deac/instiki
1
0
Fork 0
Code Issues Pull requests Releases Wiki Activity
instiki/public/MathJax/config/TeX-AMS_HTML-full.js
Jacques Distler 7d3f9db8f0 Update MathJax to Version 1.1-beta
2011-01-27 19:12:00 -06:00

57 lines
188 KiB
JavaScript
Raw Blame History

/*
* /MathJax/config/TeX-AMS_HTML-full.js
*
* Copyright (c) 2010-11 Design Science, Inc.
*
* Part of the MathJax library.
* See http://www.mathjax.org for details.
*
* Licensed under the Apache License, Version 2.0;
* you may not use this file except in compliance with the License.
*
* http://www.apache.org/licenses/LICENSE-2.0
*/
MathJax.Ajax.Preloading(
"[MathJax]/jax/input/TeX/config.js",
"[MathJax]/jax/output/HTML-CSS/config.js",
"[MathJax]/extensions/tex2jax.js",
"[MathJax]/extensions/MathZoom.js",
"[MathJax]/extensions/MathMenu.js",
"[MathJax]/jax/element/mml/jax.js",
"[MathJax]/extensions/TeX/noErrors.js",
"[MathJax]/extensions/TeX/noUndefined.js",
"[MathJax]/jax/input/TeX/jax.js",
"[MathJax]/extensions/TeX/AMSmath.js",
"[MathJax]/extensions/TeX/AMSsymbols.js",
"[MathJax]/jax/output/HTML-CSS/jax.js",
"[MathJax]/jax/output/HTML-CSS/autoload/mtable.js"
);
MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.0.4",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%"}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.0.6",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",showMathMenu:true,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",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}(function(b,c){var a;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),l=["[Math]"],k;var h=document.createElement("span",{className:"MathJax_Preview"});var j=e.root.Get("displaystyle");if(e.inputJax.id==="TeX"){if(j){k=a.displayMathDelimiters;l=[k[0]+e.originalText+k[1]];if(a.multilineDisplay){l=l[0].split(/\n/)}}else{k=a.inlineMathDelimiters;l=[k[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+k[1]]}}for(var g=0,d=l.length;g<d;g++){h.appendChild(document.createTextNode(l[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;MathJax.Hub.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}})(MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");
MathJax.Extension.tex2jax={version:"1.0.1",config:{element:null,inlineMath:[["$","$"],["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){MathJax.Hub.Insert(this.config,(MathJax.Hub.config.tex2jax||{}));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=this.config.element||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?"|\\\\*\\\\\\$":""),"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,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){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)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);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(b,c){var d=this.match[b[0]];if(d!=null){this.search={end:d.end,mode:d.mode,open:c,olen:b[0].length,opos:this.pattern.lastIndex-b[0].length};this.switchPattern(d.pattern)}else{if(b[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+b[1]+"}",mode:"; mode=display",open:c,olen:0,opos:this.pattern.lastIndex-b[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{var a=b[0].replace(/\\(.)/g,"$1");c.nodeValue=c.nodeValue.substr(0,b.index)+a+c.nodeValue.substr(b.index+b[0].length);this.pattern.lastIndex-=b[0].length-a.length}}return c},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{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;if(MathJax.Hub.Browser.isMSIE){a.text=b}else{a.appendChild(document.createTextNode(b))}this.insertNode(a);return a},filterTeX:function(a){return a}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
(function(a,c,e,b,h){var i="1.0";var g=a.Insert({delay:400,styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-family":"serif","font-size":"85%","font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}},(a.config.MathZoom||{}));var d=function(j){if(!j){j=window.event}if(j){if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false}return false};var f=MathJax.Extension.MathZoom={version:i,settings:a.config.menuSettings,HandleEvent:function(l,j,k){if(!l){l=window.event}if(f.settings.CTRL&&!l.ctrlKey){return true}if(f.settings.ALT&&!l.altKey){return true}if(f.settings.CMD&&!l.metaKey){return true}if(f.settings.Shift&&!l.shiftKey){return true}return f[j](l,k)},Click:function(k,j){if(this.settings.zoom==="Click"){return this.Zoom(j,k)}},DblClick:function(k,j){if(this.settings.zoom==="Double-Click"){return this.Zoom(j,k)}},Mouseover:function(k,j){if(this.settings.zoom==="Hover"){f.oldMouseOver=j.onmouseover;j.onmouseover=null;j.onmousemove=this.Mousemove;j.onmouseout=this.Mouseout;return f.Timer(k,j)}},Mouseout:function(j){this.onmouseover=f.oldMouseOver;delete f.oldMouseOver;this.onmousemove=this.onmouseout=null;f.ClearTimer();return d(j)},Mousemove:function(j){return f.Timer(j||window.event,this)},Timer:function(k,j){this.ClearTimer();this.timer=setTimeout(MathJax.Callback(["Zoom",this,j,{}]),g.delay);return d(k)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer);delete this.timer}},Zoom:function(s,l){this.ClearTimer();this.Remove();var v=s.parentNode;if(v.className==="MathJax_MathContainer"){v=v.parentNode}if(v.parentNode.className==="MathJax_MathContainer"){v=v.parentNode.parentNode}var q=(String(v.className).match(/^MathJax_(MathML|Display)$/)?v:s).nextSibling;var m=a.getJaxFor(q),r=m.root;var o=(b&&m.outputJax.isa(b.constructor)?"HTMLCSS":(h&&m.outputJax.isa(h.constructor)?"MathML":null));if(!o){return}var j=Math.floor(0.85*document.body.clientWidth),p=Math.floor(0.85*document.body.clientHeight);var k=c.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},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":j+"px","max-height":p+"px"}},[["span"]]]]);var x=k.lastChild,u=x.firstChild,n=k.firstChild;s.parentNode.insertBefore(k,s);if(this.msieZIndexBug){var t=c.Element("img",{src:"about:blank",id:"MathJax_ZoomTracker",style:{width:0,height:0,position:"relative"}});document.body.appendChild(k);k.style.position="absolute";k.style.zIndex=g.styles["#MathJax_ZoomOverlay"]["z-index"];k=t}var w=(this["Zoom"+o])(r,u,s);if(this.msiePositionBug){if(this.msieIE8Bug){u.style.position="absolute";x.style.height=u.offsetHeight;u.style.position="";if(x.offsetHeight<=p&&x.offsetWidth<=j){x.style.overflow="visible"}}if(this.msieWidthBug){x.style.width=Math.min(j,w.w)}else{if(w.w>j){x.style.width=j}}if(x.offsetHeight>p){x.style.Height=p+"px"}if(s.nextSibling){s.parentNode.insertBefore(k,s.nextSibling)}else{v.appendChild(k)}}else{if(this.operaPositionBug){x.style.width=Math.min(j,u.offsetWidth)+"px"}}this.Position(x,w,(o==="MathML"&&v.nodeName.toLowerCase()==="div"));x.style.visibility="";if(this.settings.zoom==="Hover"){n.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}return d(l)},ZoomHTMLCSS:function(o,q,p){q.className="MathJax";b.idPostfix="-zoom";b.getScales(q,q);o.toHTML(q,q);var r=o.HTMLspanElement().bbox;b.idPostfix="";if(r.width&&r.width!=="100%"){var j=Math.floor(0.85*document.body.clientWidth);q.style.width=j+"px";q.style.display="inline-block";var k=(o.id||"MathJax-Span-"+o.spanID)+"-zoom";var l=document.getElementById(k).firstChild;while(l&&l.style.width!==r.width){l=l.nextSibling}if(l){l.style.width="100%"}}q.appendChild(this.topImg);var n=this.topImg.offsetTop;q.removeChild(this.topImg);var m=(this.msieWidthBug?b.getW(p)*b.em:p.offsetWidth);return{w:r.w*b.em,Y:-n,W:m}},ZoomMathML:function(k,l,m){k.toNativeMML(l,l);var n;l.appendChild(this.topImg);n=this.topImg.offsetTop;l.removeChild(this.topImg);var j=(this.ffMMLwidthBug?m.parentNode:m).offsetWidth;return{w:l.offsetWidth,Y:-n,W:j}},Position:function(p,n,r){var k=this.Resize(),m=k.x,l=k.y,j=n.W;if(this.msiePositionBug){j=-j}if(r&&this.ffMMLcenterBug){j=0}var q=-Math.floor((p.offsetWidth-j)/2),o=n.Y;p.style.left=Math.max(q,20-m)+"px";p.style.top=Math.max(o,20-l)+"px"},Resize:function(l){if(f.onresize){f.onresize(l)}var j=0,o=0,n=document.getElementById("MathJax_ZoomFrame"),k=document.getElementById("MathJax_ZoomOverlay");var m=(f.msieZIndexBug?document.getElementById("MathJax_ZoomTracker"):n);if(f.operaPositionBug){n.style.border="1px solid"}if(m.offsetParent){do{j+=m.offsetLeft;o+=m.offsetTop}while(m=m.offsetParent)}if(f.operaPositionBug){n.style.border=""}if(f.msieZIndexBug){n.style.left=j+"px";n.style.top=o+"px"}k.style.left=(-j)+"px";k.style.top=(-o)+"px";if(f.msiePositionBug){setTimeout(f.SetWH,0)}else{f.SetWH()}return{x:j,y:o}},SetWH:function(){var j=document.getElementById("MathJax_ZoomOverlay");j.style.width=j.style.height="1px";j.style.width=document.body.scrollWidth+"px";j.style.height=document.body.scrollHeight+"px"},Remove:function(k){var l=document.getElementById("MathJax_ZoomFrame");if(l){l.parentNode.removeChild(l);l=document.getElementById("MathJax_ZoomTracker");if(l){l.parentNode.removeChild(l)}if(f.operaRefreshBug){var j=c.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(j)}if(window.removeEventListener){removeEventListener("resize",f.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",f.Resize)}else{window.onresize=f.onresize;delete f.onresize}}}return d(k)}};a.Register.StartupHook("HTML-CSS Jax Ready",function(){b=MathJax.OutputJax["HTML-CSS"];b.Augment({HandleEvent:f.HandleEvent})});a.Register.StartupHook("NativeMML Jax Ready",function(){h=MathJax.OutputJax.NativeMML;h.Augment({HandleEvent:f.HandleEvent,MSIEmouseup:function(l,k,j){if(this.trapUp){delete this.trapUp;return true}if(this.MSIEzoomKeys(l)){return true}return false},MSIEclick:function(l,k,j){if(this.trapClick){delete this.trapClick;return true}if(!this.MSIEzoomKeys(l)){return false}if(!this.settings.zoom.match(/Click/)){return false}return(f.Click(l,k)===false)},MSIEdblclick:function(l,k,j){if(!this.MSIEzoomKeys(l)){return false}return(f.DblClick(l,k)===false)},MSIEmouseover:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEmouseout:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.ClearTimer();return true},MSIEmousemove:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEzoomKeys:function(j){if(this.settings.CTRL&&!j.ctrlKey){return false}if(this.settings.CMD&&!j.metaKey){return false}if(this.settings.ALT&&!j.altKey){return false}if(this.settings.Shift&&!j.shiftKey){return false}return true}})});a.Browser.Select({MSIE:function(j){var k=(document.compatMode==="BackCompat");var l=j.versionAtLeast("8.0")&&document.documentMode>7;f.msiePositionBug=true;f.msieWidthBug=!k;f.msieIE8Bug=l;f.msieZIndexBug=!l;f.msieInlineBlockAlignBug=(!l||k)},Opera:function(j){f.operaPositionBug=true;f.operaRefreshBug=true},Firefox:function(j){f.ffMMLwidthBug=true;f.ffMMLcenterBug=true}});f.topImg=(f.msieInlineBlockAlignBug?c.Element("img",{style:{width:0,height:0},src:"about:blank"}):c.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(f.operaPositionBug){f.topImg.style.border="1px solid"}MathJax.Callback.Queue(["Styles",e,g.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",e,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(b,c,f){var k="1.0.2";var i=b.Browser.isPC,g=b.Browser.isMSIE;var e=(i?null:"5px");var j=b.Insert({delay:150,helpURL:"http://www.mathjax.org/help/user/",showRenderer:true,showFontMenu:false,showContext:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(i?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":e,"-webkit-border-radius":e,"-moz-border-radius":e,"-khtml-border-radius":e,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(i?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(i?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(g?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(g?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(i?"1em":".7em")},".MathJax_MenuLabel":{padding:(i?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(i?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(i?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(i?"Highlight":"#606872"),color:(i?"HighlightText":"white")}}},(b.config.MathMenu||{}));var d=function(l){if(!l){l=window.event}if(l){if(l.preventDefault){l.preventDefault()}if(l.stopPropagation){l.stopPropagation()}l.cancelBubble=true;l.returnValue=false}return false};var a=MathJax.Menu=MathJax.Object.Subclass({version:k,items:[],posted:false,title:null,margin:5,Init:function(l){this.items=[].slice.call(arguments,0)},With:function(l){if(l){b.Insert(this,l)}return this},Post:function(n,v){if(!n){n=window.event}var t=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var l=document.getElementById("MathJax_MenuFrame");if(!l){l=a.Background(this)}var o=c.addElement(l,"div",{onmouseup:a.Mouseup,ondblclick:this.False,ondragstart:this.False,onselectstart:this.False,oncontextmenu:this.False,menuItem:this,className:"MathJax_Menu"},t);for(var q=0,p=this.items.length;q<p;q++){this.items[q].Create(o)}this.posted=true;o.style.width=(o.offsetWidth+2)+"px";var u=n.pageX,s=n.pageY;if(!u&&!s){u=n.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;s=n.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!v){if(u+o.offsetWidth>document.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o<l;o++){var p=n[o].menuItem;if(p&&p.menu&&p.menu.posted){p.Deactivate(n[o])}}l=r.length-1;while(l>=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n<l;n++){var o=r[n].menuItem;if(o&&o.variable===this.variable){r[n].firstChild.style.display="none"}}q.firstChild.display="";j.settings[this.variable]=this.value;a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(p,q);return this.False(p)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(m,l,n){this.name=m;this.variable=l;this.With(n)},Label:function(m,n){var l={className:"MathJax_MenuCheck"};if(!j.settings[this.variable]){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(l,m){if(!this.disabled){m.firstChild.display=(j.settings[this.variable]?"none":"");j.settings[this.variable]=!j.settings[this.variable];a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(l,m);return this.False(l)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(l,m){this.name=l;this.With(m)},Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuRule";return null}});a.About=function(){var o=MathJax.OutputJax["HTML-CSS"]||{fontInUse:""};var q=(o.webFonts?"":"local "),m=(o.webFonts?" web":"");var n=(o.imgFonts?"Image":q+o.fontInUse+m);var l=[];a.About.GetJax(l,MathJax.InputJax,"Input");a.About.GetJax(l,MathJax.OutputJax,"Output");a.About.GetJax(l,MathJax.ElementJax,"Element");a.About.div=a.Background(a.About);var r=MathJax.HTML.addElement(a.About.div,"div",{style:{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+n+" fonts",["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},l],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["wwww.mathjax.org"]]]);var s=(document.documentElement||{});var p=window.innerHeight||s.clientHeight||s.scrollHeight||0;if(a.prototype.msieAboutBug){r.style.width="20em";r.style.position="absolute";r.style.left=Math.floor((document.documentElement.scrollWidth-r.offsetWidth)/2)+"px";r.style.top=(Math.floor((p-r.offsetHeight)/3)+document.body.scrollTop)+"px"}else{r.style.marginLeft=Math.floor(-r.offsetWidth/2)+"px";r.style.top=Math.floor((p-r.offsetHeight)/3)+"px"}};a.About.Remove=function(l){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(l,n,m){for(var o in n){if(n.hasOwnProperty(o)){if(n[o].isa&&n[o].isa(n)){l.push(n[o].id+" "+m+" Jax v"+n[o].version,["br"])}}}return l};a.Help=function(){window.open(j.helpURL,"MathJaxHelp")};a.ShowSource=function(n){if(!n){n=window.event}if(!a.jax){return}if(j.settings.format==="MathML"){var l=MathJax.ElementJax.mml;if(l&&typeof(l.mbase.prototype.toMathML)!=="undefined"){a.ShowSource.Text(a.jax.root.toMathML(),n)}else{if(!f.loadingToMathML){f.loadingToMathML=true;var m={screenX:n.screenX,screenY:n.screenY};a.ShowSource.Window(n);MathJax.Callback.Queue(f.Require("[MathJax]/extensions/toMathML.js"),function(){delete f.loadingToMathML},[this,arguments.callee,m]);return}}}else{if(a.jax.originalText==null){alert("No TeX form available");return}a.ShowSource.Text(a.jax.originalText,n)}};a.ShowSource.Window=function(m){if(!a.ShowSource.w){var n=[],l=j.windowSettings;for(var o in l){if(l.hasOwnProperty(o)){n.push(o+"="+l[o])}}a.ShowSource.w=window.open("","_blank",n.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(r,q){var n=a.ShowSource.Window(q);r=r.replace(/^\s*/,"").replace(/\s*$/,"");r=r.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");n.document.open();n.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");n.document.write("<table><tr><td><pre>"+r+"</pre></td></tr></table>");n.document.write("</body></html>");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o<n;o++){if(l[o]===p){l.splice(o,1);break}}l.unshift(p)}],["Reprocess",b])}};a.Font=function(){var l=MathJax.OutputJax["HTML-CSS"];if(!l){return}document.location.reload()};b.Browser.Select({MSIE:function(l){var m=(document.compatMode==="BackCompat");var n=l.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m})}});j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help));a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax);
MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.0.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g<f;g++){this.SetData(this.data.length,arguments[g])}}},SetData:function(f,g){if(g!=null){if(!(g instanceof a.mbase)){g=(this.isToken?a.chars(g):a.mtext(g))}g.parent=this;g.setInherit(this.inheritFromMe?this:this.inherit)}this.data[f]=g},Parent:function(){var f=this.parent;while(f&&f.inferred){f=f.parent}return f},Get:function(g,k){if(typeof(this[g])!=="undefined"){return this[g]}var h=this.Parent();if(h&&h["adjustChild_"+g]!=null){return(h["adjustChild_"+g])(h.childPosition(this))}var j=this.inherit;var f=j;while(j){if(typeof(j[g])!=="undefined"){var i=j.noInherit[this.type];if(!(i&&i[g])){return j[g]}}f=j;j=j.inherit}if(!k){if(this.defaults[g]===a.AUTO){return this.autoDefault(g)}if(this.defaults[g]!==a.INHERIT&&this.defaults[g]!=null){return this.defaults[g]}if(f){return f.defaults[g]}}return null},hasValue:function(f){return(this.Get(f,true)!=null)},getValues:function(){var g={};for(var h=0,f=arguments.length;h<f;h++){g[arguments[h]]=this.Get(arguments[h])}return g},adjustChild_scriptlevel:function(f){return this.Get("scriptlevel")},adjustChild_displaystyle:function(f){return this.Get("displaystyle")},adjustChild_texprimestyle:function(f){return this.Get("texprimestyle")},childPosition:function(h){if(h.parent.inferred){h=h.parent}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]===h){return g}}return null},setInherit:function(h){if(h!==this.inherit&&this.inherit==null){this.inherit=h;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&this.data[g].setInherit){this.data[g].setInherit(h)}}}},setTeXclass:function(f){this.getPrevClass(f);return(typeof(this.texClass)!=="undefined"?this:f)},getPrevClass:function(f){if(f){this.prevClass=f.Get("texClass");this.prevLevel=f.Get("scriptlevel")}},updateTeXclass:function(f){if(f){this.prevClass=f.prevClass;delete f.prevClass;this.prevLevel=f.prevLevel;delete f.prevLevel;this.texClass=f.Get("texClass")}},texSpacing:function(){var g=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var f=(this.Get("texClass")||a.TEXCLASS.ORD);if(g===a.TEXCLASS.NONE||f===a.TEXCLASS.NONE){return""}if(g===a.TEXCLASS.VCENTER){g=a.TEXCLASS.ORD}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}var h=this.TEXSPACE[g][f];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f<this.data.length;f++){if(!this.data[f].isSpacelike()){return d}}return b},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(f){if(this.data[0]){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.data[0])}return f},setBaseTeXclasses:function(h){this.getPrevClass(h);this.texClass=null;if(this.isEmbellished()){h=this.data[0].setTeXclass(h);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}h=this}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}return h},setSeparateTeXclasses:function(h){this.getPrevClass(h);for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(g){if(g==="mathvariant"){var f=(this.data[0]||"").toString();return(f.length===1||(f.length===2&&f.charCodeAt(0)===this.PLANE1)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:b,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:d,separator:d,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:d,symmetric:b,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:d,movablelimits:d,accent:d,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(h,o){var n=this.def;if(!n){if(h==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var l=this.data.join("");var g=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var j=0,f=g.length;j<f;j++){var k=this.OPTABLE[g[j]][l];if(k){n=this.makeDef(k);break}}if(!n){n=this.CheckRange(l)}if(!n&&o){n={}}else{if(!n){n=MathJax.Hub.Insert({},this.defaultDef)}n.form=g[0];this.def=n}}this.useMMLspacing&=~(this.SPACE_ATTR[h]||0);if(n[h]!=null){return n[h]}else{if(!o){return this.defaultDef[h]}}return""},CheckRange:function(k){var l=k.charCodeAt(0);if(k.charAt(0)===a.PLANE1){l=k.charCodeAt(1)+119808-56320}for(var h=0,f=this.RANGES.length;h<f&&this.RANGES[h][0]<=l;h++){if(l<=this.RANGES[h][1]){if(this.RANGES[h][3]){var g=a.optableDir+"/"+this.RANGES[h][3]+".js";this.RANGES[h][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(g))}var j=(["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER"])[this.RANGES[h][2]];j=this.OPTABLE.infix[k]=a.mo.OPTYPES[j==="BIN"?"BIN3":j];return this.makeDef(j)}}return null},makeDef:function(g){if(g[2]==null){g[2]=this.defaultDef.texClass}if(!g[3]){g[3]={}}var f=MathJax.Hub.Insert({},g[3]);f.lspace=this.SPACE[g[0]];f.rspace=this.SPACE[g[1]];f.texClass=g[2];return f},getForm:function(){var f=this,h=this.parent,g=this.Parent();while(g&&g.isEmbellished()){f=h;h=g.parent;g=g.Parent()}if(h&&h.type==="mrow"&&h.NonSpaceLength()!==1){if(h.FirstNonSpace()===f){return a.FORM.PREFIX}if(h.LastNonSpace()===f){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return b},lineBreak:function(){var f=this.getValues("linebreak","linebreakstyle");if(f.linebreak===a.LINEBREAK.NEWLINE){if(f.linebreakstyle===a.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){f.linebreakstyle=this.Get("infixlinebreakstyle")}return f.linebreakstyle}return"none"},setTeXclass:function(f){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(f){this.prevClass=f.texClass||a.TEXCLASS.ORD;this.prevLevel=f.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){f.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:b,isSpacelike:function(){return b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},lineBreak:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE?a.LINEBREAKSTYLE.AFTER:"none")}});a.ms=a.mbase.Subclass({type:"ms",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:d,isEmbellished:function(){var g=d;for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]==null){continue}if(this.data[h].isEmbellished()){if(g){return d}g=b;this.core=h}else{if(!this.data[h].isSpacelike()){return d}}}return g},NonSpaceLength:function(){var h=0;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){h++}}return h},FirstNonSpace:function(){for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){return this.data[g]}}return null},LastNonSpace:function(){for(var f=this.data.length-1;f>=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){h=this.data[g].setTeXclass(h)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return h}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:d},adjustChild_displaystyle:function(f){return d},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(!this.Get("displaystyle")||f>0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length<this.data.length){g.separators+=g.separators.charAt(g.separators.length-1)}}if(this.data[0]){j=this.data[0].setTeXclass(j)}for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){if(g.separators!==""){this.SetData("sep"+h,a.mo(g.separators.charAt(h-1)));j=this.data["sep"+h].setTeXclass(j)}j=this.data[h].setTeXclass(j)}}if(g.close!==""){this.SetData("close",a.mo(g.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));j=this.data.close.setTeXclass(j)}this.updateTeXclass(this.data.open);return j}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:b,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!((arguments[g] instanceof a.mtr)||(arguments[g] instanceof a.mlabeledtr))){arguments[g]=a.mtd(arguments[g])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:b,noInherit:{mrow:{rowalign:b,columnalign:b,groupalign:b},mtable:{rowalign:b,columnalign:b,groupalign:b}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!(arguments[g] instanceof a.mtd)){arguments[g]=a.mtd(arguments[g])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:b,noInherit:{mrow:{groupalign:b},mtable:{groupalign:b}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return b}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},setTeXclass:a.mbase.setSeparateTeXclasses});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:b,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:d},autoDefault:function(f){if(f==="displaystyle"){return this.Get("display")==="block"}return""},setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var f=this.value();if(f<=65535){return String.fromCharCode(f)}return this.PLANE1+String.fromCharCode(f-119808+56320)}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:function(f){this.getPrevClass(f);this.data[0].setTeXclass();return this}});var c=a.TEXCLASS;var e={ORD:[0,0,c.ORD],ORD11:[1,1,c.ORD],ORD21:[2,1,c.ORD],ORD02:[0,2,c.ORD],ORD55:[5,5,c.ORD],OP:[1,2,c.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,c.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,c.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,c.OP,{largeop:true,symmetric:true}],BIN3:[3,3,c.BIN],BIN4:[4,4,c.BIN],BIN01:[0,1,c.BIN],TALLBIN:[4,4,c.BIN,{stretchy:true}],BINOP:[4,4,c.BIN,{largeop:true,movablelimits:true}],REL:[5,5,c.REL],REL1:[1,1,c.REL,{stretchy:true}],REL4:[4,4,c.REL],WIDEREL:[5,5,c.REL,{stretchy:true}],RELACCENT:[5,5,c.REL,{accent:true,stretchy:true}],OPEN:[0,0,c.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,c.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,c.INNER],PUNCT:[0,3,c.PUNCT],ACCENT:[0,0,c.ORD,{accent:true}],WIDEACCENT:[0,0,c.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,c.REL,"BasicLatin"],[160,255,c.ORD,"Latin1Supplement"],[256,383,c.ORD],[384,591,c.ORD],[688,767,c.ORD,"SpacingModLetters"],[768,879,c.ORD,"CombDiacritMarks"],[880,1023,c.ORD,"GreekAndCoptic"],[7680,7935,c.ORD],[8192,8303,c.PUNCT,"GeneralPunctuation"],[8304,8351,c.ORD],[8352,8399,c.ORD],[8400,8447,c.ORD,"CombDiactForSymbols"],[8448,8527,c.ORD,"LetterlikeSymbols"],[8528,8591,c.ORD],[8592,8703,c.REL,"Arrows"],[8704,8959,c.BIN,"MathOperators"],[8960,9215,c.ORD,"MiscTechnical"],[9312,9471,c.ORD],[9632,9727,c.ORD,"GeometricShapes"],[9984,10175,c.ORD,"Dingbats"],[10176,10223,c.ORD,"MiscMathSymbolsA"],[10496,10623,c.REL,"SupplementalArrowsB"],[10624,10751,c.ORD,"MiscMathSymbolsB"],[10752,11007,c.BIN,"SuppMathOperators"],[11008,11263,c.ORD],[119808,120831,c.ORD]],OPTABLE:{prefix:{"\u2111":e.ORD11,"\u2113":e.ORD11,"\u211C":e.ORD11,"\u2200":e.ORD21,"\u2202":e.ORD21,"\u2203":e.ORD21,"\u2207":e.ORD21,"\u220F":e.OP,"\u2210":e.OP,"\u2211":e.OP,"\u2212":e.BIN01,"\u2213":e.BIN01,"\u221A":[1,1,c.ORD,{stretchy:true}],"\u2220":e.ORD,"\u222B":e.INTEGRAL,"\u222E":e.INTEGRAL,"\u22C0":e.OP,"\u22C1":e.OP,"\u22C2":e.OP,"\u22C3":e.OP,"\u2308":e.OPEN,"\u230A":e.OPEN,"\u27E8":e.OPEN,"\u2A00":e.OP,"\u2A01":e.OP,"\u2A02":e.OP,"\u2A04":e.OP,"\u2A06":e.OP,"\u00AC":e.ORD21,"\u00B1":e.BIN01,"(":e.OPEN,"+":e.BIN01,"-":e.BIN01,"[":e.OPEN,"{":e.OPEN,"|":e.OPEN},postfix:{"!":[1,0,c.CLOSE],"&":e.ORD,"\u2032":e.ORD02,"\u203E":e.WIDEACCENT,"\u2309":e.CLOSE,"\u230B":e.CLOSE,"\u23DE":e.WIDEACCENT,"\u23DF":e.WIDEACCENT,"\u266D":e.ORD02,"\u266E":e.ORD02,"\u266F":e.ORD02,"\u27E9":e.CLOSE,"\u02C6":e.WIDEACCENT,"\u02C7":e.WIDEACCENT,"\u02D8":e.ACCENT,"\u02D9":e.ACCENT,"\u02DC":e.WIDEACCENT,"\u0302":e.ACCENT,"\u00A8":e.ACCENT,"\u00AF":e.WIDEACCENT,")":e.CLOSE,"]":e.CLOSE,"^":e.WIDEACCENT,_:e.WIDEACCENT,"`":e.ACCENT,"|":e.CLOSE,"}":e.CLOSE,"~":e.WIDEACCENT},infix:{"%":[3,3,c.ORD],"\u2022":e.BIN4,"\u2026":e.INNER,"\u2044":e.TALLBIN,"\u2061":e.ORD,"\u2062":e.ORD,"\u2063":[0,0,c.ORD,{separator:true}],"\u2064":e.ORD,"\u2190":e.RELACCENT,"\u2191":e.WIDEREL,"\u2192":e.RELACCENT,"\u2193":e.WIDEREL,"\u2194":e.RELACCENT,"\u2195":e.WIDEREL,"\u2196":e.WIDEREL,"\u2197":e.WIDEREL,"\u2198":e.WIDEREL,"\u2199":e.WIDEREL,"\u21A6":e.WIDEREL,"\u21A9":e.WIDEREL,"\u21AA":e.WIDEREL,"\u21BC":e.RELACCENT,"\u21BD":e.WIDEREL,"\u21C0":e.RELACCENT,"\u21C1":e.WIDEREL,"\u21CC":e.WIDEREL,"\u21D0":e.WIDEREL,"\u21D1":e.WIDEREL,"\u21D2":e.WIDEREL,"\u21D3":e.WIDEREL,"\u21D4":e.WIDEREL,"\u21D5":e.WIDEREL,"\u2208":e.REL,"\u2209":e.REL,"\u220B":e.REL,"\u2212":e.BIN4,"\u2213":e.BIN4,"\u2215":e.TALLBIN,"\u2216":e.BIN4,"\u2217":e.BIN4,"\u2218":e.BIN4,"\u2219":e.BIN4,"\u221D":e.REL,"\u2223":e.REL,"\u2225":e.REL,"\u2227":e.BIN4,"\u2228":e.BIN4,"\u2229":e.BIN4,"\u222A":e.BIN4,"\u223C":e.REL,"\u2240":e.BIN4,"\u2243":e.REL,"\u2245":e.REL,"\u2248":e.REL,"\u224D":e.REL,"\u2250":e.REL,"\u2260":e.REL,"\u2261":e.REL,"\u2264":e.REL,"\u2265":e.REL,"\u226A":e.REL,"\u226B":e.REL,"\u227A":e.REL,"\u227B":e.REL,"\u2282":e.REL,"\u2283":e.REL,"\u2286":e.REL,"\u2287":e.REL,"\u228E":e.BIN4,"\u2291":e.REL,"\u2292":e.REL,"\u2293":e.BIN4,"\u2294":e.BIN4,"\u2295":e.BIN4,"\u2296":e.BIN4,"\u2297":e.BIN4,"\u2298":e.BIN4,"\u2299":e.BIN4,"\u22A2":e.REL,"\u22A3":e.REL,"\u22A4":e.ORD55,"\u22A5":e.REL,"\u22A8":e.REL,"\u22C4":e.BIN4,"\u22C5":e.BIN4,"\u22C6":e.BIN4,"\u22C8":e.REL,"\u22EE":e.ORD55,"\u22EF":e.INNER,"\u22F1":[5,5,c.INNER],"\u2500":[0,0,c.ORD,{stretchy:true}],"\u25B3":e.BIN4,"\u25B5":e.BIN4,"\u25B9":e.BIN4,"\u25BD":e.BIN4,"\u25BF":e.BIN4,"\u25C3":e.BIN4,"\u2758":[4,4,c.REL,{fence:true,stretchy:true,symmetric:true}],"\u27F5":e.REL1,"\u27F6":e.REL1,"\u27F7":e.REL1,"\u27F8":e.REL1,"\u27F9":e.REL1,"\u27FA":e.REL1,"\u2A2F":e.BIN4,"\u2A3F":e.BIN4,"\u2AAF":e.REL,"\u2AB0":e.REL,"\u00B1":e.BIN4,"\u00B7":e.BIN4,"\u00D7":e.BIN4,"\u00F7":e.BIN4,"*":e.BIN3,"+":e.BIN4,",":[0,3,c.PUNCT,{separator:true}],"-":e.BIN4,".":[3,3,c.ORD],"/":e.ORD11,":":[1,2,c.REL],";":[0,3,c.PUNCT,{separator:true}],"<":e.REL,"=":e.REL,">":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u02C9":e.ACCENT,"\u02CA":e.ACCENT,"\u02CB":e.ACCENT,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2118":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u27EE":e.OPEN,"\u27EF":e.CLOSE,"\u27FC":e.REL4,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
(function(){var c="1.0";MathJax.Extension["TeX/noErrors"]={version:c,config:MathJax.Hub.Insert({multiLine:true,inlineDelimiters:["",""],style:{"font-family":"serif","font-size":"80%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}},((MathJax.Hub.config.TeX||{}).noErrors||{}))};var a=MathJax.Extension["TeX/noErrors"].config;var b=String.fromCharCode(160);MathJax.Hub.Config({TeX:{Augment:{formatError:function(f,e,g,d){var i=a.inlineDelimiters;var h=(g||a.multiLine);if(!g){e=i[0]+e+i[1]}if(h){e=e.replace(/ /g,b)}else{e=e.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(e).With({isError:true,multiLine:h})}}},"HTML-CSS":{styles:{".MathJax .merror":MathJax.Hub.Insert({"font-style":null,"background-color":null,"vertical-align":(MathJax.Hub.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})})();MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var b=MathJax.OutputJax["HTML-CSS"];var c=a.math.prototype.toHTML;a.math.Augment({toHTML:function(d,e){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toHTML(d)}return c.call(this,d,e)}});a.merror.Augment({toHTML:function(j){if(!this.isError){return a.mbase.prototype.toHTML.call(this,j)}j=this.HTMLcreateSpan(j);if(this.multiLine){j.style.display="inline-block"}var l=this.data[0].data[0].data.join("").split(/\n/);for(var g=0,e=l.length;g<e;g++){b.addText(j,l[g]);if(g!==e-1){b.addElement(j,"br")}}var n=b.getHD(j.parentNode),d=b.getW(j.parentNode);if(e>1){var k=(n.h+n.d)/2,h=b.TeX.x_height/2;var f=b.config.styles[".MathJax .merror"]["font-size"];if(f&&f.match(/%/)){h*=parseInt(f)/100}j.parentNode.style.verticalAlign=b.Em(n.d+(h-k));n.h=h+k;n.d=k-h}j.bbox={h:n.h,d:n.d,w:d,lw:0,rw:d};return j}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Hub.Register.StartupHook("NativeMML Jax Ready",function(){var b=MathJax.ElementJax.mml;var a=MathJax.Extension["TeX/noErrors"].config;var c=b.math.prototype.toNativeMML;b.math.Augment({toNativeMML:function(d){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toNativeMML(d)}return c.call(this,d)}});b.merror.Augment({toNativeMML:function(g){if(!this.isError){return b.mbase.prototype.toNativeMML.call(this,g)}g=g.appendChild(document.createElement("span"));var h=this.data[0].data[0].data.join("").split(/\n/);for(var f=0,e=h.length;f<e;f++){g.appendChild(document.createTextNode(h[f]));if(f!==e-1){g.appendChild(document.createElement("br"))}}if(this.multiLine){g.style.display="inline-block";if(e>1){g.style.verticalAlign="middle"}}for(var j in a.style){if(a.style.hasOwnProperty(j)){var d=j.replace(/-./g,function(i){return i.charAt(1).toUpperCase()});g.style[d]=a.style[j]}}return g}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");
MathJax.Extension["TeX/noUndefined"]={version:"1.0",config:MathJax.Hub.Insert({attributes:{mathcolor:"red"}},((MathJax.Hub.config.TeX||{}).noUndefined||{}))};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");
(function(d){var c=true,f=false,i,h=String.fromCharCode(160);var e=MathJax.Object.Subclass({Init:function(k){this.global={};this.data=[b.start().With({global:this.global})];if(k){this.data[0].env=k}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l<k;l++){n=arguments[l];if(n instanceof i.mbase){n=b.mml(n)}n.global=this.global;o=(this.data.length?this.Top().checkItem(n):c);if(o instanceof Array){this.Pop();this.Push.apply(this,o)}else{if(o instanceof b){this.Pop();this.Push(o)}else{if(o){this.data.push(n);if(n.env){for(var p in this.env){if(this.env.hasOwnProperty(p)){n.env[p]=this.env[p]}}this.env=n.env}else{n.env=this.env}}}}}},Pop:function(){var k=this.data.pop();if(!k.isOpen){delete k.env}this.env=(this.data.length?this.Top().env:{});return k},Top:function(k){if(k==null){k=1}if(this.data.length<k){return null}return this.data[this.data.length-k]},Prev:function(k){var l=this.Top();if(k){return l.data[l.data.length-1]}else{return l.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",closeError:"Extra close brace or missing open brace",rightError:"Missing \\left or extra \\right",Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(k,l){if(k==null){k=c}if(this.data.length===1&&!l){return this.data[0]}return i.mrow.apply(i,this.data).With((k?{inferred:c}:{}))},checkItem:function(k){if(k.type==="over"&&this.isOpen){k.num=this.mmlData(f);this.data=[]}if(k.type==="cell"&&this.isOpen){d.Error("Misplaced "+k.name)}if(k.isClose&&this[k.type+"Error"]){d.Error(this[k.type+"Error"])}if(!k.isNotStack){return c}this.Push(k.data[0]);return f},With:function(k){for(var l in k){if(k.hasOwnProperty(l)){this[l]=k[l]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:c,checkItem:function(k){if(k.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,k)}});b.stop=b.Subclass({type:"stop",isClose:c});b.open=b.Subclass({type:"open",isOpen:c,stopError:"Extra open brace or missing close brace",checkItem:function(l){if(l.type==="close"){var k=this.mmlData();return b.mml(i.TeXAtom(k))}return this.SUPER(arguments).checkItem.call(this,l)}});b.close=b.Subclass({type:"close",isClose:c});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(l){var k=["","subscript","superscript"][this.position];if(l.type==="open"||l.type==="left"){return c}if(l.type==="mml"){this.data[0].SetData(this.position,l.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error("Missing open brace for "+k)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:c,name:"\\over",checkItem:function(m,k){if(m.type==="over"){d.Error("Ambiguous use of "+m.name)}if(m.isClose){var l=i.mfrac(this.num,this.mmlData(f));if(this.thickness!=null){l.linethickness=this.thickness}if(this.open||this.close){l.texClass=i.TEXCLASS.INNER;l.texWithDelims=c;l=i.mfenced(l).With({open:this.open,close:this.close})}return[b.mml(l),m]}return this.SUPER(arguments).checkItem.call(this,m)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:c,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(l){if(l.type==="right"){var k=i.mfenced(this.data.length===1?this.data[0]:i.mrow.apply(i,this.data));return b.mml(k.With({open:this.delim,close:l.delim}))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:c,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:c,checkItem:function(k){if(k.type==="end"){if(k.name!==this.name){d.Error("\\begin{"+this.name+"} ended with \\end{"+k.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(k.type==="stop"){d.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,k)}});b.end=b.Subclass({type:"end",isClose:c});b.style=b.Subclass({type:"style",checkItem:function(l){if(!l.isClose){return this.SUPER(arguments).checkItem.call(this,l)}var k=i.mstyle.apply(i,this.data).With(this.styles);return[b.mml(k),l]}});b.position=b.Subclass({type:"position",checkItem:function(l){if(l.isClose){d.Error("Missing box for "+this.name)}if(l.isNotStack){var k=l.mmlData();switch(this.move){case"vertical":k=i.mpadded(k).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(k)];case"horizontal":return[b.mml(this.left),l,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,l)}});b.array=b.Subclass({type:"array",isOpen:c,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(l){if(l.isClose){if(l.isEntry){this.EndEntry();this.clearEnv();return f}if(l.isCR){this.EndEntry();this.EndRow();this.clearEnv();return f}this.EndTable();this.clearEnv();var k=i.mtable.apply(i,this.table).With(this.arraydef);if(this.open||this.close){k=i.mfenced(k).With({open:this.open,close:this.close})}k=b.mml(k);if(this.requireClose){if(l.type==="close"){return k}d.Error("Missing close brace")}return[k,l]}return this.SUPER(arguments).checkItem.call(this,l)},EndEntry:function(){this.row.push(i.mtd.apply(i,this.data));this.data=[]},EndRow:function(){this.table.push(i.mtr.apply(i,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var k=this.arraydef.rowlines.split(/ /);if(k.length===this.table.length){this.arraydef.frame=k.pop();this.arraydef.rowlines=k.join(" ")}else{if(k.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var k in this.env){if(this.env.hasOwnProperty(k)){delete this.env[k]}}}});b.cell=b.Subclass({type:"cell",isClose:c});b.mml=b.Subclass({type:"mml",isNotStack:c,Push:function(){for(var l=0,k=arguments.length;l<k;l++){if(arguments[l].type!=="mo"&&arguments[l].isEmbellished()){arguments[l]=i.TeXAtom(arguments[l]).With({isEmbellishedWrapper:c})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var j=function(){i=MathJax.ElementJax.mml;MathJax.Hub.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:i.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:i.VARIANT.NORMAL}],Re:["211C",{mathvariant:i.VARIANT.NORMAL}],Im:["2111",{mathvariant:i.VARIANT.NORMAL}],partial:["2202",{mathvariant:i.VARIANT.NORMAL}],infty:["221E",{mathvariant:i.VARIANT.NORMAL}],prime:["2032",{mathvariant:i.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:i.VARIANT.NORMAL}],nabla:["2207",{mathvariant:i.VARIANT.NORMAL}],top:["22A4",{mathvariant:i.VARIANT.NORMAL}],bot:["22A5",{mathvariant:i.VARIANT.NORMAL}],angle:["2220",{mathvariant:i.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:i.VARIANT.NORMAL}],backslash:["2216",{mathvariant:i.VARIANT.NORMAL}],forall:["2200",{mathvariant:i.VARIANT.NORMAL}],exists:["2203",{mathvariant:i.VARIANT.NORMAL}],neg:["00AC",{mathvariant:i.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:i.VARIANT.NORMAL}],flat:["266D",{mathvariant:i.VARIANT.NORMAL}],natural:["266E",{mathvariant:i.VARIANT.NORMAL}],sharp:["266F",{mathvariant:i.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:i.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:i.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:i.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:i.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigvee:["22C1",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigwedge:["22C0",{texClass:i.TEXCLASS.OP,movesupsub:c}],biguplus:["2A04",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcap:["22C2",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcup:["22C3",{texClass:i.TEXCLASS.OP,movesupsub:c}],"int":["222B",{texClass:i.TEXCLASS.OP}],intop:["222B",{texClass:i.TEXCLASS.OP,movesupsub:c,movablelimits:c}],iint:["222C",{texClass:i.TEXCLASS.OP}],iiint:["222D",{texClass:i.TEXCLASS.OP}],prod:["220F",{texClass:i.TEXCLASS.OP,movesupsub:c}],sum:["2211",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigotimes:["2A02",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigoplus:["2A01",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigodot:["2A00",{texClass:i.TEXCLASS.OP,movesupsub:c}],oint:["222E",{texClass:i.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:i.TEXCLASS.OP,movesupsub:c}],smallint:["222B",{largeop:f}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:f}],oslash:["2298",{largeop:f}],otimes:["2297",{largeop:f}],ominus:["2296",{largeop:f}],oplus:["2295",{largeop:f}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:i.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:i.TEXCLASS.PUNCT}],colon:["003A",{texClass:i.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:i.TEXCLASS.ORD}],"\\|":["2225",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",c,0],textstyle:["SetStyle","T",f,0],scriptstyle:["SetStyle","S",f,1],scriptscriptstyle:["SetStyle","SS",f,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont",i.VARIANT.ITALIC],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim&thinsp;inf"],limsup:["NamedOp",null,"lim&thinsp;sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.THINMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em"],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],def:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Macro","",1],nonumber:["Macro",""],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],require:"Require"},environment:{array:["Array"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",i.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",i.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){g.macros[l]=["Macro",k[l]]}else{g.macros[l]=["Macro"].concat(k[l])}}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.i<this.string.length){k=this.string.charAt(this.i++);if(g.special[k]){this[g.special[k]](k)}else{if(g.letter.test(k)){this.Variable(k)}else{if(g.digit.test(k)){this.Number(k)}else{this.Other(k)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(q){var k=this.GetCS(),p,n;if(g.macros[k]){var m=g.macros[k];if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,["\\"+k].concat(m.slice(1)))}else{if(g.mathchar0mi[k]){p=g.mathchar0mi[k];n={mathvariant:i.VARIANT.ITALIC};if(p instanceof Array){n=p[1];p=p[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.mathchar0mo[k]){p=g.mathchar0mo[k];n={stretchy:f};if(p instanceof Array){n=p[1];n.stretchy=f;p=p[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+p)).With(n)))}else{if(g.mathchar7[k]){p=g.mathchar7[k];n={mathvariant:i.VARIANT.NORMAL};if(p instanceof Array){n=p[1];p=p[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.delimiter["\\"+k]!=null){var o=g.delimiter["\\"+k];n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:f,stretchy:f}).With(n)))}else{this.csUndefined("\\"+k)}}}}}},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(g.number);if(l){k=i.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=i.mo(i.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(i.mtext(i.chars(h)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=i.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.over}else{l=i.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.under}else{l=i.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(m){var l=this.stack.Prev();if(!l){l=i.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(i.mo(i.chars(k)).With({isPrime:c,variantForm:d.isSTIX}));this.Push(i.msubsup(l,null,k))},Comment:function(k){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(k){d.Error("You can't use 'macro parameter character #' in math mode")},Other:function(m){var l={stretchy:false},k;if(this.stack.env.font){l.mathvariant=this.stack.env.font}if(g.remap[m]){m=g.remap[m];if(m instanceof Array){l=m[1];m=m[0]}k=i.mo(i.entity("#x"+m))}else{k=i.mo(m)}if(k.autoDefault("texClass",true)==""){k=i.TeXAtom(k)}this.Push(this.mmlToken(k.With(l)))},SetFont:function(l,k){this.stack.env.font=k},SetStyle:function(l,k,m,n){this.stack.env.style=k;this.stack.env.level=n;this.Push(b.style().With({styles:{displaystyle:m,scriptlevel:n}}))},SetSize:function(k,l){this.stack.env.size=l;this.Push(b.style().With({styles:{mathsize:l+"em"}}))},Color:function(m){var l=this.GetArgument(m);var k=this.stack.env.color;this.stack.env.color=l;var n=this.ParseArg(m);if(k){this.stack.env.color}else{delete this.stack.env.color}this.Push(i.mstyle(n).With({mathcolor:l}))},Spacer:function(k,l){this.Push(i.mspace().With({width:l,mathsize:i.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(k){this.Push(b[k.substr(1)]().With({delim:this.GetDelimiter(k)}))},NamedOp:function(m,l,o){var n=(l!=null&&l===0?f:c);if(!o){o=m.substr(1)}l=((l||l==null)?c:f);o=o.replace(/&thinsp;/,String.fromCharCode(8198));var k=i.mo(o).With({movablelimits:l,movesupsub:n,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});k.useMMLspacing&=~k.SPACE_ATTR.form;this.Push(this.mmlToken(k))},Limits:function(l,k){var m=this.stack.Prev("nopop");if(m.texClass!==i.TEXCLASS.OP){d.Error(l+" is allowed only on operators")}m.movesupsub=(k?c:f);m.movablelimits=f},Over:function(m,l,n){var k=b.over().With({name:m});if(l||n){k.open=l;k.close=n}else{if(m.match(/withdelims$/)){k.open=this.GetDelimiter(m);k.close=this.GetDelimiter(m)}}if(m.match(/^\\above/)){k.thickness=this.GetDimen(m)}else{if(m.match(/^\\atop/)||l||n){k.thickness=0}}this.Push(k)},Frac:function(l){var k=this.ParseArg(l);var m=this.ParseArg(l);this.Push(i.mfrac(k,m))},Sqrt:function(l){var m=this.GetBrackets(l),k=this.ParseArg(l);if(m==""){k=i.msqrt.apply(i,k.array())}else{k=i.mroot(k,this.parseRoot(m))}this.Push(k)},Root:function(l){var m=this.GetUpTo(l,"\\of");var k=this.ParseArg(l);this.Push(i.mroot(k,this.parseRoot(m)))},parseRoot:function(p){var l=this.stack.env,k=l.inRoot;l.inRoot=true;var o=d.Parse(p,l);p=o.mml();var m=o.stack.global;if(m.leftRoot||m.upRoot){p=i.mpadded(p);if(m.leftRoot){p.width=m.leftRoot}if(m.upRoot){p.voffset=m.upRoot;p.height=m.upRoot}}l.inRoot=k;return p},MoveRoot:function(k,m){if(!this.stack.env.inRoot){d.Error(k+" can appear only within a root")}if(this.stack.global[m]){d.Error("Multiple use of "+k)}var l=this.GetArgument(k);if(!l.match(/-?[0-9]+/)){d.Error("The argument to "+k+" must be an integer")}l=(l/15)+"em";if(l.substr(0,1)!=="-"){l="+"+l}this.stack.global[m]=l},Accent:function(m,k,o){var n=this.ParseArg(m);var l=this.mmlToken(i.mo(i.entity("#x"+k)).With({accent:c}));l.stretchy=(o?c:f);this.Push(i.munderover(n,null,l).With({accent:c}))},UnderOver:function(m,p,k){var o={o:"over",u:"under"}[m.charAt(1)];var n=this.ParseArg(m);if(n.Get("movablelimits")){n.movablelimits=false}var l=i.munderover(n,null,null);if(k){l.movesupsub=c}l.data[l[o]]=this.mmlToken(i.mo(i.entity("#x"+p)).With({stretchy:c,accent:(o=="under")}));this.Push(l)},Overset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,null,m))},Underset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,m,null))},TeXAtom:function(n,p){var o={texClass:p},m;if(p==i.TEXCLASS.OP){o.movesupsub=o.movablelimits=c;var k=this.GetArgument(n);var l=k.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(l){m=this.mmlToken(i.mo(l[1]).With({movablelimits:c,movesupsub:c,mathvariant:i.VARIANT.NORMAL,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP}));m.useMMLspacing&=~m.SPACE_ATTR.form}else{m=i.TeXAtom(d.Parse(k,this.stack.env).mml()).With(o)}}else{m=i.TeXAtom(this.ParseArg(n)).With(o)}this.Push(m)},Strut:function(k){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(l,k,m){var n=i.mphantom(this.ParseArg(l));if(k||m){n=i.mpadded(n);if(m){n.height=n.depth=0}if(k){n.width=0}}this.Push(n)},Smash:function(m){var l=this.trimSpaces(this.GetBrackets(m));var k=i.mpadded(this.ParseArg(m));switch(l){case"b":k.depth=0;break;case"t":k.height=0;break;default:k.height=k.depth=0}this.Push(k)},Lap:function(l){var k=i.mpadded(this.ParseArg(l)).With({width:0});if(l==="\\llap"){k.lspace="-1 width"}this.Push(k)},RaiseLower:function(k){var l=this.GetDimen(k);var m=b.position().With({name:k,move:"vertical"});if(l.charAt(0)==="-"){l=l.slice(1);k={raise:"\\lower",lower:"\\raise"}[k.substr(1)]}if(k==="\\lower"){m.dh="-"+l;m.dd=l}else{m.dh=l;m.dd="-"+l}this.Push(m)},MoveLeftRight:function(k){var n=this.GetDimen(k);var m=(n.charAt(0)==="-"?n.slice(1):"-"+n);if(k==="\\moveleft"){var l=n;n=m;m=l}this.Push(b.position().With({name:k,move:"horizontal",left:i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:1}),right:i.mspace().With({width:m,mathsize:i.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(k){this.Push(i.mspace().With({width:this.GetDimen(k),mathsize:i.SIZE.NORMAL,scriptlevel:0}))},Rule:function(m,o){var k=this.GetDimen(m),n=this.GetDimen(m),q=this.GetDimen(m);var l,p={width:k,height:n,depth:q};if(o!=="blank"){l=i.mpadded(i.mrow()).With(p);if(parseFloat(k)&&parseFloat(n)+parseFloat(q)){l=i.mstyle(l).With({mathbackground:(this.stack.env.color||"black")})}}else{l=i.mspace().With(p)}this.Push(l)},MakeBig:function(k,n,l){l*=g.p_height;l=String(l).replace(/(\.\d\d\d).+/,"$1")+"em";var m=this.GetDelimiter(k);this.Push(i.TeXAtom(i.mo(m).With({minsize:l,maxsize:l,scriptlevel:0,fence:c,stretchy:c,symmetric:c})).With({texClass:n}))},BuildRel:function(k){var l=this.ParseUpTo(k,"\\over");var m=this.ParseArg(k);this.Push(i.TeXAtom(i.munderover(m,null,l)).With({mclass:i.TEXCLASS.REL}))},HBox:function(k,l){this.Push.apply(this,this.InternalMath(this.GetArgument(k),l))},FBox:function(k){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(k))).With({notation:"box"}))},Require:function(k){var l=this.GetArgument(k);this.Extension(null,l)},Extension:function(k,l,m){if(k&&!typeof(k)==="string"){k=k.name}l=d.extensionDir+"/"+l;if(!l.match(/\.js$/)){l+=".js"}if(!MathJax.Ajax.loaded[MathJax.Ajax.fileURL(l)]){if(k!=null){delete g[m||"macros"][k.replace(/^\\/,"")]}MathJax.Hub.RestartAfter(MathJax.Ajax.Require(l))}},Macro:function(l,o,n){if(n){var k=[];for(var m=0;m<n;m++){k.push(this.GetArgument(l))}o=this.SubstituteArgs(k,o)}this.string=this.AddArgs(o,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,q,m,k){var r=this.GetNext();if(r===""){d.Error("Missing argument for "+l)}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:c,arraydef:{rowspacing:(m||"4pt"),columnspacing:(q||"1em")}});if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=c}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(k){this.Push(b.cell().With({isEntry:c,name:k}))},Cr:function(k){this.Push(b.cell().With({isCR:c,name:k}))},HLine:function(l,m){if(m==null){m="solid"}var n=this.stack.Top();if(n.type!=="array"||n.data.length){d.Error("Misplaced "+l)}if(n.table.length==0){n.arraydef.frame=m}else{var k=(n.arraydef.rowlines?n.arraydef.rowlines.split(/ /):[]);while(k.length<n.table.length){k.push("none")}k[n.table.length-1]=m;n.arraydef.rowlines=k.join(" ")}},Begin:function(l){var m=this.GetArgument(l);if(m.match(/[^a-z*]/i)){d.Error('Invalid environment name "'+m+'"')}if(!g.environment[m]){d.Error('Unknown environment "'+m+'"')}if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var n=g.environment[m];if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(m,o,t,r,s,n,k,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){var l=(u.charAt(0)+u.charAt(u.length-1)).replace(/[^|:]/g,"");if(l!==""){q.arraydef.frame={"|":"solid",":":"dashed"}[l.charAt(0)];q.arraydef.framespacing=".5em .5ex"}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(k==="D"){q.arraydef.displaystyle=c}if(k==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=f}this.Push(m);return q},convertDelimiter:function(k){if(k){k=g.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":n++;break;case"}":if(n==0){d.Error("Extra close brace")}if(--n==0){return this.string.slice(k,this.i-1)}break}}d.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(l){if(this.GetNext()!="["){return""}var k=++this.i,m=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":m++;break;case"\\":this.i++;break;case"}":if(m--<=0){d.Error("Extra close brace while looking for ']'")}break;case"]":if(m==0){return this.string.slice(k,this.i-1)}break}}d.Error("Couldn't find closing ']' for argument to "+l)},GetDelimiter:function(k){while(this.nextIsSpace()){this.i++}var l=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(l=="\\"){l+=this.GetCS(k)}if(g.delimiter[l]!=null){return this.convertDelimiter(l)}}d.Error("Missing or unrecognized delimiter for "+k)},GetDimen:function(l){var m;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){m=this.GetArgument(l);if(m.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return m.replace(/ /g,"")}}else{m=this.string.slice(this.i);var k=m.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(k){this.i+=k[0].length;return k[1].replace(/ /g,"")}}d.Error("Missing dimension or its units for "+l)},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error("Extra close brace while looking for "+o)}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error("Couldn't find "+o+" for "+n)},ParseArg:function(k){return d.Parse(this.GetArgument(k),this.stack.env).mml()},ParseUpTo:function(k,l){return d.Parse(this.GetUpTo(k,l),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:f};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\$|\\\(/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(i.TeXAtom(d.Parse(q.slice(l,o-1)).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="\\"){r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(i.TeXAtom(d.Parse(q.slice(l,o-2)).mml().With(p)));n="";l=o}}}}}if(n!==""){d.Error("Math not terminated in text box")}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(l,k){l=l.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(l)).With(k)},SubstituteArgs:function(l,k){var o="";var n="";var p;var m=0;while(m<k.length){p=k.charAt(m++);if(p==="\\"){o+=p+k.charAt(m++)}else{if(p==="#"){p=k.charAt(m++);if(p==="#"){o+=p}else{if(!p.match(/[1-9]/)||p>l.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},Translate:function(k){var l,n=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(MathJax.Hub.Browser.isKonqueror){n=n.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}var o=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);n=d.prefilterMath(n,o,k);try{l=d.Parse(n).mml()}catch(m){if(!m.texError){throw m}l=this.formatError(m,n,o,k)}if(l.inferred){l=i.apply(MathJax.ElementJax,l.data)}else{l=i(l)}if(o){l.root.display="block"}return this.postfilterMath(l,o,k)},prefilterMath:function(l,m,k){return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(m,l,n,k){return i.merror(m.message.replace(/\n.*/,""))},Error:function(k){throw MathJax.Hub.Insert(Error(k),{texError:c})},Macro:function(k,l,m){g.macros[k]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(l){for(var n=0,k=l.data.length;n<k;n++){if(l.data[n]){if(l.isa(i.mrow)){while(n+1<k&&l.data[n+1]&&l.data[n].isa(i.mo)&&l.data[n+1].isa(i.mo)&&l.data[n].Get("texClass")===i.TEXCLASS.REL&&l.data[n+1].Get("texClass")===i.TEXCLASS.REL){l.data[n].Append.apply(l.data[n],l.data[n+1].data);l.data.splice(n+1,1);k--}}if(!l.data[n].isToken){this.combineRelations(l.data[n])}}}}});d.loadComplete("jax.js")})(MathJax.InputJax.TeX);
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var e="1.0";var a=MathJax.ElementJax.mml;var f=MathJax.InputJax.TeX;var c=f.Definitions;var d=f.Stack.Item;var b=function(g){return g.join("em ")+"em"};MathJax.Hub.Insert(c,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",a.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",a.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["Macro","\\mathop{\\rm inj\\,lim}"],projlim:["Macro","\\mathop{\\rm proj\\,lim}"],varliminf:["Macro","\\mathop{\\underline{\\rm lim}}"],varlimsup:["Macro","\\mathop{\\overline{\\rm lim}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0em",""],tbinom:["Genfrac","(",")","0em",1],dbinom:["Genfrac","(",")","0em",0],cfrac:"CFrac",shoveleft:["HandleShove",a.ALIGN.LEFT],shoveright:["HandleShove",a.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",b([5/18])],gather:["AMSarray",null,true,true,"c"],"gather*":["AMSarray",null,false,true,"c"],alignat:["AlignAt",null,true,true],"alignat*":["AlignAt",null,false,true],alignedat:["AlignAt",null,false,false],aligned:["Array",null,null,null,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".5em","D"],gathered:["Array",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,b([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",b([1/3]),".2em","S",1]},delimiter:{"\\lvert":["2223",{texClass:a.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:a.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:a.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:a.TEXCLASS.CLOSE}]}});f.Parse.Augment({HandleTag:function(h){var g=this.trimSpaces(this.GetArgument(h));if(g==="*"){g=this.GetArgument(h)}else{g="("+g+")"}if(this.stack.global.notag){f.Error(h+" not allowed in "+this.stack.global.notag+" environment")}if(this.stack.global.tag){f.Error("Multiple "+h)}this.stack.global.tag=a.mtd.apply(a,this.InternalMath(g))},HandleNoTag:function(g){if(this.stack.global.tag){delete this.stack.global.tag}},HandleDeclareOp:function(h){var g="";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}if(i.charAt(0)=="\\"){i=i.substr(1)}var j=this.GetArgument(h);j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");f.Definitions.macros[i]=["Macro","\\mathop{\\rm "+j+"}"+g]},HandleOperatorName:function(h){var g="\\nolimits";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}i=i.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+i+"}"+g+" "+this.string.slice(this.i);this.i=0},HandleShove:function(h,g){var i=this.stack.Top();if(i.type!=="multline"||i.data.length){f.Error(h+" must come at the beginning of the line")}i.data.shove=g},CFrac:function(j){var g=this.trimSpaces(this.GetBrackets(j)),i=this.GetArgument(j),k=this.GetArgument(j);var h=a.mfrac(f.Parse("\\strut\\textstyle{"+i+"}",this.stack.env).mml(),f.Parse("\\strut\\textstyle{"+k+"}",this.stack.env).mml());g=({l:a.ALIGN.LEFT,r:a.ALIGN.RIGHT,"":""})[g];if(g==null){f.Error("Illegal alignment specified in "+j)}if(g){h.numalign=h.denomalign=g}this.Push(h)},Genfrac:function(h,j,o,l,g){if(j==null){j=this.GetDelimiterArg(h)}else{j=this.convertDelimiter(j)}if(o==null){o=this.GetDelimiterArg(h)}else{o=this.convertDelimiter(o)}if(l==null){l=this.GetArgument(h)}if(g==null){g=this.trimSpaces(this.GetArgument(h))}var k=this.ParseArg(h);var n=this.ParseArg(h);var i=a.mfrac(k,n);if(l!==""){i.linethickness=l}if(j||o){i=a.mfenced(i).With({open:j,close:o})}if(g!==""){var m=(["D","T","S","SS"])[g];if(m==null){f.Error("Bad math style for "+h)}i=a.mstyle(i);if(m==="D"){i.displaystyle=true;i.scriptlevel=0}else{i.displaystyle=false;i.scriptlevel=g-1}}this.Push(i)},Multline:function(h,g){this.Push(h);return d.multline().With({arraydef:{displaystyle:true,rowspacing:".5em",width:f.config.MultLineWidth,columnwidth:"100%",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AMSarray:function(i,h,g,k,j){this.Push(i);k=k.replace(/[^clr]/g,"").split("").join(" ");k=k.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return d.AMSarray(i.name,h,g,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:k,columnspacing:(j||"1em"),rowspacing:"3pt",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AlignAt:function(i,h,g){var j=this.GetArgument("\\begin{"+i.name+"}");if(j.match(/[^0-9]/)){f.Error("Argument to \\begin{"+i.name+"} must me a positive integer")}align="";spacing=[];while(j>0){align+="rl";spacing.push("0em 0em");j--}spacing=spacing.join(" ");if(g){return this.AMSarray(i,h,g,align,spacing)}return this.Array(i,null,null,align,spacing,".5em","D")},MultiIntegral:function(g,k){var j=this.GetNext();if(j==="\\"){var h=this.i;j=this.GetArgument(g);this.i=h;if(j==="\\limits"){if(g==="\\idotsint"){k="\\!\\!\\mathop{\\,\\,"+k+"}"}else{k="\\!\\!\\!\\mathop{\\,\\,\\,"+k+"}"}}}this.string=k+" "+this.string.slice(this.i);this.i=0},xArrow:function(i,m,k,g){var j={width:"+"+(k+g)+"mu",lspace:k+"mu"};var n=this.GetBrackets(i),o=this.ParseArg(i);var p=a.mo(a.chars(String.fromCharCode(m))).With({stretchy:true,texClass:a.TEXCLASS.REL});var h=a.munderover(p);h.SetData(h.over,a.mpadded(o).With(j).With({voffset:".15em"}));if(n){n=f.Parse(n,this.stack.env).mml();h.SetData(h.under,a.mpadded(n).With(j).With({voffset:"-.24em"}))}this.Push(h)},GetDelimiterArg:function(g){var h=this.trimSpaces(this.GetArgument(g));if(h==""){return null}if(!c.delimiter[h]){f.Error("Missing or unrecognized delimiter for "+g)}return this.convertDelimiter(h)}});d.multline=d.array.Subclass({type:"multline",EndEntry:function(){var g=a.mtd.apply(a,this.data);if(this.data.shove){g.columnalign=this.data.shove}this.row.push(g);this.data=[]},EndRow:function(){if(this.row.length!=1){f.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var h=this.table.length-1,j;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=a.ALIGN.LEFT}if(!this.table[h][0].columnalign){this.table[h][0].columnalign=a.ALIGN.RIGHT}var g=a.mtr;if(this.global.tag){this.table[0]=[this.global.tag].concat(this.table[0]);delete this.global.tag;g=a.mlabeledtr}this.table[0]=g.apply(a,this.table[0]);for(j=1,h=this.table.length;j<h;j++){this.table[j]=a.mtr.apply(a,this.table[j])}}}});d.AMSarray=d.array.Subclass({type:"AMSarray",Init:function(j,i,h,g){this.SUPER(arguments).Init.apply(this);this.numbered=i;this.save_notag=g.global.notag;g.global.notag=(h?null:j)},EndRow:function(){var g=a.mtr;if(this.global.tag){this.row=[this.global.tag].concat(this.row);g=a.mlabeledtr;delete this.global.tag}this.table.push(g.apply(a,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notag=this.save_notag}});d.start.Augment({oldCheckItem:d.start.prototype.checkItem,checkItem:function(h){if(h.type==="stop"){var g=this.mmlData();if(this.global.tag){var j=[this.global.tag,a.mtd(g)];delete this.global.tag;var i={side:f.config.TagSide,minlabelspacing:f.config.TagIndent,columnalign:g.displayAlign};if(g.displayAlign===a.INDENTALIGN.LEFT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth=g.displayIndent+" fit";i.columnspacing="0";j=[j[0],a.mtd(),j[1]]}}else{if(g.displayAlign===a.INDENTALIGN.RIGHT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth="fit "+g.displayIndent;i.columnspacing="0";j[2]=a.mtd()}}}g=a.mtable(a.mlabeledtr.apply(a,j)).With(i)}return d.mml(g)}return this.SUPER(arguments).checkItem.call(this,h)}});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.0";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{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",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:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});if(MathJax.Hub.Browser.isMSIE){MathJax.InputJax.TeX.Definitions.mathchar0mi.digamma=["03DC",{variantForm:true}];MathJax.InputJax.TeX.Definitions.mathchar0mi.varkappa=["03F0",{variantForm:true}]}});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=MathJax.InputJax.TeX.Definitions;var c=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){c["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(c["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){b.mathchar0mi.varnothing="2205";b.mathchar0mi.hslash="210F";b.mathchar0mi.blacktriangle="25B4";b.mathchar0mi.blacktriangledown="25BE";b.mathchar0mi.square="25FB";b.mathchar0mi.blacksquare="25FC";b.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];b.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];b.mathchar0mo.blacktriangleleft="25C2";b.mathchar0mo.blacktriangleright="25B8";b.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(c["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":e.FONTDATA.FONTS[h].family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&e.FONTDATA.FONTS[h].isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{useOldImageData:true,styles:{".MathJax":{display:"inline","font-family":"serif","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:b(),Config:function(){this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DEFAULTFAMILY:"serif",DEFAULTWEIGHT:"normal",DEFAULTSTYLE:"normal",DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;if(!i){i=window.event}var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;var i=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=i+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&i!==100){this.em=a.mbase.prototype.em=f*i/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="pc"){return f*this.pxPerInch/e.em/12}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(u,o,z,A,r){var i=this.createStack(u,true);var q=this.createBox(i),p=this.createBox(i);this.createChar(q,(z.top||z.ext),A,r);this.createChar(p,(z.bot||z.ext),A,r);var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+p.bbox.h+p.bbox.d;var l=-q.bbox.h;this.placeBox(q,0,l,true);l-=q.bbox.d;if(z.mid){x=this.createBox(i);this.createChar(x,z.mid,A,r);v+=x.bbox.h+x.bbox.d}if(o>v){g=this.Element("span");this.createChar(g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;this.placeBox(this.addBox(i,g.cloneNode(true)),0,l,true)}l+=m-g.bbox.d;if(z.mid&&t){this.placeBox(x,0,l-x.bbox.h,true);s=j;l+=-(x.bbox.h+x.bbox.d)+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){this.placeBox(x,0,l-x.bbox.h,true);l+=-(x.bbox.h+x.bbox.d)}l+=(v-o)/2}this.placeBox(p,0,l-p.bbox.h,true);l-=p.bbox.h+p.bbox.d;u.bbox={w:Math.max(q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:Math.max(q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u.isMultiChar=true;this.setStackWidth(i,u.bbox.w)},extendDelimiterH:function(t,g,y,A,q){var j=this.createStack(t,true);var h=this.createBox(j),u=this.createBox(j);this.createChar(h,(y.left||y.rep),A,q);this.createChar(u,(y.right||y.rep),A,q);var f=this.Element("span");this.createChar(f,y.rep,A,q);var v={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(h,-h.bbox.lw,0,true);var o=(h.bbox.rw-h.bbox.lw)+(u.bbox.rw-u.bbox.lw)-0.05,m=h.bbox.rw-h.bbox.lw-0.025;if(y.mid){v=this.createBox(j);this.createChar(v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){this.placeBox(this.addBox(j,f.cloneNode(true)),m,0,true);m+=i}if(y.mid&&s){this.placeBox(v,m,0,true);m+=v.bbox.w-p;r=l}}}else{m-=(o-g)/2;if(y.mid){this.placeBox(v,m,0,true);m+=v.bbox.w}m-=(o-g)/2}this.placeBox(u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:Math.max(h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:Math.max(h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t.isMultiChar=true;this.setStackWidth(j,t.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||this.FONTDATA.DEFAULTSTYLE,i=f.weight||this.FONTDATA.DEFAULTWEIGHT;if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,k,j,i){var h=k[5];if(h.img){return this.handleImg(g,f,k,j,i)}if(h.c==null){if(j<=65535){h.c=String.fromCharCode(j)}else{h.c=this.PLANE1+String.fromCharCode(j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length){return i+h.c}e.createShift(g,k[3]/1000);e.createShift(g,(k[4]-k[3])/1000);this.addText(g,h.c);e.createShift(g,-k[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.FONTDATA.DEFAULTFAMILY+",serif"});k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(l)}}var o=this.HTMLcomputeBBox(l);var k=l.bbox.h,n=l.bbox.d;for(g=0,f=o.length;g<f;g++){o[g].HTMLstretchV(l,k,n)}if(o.length){this.HTMLcomputeBBox(l,true)}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLlineBreaks:function(){var k=[[0,this]];for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){var l=this.data[h].lineBreak();if(l!=="none"){var g=(l==="after"?h+1:h);if(k.length===0||k[k.length-1]!==g){k.push([g,this.data[h]])}else{k[k.length-1]=[g,this.data[h]]}}}}k.push([this.data.length,k[k.length-1][1]]);return k},toHTMLmultiline:function(f){a.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(l,k,j,f){if(j==null){j=0}if(f==null){f=this.data.length}var h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=f.HTMLspanElement();if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(k){var m=this.getValues("mathcolor","color");if(this.mathbackground){m.mathbackground=this.mathbackground}if(this.background){m.background=this.background}if(this.style&&k.style.backgroundColor){m.mathbackground=k.style.backgroundColor;k.style.backgroundColor="transparent"}if(m.color&&!this.mathcolor){m.mathcolor=m.color}if(m.background&&!this.mathbackground){m.mathbackground=m.background}if(m.mathcolor){k.style.color=m.mathcolor}if(m.mathbackground&&m.mathbackground!==a.COLOR.TRANSPARENT){var n=1/e.em,j=0,i=0;if(this.isToken){j=k.bbox.lw;i=k.bbox.rw-k.bbox.w}if(k.style.paddingLeft!==""){j+=parseFloat(k.style.paddingLeft)*(k.scale||1)}if(k.style.paddingRight!==""){i-=parseFloat(k.style.paddingRight)*(k.scale||1)}var h=Math.max(0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.msieCharPaddingWidthBug&&k.style.paddingLeft!==""){h+=parseFloat(k.style.paddingLeft)*(k.scale||1)}var l=k.bbox.h+k.bbox.d,f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var g=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:m.mathbackground,width:e.Em(h),height:e.Em(l),verticalAlign:e.Em(f),marginLeft:e.Em(j),marginRight:e.Em(i)}});if(e.msieInlineBlockAlignBug){g.style.position="relative";g.style.width=g.style.height=0;g.style.verticalAlign=g.style.marginLeft=g.style.marginRight="";e.placeBox(e.addElement(g,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",width:e.Em(h),height:e.Em(l),background:m.mathbackground}}),j,k.bbox.h+n)}k.parentNode.insertBefore(g,k);return g}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return e.FONTDATA.VARIANT[g]}},{HTMLautoload:function(){var f=e.autoloadDir+"/"+this.type+".js";d.RestartAfter(c.Require(f))},HTMLautoloadFile:function(f){var g=e.autoloadDir+"/"+f+".js";d.RestartAfter(c.Require(g))},HTMLstretchH:function(g,f){this.HTMLremoveColor();return this.toHTML(g,f)},HTMLstretchV:function(g,f,i){this.HTMLremoveColor();return this.toHTML(g,f,i)}});a.chars.Augment({toHTML:function(g,f){this.HTMLhandleVariant(g,f,this.data.join("").replace(/[\u2061-\u2064]/g,""))}});a.entity.Augment({toHTML:function(g,f){this.HTMLhandleVariant(g,f,this.toString().replace(/[\u2061-\u2064]/g,""))}});a.mi.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));j.bbox=null;var h=this.HTMLgetVariant();for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(j,h)}}if(!j.bbox){j.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete j.bbox.skew}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});a.mn.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));j.bbox=null;var h=this.HTMLgetVariant();for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(j,h)}}if(!j.bbox){j.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete j.bbox.skew}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});a.mo.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));if(this.data.length==0){return k}else{k.bbox=null}var n=this.data.join("");var j=this.HTMLgetVariant();var g=this.getValues("largeop","displaystyle");if(g.largeop){j=e.FONTDATA.VARIANT[g.displaystyle?"-largeOp":"-smallOp"]}for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){this.data[h].toHTML(k,j)}}if(!k.bbox){k.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(n.length!==1){delete k.bbox.skew}if(e.AccentBug&&k.bbox.w===0&&n.length===1&&k.firstChild){k.firstChild.nodeValue+=e.NBSP;e.createSpace(k,0,0,-k.offsetWidth/e.em)}if(g.largeop){var l=(k.bbox.h-k.bbox.d)/2-e.TeX.axis_height*k.scale;if(e.safariVerticalAlignBug&&k.lastChild.nodeName==="IMG"){k.lastChild.style.verticalAlign=e.Em(parseFloat(k.lastChild.style.verticalAlign||0)/e.em-l/k.scale)}else{if(e.konquerorVerticalAlignBug&&k.lastChild.nodeName==="IMG"){k.style.position="relative";k.lastChild.style.position="relative";k.lastChild.style.top=e.Em(l/k.scale)}else{k.style.verticalAlign=e.Em(-l/k.scale)}}k.bbox.h-=l;k.bbox.d+=l;if(k.bbox.rw>k.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){this.data[h].toHTML(k,j)}}if(!k.bbox){k.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete k.bbox.skew}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});a.ms.Augment({toHTML:a.mbase.HTMLautoload});a.mglyph.Augment({toHTML:a.mbase.HTMLautoload});a.mspace.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));var g=this.getValues("height","depth","width");g.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){g.mathbackground=this.background}var i=e.length2em(g.height),k=e.length2em(g.depth),f=e.length2em(g.width);e.createSpace(j,i,k,f,g.mathbackground);return j}});a.mphantom.Augment({toHTML:function(j,g,l){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){var k=e.Measured(this.data[0].toHTML(j),j);if(l!=null){e.Remeasured(this.data[0].HTMLstretchV(j,g,l),j)}else{if(g!=null){e.Remeasured(this.data[0].HTMLstretchH(j,g),j)}}j.bbox={w:k.bbox.w,h:k.bbox.h,d:k.bbox.d,lw:0,rw:0};for(var h=0,f=j.childNodes.length;h<f;h++){j.childNodes[h].style.visibility="hidden"}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mpadded.Augment({toHTML:function(j,h,l){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){var g=e.createStack(j,true);var k=e.createBox(g);e.Measured(this.data[0].toHTML(k),k);if(l!=null){e.Remeasured(this.data[0].HTMLstretchV(k,h,l),k)}else{if(h!=null){e.Remeasured(this.data[0].HTMLstretchH(k,h),k)}}var i=this.getValues("height","depth","width","lspace","voffset"),f=0,m=0;if(i.lspace){f=this.HTMLlength2em(k,i.lspace)}if(i.voffset){m=this.HTMLlength2em(k,i.voffset)}e.placeBox(k,f,m);j.bbox={h:k.bbox.h,d:k.bbox.d,w:k.bbox.w,lw:Math.min(0,k.bbox.lw+f),rw:Math.max(k.bbox.w,k.bbox.rw+f),H:Math.max((k.bbox.H==null?-e.BIGDIMEN:k.bbox.H),k.bbox.h+m),D:Math.max((k.bbox.D==null?-e.BIGDIMEN:k.bbox.D),k.bbox.d-m)};if(i.height!==""){j.bbox.h=this.HTMLlength2em(k,i.height,"h",0)}if(i.depth!==""){j.bbox.d=this.HTMLlength2em(k,i.depth,"d",0)}if(i.width!==""){j.bbox.w=this.HTMLlength2em(k,i.width,"w",0)}if(j.bbox.H<=j.bbox.h){delete j.bbox.H}if(j.bbox.D<=j.bbox.d){delete j.bbox.D}e.setStackWidth(g,j.bbox.w)}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLlength2em:function(j,k,l,f){if(f==null){f=-e.BIGDIMEN}var h=String(k).match(/width|height|depth/);var i=(h?j.bbox[h[0].charAt(0)]:(l?j.bbox[l]:null));var g=e.length2em(k,i);if(l&&String(k).match(/^\s*[-+]/)){return Math.max(f,j.bbox[l]+g)}else{return g}},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mrow.Augment({HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f);this.HTMLhandleColor(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(r<s){n+=(s-r)/2;m+=(s-r)/2}}else{s=Math.max((x?2:0)*w+o,o/2+1.5*w);r=(n-k.bbox.d)-(B+o/2);if(r<s){n+=s-r}r=(B-o/2)-(j.bbox.h-m);if(r<s){m+=s-r}var i=e.createBox(h);e.createRule(i,o,0,g+2*o);e.placeBox(i,0,B-o/2)}e.alignBox(k,f.numalign,n);e.alignBox(j,f.denomalign,-m)}this.HTMLhandleSpace(y);this.HTMLhandleColor(y);return y},HTMLcanStretch:function(f){return false},HTMLhandleSpace:function(f){if(!this.texWithDelims){var g=(this.useMMLspacing?0:e.length2em(this.texSpacing()||0))+0.12;f.style.paddingLeft=e.Em(g);f.style.paddingRight=".12em"}}});a.msqrt.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);var r=e.createStack(n);var h=e.createBox(r),l=e.createBox(r),k=e.createBox(r);this.HTMLmeasureChild(0,h);var j=this.HTMLgetScale();var s=e.TeX.rule_thickness*j,g,f,o,i;if(this.Get("displaystyle")){g=e.TeX.x_height*j}else{g=s}f=Math.max(s+g/4,1.5*e.TeX.min_rule_thickness/this.em);o=h.bbox.h+h.bbox.d+f+s;i=h.bbox.w;e.createDelimiter(k,8730,o,j);e.Measured(k);var m=0;if(k.isMultiChar||(e.AdjustSurd&&e.imgFonts)){k.bbox.w*=0.95}if(k.bbox.h+k.bbox.d>o){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||i<u.HW[0][0]*j||j<0.75){e.createRule(l,s,0,i)}else{e.createDelimiter(l,e.FONTDATA.RULECHAR,i,j)}o=h.bbox.h+f+s;m=this.HTMLaddRoot(r,k,m,k.bbox.h+k.bbox.d-o,j);e.placeBox(k,m,o-k.bbox.h);e.placeBox(l,m+k.bbox.w,o-l.bbox.h+e.rfuzz);e.placeBox(h,m+k.bbox.w,0);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n},HTMLaddRoot:function(h,g,f,j,i){return f}});a.mroot.Augment({toHTML:a.msqrt.prototype.toHTML,HTMLaddRoot:function(o,g,m,k,f){var i=e.createBox(o);if(this.data[1]){var l=this.data[1].toHTML(i);l.style.paddingRight=l.style.paddingLeft="";e.Measured(l,i)}else{i.bbox=this.HTMLzeroBBox()}var j=this.HTMLrootHeight(g.bbox.h+g.bbox.d,f,i)-k;var n=Math.min(i.bbox.w,i.bbox.rw);m=Math.max(n,g.offset);e.placeBox(i,m-n,j);return m-g.offset},HTMLrootHeight:function(h,g,f){return 0.45*(h-0.9*g)+0.6*g+Math.max(0,f.bbox.d-0.075)}});a.mfenced.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data.open){this.data.open.toHTML(k)}if(this.data[0]!=null){this.data[0].toHTML(k)}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){if(this.data["sep"+g]){this.data["sep"+g].toHTML(k)}this.data[g].toHTML(k)}}if(this.data.close){this.data.close.toHTML(k)}var n=this.HTMLcomputeBBox(k);var j=k.bbox.h,l=k.bbox.d;for(g=0,f=n.length;g<f;g++){n[g].HTMLstretchV(k,j,l)}if(n.length){this.HTMLcomputeBBox(k,true)}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcomputeBBox:function(k,j){var g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.munderover.Augment({toHTML:function(G,B,z){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,G)}G=this.HTMLcreateSpan(G);var K=this.HTMLgetScale();var j=e.createStack(G);var l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(g==-e.BIGDIMEN){g=F}if(z==null&&B!=null){g=F=B}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}o=e.TeX.big_op_spacing5*K;var u=(H!=this.base&&f[this.ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q.insertBefore(e.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild)}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(g-q.bbox.w)/2,right:g-q.bbox.w}[f.align];p=v;n=0;if(H==this.over){if(u){E=Math.max(w*K*A,2.5/this.em);o=0;if(h.bbox.skew){p+=h.bbox.skew}}else{s=e.TeX.big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E=Math.max(s,r-Math.max(0,q.bbox.d))}E=Math.max(E,1.5/this.em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==this.under){if(u){E=3*w*K*A;o=0}else{s=e.TeX.big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E=Math.max(s,r-q.bbox.h)}E=Math.max(E,1.5/this.em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}e.placeBox(q,p,n)}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(C,A,w){C=this.HTMLcreateSpan(C);var G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var m=i.bbox.h-y,l=i.bbox.d+x,F=0,z;if(i.bbox.ic){F=i.bbox.ic}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&i.bbox.scale===1&&!this.data[this.base].Get("largeop")){m=l=0}}var B=this.getValues("subscriptshift","superscriptshift");B.subscriptshift=(B.subscriptshift===""?0:e.length2em(B.subscriptshift));B.superscriptshift=(B.superscriptshift===""?0:e.length2em(B.superscriptshift));if(!f){if(k){l=Math.max(l,e.TeX.sub1*G,k.bbox.h-(4/5)*E,B.subscriptshift);e.placeBox(k,i.bbox.w+o-F,-l,k.bbox)}}else{if(!k){g=this.getValues("displaystyle","texprimestyle");z=e.TeX[(g.displaystyle?"sup1":(g.texprimestyle?"sup3":"sup2"))];m=Math.max(m,z*G,f.bbox.d+(1/4)*E,B.superscriptshift);e.placeBox(f,i.bbox.w+o,m,f.bbox)}else{l=Math.max(l,e.TeX.sub2*G);var n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieCharPaddingWidthBug:(h&&!g),msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0.2"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?(j.isPC?"svg":"otf"):false)});if(k){var i=MathJax.Hub.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{MathJax.Hub.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:"svg",safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var h=0,g=j.length;h<g;h++){if(j[h]==="STIX"){j.splice(h,1);g--;h--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=j[0]}}})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}});if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);
(function(a,b){var c="1.0";a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var aL=b.FONTDATA.baselineskip*am*aJ.useHeight,Z=b.FONTDATA.lineH*am,af=b.FONTDATA.lineD*am;for(aF=0,aC=this.data.length;aF<aC;aF++){R=this.data[aF];ay=(R.type==="mlabeledtr"?aH:0);O[aF]=[];w[aF]=I[aF]=0;for(aE=ay,t=R.data.length+ay;aE<t;aE++){if(l[aE]==null){if(aE>v){v=aE}K[aE]=b.createStack(b.createBox(ag));l[aE]=-b.BIGDIMEN}O[aF][aE]=b.createBox(K[aE]);b.Measured(R.data[aE-ay].toHTML(O[aF][aE]),O[aF][aE]);if(R.data[aE-ay].isMultiline){O[aF][aE].style.width="100%"}if(O[aF][aE].bbox.h>w[aF]){w[aF]=O[aF][aE].bbox.h}if(O[aF][aE].bbox.d>I[aF]){I[aF]=O[aF][aE].bbox.d}if(O[aF][aE].bbox.w>l[aE]){l[aE]=O[aF][aE].bbox.w}}}if(w[0]+I[0]){w[0]=Math.max(w[0],Z)}if(w[O.length-1]+I[O.length-1]){I[O.length-1]=Math.max(I[O.length-1],af)}var al=aJ.columnspacing.split(/ /),S=aJ.rowspacing.split(/ /),ah=aJ.columnalign.split(/ /),L=aJ.rowalign.split(/ /),N=aJ.columnlines.split(/ /),k=aJ.rowlines.split(/ /),ap=aJ.columnwidth.split(/ /),au=[];for(aF=0,aC=al.length;aF<aC;aF++){al[aF]=b.length2em(al[aF])}for(aF=0,aC=S.length;aF<aC;aF++){S[aF]=b.length2em(S[aF])}while(al.length<v){al.push(al[al.length-1])}while(ah.length<=v){ah.push(ah[ah.length-1])}while(N.length<v){N.push(N[N.length-1])}while(ap.length<=v){ap.push(ap[ap.length-1])}while(S.length<O.length){S.push(S[S.length-1])}while(L.length<=O.length){L.push(L[L.length-1])}while(k.length<O.length){k.push(k[k.length-1])}if(K[aH]){ah[aH]=(aJ.side.substr(0,1)==="l"?"left":"right");al[aH]=-l[aH]}for(aF=0,aC=O.length;aF<aC;aF++){R=this.data[aF];au[aF]=[];if(R.rowalign){L[aF]=R.rowalign}if(R.columnalign){au[aF]=R.columnalign.split(/ /);while(au[aF].length<=v){au[aF].push(au[aF][au[aF].length-1])}}}var az=w[0]+I[O.length-1];for(aF=0,aC=O.length-1;aF<aC;aF++){az+=Math.max((w[aF]+I[aF]?aL:0),I[aF]+w[aF+1]+S[aF])}var ac=0,aa=0,aA,aI=az;if(aJ.frame!=="none"||(aJ.columnlines+aJ.rowlines).match(/solid|dashed/)){ac=b.length2em(aJ.framespacing.split(/[, ]+/)[0]);aa=b.length2em(aJ.framespacing.split(/[, ]+/)[1]);aI=az+2*aa}var h,ax;if(String(aJ.align).match(/^\d+$/)){h=az/2+b.TeX.axis_height*am-w[0];ax=-(az/2+aa)}else{h=({top:-(w[0]+aa),bottom:az+aa-w[0],center:az/2-w[0],baseline:az/2-w[0],axis:az/2+b.TeX.axis_height*am-w[0]})[aJ.align];ax=({top:-(az+2*aa),bottom:0,center:-(az/2+aa),baseline:-(az/2+aa),axis:b.TeX.axis_height*am-az/2-aa})[aJ.align]}var aq,aw=0,U=0,V=0,aB=0,aG=0,o=[],B=[],ai=1;if(aJ.equalcolumns&&aJ.width!=="auto"){if(r){aq=(100/(v+1)).toFixed(2).replace(/\.?0+$/,"")+"%";for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){ap[aF]=aq}aq=0;aw=1;aG=v+1;for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq+=al[aF]}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq-=al[aF]}aq/=v+1;for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){l[aF]=aq}}}else{for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){if(ap[aF]==="auto"){U+=l[aF]}else{if(ap[aF]==="fit"){B[aG]=aF;aG++;U+=l[aF]}else{if(ap[aF].match(/%$/)){o[aB]=aF;aB++;V+=l[aF];aw+=b.length2em(ap[aF],1)}else{l[aF]=b.length2em(ap[aF]);U+=l[aF]}}}}if(r){aq=0;for(aF=0,aC=Math.min(v,al.length);aF<aC;aF++){aq+=al[aF]}if(aw>0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq-=al[aF]}}for(aF=0,aC=o.length;aF<aC;aF++){l[o[aF]]=b.length2em(ap[o[aF]],aq*ai);U+=l[o[aF]]}if(Math.abs(aq-U)>0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF<aC;aF++){l[B[aF]]+=aq}}else{aq=aq/U;for(aE=0;aE<=v;aE++){l[aE]*=aq}}}if(aJ.equalcolumns){var ad=Math.max.apply(Math,l);for(aE=0;aE<=v;aE++){l[aE]=ad}}}}if(aJ.equalrows){var T=Math.max.apply(Math,w),ao=Math.max.apply(Math,I);for(aF=0,aC=O.length;aF<aC;aF++){ay=((T+ao)-(w[aF]+I[aF]))/2;w[aF]+=ay;I[aF]+=ay}}var ar=h,n,u,aD;ay=(K[aH]?aH:0);for(aE=ay;aE<=v;aE++){for(aF=0,aC=O.length;aF<aC;aF++){if(O[aF][aE]){ay=(this.data[aF].type==="mlabeledtr"?aH:0);var ak=this.data[aF].data[aE-ay];if(ak.HTMLcanStretch("Horizontal")){O[aF][aE].bbox=ak.HTMLstretchH(K[aE],l[aE]).bbox}else{if(ak.HTMLcanStretch("Vertical")){var z=ak.CoreMO();var ab=z.symmetric;z.symmetric=false;O[aF][aE].bbox=ak.HTMLstretchV(K[aE],w[aF],I[aF]).bbox;z.symmetric=ab}}aD=ak.rowalign||this.data[aF].rowalign||L[aF];n=({top:w[aF]-O[aF][aE].bbox.h,bottom:O[aF][aE].bbox.d-I[aF],center:((w[aF]-I[aF])-(O[aF][aE].bbox.h-O[aF][aE].bbox.d))/2,baseline:0,axis:0})[aD];aD=(ak.columnalign||au[aF][aE]||ah[aE]);b.alignBox(O[aF][aE],aD,ar+n)}if(aF<O.length-1){ar-=Math.max((w[aF]+I[aF]?aL:0),I[aF]+w[aF+1]+S[aF])}}ar=h}if(r){var q=b.createBox(ag);q.style.left=q.style.top=0;q.style.right=b.Em(aq+2*ac);q.style.display="inline-block";q.style.height="0px";if(b.msieRelativeWidthBug){q=b.createBox(q);q.style.position="relative";q.style.height="1em";q.style.width="100%";q.bbox=ag.bbox}var an=0,av=ac,aK,g;if(aG){aK=100*(1-aw)/aG,g=U/aG}else{aK=100*(1-aw)/(v+1);g=U/(v+1)}for(aE=0;aE<=v;aE++){b.placeBox(K[aE].parentNode,0,0);K[aE].style.position="relative";K[aE].style.left=b.Em(av);K[aE].style.width="100%";K[aE].parentNode.parentNode.removeChild(K[aE].parentNode);var e=b.createBox(q);b.addBox(e,K[aE]);K[aE]=e;var ae=e.style;ae.display="inline-block";ae.left=an+"%";if(ap[aE].match(/%$/)){var G=parseFloat(ap[aE])*ai;if(aG===0){ae.width=(aK+G)+"%";an+=aK+G;e=b.createBox(e);b.addBox(e,K[aE].firstChild);e.style.left=0;e.style.right=b.Em(g);av-=g}else{ae.width=G+"%";an+=G}}else{if(ap[aE]==="fit"||aG===0){ae.width=aK+"%";e=b.createBox(e);b.addBox(e,K[aE].firstChild);e.style.left=0;e.style.right=b.Em(g-l[aE]);av+=l[aE]-g;an+=aK}else{ae.width=b.Em(l[aE]);av+=l[aE]}}if(b.msieRelativeWidthBug){b.addText(e.firstChild,b.NBSP);e.firstChild.style.position="relative"}av+=al[aE];if(N[aE]!=="none"&&aE<v&&aE!==aH){u=b.createBox(q);u.style.left=an+"%";u=b.createRule(u,aI,0,1.25/b.em);u.style.position="absolute";u.bbox={h:aI,d:0,w:0,rw:1.25/b.em,lw:0};u.parentNode.bbox=ag.bbox;b.placeBox(u,av-al[aE]/2,ax,true);u.style.borderStyle=N[aE]}}}else{var at=ac;for(aE=0;aE<=v;aE++){if(!K[aE].bbox.width){b.setStackWidth(K[aE],l[aE])}if(ap[aE]!=="auto"&&ap[aE]!=="fit"){K[aE].bbox.width=l[aE];K[aE].bbox.isFixed=true}b.placeBox(K[aE].parentNode,at,0);at+=l[aE]+al[aE];if(N[aE]!=="none"&&aE<v&&aE!==aH){u=b.createRule(ag,aI,0,1.25/b.em);b.addBox(ag,u);u.bbox={h:aI,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(u,at-al[aE]/2,ax,true);u.style.borderStyle=N[aE]}}}aA=ag.bbox.w+ac;var d;if(aJ.frame!=="none"){d=b.createFrame(ag,aI,0,aA,1.25/b.em,aJ.frame);b.addBox(ag,d);b.placeBox(d,0,ax,true);if(r){d.style.width="100%"}}ar=h;for(aF=0,aC=O.length-1;aF<aC;aF++){n=Math.max(aL,I[aF]+w[aF+1]+S[aF]);if(k[aF]!=="none"){u=b.createRule(ag,1.25/b.em,0,aA);b.addBox(ag,u);u.bbox={h:1.25/b.em,d:0,w:aA,rw:aA,lw:0};b.placeBox(u,0,ar-I[aF]-(n-I[aF]-w[aF+1])/2,true);if(k[aF]==="dashed"||r){u.style.borderTop=u.style.height+" "+k[aF];u.style.height=0;u.style.width=u.style.borderLeftWidth;u.style.borderLeft="";if(r){u.style.width="100%"}}}ar-=n}if(r){X.bbox.width=aJ.width;ag.style.width="100%"}if(K[aH]){var Q=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(Q.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){Q.indentalign=Q.indentalignfirst}if(Q.indentalign===a.INDENTALIGN.AUTO){Q.indentalign=this.displayAlign}if(Q.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){Q.indentshift=Q.indentshiftfirst}if(Q.indentshift==="auto"){Q.indentshift=this.displayIndent}var E=b.createStack(X,false,"100%");b.addBox(E,ag);b.alignBox(ag,Q.indentalign,0);if(Q.indentshift&&Q.indentalign!==a.INDENTALIGN.CENTER){ag.style[{left:"Left",right:"Right"}[Q.indentalign]]=b.Em(b.length2em(Q.indentshift))}K[aH].parentNode.parentNode.removeChild(K[aH].parentNode);b.addBox(E,K[aH]);b.alignBox(K[aH],ah[aH],0);if(b.msieRelativeWidthBug){ag.style.top=K[aH].style.top=""}if(r){ag.style.width=aJ.width;X.bbox.width="100%"}K[aH].style.marginRight=K[aH].style.marginLeft=b.Em(b.length2em(aJ.minlabelspacing))}if(!r){this.HTMLhandleSpace(X)}var aj=this.HTMLhandleColor(X);if(aj&&r){if(!d){d=b.createFrame(ag,aI,0,aA,0,"none");b.addBox(ag,d);b.placeBox(d,0,ax,true);d.style.width="100%"}d.style.backgroundColor=aj.style.backgroundColor;d.parentNode.insertBefore(d,d.parentNode.firstChild);aj.parentNode.removeChild(aj)}return X},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=b.Measured(this.data[0].toHTML(e),e);if(g!=null){b.Remeasured(this.data[0].HTMLstretchV(e,d,g),e)}else{if(d!=null){b.Remeasured(this.data[0].HTMLstretchH(e,d),e)}}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.ElementJax.mml,MathJax.OutputJax["HTML-CSS"]);
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML-full.js");
Reference in a new issue View git blame Copy permalink