/*
 *  /MathJax/config/TeX-AMS-MML_SVG.js
 *  
 *  Copyright (c) 2010-2014 The MathJax Consortium
 *
 *  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/input/MathML/config.js",
  "[MathJax]/jax/output/SVG/config.js",
  "[MathJax]/extensions/tex2jax.js",
  "[MathJax]/extensions/mml2jax.js",
  "[MathJax]/extensions/MathEvents.js",
  "[MathJax]/extensions/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.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/input/MathML/jax.js"
);

MathJax.Hub.Config({"v1.0-compatible":false});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.4.0",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.4.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.4.0",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:10,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js");
MathJax.Extension.tex2jax={version:"2.4.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],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])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
MathJax.Extension.mml2jax={version:"2.4.0",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.PushMathElements(h,e,f.name+":math")}}}catch(g){}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.PushMathElements(h,e,a.nodeName.substr(6)+":math")}}}}this.ProcessMathArray(h)},PushMathElements:function(f,d,a,c){var h,g=MathJax.Hub.config.preRemoveClass;if(c){if(!d.getElementsByTagNameNS){return}h=d.getElementsByTagNameNS(c,a)}else{h=d.getElementsByTagName(a)}for(var e=0,b=h.length;e<b;e++){var j=h[e].parentNode;if(j&&j.className!==g&&!h[e].prefix===!c){f.push(h[e])}}},ProcessMathArray:function(c){var b,a=c.length;if(a){if(this.MathTagBug){for(b=0;b<a;b++){if(c[b].nodeName==="MATH"){this.ProcessMathFlattened(c[b])}else{this.ProcessMath(c[b])}}}else{for(b=0;b<a;b++){this.ProcessMath(c[b])}}}},ProcessMath:function(e){var d=e.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified&&d.nodeName.substr(0,10)!=="_moz-math-"){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(f,b){var g=this.config.preview;if(g==="none"){return}var a=false;if(g==="mathml"){a=true;if(this.MathTagBug){g="alttext"}else{g=f.cloneNode(false)}}if(g==="alttext"||g==="altimg"){a=true;var c=this.filterPreview(f.getAttribute("alttext"));if(g==="alttext"){if(c!=null){g=MathJax.HTML.TextNode(c)}else{g=null}}else{var h=f.getAttribute("altimg");if(h!=null){var e={width:f.getAttribute("altimg-width"),height:f.getAttribute("altimg-height")};g=MathJax.HTML.Element("img",{src:h,alt:c,style:e})}else{g=null}}}if(g){var d;if(a){d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass});d.appendChild(g)}else{d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},g)}b.parentNode.insertBefore(d,b)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
(function(d,h,l,g,m,b,j){var q="2.4.0";var i=MathJax.Extension;var c=i.MathEvents={version:q};var k=d.config.menuSettings;var p={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:l.urlRev(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(r){return n.Handler(r,"Mousedown",this)},Mouseup:function(r){return n.Handler(r,"Mouseup",this)},Mousemove:function(r){return n.Handler(r,"Mousemove",this)},Mouseover:function(r){return n.Handler(r,"Mouseover",this)},Mouseout:function(r){return n.Handler(r,"Mouseout",this)},Click:function(r){return n.Handler(r,"Click",this)},DblClick:function(r){return n.Handler(r,"DblClick",this)},Menu:function(r){return n.Handler(r,"ContextMenu",this)},Handler:function(u,s,t){if(l.loadingMathMenu){return n.False(u)}var r=b[t.jaxID];if(!u){u=window.event}u.isContextMenu=(s==="ContextMenu");if(r[s]){return r[s](u,t)}if(i.MathZoom){return i.MathZoom.HandleEvent(u,s,t)}},False:function(r){if(!r){r=window.event}if(r){if(r.preventDefault){r.preventDefault()}else{r.returnValue=false}if(r.stopPropagation){r.stopPropagation()}r.cancelBubble=true}return false},ContextMenu:function(u,F,x){var C=b[F.jaxID],w=C.getJaxFromMath(F);var G=(C.config.showMathMenu!=null?C:d).config.showMathMenu;if(!G||(k.context!=="MathJax"&&!x)){return}if(c.msieEventBug){u=window.event||u}n.ClearSelection();f.ClearHoverTimer();if(w.hover){if(w.hover.remove){clearTimeout(w.hover.remove);delete w.hover.remove}w.hover.nofade=true}var v=MathJax.Menu;var H,E;if(v){if(v.loadingDomain){return n.False(u)}H=m.loadDomain("MathMenu");if(!H){v.jax=w;var s=v.menu.Find("Show Math As").menu;s.items[0].name=w.sourceMenuTitle;s.items[0].format=(w.sourceMenuFormat||"MathML");s.items[1].name=j[w.inputJax].sourceMenuTitle;s.items[5].disabled=!j[w.inputJax].annotationEncoding;var B=s.items[2];B.disabled=true;var r=B.menu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var A=0,z=r.length;A<z;A++){var t=r[A].name[1];if(w.root&&w.root.getAnnotation(t)!==null){B.disabled=false;r[A].hidden=false}else{r[A].hidden=true}}var y=v.menu.Find("Math Settings","MathPlayer");y.hidden=!(w.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return v.menu.Post(u)}v.loadingDomain=true;E=function(){delete v.loadingDomain}}else{if(l.loadingMathMenu){return n.False(u)}l.loadingMathMenu=true;H=l.Require("[MathJax]/extensions/MathMenu.js");E=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var D={pageX:u.pageX,pageY:u.pageY,clientX:u.clientX,clientY:u.clientY};g.Queue(H,E,["ContextMenu",n,D,F,x]);return n.False(u)},AltContextMenu:function(t,s){var u=b[s.jaxID];var r=(u.config.showMathMenu!=null?u:d).config.showMathMenu;if(r){r=(u.config.showMathMenuMSIE!=null?u:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&r){if(!c.noContextMenuBug||t.button!==n.RIGHTBUTTON){return}}else{if(!t[n.MENUKEY]||t.button!==n.LEFTBUTTON){return}}return u.ContextMenu(t,s,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(t){t.appendChild(c.topImg);var s=c.topImg.offsetTop,u=t.offsetHeight-s,r=t.offsetWidth;t.removeChild(c.topImg);return{w:r,h:s,d:u}}};var f=c.Hover={Mouseover:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.ReHover(r)}else{f.HoverTimer(r,s)}return n.False(t)}}},Mouseout:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.UnHover(r)}else{f.ClearHoverTimer()}return n.False(t)}}},Mousemove:function(t,s){if(k.discoverable||k.zoom==="Hover"){var r=this.getJaxFromMath(s);if(r.hover){return}if(f.lastX==t.clientX&&f.lastY==t.clientY){return}f.lastX=t.clientX;f.lastY=t.clientY;f.HoverTimer(r,s);return n.False(t)}},HoverTimer:function(r,s){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,r,s]),p.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(r,v){if(i.MathZoom&&i.MathZoom.Hover({},v)){return}var u=b[r.outputJax],w=u.getHoverSpan(r,v),z=u.getHoverBBox(r,w,v),x=(u.config.showMathMenu!=null?u:d).config.showMathMenu;var B=p.frame.x,A=p.frame.y,y=p.frame.bwidth;if(c.msieBorderWidthBug){y=0}r.hover={opacity:0,id:r.inputID+"-Hover"};var s=h.Element("span",{id:r.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-z.h-A-y-(z.y||0)),left:this.Px(-B-y+(z.x||0)),width:this.Px(z.w+2*B),height:this.Px(z.h+z.d+2*A),opacity:0,filter:"alpha(opacity=0)"}}]]);var t=h.Element("span",{isMathJax:true,id:r.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:v,src:p.button.src,onclick:this.HoverMenu,jax:u.id,style:{left:this.Px(z.w+B+y+(z.x||0)+p.button.x),top:this.Px(-z.h-A-y-(z.y||0)-p.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(z.width){s.style.width=t.style.width=z.width;s.style.marginRight=t.style.marginRight="-"+z.width;s.firstChild.style.width=z.width;t.firstChild.style.left="";t.firstChild.style.right=this.Px(p.button.wx)}w.parentNode.insertBefore(s,w);if(x){w.parentNode.insertBefore(t,w)}if(w.style){w.style.position="relative"}this.ReHover(r)},ReHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}r.hover.remove=setTimeout(g(["UnHover",this,r]),p.fadeoutDelay);this.HoverFadeTimer(r,p.fadeinInc)},UnHover:function(r){if(!r.hover.nofade){this.HoverFadeTimer(r,-p.fadeoutInc,p.fadeoutStart)}},HoverFade:function(r){delete r.hover.timer;r.hover.opacity=Math.max(0,Math.min(1,r.hover.opacity+r.hover.inc));r.hover.opacity=Math.floor(1000*r.hover.opacity)/1000;var t=document.getElementById(r.hover.id),s=document.getElementById(r.hover.id+"Menu");t.firstChild.style.opacity=r.hover.opacity;t.firstChild.style.filter="alpha(opacity="+Math.floor(100*r.hover.opacity)+")";if(s){s.firstChild.style.opacity=r.hover.opacity;s.firstChild.style.filter=t.style.filter}if(r.hover.opacity===1){return}if(r.hover.opacity>0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last<a.delay&&a.up);a.last=r;a.up=false;if(t){a.timeout=setTimeout(a.menu,a.delay,s,this);s.preventDefault()}},end:function(s){var r=new Date().getTime();a.up=(r-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;s.preventDefault();return n.Handler((s.touches[0]||s.touch),"DblClick",this)}},menu:function(s,r){delete a.timeout;a.last=0;a.up=false;return n.Handler((s.touches[0]||s.touch),"ContextMenu",r)}};if(d.Browser.isMobile){var o=p.styles[".MathJax_Hover_Arrow"];o.width="25px";o.height="18px";p.button.x=-6}d.Browser.Select({MSIE:function(r){var t=(document.documentMode||0);var s=r.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=r.isIE9;c.msieAlignBug=(!s||t<8);if(t<9){n.LEFTBUTTON=1}},Safari:function(r){c.safariContextMenuBug=true},Opera:function(r){c.operaPositionBug=true},Konqueror:function(r){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=p=d.CombineConfig("MathEvents",p);var e=function(){var r=p.styles[".MathJax_Hover_Frame"];r.border=p.frame.bwidth+"px solid "+p.frame.bcolor+" ! important";r["box-shadow"]=r["-webkit-box-shadow"]=r["-moz-box-shadow"]=r["-khtml-box-shadow"]="0px 0px "+p.frame.hwidth+" 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(function(a,d,f,c,j){var k="2.4.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"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)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.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}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.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(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(c,g,k,f,b){var q="2.4.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:q,signal:j};var o=function(r){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",r]].concat([].slice.call(arguments,1)))};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var p=c.CombineConfig("MathMenu",{delay:150,closeImg:k.urlRev(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",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,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","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_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"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":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"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:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(n?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:q,items:[],posted:false,title:null,margin:5,Init:function(r){this.items=[].slice.call(arguments,0)},With:function(r){if(r){c.Insert(this,r)}return this},Post:function(s,C,A){if(!s){s=window.event}var r=document.getElementById("MathJax_MenuFrame");if(!r){r=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax]);a.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var t=g.Element("div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});if(!A){MathJax.Localization.setCSS(t)}for(var v=0,u=this.items.length;v<u;v++){this.items[v].Create(t)}if(a.isMobile){g.addElement(t,"span",{className:"MathJax_Menu_Close",menu:C,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}r.appendChild(t);this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var B=s.pageX,z=s.pageY;if(!B&&!z){B=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!C){if(B+t.offsetWidth>document.body.offsetWidth-this.margin){B=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){B=Math.max(5,B-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",D=C.offsetWidth;B=(a.isMobile?30:D-2);z=0;while(C&&C!==r){B+=C.offsetLeft;z+=C.offsetTop;C=C.parentNode}if(!a.isMobile){if((a.isRTL&&B-D-t.offsetWidth>this.margin)||(!a.isRTL&&B+t.offsetWidth>document.body.offsetWidth-this.margin)){w="right";B=Math.max(this.margin,B-D-t.offsetWidth+6)}}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=B+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return 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clarify"])}l=m.sub}else{if(m.movesupsub){if(m.type!=="munderover"||m.data[m.under]){if(m.movablelimits&&m.isa(h.mi)){m=this.mi2mo(m)}m=h.munderover(m,null,null).With({movesupsub:true})}l=m.under}else{m=h.msubsup(m,null,null);l=m.sub}}this.Push(b.subsup(m).With({position:l,primes:o}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var n=this.stack.Prev("nopop");if(!n||n.texClass!==h.TEXCLASS.OP){d.Error(["MisplacedLimits","%1 is allowed only on 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o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}var m=h.munderover(o,null,null);if(l){m.movesupsub=true}m.data[m[p]]=this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p=="under")}));this.Push(m)},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ 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l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({mclass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,t,q,s,n,l,u){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(s||"1em")}});if(u){p.isCases=true}if(o||t){p.open=o;p.close=t}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"");if(p&&!p.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(p){var n=p.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex 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u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};c.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser);
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_SVG.js");
