MathJax"===a.context&&!a.mpContext&&b){if(!p.noContextMenuBug||h.button!==d.RIGHTBUTTON)return}else if(!h[d.MENUKEY]||h.button!==d.LEFTBUTTON)return;return e.ContextMenu(h,f,!0)}},ClearSelection:function(){p.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0);document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(a){a.appendChild(p.topImg);var h=p.topImg.offsetTop,d=a.offsetHeight-h,f=a.offsetWidth;a.removeChild(p.topImg);return{w:f,h:h,d:d}}},u=p.Hover={Mouseover:function(h,f){if(a.discoverable||"Hover"===a.zoom){var e=h.fromElement||h.relatedTarget,b=h.toElement||h.target;if(e&&b&&(e.isMathJax!=b.isMathJax||c.getJaxFor(e)!==c.getJaxFor(b)))return e=this.getJaxFromMath(f),e.hover?u.ReHover(e):u.HoverTimer(e,f),d.False(h)}},Mouseout:function(h,f){if(a.discoverable||"Hover"===a.zoom){var e=h.fromElement||h.relatedTarget,b=h.toElement||h.target;if(e&&b&&(e.isMathJax!=b.isMathJax||c.getJaxFor(e)!==c.getJaxFor(b)))return e=this.getJaxFromMath(f),e.hover?u.UnHover(e):u.ClearHoverTimer(),d.False(h)}},Mousemove:function(h,f){if(a.discoverable||"Hover"===a.zoom){var e=this.getJaxFromMath(f);if(!e.hover&&(u.lastX!=h.clientX||u.lastY!=h.clientY))return u.lastX=h.clientX,u.lastY=h.clientY,u.HoverTimer(e,f),d.False(h)}},HoverTimer:function(a,d){this.ClearHoverTimer();this.hoverTimer=setTimeout(k(["Hover",this,a,d]),h.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(a,d){if(!t.MathZoom||!t.MathZoom.Hover({},d)){var f=l[a.outputJax],e=f.getHoverSpan(a,d),b=f.getHoverBBox(a,e,d),u=(null!=f.config.showMathMenu?f:c).config.showMathMenu,k=h.frame.x,n=h.frame.y,m=h.frame.bwidth;p.msieBorderWidthBug&&(m=0);a.hover={opacity:0,id:a.inputID+"-Hover"};var z=g.Element("span",{id:a.hover.id,isMathJax:!0,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:!0,style:{display:"inline-block",position:"absolute",top:this.Px(-b.h-n-m-(b.y||0)),left:this.Px(-k-m+(b.x||0)),width:this.Px(b.w+2*k),height:this.Px(b.h+b.d+2*n),opacity:0,filter:"alpha(opacity\x3d0)"}}]]),f=g.Element("span",{isMathJax:!0,id:a.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:!0,math:d,src:h.button.src,onclick:this.HoverMenu,jax:f.id,style:{left:this.Px(b.w+k+m+(b.x||0)+h.button.x),top:this.Px(-b.h-n-m-(b.y||0)-h.button.y),opacity:0,filter:"alpha(opacity\x3d0)"}}]]);b.width&&(z.style.width=f.style.width=b.width,z.style.marginRight=f.style.marginRight="-"+b.width,z.firstChild.style.width=b.width,f.firstChild.style.left="",f.firstChild.style.right=this.Px(h.button.wx));e.parentNode.insertBefore(z,e);u&&e.parentNode.insertBefore(f,e);e.style&&(e.style.position="relative");this.ReHover(a)}},ReHover:function(a){a.hover.remove&&clearTimeout(a.hover.remove);a.hover.remove=setTimeout(k(["UnHover",this,a]),h.fadeoutDelay);this.HoverFadeTimer(a,h.fadeinInc)},UnHover:function(a){a.hover.nofade||this.HoverFadeTimer(a,-h.fadeoutInc,h.fadeoutStart)},HoverFade:function(a){delete a.hover.timer;a.hover.opacity=Math.max(0,Math.min(1,a.hover.opacity+a.hover.inc));a.hover.opacity=Math.floor(1E3*a.hover.opacity)/1E3;var h=document.getElementById(a.hover.id),d=document.getElementById(a.hover.id+"Menu");h.firstChild.style.opacity=a.hover.opacity;h.firstChild.style.filter="alpha(opacity\x3d"+Math.floor(100*a.hover.opacity)+")";d&&(d.firstChild.style.opacity=a.hover.opacity,d.firstChild.style.filter=h.style.filter);1!==a.hover.opacity&&(0<a.hover.opacity?this.HoverFadeTimer(a,a.hover.inc):(h.parentNode.removeChild(h),d&&d.parentNode.removeChild(d),a.hover.remove&&clearTimeout(a.hover.remove),delete a.hover))},HoverFadeTimer:function(a,d,f){a.hover.inc=d;a.hover.timer||(a.hover.timer=setTimeout(k(["HoverFade",this,a]),f||h.fadeDelay))},HoverMenu:function(a){a||(a=window.event);return l[this.jax].ContextMenu(a,this.math,!0)},ClearHover:function(a){a.hover.remove&&clearTimeout(a.hover.remove);a.hover.timer&&clearTimeout(a.hover.timer);u.ClearHoverTimer();delete a.hover},Px:function(a){return.006>Math.abs(a)?"0px":a.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){(new Image).src=h.button.src}},e=p.Touch={last:0,delay:500,start:function(a){var h=(new Date).getTime(),d=h-e.last<e.delay&&e.up;e.last=h;e.up=!1;d&&(e.timeout=setTimeout(e.menu,e.delay,a,this),a.preventDefault())},end:function(a){var h=(new Date).getTime();e.up=h-e.last<e.delay;if(e.timeout)return clearTimeout(e.timeout),delete e.timeout,e.last=0,e.up=!1,a.preventDefault(),d.Handler(a.touches[0]||a.touch,"DblClick",this)},menu:function(a,h){delete e.timeout;e.last=0;e.up=!1;return d.Handler(a.touches[0]||a.touch,"ContextMenu",h)}};if(c.Browser.isMobile){var f=h.styles[".MathJax_Hover_Arrow"];f.width="25px";f.height="18px";h.button.x=-6}c.Browser.Select({MSIE:function(a){var h=document.documentMode||0,f=a.versionAtLeast("8.0");p.msieBorderWidthBug="BackCompat"===document.compatMode;p.msieEventBug=a.isIE9;p.msieAlignBug=!f||8>h;9>h&&(d.LEFTBUTTON=1)},Safari:function(a){p.safariContextMenuBug=!0},Opera:function(a){p.operaPositionBug=!0},Konqueror:function(a){p.noContextMenuBug=!0}});p.topImg=p.msieAlignBug?g.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):g.Element("span",{style:{width:0,height:0,display:"inline-block"}});p.operaPositionBug&&(p.topImg.style.border="1px solid");p.config=h=c.CombineConfig("MathEvents",h);k.Queue(c.Register.StartupHook("End Config",{}),[function(){var a=h.styles[".MathJax_Hover_Frame"];a.border=h.frame.bwidth+"px solid "+h.frame.bcolor+" ! important";a["box-shadow"]=a["-webkit-box-shadow"]=a["-moz-box-shadow"]=a["-khtml-box-shadow"]="0px 0px "+h.frame.hwidth+" "+h.frame.hcolor}],["getImages",u],["Styles",b,h.styles],["Post",c.Startup.signal,"MathEvents 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a.settings.CTRL&&!h.ctrlKey||a.settings.ALT&&!h.altKey||a.settings.CMD&&!h.metaKey||a.settings.Shift&&!h.shiftKey||!a[d]?!0:a[d](h,b)},Click:function(a,d){if("Click"===this.settings.zoom)return this.Zoom(a,d)},DblClick:function(a,d){if("Double-Click"===this.settings.zoom)return this.Zoom(a,d)},Hover:function(a,d){return"Hover"===this.settings.zoom?(this.Zoom(a,d),!0):!1},Zoom:function(a,d){this.Remove();t.ClearHoverTimer();p.ClearSelection();var b=MathJax.OutputJax[d.jaxID],e=b.getJaxFromMath(d);e.hover&&t.UnHover(e);var f=Math.floor(.85*document.body.clientWidth),k=Math.floor(.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight)),y=g.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":f+"px","max-height":k+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),v=y.lastChild,r=v.firstChild,n=y.firstChild;d.parentNode.insertBefore(y,d);d.parentNode.insertBefore(d,y);r.addEventListener&&r.addEventListener("mousedown",this.Remove,!0);if(this.msieTrapEventBug){var w=g.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});y.insertBefore(w,v)}this.msieZIndexBug&&(g.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}}),y.style.position="relative",y.style.zIndex=l.styles["#MathJax_ZoomOverlay"]["z-index"]);b=b.Zoom(e,r,d,f,k);this.msiePositionBug&&(this.msieSizeBug&&(v.style.height=b.zH+"px",v.style.width=b.zW+"px"),v.offsetHeight>k&&(v.style.height=k+"px",v.style.width=b.zW+this.scrollSize+"px"),v.offsetWidth>f&&(v.style.width=f+"px",v.style.height=b.zH+this.scrollSize+"px"));this.operaPositionBug&&(v.style.width=Math.min(f,b.zW)+"px");v.offsetWidth&&v.offsetWidth<f&&v.offsetHeight<k&&(v.style.overflow="visible");this.Position(v,b);this.msieTrapEventBug&&(w.style.height=v.clientHeight+"px",w.style.width=v.clientWidth+"px",w.style.left=parseFloat(v.style.left)+v.clientLeft+"px",w.style.top=parseFloat(v.style.top)+v.clientTop+"px");v.style.visibility="";"Hover"===this.settings.zoom&&(n.onmouseover=this.Remove);window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize);c.signal.Post(["math 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d=a.scroll_parent||document.documentElement||document.body;a.style.width=d.scrollWidth+"px";a.style.height=Math.max(d.clientHeight,d.scrollHeight)+"px"},getOverflow:window.getComputedStyle?function(a){return getComputedStyle(a).overflow}:function(a){return(a.currentStyle||{overflow:"visible"}).overflow},getBorder:function(a){var d={thin:1,medium:2,thick:3},b=window.getComputedStyle?getComputedStyle(a):a.currentStyle||{borderLeftWidth:0,borderTopWidth:0};a=b.borderLeftWidth;b=b.borderTopWidth;a=d[a]?d[a]:parseInt(a);b=d[b]?d[b]:parseInt(b);return{x:a,y:b}},getXY:function(h){var d=0,b=0,e;for(e=h;e.offsetParent;)d+=e.offsetLeft,e=e.offsetParent;a.operaPositionBug&&(h.style.border="1px solid");for(e=h;e.offsetParent;)b+=e.offsetTop,e=e.offsetParent;a.operaPositionBug&&(h.style.border="");return{x:d,y:b}},Remove:function(h){var d=document.getElementById("MathJax_ZoomFrame");if(d){var b=MathJax.OutputJax[d.previousSibling.jaxID].getJaxFromMath(d.previousSibling);c.signal.Post(["math 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d=document.getElementById("MathJax_MenuFrame").childNodes,e=h.parentNode.childNodes,b=0,c=e.length;b<c;b++){var k=e[b].menuItem;k&&k.menu&&k.menu.posted&&k.Deactivate(e[b])}for(c=d.length-1;0<=c&&h.parentNode.menuItem!==d[c].menuItem;)d[c].menuItem.posted=!1,d[c].parentNode.removeChild(d[c]),c--;this.Timer&&!f.isMobile&&this.Timer(a,h)}},Mouseout:function(a,h){this.menu&&this.menu.posted||this.Deactivate(h);this.timer&&(clearTimeout(this.timer),delete this.timer)},Mouseup:function(a,h){return this.Remove(a,h)},Touchstart:function(a,h){return this.TouchEvent(a,h,"Mousedown")},Touchend:function(a,h){return this.TouchEvent(a,h,"Mouseup")},TouchEvent:function(a,h,d){this!==q.lastItem&&(q.lastMenu&&f.Event(a,q.lastMenu,"Mouseout"),f.Event(a,h,"Mouseover",!0),q.lastItem=this,q.lastMenu=h);if(this.nativeTouch)return null;f.Event(a,h,d);return!1},Remove:function(a,h){h=h.parentNode.menuItem;return h.Remove(a,h)},Activate:function(a){this.Deactivate(a);a.className+=" MathJax_MenuActive"},Deactivate:function(a){a.className=a.className.replace(/ MathJax_MenuActive/,"")},With:function(a){a&&c.Insert(this,a);return this}});f.ITEM.COMMAND=f.ITEM.Subclass({action:function(){},Init:function(a,h,d){a instanceof Array||(a=[a,a]);this.name=a;this.action=h;this.With(d)},Label:function(a,h){return[this.Name()]},Mouseup:function(a,h){this.disabled||(this.Remove(a,h),l.Post(["command",this]),this.action.call(this,a));return u(a)}});f.ITEM.SUBMENU=f.ITEM.Subclass({menu:null,marker:t&&!c.Browser.isSafari?"\u25b6":"\u25b8",Init:function(a,h){a instanceof Array||(a=[a,a]);this.name=a;var d=1;h instanceof f.ITEM||(this.With(h),d++);this.menu=f.apply(f,[].slice.call(arguments,d))},Label:function(a,h){this.menu.posted=!1;return[this.Name()+" 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f={className:"MathJax_MenuRadioCheck"};d.settings[this.variable]!==this.value&&(f={style:{display:"none"}});return[["span",f,[this.marker]]," "+this.Name()]},Mouseup:function(a,h){if(!this.disabled){for(var e=h.parentNode.childNodes,b=0,c=e.length;b<c;b++){var k=e[b].menuItem;k&&k.variable===this.variable&&(e[b].firstChild.style.display="none")}h.firstChild.display="";d.settings[this.variable]=this.value;f.cookie[this.variable]=d.settings[this.variable];f.saveCookie();l.Post(["radio button",this])}this.Remove(a,h);this.action&&!this.disabled&&this.action.call(f,this);return u(a)}});f.ITEM.CHECKBOX=f.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(a,h,d){a instanceof Array||(a=[a,a]);this.name=a;this.variable=h;this.With(d)},Label:function(a,h){var f={className:"MathJax_MenuCheck"};d.settings[this.variable]||(f={style:{display:"none"}});return[["span",f,[this.marker]]," "+this.Name()]},Mouseup:function(a,h){this.disabled||(h.firstChild.display=d.settings[this.variable]?"none":"",d.settings[this.variable]=!d.settings[this.variable],f.cookie[this.variable]=d.settings[this.variable],f.saveCookie(),l.Post(["checkbox",this]));this.Remove(a,h);this.action&&!this.disabled&&this.action.call(f,this);return u(a)}});f.ITEM.LABEL=f.ITEM.Subclass({Init:function(a,h){a instanceof Array||(a=[a,a]);this.name=a;this.With(h)},Label:function(a,h){delete a.onmouseover;delete a.onmouseout;delete a.onmousedown;a.className+=" MathJax_MenuLabel";return[this.Name()]}});f.ITEM.RULE=f.ITEM.Subclass({Label:function(a,h){delete a.onmouseover;delete a.onmouseout;delete a.onmousedown;a.className+=" MathJax_MenuRule";return null}});f.About=function(){var a=n["HTML-CSS"]||{},h=(a.imgFonts?"image":a.fontInUse?(a.webFonts?"web":"local")+" "+a.fontInUse:n.SVG?"web SVG":"generic")+" fonts",a=!a.webFonts||a.imgFonts?null:a.allowWebFonts.replace(/otf/,"woff or otf")+" fonts",e=["MathJax.js v"+MathJax.fileversion,["br"]];e.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);f.About.GetJax(e,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);f.About.GetJax(e,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);f.About.GetJax(e,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);e.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);f.About.GetJax(e,MathJax.Extension,["Extension","%1 Extension v%2"],!0);e.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(a?" \u2014 "+m(a.replace(/ /g,""),a):"")]]);f.About.div=f.Background(f.About);h=g.addElement(f.About.div,"div",{id:"MathJax_About"},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],m(h.replace(/ /g,""),"using "+h),["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},e],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["img",{src:d.closeImg,style:{width:"21px",height:"21px",position:"absolute",top:".2em",right:".2em"},onclick:f.About.Remove}]]);MathJax.Localization.setCSS(h);a=document.documentElement||{};a=window.innerHeight||a.clientHeight||a.scrollHeight||0;f.prototype.msieAboutBug?(h.style.width="20em",h.style.position="absolute",h.style.left=Math.floor((document.documentElement.scrollWidth-h.offsetWidth)/2)+"px",h.style.top=Math.floor((a-h.offsetHeight)/3)+document.body.scrollTop+"px"):(h.style.marginLeft=Math.floor(-h.offsetWidth/2)+"px",h.style.top=Math.floor((a-h.offsetHeight)/3)+"px")};f.About.Remove=function(a){f.About.div&&(document.body.removeChild(f.About.div),delete f.About.div)};f.About.GetJax=function(a,h,d,f){var e=[],b;for(b in h)h.hasOwnProperty(b)&&h[b]&&(f&&h[b].version||h[b].isa&&h[b].isa(h))&&e.push(m(d[0],d[1],h[b].id||b,h[b].version));e.sort();h=0;for(d=e.length;h<d;h++)a.push(e[h],["br"]);return a};f.Help=function(){b.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog()})};f.ShowSource=function(a){a||(a=window.event);var h={screenX:a.screenX,screenY:a.screenY};if(f.jax)if("MathML"===this.format){var d=MathJax.ElementJax.mml;if(d&&"undefined"!==typeof d.mbase.prototype.toMathML)try{f.ShowSource.Text(f.jax.root.toMathML(),a)}catch(e){if(!e.restart)throw e;k.After([this,f.ShowSource,h],e.restart)}else b.loadingToMathML||(b.loadingToMathML=!0,f.ShowSource.Window(a),k.Queue(b.Require("[MathJax]/extensions/toMathML.js"),function(){delete b.loadingToMathML;d.mbase.prototype.toMathML||(d.mbase.prototype.toMathML=function(){})},[this,f.ShowSource,h]))}else"Error"===this.format?f.ShowSource.Text(f.jax.errorText,a):null==f.jax.originalText?alert(m("NoOriginalForm","No original form available")):f.ShowSource.Text(f.jax.originalText,a)};f.ShowSource.Window=function(a){if(!f.ShowSource.w){a=[];var h=d.windowSettings,e;for(e in h)h.hasOwnProperty(e)&&a.push(e+"\x3d"+h[e]);f.ShowSource.w=window.open("","_blank",a.join(","))}return f.ShowSource.w};f.ShowSource.Text=function(a,h){var d=f.ShowSource.Window(h);delete f.ShowSource.w;a=a.replace(/^\s*/,"").replace(/\s*$/,"");a=a.replace(/&/g,"\x26amp;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;");var e=m("EqSource","MathJax Equation Source");if(f.isMobile)d.document.open(),d.document.write("\x3chtml\x3e\x3chead\x3e\x3cmeta name\x3d'viewport' content\x3d'width\x3ddevice-width, initial-scale\x3d1.0' /\x3e\x3ctitle\x3e"+e+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e"),d.document.write("\x3cpre\x3e"+a+"\x3c/pre\x3e"),d.document.write("\x3chr\x3e\x3cinput type\x3d'button' value\x3d'"+m("Close","Close")+"' onclick\x3d'window.close()' /\x3e"),d.document.write("\x3c/body\x3e\x3c/html\x3e"),d.document.close();else{d.document.open();d.document.write("\x3chtml\x3e\x3chead\x3e\x3ctitle\x3e"+e+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e");d.document.write("\x3ctable\x3e\x3ctr\x3e\x3ctd\x3e\x3cpre\x3e"+a+"\x3c/pre\x3e\x3c/td\x3e\x3c/tr\x3e\x3c/table\x3e");d.document.write("\x3c/body\x3e\x3c/html\x3e");d.document.close();var b=d.document.body.firstChild;setTimeout(function(){var a=d.outerHeight-d.innerHeight||30,f=d.outerWidth-d.innerWidth||30,f=Math.max(100,Math.min(Math.floor(.5*screen.width),b.offsetWidth+f+25)),a=Math.max(40,Math.min(Math.floor(.5*screen.height),b.offsetHeight+a+25));d.resizeTo(f,a);h&&null!=h.screenX&&(f=Math.max(0,Math.min(h.screenX-Math.floor(f/2),screen.width-f-20)),a=Math.max(0,Math.min(h.screenY-Math.floor(a/2),screen.height-a-20)),d.moveTo(f,a))},50)}};f.Scale=function(){var a=n["HTML-CSS"],h=n.NativeMML,d=n.SVG,e=(a||h||d||{config:{scale:100}}).config.scale,b=prompt(m("ScaleMath","Scale all mathematics (compared to surrounding text) by"),e+"%");b&&(b.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(b=parseFloat(b))?b!==e&&(a&&(a.config.scale=b),h&&(h.config.scale=b),d&&(d.config.scale=b),f.cookie.scale=b,f.saveCookie(),c.Reprocess()):alert(m("NonZeroScale","The scale should not be zero")):alert(m("PercentScale","The scale should be a percentage (e.g., 120%%)")))};f.Zoom=function(){MathJax.Extension.MathZoom||b.Require("[MathJax]/extensions/MathZoom.js")};f.Renderer=function(){var h=c.outputJax["jax/mml"];if(h[0]!==d.settings.renderer){var e=c.Browser,b,k=f.Renderer.Messages,u;switch(d.settings.renderer){case "NativeMML":d.settings.warnedMML||(e.isChrome&&"24."!==e.version.substr(0,3)?b=k.MML.WebKit:e.isSafari&&!e.versionAtLeast("5.0")?b=k.MML.WebKit:e.isMSIE?e.hasMathPlayer||(b=k.MML.MSIE):b=k.MML[e],u="warnedMML");break;case "SVG":d.settings.warnedSVG||!e.isMSIE||a||(b=k.SVG.MSIE)}if(b){b=m(b[0],b[1]);b=b+"\n\n"+m("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");f.cookie.renderer=h[0].id;f.saveCookie();if(!confirm(b)){f.cookie.renderer=d.settings.renderer=g.Cookie.Get("menu").renderer;f.saveCookie();return}u&&(f.cookie.warned=d.settings.warned=!0);f.cookie.renderer=d.settings.renderer;f.saveCookie()}c.Queue(["setRenderer",c,d.settings.renderer,"jax/mml"],["Rerender",c])}};f.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}};f.Font=function(){n["HTML-CSS"]&&document.location.reload()};f.Locale=function(){MathJax.Localization.setLocale(d.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};f.LoadLocale=function(){var a=prompt(m("LoadURL","Load translation data from this URL:"));a&&(a.match(/\.js$/)||alert(m("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'")),b.Require(a,function(h){h!=b.STATUS.OK&&alert(m("BadData","Failed to load translation data from %1",a))}))};f.MPEvents=function(h){var e=d.settings.discoverable,b=f.MPEvents.Messages;a?!e&&"Menu Events"===h.name[1]&&d.settings.mpContext&&alert(m.apply(m,b.IE9warning)):d.settings.mpMouse&&!confirm(m.apply(m,b.IE8warning))?(delete f.cookie.mpContext,delete d.settings.mpContext,delete f.cookie.mpMouse,delete d.settings.mpMouse,f.saveCookie()):(d.settings.mpContext=d.settings.mpMouse,f.cookie.mpContext=f.cookie.mpMouse=d.settings.mpMouse,f.saveCookie(),MathJax.Hub.Queue(["Rerender",MathJax.Hub]))};f.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};c.Browser.Select({MSIE:function(h){var e="BackCompat"===document.compatMode;h=h.versionAtLeast("8.0")&&7<document.documentMode;f.Augment({margin:20,msieBackgroundBug:9>document.documentMode,msieFixedPositionBug:e||!h,msieAboutBug:e});a&&(delete d.styles["#MathJax_About"].filter,delete d.styles[".MathJax_Menu"].filter)},Firefox:function(a){f.skipMouseover=a.isMobile&&a.versionAtLeast("6.0");f.skipMousedown=a.isMobile}});f.isMobile=c.Browser.isMobile;f.noContextMenu=c.Browser.noContextMenu;f.CreateLocaleMenu=function(){if(f.menu){var a=f.menu.Find("Language").menu,h=a.items,d=[],e=MathJax.Localization.strings,b;for(b in e)e.hasOwnProperty(b)&&d.push(b);d=d.sort();a.items=[];b=0;for(var c=d.length;b<c;b++){var k=e[d[b]].menuTitle,k=k?k+(" ("+d[b]+")"):d[b];a.items.push(q.RADIO([d[b],k],"locale",{action:f.Locale}))}a.items.push(h[h.length-2],h[h.length-1])}};c.Register.StartupHook("End Config",function(){d.settings=c.config.menuSettings;"undefined"!==typeof d.settings.showRenderer&&(d.showRenderer=d.settings.showRenderer);"undefined"!==typeof d.settings.showFontMenu&&(d.showFontMenu=d.settings.showFontMenu);"undefined"!==typeof d.settings.showContext&&(d.showContext=d.settings.showContext);f.getCookie();f.menu=f(q.SUBMENU(["Show","Show Math As"],q.COMMAND(["MathMLcode","MathML Code"],f.ShowSource,{nativeTouch:!0,format:"MathML"}),q.COMMAND(["Original","Original Form"],f.ShowSource,{nativeTouch:!0}),q.RULE(),q.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints")),q.RULE(),q.SUBMENU(["Settings","Math Settings"],q.SUBMENU(["ZoomTrigger","Zoom Trigger"],q.RADIO(["Hover","Hover"],"zoom",{action:f.Zoom}),q.RADIO(["Click","Click"],"zoom",{action:f.Zoom}),q.RADIO(["DoubleClick","Double-Click"],"zoom",{action:f.Zoom}),q.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),q.RULE(),q.LABEL(["TriggerRequires","Trigger Requires:"]),q.CHECKBOX(c.Browser.isMac?["Option","Option"]:["Alt","Alt"],"ALT"),q.CHECKBOX(["Command","Command"],"CMD",{hidden:!c.Browser.isMac}),q.CHECKBOX(["Control","Control"],"CTRL",{hidden:c.Browser.isMac}),q.CHECKBOX(["Shift","Shift"],"Shift")),q.SUBMENU(["ZoomFactor","Zoom Factor"],q.RADIO("125%","zscale"),q.RADIO("133%","zscale"),q.RADIO("150%","zscale"),q.RADIO("175%","zscale"),q.RADIO("200%","zscale"),q.RADIO("250%","zscale"),q.RADIO("300%","zscale"),q.RADIO("400%","zscale")),q.RULE(),q.SUBMENU(["Renderer","Math Renderer"],{hidden:!d.showRenderer},q.RADIO("HTML-CSS","renderer",{action:f.Renderer}),q.RADIO("MathML","renderer",{action:f.Renderer,value:"NativeMML"}),q.RADIO("SVG","renderer",{action:f.Renderer})),q.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!d.showMathPlayer,disabled:!c.Browser.hasMathPlayer},q.LABEL(["MPHandles","Let MathPlayer Handle:"]),q.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:f.MPEvents,hidden:!a}),q.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:f.MPEvents,hidden:!a}),q.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:f.MPEvents,hidden:a})),q.SUBMENU(["FontPrefs","Font Preference"],{hidden:!d.showFontMenu},q.LABEL(["ForHTMLCSS","For HTML-CSS:"]),q.RADIO(["Auto","Auto"],"font",{action:f.Font}),q.RULE(),q.RADIO(["TeXLocal","TeX (local)"],"font",{action:f.Font}),q.RADIO(["TeXWeb","TeX (web)"],"font",{action:f.Font}),q.RADIO(["TeXImage","TeX (image)"],"font",{action:f.Font}),q.RULE(),q.RADIO(["STIXlocal","STIX (local)"],"font",{action:f.Font})),q.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!d.showContext},q.RADIO("MathJax","context"),q.RADIO(["Browser","Browser"],"context")),q.COMMAND(["Scale","Scale All Math ..."],f.Scale),q.RULE().With({hidden:!d.showDiscoverable,name:["","discover_rule"]}),q.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!d.showDiscoverable})),q.SUBMENU(["Locale","Language"],{hidden:!d.showLocale},q.RADIO("en","locale",{action:f.Locale}),q.RULE().With({hidden:!d.showLocaleURL,name:["","localURL_rule"]}),q.COMMAND(["LoadLocale","Load from URL ..."],f.LoadLocale,{hidden:!d.showLocaleURL})),q.RULE(),q.COMMAND(["About","About MathJax"],f.About),q.COMMAND(["Help","MathJax Help"],f.Help));if(f.isMobile){var h=d.settings,e=f.menu.Find("Math Settings","Zoom Trigger").menu;e.items[0].disabled=e.items[1].disabled=!0;if("Hover"===h.zoom||"Click"==h.zoom)h.zoom="None";e.items=e.items.slice(0,4);navigator.appVersion.match(/[ (]Android[) ]/)&&f.ITEM.SUBMENU.Augment({marker:"\u00bb"})}f.CreateLocaleMenu()});f.showRenderer=function(a){f.cookie.showRenderer=d.showRenderer=a;f.saveCookie();f.menu.Find("Math Settings","Math Renderer").hidden=!a};f.showMathPlayer=function(a){f.cookie.showMathPlayer=d.showMathPlayer=a;f.saveCookie();f.menu.Find("Math 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a=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=a.offsetWidth/5;this.hiddenDiv.removeChild(a);this.startMarker=this.createStrut(this.Element("span"),10,!0);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");this.operaHeightBug&&this.createStrut(this.HDspan,0);if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(b){}}else this.HDimg=this.createStrut(this.HDspan,0);this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(a){for(var 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b=a.jax[this.id],d,c=b.length,e,f,q,k,l,r,B=!1,w=this.config.linebreaks.automatic,n=this.config.linebreaks.width;w?((B=null!=n.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?n=n.replace(/\s*container\s*/,""):r=this.defaultWidth,""===n&&(n="100%")):r=1E5;for(d=0;d<c;d++)if(e=b[d],e.parentNode&&((f=e.previousSibling)&&String(f.className).match(/^MathJax(_Display)?( 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h=MathJax.Callback.Queue();h.Push(["Require",c,this.fontDir+"/"+a]);this.imgFonts&&(MathJax.isPacked||(a=a.replace(/\/([^\/]*)$/,b.imgPacked+"/$1")),h.Push(["Require",c,this.webfontDir+"/png/"+a]));g.RestartAfter(h.Push({}))},loadWebFont:function(a){a.available=a.isWebFont=!0;b.FontFaceBug&&(a.family=a.name,b.msieFontCSSBug&&(a.family+="-Web"));g.RestartAfter(this.Font.loadWebFont(a))},loadWebFontError:function(a,b){g.Startup.signal.Post("HTML-CSS Jax - disable web fonts");a.isWebFont=!1;this.config.imageFont&&this.config.imageFont===this.fontInUse?(this.imgFonts=!0,g.Startup.signal.Post("HTML-CSS Jax - switch to image fonts"),g.Startup.signal.Post("HTML-CSS Jax - using image fonts"),n(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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d=this.HTMLspanElement();""!=d.style.fontSize&&(c.fontsize=d.style.fontSize)}c.fontsize&&!this.mathsize&&(c.mathsize=c.fontsize);0!==c.scriptlevel&&(2<c.scriptlevel&&(c.scriptlevel=2),a=Math.pow(this.Get("scriptsizemultiplier"),c.scriptlevel),c.scriptminsize=b.length2em(this.Get("scriptminsize")),a<c.scriptminsize&&(a=c.scriptminsize));this.isToken&&(a*=b.length2em(c.mathsize));return a},HTMLgetMu:function(a){var b=1,c=this.getValues("scriptlevel","scriptsizemultiplier");a.scale&&1!==a.scale&&(b=1/a.scale);0!==c.scriptlevel&&(2<c.scriptlevel&&(c.scriptlevel=2),b=Math.sqrt(Math.pow(c.scriptsizemultiplier,c.scriptlevel)));return b},HTMLgetVariant:function(){var a=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");a.hasVariant=this.Get("mathvariant",!0);a.hasVariant||(a.family=a.fontfamily,a.weight=a.fontweight,a.style=a.fontstyle);if(this.style){var c=this.HTMLspanElement();!a.family&&c.style.fontFamily&&(a.family=c.style.fontFamily);!a.weight&&c.style.fontWeight&&(a.weight=c.style.fontWeight);!a.style&&c.style.fontStyle&&(a.style=c.style.fontStyle)}a.weight&&a.weight.match(/^\d+$/)&&(a.weight=600<parseInt(a.weight)?"bold":"normal");c=a.mathvariant;this.variantForm&&(c="-"+b.fontInUse+"-variant");if(a.family&&!a.hasVariant)return!a.weight&&a.mathvariant.match(/bold/)&&(a.weight="bold"),!a.style&&a.mathvariant.match(/italic/)&&(a.style="italic"),{FONTS:[],fonts:[],noRemap:!0,defaultFont:{family:a.family,style:a.style,weight:a.weight}};"bold"===a.weight?c={normal:k.VARIANT.BOLD,italic:k.VARIANT.BOLDITALIC,fraktur:k.VARIANT.BOLDFRAKTUR,script:k.VARIANT.BOLDSCRIPT,"sans-serif":k.VARIANT.BOLDSANSSERIF,"sans-serif-italic":k.VARIANT.SANSSERIFBOLDITALIC}[c]||c:"normal"===a.weight&&(c={bold:k.VARIANT.normal,"bold-italic":k.VARIANT.ITALIC,"bold-fraktur":k.VARIANT.FRAKTUR,"bold-script":k.VARIANT.SCRIPT,"bold-sans-serif":k.VARIANT.SANSSERIF,"sans-serif-bold-italic":k.VARIANT.SANSSERIFITALIC}[c]||c);"italic"===a.style?c={normal:k.VARIANT.ITALIC,bold:k.VARIANT.BOLDITALIC,"sans-serif":k.VARIANT.SANSSERIFITALIC,"bold-sans-serif":k.VARIANT.SANSSERIFBOLDITALIC}[c]||c:"normal"===a.style&&(c={italic:k.VARIANT.NORMAL,"bold-italic":k.VARIANT.BOLD,"sans-serif-italic":k.VARIANT.SANSSERIF,"sans-serif-bold-italic":k.VARIANT.BOLDSANSSERIF}[c]||c);c 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e=this.toString().replace(/[\u2061-\u2064]/g,"");d&&(e=d(e,g));c.fontInherit?(b.addElement(a,"span",{style:{"font-size":Math.floor(100/b.scale+.5)+"%"}},[e]),c.bold&&(a.lastChild.style.fontWeight="bold"),c.italic&&(a.lastChild.style.fontStyle="italic"),c=b.getHD(a),d=b.getW(a),a.bbox={h:c.h,d:c.d,w:d,lw:0,rw:d,exactW:!0}):this.HTMLhandleVariant(a,c,e)}});k.mi.Augment({toHTML:function(a){a=this.HTMLhandleSize(this.HTMLcreateSpan(a));a.bbox=null;for(var c=this.HTMLgetVariant(),d=0,g=this.data.length;d<g;d++)this.data[d]&&this.data[d].toHTML(a,c);a.bbox||(a.bbox=this.HTMLzeroBBox());d=this.data.join("");g=a.bbox;g.skew&&1!==d.length&&delete g.skew;g.rw>g.w&&1===d.length&&!c.noIC&&(g.ic=g.rw-g.w,b.createBlank(a,g.ic),g.w=g.rw);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});k.mn.Augment({toHTML:function(a){a=this.HTMLhandleSize(this.HTMLcreateSpan(a));a.bbox=null;for(var 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m=e.data[e.over],n=e.data[e.under];m&&this===m.CoreMO()&&e.Get("accent")?l=b.FONTDATA.REMAPACCENT:n&&this===n.CoreMO()&&e.Get("accentunder")&&(l=b.FONTDATA.REMAPACCENTUNDER)}f&&c.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(d=b.FONTDATA.VARIANT["-"+b.fontInUse+"-variant"]);e=0;for(f=this.data.length;e<f;e++)this.data[e]&&this.data[e].toHTML(a,d,this.HTMLremap,l);a.bbox||(a.bbox=this.HTMLzeroBBox());1!==c.length&&delete a.bbox.skew;b.AccentBug&&0===a.bbox.w&&1===c.length&&a.firstChild&&(a.firstChild.nodeValue+=b.NBSP,b.createSpace(a,0,0,-a.offsetWidth/b.em));g.largeop&&(c=(a.bbox.h-a.bbox.d)/2-b.TeX.axis_height*a.scale,b.safariVerticalAlignBug&&"IMG"===a.lastChild.nodeName?a.lastChild.style.verticalAlign=b.Em(b.unEm(a.lastChild.style.verticalAlign||0)/b.em-c/a.scale):b.konquerorVerticalAlignBug&&"IMG"===a.lastChild.nodeName?(a.style.position="relative",a.lastChild.style.position="relative",a.lastChild.style.top=b.Em(c/a.scale)):a.style.verticalAlign=b.Em(-c/a.scale),a.bbox.h-=c,a.bbox.d+=c,a.bbox.rw>a.bbox.w&&(a.bbox.ic=a.bbox.rw-a.bbox.w,b.createBlank(a,a.bbox.ic),a.bbox.w=a.bbox.rw));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},CoreParent:function(){for(var a=this;a&&a.isEmbellished()&&a.CoreMO()===this&&!a.isa(k.math);)a=a.Parent();return a},CoreText:function(a){if(!a)return"";if(a.isEmbellished())return a.CoreMO().data.join("");for(;(a.isa(k.mrow)||a.isa(k.TeXAtom)||a.isa(k.mstyle)||a.isa(k.mphantom))&&1===a.data.length&&a.data[0];)a=a.data[0];return a.isToken?a.data.join(""):""},HTMLremapChars:{"*":"\u2217",'"':"\u2033","\u00b0":"\u2218","\u00b2":"2","\u00b3":"3","\u00b4":"\u2032","\u00b9":"1"},HTMLremap:function(a,b){a=a.replace(/-/g,"\u2212");b&&(a=a.replace(/'/g,"\u2032").replace(/`/g,"\u2035"),1===a.length&&(a=b[a]||a));return a},HTMLcanStretch:function(a){if(!this.Get("stretchy"))return!1;var c=this.data.join("");if(1<c.length)return!1;var d=this.CoreParent();if(d&&d.isa(k.munderover)&&1===this.CoreText(d.data[d.base]).length){var g=d.data[d.over],e=d.data[d.under];g&&this===g.CoreMO()&&d.Get("accent")?c=b.FONTDATA.REMAPACCENT[c]||c:e&&this===e.CoreMO()&&d.Get("accentunder")&&(c=b.FONTDATA.REMAPACCENTUNDER[c]||c)}return(c=b.FONTDATA.DELIMITERS[c.charCodeAt(0)])&&c.dir==a.substr(0,1)},HTMLstretchV:function(a,c,d){this.HTMLremoveColor();var g=this.getValues("symmetric","maxsize","minsize"),e=this.HTMLspanElement(),f=this.HTMLgetMu(e),k,l=b.TeX.axis_height,m=e.scale;k=g.symmetric?2*Math.max(c-l,d+l):c+d;g.maxsize=b.length2em(g.maxsize,f,e.bbox.h+e.bbox.d);g.minsize=b.length2em(g.minsize,f,e.bbox.h+e.bbox.d);k=Math.max(g.minsize,Math.min(g.maxsize,k));e=this.HTMLcreateSpan(a);b.createDelimiter(e,this.data.join("").charCodeAt(0),k,m);k=g.symmetric?(e.bbox.h+e.bbox.d)/2+l:(e.bbox.h+e.bbox.d)*c/(c+d);b.positionDelimiter(e,k);this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:function(a,c){this.HTMLremoveColor();var d=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===d.fontweight||600<=parseInt(d.fontweight))&&!this.Get("mathvariant",!0)&&(d.mathvariant=k.VARIANT.BOLD);var g=this.HTMLspanElement(),e=this.HTMLgetMu(g),f=g.scale;d.maxsize=b.length2em(d.maxsize,e,g.bbox.w);d.minsize=b.length2em(d.minsize,e,g.bbox.w);c=Math.max(d.minsize,Math.min(d.maxsize,c));g=this.HTMLcreateSpan(a);b.createDelimiter(g,this.data.join("").charCodeAt(0),c,f,d.mathvariant);this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});k.mtext.Augment({toHTML:function(a){a=this.HTMLhandleSize(this.HTMLcreateSpan(a));var c=this.HTMLgetVariant();if(b.config.mtextFontInherit||"merror"===this.Parent().type)c={bold:c.bold,italic:c.italic,fontInherit:!0};for(var d=0,g=this.data.length;d<g;d++)this.data[d]&&this.data[d].toHTML(a,c);a.bbox||(a.bbox=this.HTMLzeroBBox());1!==this.data.join("").length&&delete a.bbox.skew;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});k.merror.Augment({toHTML:function(a){var c=MathJax.HTML.addElement(a,"span",{style:{display:"inline-block"}});a=this.SUPER(arguments).toHTML.call(this,c);var d=b.getHD(c),g=b.getW(c);c.bbox={h:d.h,d:d.d,w:g,lw:0,rw:g,exactW:!0};c.id=a.id;a.id=null;return c}});k.ms.Augment({toHTML:k.mbase.HTMLautoload});k.mglyph.Augment({toHTML:k.mbase.HTMLautoload});k.mspace.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=this.getValues("height","depth","width"),d=this.HTMLgetMu(a);c.mathbackground=this.mathbackground;this.background&&!this.mathbackground&&(c.mathbackground=this.background);var g=b.length2em(c.height,d),e=b.length2em(c.depth,d),d=b.length2em(c.width,d);b.createSpace(a,g,e,d,c.mathbackground,!0);return a}});k.mphantom.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var g=this.data[0].toHTML(a);null!=d?b.Remeasured(this.data[0].HTMLstretchV(a,c,d),a):null!=c?b.Remeasured(this.data[0].HTMLstretchH(a,c),a):g=b.Measured(g,a);a.bbox={w:g.bbox.w,h:g.bbox.h,d:g.bbox.d,lw:0,rw:0,exactW:!0};c=0;for(d=a.childNodes.length;c<d;c++)a.childNodes[c].style.visibility="hidden"}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mpadded.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var g=b.createStack(a,!0),e=b.createBox(g),f=this.data[0].toHTML(e);null!=d?b.Remeasured(this.data[0].HTMLstretchV(e,c,d),e):null!=c?b.Remeasured(this.data[0].HTMLstretchH(e,c),e):b.Measured(f,e);c=this.getValues("height","depth","width","lspace","voffset");var f=d=0,k=this.HTMLgetMu(a);c.lspace&&(d=this.HTMLlength2em(e,c.lspace,k));c.voffset&&(f=this.HTMLlength2em(e,c.voffset,k));b.placeBox(e,d,f);a.bbox={h:e.bbox.h,d:e.bbox.d,w:e.bbox.w,exactW:!0,lw:Math.min(0,e.bbox.lw+d),rw:Math.max(e.bbox.w,e.bbox.rw+d),H:Math.max(null==e.bbox.H?-b.BIGDIMEN:e.bbox.H,e.bbox.h+f),D:Math.max(null==e.bbox.D?-b.BIGDIMEN:e.bbox.D,e.bbox.d-f)};""!==c.height&&(a.bbox.h=this.HTMLlength2em(e,c.height,k,"h",0));""!==c.depth&&(a.bbox.d=this.HTMLlength2em(e,c.depth,k,"d",0));""!==c.width&&(a.bbox.w=this.HTMLlength2em(e,c.width,k,"w",0));a.bbox.H<=a.bbox.h&&delete a.bbox.H;a.bbox.D<=a.bbox.d&&delete a.bbox.D;e=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;a.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||e.exec(c.height)||e.exec(c.width)||e.exec(c.depth));b.setStackWidth(g,a.bbox.w)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLlength2em:function(a,c,d,g,e){null==e&&(e=-b.BIGDIMEN);var f=String(c).match(/width|height|depth/),f=f?a.bbox[f[0].charAt(0)]:g?a.bbox[g]:0;d=b.length2em(c,d,f);return g&&String(c).match(/^\s*[-+]/)?Math.max(e,a.bbox[g]+d):d},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mrow.Augment({HTMLlineBreaks:function(a){return this.parent.linebreakContainer?b.config.linebreaks.automatic&&a.bbox.w>b.linebreakWidth||this.hasNewline():!1},HTMLstretchH:function(a,b){this.HTMLremoveColor();var c=this.HTMLspanElement();this.data[this.core].HTMLstretchH(c,b);this.HTMLcomputeBBox(c,!0);this.HTMLhandleColor(c);return c},HTMLstretchV:function(a,b,c){this.HTMLremoveColor();a=this.HTMLspanElement();this.data[this.core].HTMLstretchV(a,b,c);this.HTMLcomputeBBox(a,!0);this.HTMLhandleColor(a);return a}});k.mstyle.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var g=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=g.bbox}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mfrac.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),g=b.createBox(c);b.MeasureSpans([this.HTMLboxChild(0,d),this.HTMLboxChild(1,g)]);var e=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),f=this.HTMLgetScale(),k=e.displaystyle,l=b.TeX.axis_height*f;if(e.bevelled){var e=k?.4:.15,m=Math.max(d.bbox.h+d.bbox.d,g.bbox.h+g.bbox.d)+2*e,c=b.createBox(c);b.createDelimiter(c,47,m);b.placeBox(d,0,(d.bbox.d-d.bbox.h)/2+l+e);b.placeBox(c,d.bbox.w-e/2,(c.bbox.d-c.bbox.h)/2+l);b.placeBox(g,d.bbox.w+c.bbox.w-e,(g.bbox.d-g.bbox.h)/2+l-e)}else{var m=Math.max(d.bbox.w,g.bbox.w),r=b.thickness2em(e.linethickness,f),n,p,t=b.TeX.min_rule_thickness/this.em;k?(n=b.TeX.num1,p=b.TeX.denom1):(n=0===r?b.TeX.num3:b.TeX.num2,p=b.TeX.denom2);n*=f;p*=f;0===r?(f=Math.max((k?7:3)*b.TeX.rule_thickness,2*t),k=n-d.bbox.d-(g.bbox.h-p),k<f&&(n+=(f-k)/2,p+=(f-k)/2)):(f=Math.max((k?2:0)*t+r,r/2+1.5*t),k=n-d.bbox.d-(l+r/2),k<f&&(n+=f-k),k=l-r/2-(g.bbox.h-p),k<f&&(p+=f-k),c=b.createBox(c),b.createRule(c,r,0,m+2*r),b.placeBox(c,0,l-r/2));b.alignBox(d,e.numalign,n);b.alignBox(g,e.denomalign,-p)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcanStretch:function(a){return!1},HTMLhandleSpace:function(a){if(!this.texWithDelims){var c=(this.useMMLspacing?0:b.length2em(this.texSpacing()||0))+.12;a.style.paddingLeft=b.Em(c);a.style.paddingRight=b.Em(.12)}}});k.msqrt.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),g=b.createBox(c),e=b.createBox(c),f=this.HTMLgetScale(),k=b.TeX.rule_thickness*f,l,m,n;l=this.Get("displaystyle")?b.TeX.x_height*f:k;l=Math.max(k+l/4,1.5*b.TeX.min_rule_thickness/this.em);var p=this.HTMLboxChild(0,d);m=p.bbox.h+p.bbox.d+l+k;b.createDelimiter(e,8730,m,f);b.MeasureSpans([p,e]);n=p.bbox.w;var t=0;if(e.isMultiChar||b.AdjustSurd&&b.imgFonts)e.bbox.w*=.95;e.bbox.h+e.bbox.d>m&&(l=(e.bbox.h+e.bbox.d-(m-k))/2);m=b.FONTDATA.DELIMITERS[b.FONTDATA.RULECHAR];!m||n<m.HW[0][0]*f||.75>f?b.createRule(g,0,k,n):b.createDelimiter(g,b.FONTDATA.RULECHAR,n,f);m=p.bbox.h+l+k;l=m*b.rfuzz;e.isMultiChar&&(l=b.rfuzz);t=this.HTMLaddRoot(c,e,t,e.bbox.h+e.bbox.d-m,f);b.placeBox(e,t,m-e.bbox.h);b.placeBox(g,t+e.bbox.w,m-g.bbox.h+l);b.placeBox(d,t+e.bbox.w,0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLaddRoot:function(a,b,c,g,e){return c}});k.mroot.Augment({toHTML:k.msqrt.prototype.toHTML,HTMLaddRoot:function(a,c,d,g,e){a=b.createBox(a);this.data[1]?(d=this.data[1].toHTML(a),d.style.paddingRight=d.style.paddingLeft="",b.Measured(d,a)):a.bbox=this.HTMLzeroBBox();g=this.HTMLrootHeight(c.bbox.h+c.bbox.d,e,a)-g;e=Math.min(a.bbox.w,a.bbox.rw);d=Math.max(e,c.offset);b.placeBox(a,d-e,g);return d-c.offset},HTMLrootHeight:function(a,b,c){return.45*(a-.9*b)+.6*b+Math.max(0,c.bbox.d-.075)}});k.mfenced.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);this.data.open&&this.data.open.toHTML(a);null!=this.data[0]&&this.data[0].toHTML(a);for(var b=1,c=this.data.length;b<c;b++)this.data[b]&&(this.data["sep"+b]&&this.data["sep"+b].toHTML(a),this.data[b].toHTML(a));this.data.close&&this.data.close.toHTML(a);for(var g=this.HTMLcomputeBBox(a),e=a.bbox.h,f=a.bbox.d,b=0,c=g.length;b<c;b++)g[b].HTMLstretchV(a,e,f);g.length&&this.HTMLcomputeBBox(a,!0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcomputeBBox:function(a,b){var c=a.bbox={},g=[];this.HTMLcheckStretchy(this.data.open,c,g,b);this.HTMLcheckStretchy(this.data[0],c,g,b);for(var e=1,f=this.data.length;e<f;e++)this.data[e]&&(this.HTMLcheckStretchy(this.data["sep"+e],c,g,b),this.HTMLcheckStretchy(this.data[e],c,g,b));this.HTMLcheckStretchy(this.data.close,c,g,b);this.HTMLcleanBBox(c);return g},HTMLcheckStretchy:function(a,b,c,g){a&&(!g&&a.HTMLcanStretch("Vertical")&&(c.push(a),a=a.CoreMO()||a),this.HTMLcombineBBoxes(a,b))}});k.menclose.Augment({toHTML:k.mbase.HTMLautoload});k.maction.Augment({toHTML:k.mbase.HTMLautoload});k.semantics.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var g=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=g.bbox}this.HTMLhandleSpace(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.munderover.Augment({toHTML:function(a,c,d){var g=this.getValues("displaystyle","accent","accentunder","align");if(!g.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return k.msubsup.prototype.toHTML.call(this,a);a=this.HTMLcreateSpan(a);var e=this.HTMLgetScale(),f=b.createStack(a),l=[],m=[],n=[],r,p,t;p=0;for(t=this.data.length;p<t;p++)null!=this.data[p]&&(r=l[p]=b.createBox(f),m[p]=this.data[p].toHTML(r),p==this.base?(null!=d?this.data[this.base].HTMLstretchV(r,c,d):null!=c&&this.data[this.base].HTMLstretchH(r,c),n[p]=null==d&&null!=c?!1:this.data[p].HTMLcanStretch("Horizontal")):n[p]=this.data[p].HTMLcanStretch("Horizontal"));b.MeasureSpans(m);f=m=-b.BIGDIMEN;p=0;for(t=this.data.length;p<t;p++)this.data[p]&&(l[p].bbox.w>f&&(f=l[p].bbox.w),!n[p]&&f>m&&(m=f));null==d&&null!=c?m=c:m==-b.BIGDIMEN&&(m=f);p=f=0;for(t=this.data.length;p<t;p++)this.data[p]&&(r=l[p],n[p]&&(r.bbox=this.data[p].HTMLstretchH(r,m).bbox),r.bbox.w>f&&(f=r.bbox.w));c=b.TeX.rule_thickness;d=b.FONTDATA.TeX_factor;var n=l[this.base]||{bbox:this.HTMLzeroBBox()},F,A,C,z=0;n.bbox.ic&&(z=1.3*n.bbox.ic+.05);p=0;for(t=this.data.length;p<t;p++)null!=this.data[p]&&(r=l[p],m=b.TeX.big_op_spacing5*e,(C=p!=this.base&&g[this.ACCENTS[p]])&&r.bbox.w<=1/b.em+1E-4&&(r.bbox.w=r.bbox.rw-r.bbox.lw,r.bbox.noclip=!0,r.bbox.lw&&r.insertBefore(b.createSpace(r.parentNode,0,0,-r.bbox.lw),r.firstChild),b.createBlank(r,0,0,r.bbox.rw+.1)),F={left:0,center:(f-r.bbox.w)/2,right:f-r.bbox.w}[g.align],A=0,p==this.over?(C?(C=Math.max(c*e*d,2.5/this.em),m=0,n.bbox.skew&&(F+=n.bbox.skew)):(C=b.TeX.big_op_spacing1*e*d,A=b.TeX.big_op_spacing3*e*d,C=Math.max(C,A-Math.max(0,r.bbox.d))),C=Math.max(C,1.5/this.em),F+=z/2,A=n.bbox.h+r.bbox.d+C,r.bbox.h+=m):p==this.under&&(C?(C=3*c*e*d,m=0):(C=b.TeX.big_op_spacing2*e*d,A=b.TeX.big_op_spacing4*e*d,C=Math.max(C,A-r.bbox.h)),C=Math.max(C,1.5/this.em),F-=z/2,A=-(n.bbox.d+r.bbox.h+C),r.bbox.d+=m),b.placeBox(r,F,A));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.msubsup.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);var g=this.HTMLgetScale(),e=this.HTMLgetMu(a),f=b.createStack(a),k,l=[],m=b.createBox(f);this.data[this.base]?(l.push(this.data[this.base].toHTML(m)),null!=d?this.data[this.base].HTMLstretchV(m,c,d):null!=c&&this.data[this.base].HTMLstretchH(m,c)):m.bbox=this.HTMLzeroBBox();c=b.TeX.x_height*g;d=b.TeX.scriptspace*g*.75;var n;this.HTMLnotEmpty(this.data[this.sup])&&(n=b.createBox(f),l.push(this.data[this.sup].toHTML(n)));this.HTMLnotEmpty(this.data[this.sub])&&(k=b.createBox(f),l.push(this.data[this.sub].toHTML(k)));b.MeasureSpans(l);n&&(n.bbox.w+=d,n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw));k&&(k.bbox.w+=d,k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw));b.placeBox(m,0,0);var l=n?this.data[this.sup].HTMLgetScale():k?this.data[this.sub].HTMLgetScale():this.HTMLgetScale(),p=b.TeX.sup_drop*l,f=m.bbox.h-p,t=m.bbox.d+b.TeX.sub_drop*l,l=0;m.bbox.ic&&(m.bbox.w-=m.bbox.ic,l=1.3*m.bbox.ic+.05);!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||1!==this.data[this.base].data.join("").length||1!==m.bbox.scale||this.data[this.base].Get("largeop")||(f=t=0);d=this.getValues("subscriptshift","superscriptshift");d.subscriptshift=""===d.subscriptshift?0:b.length2em(d.subscriptshift,e);d.superscriptshift=""===d.superscriptshift?0:b.length2em(d.superscriptshift,e);n?k?(t=Math.max(t,b.TeX.sub2*g),g*=b.TeX.rule_thickness,f-n.bbox.d-(k.bbox.h-t)<3*g&&(t=3*g-f+n.bbox.d+k.bbox.h,p=.8*c-(f-n.bbox.d),0<p&&(f+=p,t-=p)),b.placeBox(n,m.bbox.w+l,Math.max(f,d.superscriptshift)),b.placeBox(k,m.bbox.w,-Math.max(t,d.subscriptshift))):(k=this.getValues("displaystyle","texprimestyle"),k=b.TeX[k.displaystyle?"sup1":k.texprimestyle?"sup3":"sup2"],f=Math.max(f,k*g,n.bbox.d+.25*c,d.superscriptshift),b.placeBox(n,m.bbox.w+l,f,n.bbox)):k&&(t=Math.max(t,b.TeX.sub1*g,k.bbox.h-.8*c,d.subscriptshift),b.placeBox(k,m.bbox.w,-t,k.bbox));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mmultiscripts.Augment({toHTML:k.mbase.HTMLautoload});k.mtable.Augment({toHTML:k.mbase.HTMLautoload});k["annotation-xml"].Augment({toHTML:k.mbase.HTMLautoload});k.math.Augment({toHTML:function(a,c){var d=this.Get("alttext");d&&""!==d&&c.setAttribute("aria-label",d);var l=b.addElement(a,"nobr",{isMathJax:!0});a=this.HTMLcreateSpan(l);var d=b.createStack(a),e=b.createBox(d),f;d.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";null!=this.data[0]&&(b.msieColorBug&&(this.background&&(this.data[0].background=this.background,delete this.background),this.mathbackground&&(this.data[0].mathbackground=this.mathbackground,delete this.mathbackground)),k.mbase.prototype.displayAlign=g.config.displayAlign,k.mbase.prototype.displayIndent=g.config.displayIndent,f=this.data[0].toHTML(e),f.bbox.exactW=!1,f=b.Measured(f,e));b.placeBox(e,0,0);a.style.width=b.Em((Math.round(f.bbox.w*this.em)+.25)/b.outerEm);a.style.display="inline-block";var l=1/b.em,m=b.em/b.outerEm;b.em/=m;a.bbox.h*=m;a.bbox.d*=m;a.bbox.w*=m;a.bbox.lw*=m;a.bbox.rw*=m;f&&null!=f.bbox.width&&(a.style.minWidth=f.bbox.minWidth||a.style.width,a.style.width=d.style.width=f.bbox.width,e.style.width="100%");this.HTMLhandleColor(a);f&&b.createRule(a,(f.bbox.h+l)*m,(f.bbox.d+l)*m,0);this.isMultiline||"block"!==this.Get("display")||null!=a.bbox.width||(d=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift"),d.indentalignfirst!==k.INDENTALIGN.INDENTALIGN&&(d.indentalign=d.indentalignfirst),d.indentalign===k.INDENTALIGN.AUTO&&(d.indentalign=this.displayAlign),c.style.textAlign=d.indentalign,d.indentshiftfirst!==k.INDENTSHIFT.INDENTSHIFT&&(d.indentshift=d.indentshiftfirst),"auto"===d.indentshift&&(d.indentshift=this.displayIndent),d.indentshift&&d.indentalign!==k.INDENTALIGN.CENTER&&(a.style[{left:"marginLeft",right:"marginRight"}[d.indentalign]]=b.Em(b.length2em(d.indentshift))));return a},HTMLspanElement:k.mbase.prototype.HTMLspanElement});k.TeXAtom.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);if(null!=this.data[0])if(this.texClass===k.TEXCLASS.VCENTER){var c=b.createStack(a),c=b.createBox(c);b.Measured(this.data[0].toHTML(c),c);b.placeBox(c,0,b.TeX.axis_height-(c.bbox.h+c.bbox.d)/2+c.bbox.d)}else a.bbox=this.data[0].toHTML(a).bbox;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",b,"jax.js"]),0)})});g.Register.StartupHook("End Config",function(){g.Browser.Select({MSIE:function(a){var c=document.documentMode||0,d=a.versionAtLeast("7.0"),g=a.versionAtLeast("8.0")&&7<c,e="BackCompat"===document.compatMode;9>c&&(b.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white",b.config.styles[".MathJax .MathJax_HitBox"].opacity=0,b.config.styles[".MathJax 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Version\/\d/)&&navigator.vendor.match(/Apple/),e=navigator.appVersion.match(/ Android (\d+)\.(\d+)/),e=d&&a.isMobile&&(navigator.platform.match(/iPad|iPod|iPhone/)&&!a.versionAtLeast("5.0")||null!=e&&(2>e[1]||2==e[1]&&2>e[2]));b.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:.011,AccentBug:!0,AdjustSurd:!0,negativeBBoxes:!0,safariNegativeSpaceBug:!0,safariVerticalAlignBug:!d,safariTextNodeBug:!c,forceReflow:!0,allowWebFonts:d&&!e?"otf":!1});k&&b.Augment({webFontDefault:a.isMobile?"sans-serif":"serif"});a.isPC&&b.Augment({adjustAvailableFonts:b.removeSTIXfonts,checkWebFontsTwice:!0});e&&((a=g.config["HTML-CSS"])?(a.availableFonts=[],a.preferredFont=null):g.config["HTML-CSS"]={availableFonts:[],preferredFont:null})},Chrome:function(a){b.Augment({Em:b.EmRounded,cloneNodeBug:!0,rfuzz:.011,AccentBug:!0,AdjustSurd:!0,negativeBBoxes:!0,safariNegativeSpaceBug:!0,safariWebFontSerif:[""],forceReflow:!0,allowWebFonts:a.versionAtLeast("4.0")?"otf":"svg"})},Opera:function(a){a.isMini=null!=navigator.appVersion.match("Opera Mini");b.config.styles[".MathJax .merror"]["vertical-align"]=null;b.config.styles[".MathJax span"]["z-index"]=0;b.Augment({operaHeightBug:!0,operaVerticalAlignBug:!0,operaFontSizeBug:a.versionAtLeast("10.61"),initialSkipBug:!0,FontFaceBug:!0,PaddingWidthBug:!0,allowWebFonts:a.versionAtLeast("10.0")&&!a.isMini?"otf":!1,adjustAvailableFonts:b.removeSTIXfonts})},Konqueror:function(a){b.Augment({konquerorVerticalAlignBug:!0})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){"None"!==g.config.menuSettings.zoom&&c.Require("[MathJax]/extensions/MathZoom.js")})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c=MathJax.ElementJax.mml,g=MathJax.OutputJax["HTML-CSS"];c.mtable.Augment({toHTML:function(b){b=this.HTMLcreateSpan(b);if(0===this.data.length)return b;var k=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing"),n=k.width.match(/%$/),l=g.createStack(b),m=this.HTMLgetScale(),t=this.HTMLgetMu(b),p=[],a=[],h=[],d=[],u=[],e,f,q=-1,y,v,r,B,w,F,A=[],C=g.FONTDATA.baselineskip*m*k.useHeight,z,G=g.FONTDATA.lineH*m,N=g.FONTDATA.lineD*m;e=0;for(y=this.data.length;e<y;e++)for(B=this.data[e],r="mlabeledtr"===B.type?-1:0,d[e]=[],p[e]=a[e]=0,f=r,v=B.data.length+r;f<v;f++)null==h[f]&&(f>q&&(q=f),u[f]=g.createStack(g.createBox(l)),h[f]=-g.BIGDIMEN),d[e][f]=g.createBox(u[f]),A.push(B.data[f-r].toHTML(d[e][f]));g.MeasureSpans(A);e=0;for(y=this.data.length;e<y;e++)for(B=this.data[e],f=r="mlabeledtr"===B.type?-1:0,v=B.data.length+r;f<v;f++){w=B.data[f-r];w.isMultiline&&(d[e][f].style.width="100%");if(w.isEmbellished()&&(F=w.CoreMO(),A=F.Get("minsize",!0))){var 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x=I(k.rowalign),J=I(k.columnlines),N=I(k.rowlines),D=I(k.columnwidth),H=[];e=0;for(y=A.length;e<y;e++)A[e]=g.length2em(A[e],t);e=0;for(y=G.length;e<y;e++)G[e]=g.length2em(G[e],t);for(;A.length<q;)A.push(A[A.length-1]);for(;v.length<=q;)v.push(v[v.length-1]);for(;J.length<q;)J.push(J[J.length-1]);for(;D.length<=q;)D.push(D[D.length-1]);for(;G.length<d.length;)G.push(G[G.length-1]);for(;x.length<=d.length;)x.push(x[x.length-1]);for(;N.length<d.length;)N.push(N[N.length-1]);u[-1]&&(v[-1]="l"===k.side.substr(0,1)?"left":"right",A[-1]=-h[-1]);e=0;for(y=d.length;e<y;e++)if(B=this.data[e],H[e]=[],B.rowalign&&(x[e]=B.rowalign),B.columnalign)for(H[e]=I(B.columnalign);H[e].length<=q;)H[e].push(H[e][H[e].length-1]);if(k.equalrows){B=Math.max.apply(Math,p);var 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    14.