From acf080caae8ad3deb2d02b719c668d1a42e3f098 Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Thu, 25 Aug 2011 19:45:25 -0400 Subject: [PATCH] Clean up Zoom functions, in particular some of the IE complications; move getBBox to MathEvents --- config/Accessible-full.js | 12 +++--- config/Accessible.js | 8 ++-- config/MML_HTMLorMML-full.js | 12 +++--- config/MML_HTMLorMML.js | 8 ++-- config/TeX-AMS-MML_HTMLorMML-full.js | 12 +++--- config/TeX-AMS-MML_HTMLorMML.js | 8 ++-- config/TeX-AMS_HTML-full.js | 8 ++-- config/TeX-AMS_HTML.js | 6 +-- extensions/MathEvents.js | 2 +- extensions/MathMenu.js | 2 +- extensions/MathZoom.js | 2 +- jax/output/HTML-CSS/config.js | 2 +- jax/output/HTML-CSS/jax.js | 2 +- jax/output/NativeMML/config.js | 2 +- jax/output/NativeMML/jax.js | 2 +- unpacked/extensions/MathEvents.js | 33 +++++++++++--- unpacked/extensions/MathMenu.js | 2 +- unpacked/extensions/MathZoom.js | 64 +++++++++------------------- unpacked/jax/output/HTML-CSS/jax.js | 19 +++------ unpacked/jax/output/NativeMML/jax.js | 32 +++----------- 20 files changed, 103 insertions(+), 135 deletions(-) diff --git a/config/Accessible-full.js b/config/Accessible-full.js index 03549bb59..30e1120ea 100644 --- a/config/Accessible-full.js +++ b/config/Accessible-full.js @@ -56,9 +56,9 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.2",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.5",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.12",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=0;a--){if(b[a].nodeName==="MATH"){this.ProcessMathFlattened(b[a])}else{this.ProcessMath(b[a])}}}else{for(a=b.length-1;a>=0;a--){this.ProcessMath(b[a])}}}},ProcessMath:function(e){var d=e.parentNode;var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}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";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/"/g,""")},createPreview:function(b,a){var c;if(this.config.preview==="alttext"){var d=b.getAttribute("alttext");if(d!=null){c=[this.filterText(d)]}}else{if(this.config.preview instanceof Array){c=this.config.preview}}if(c){c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c);a.parentNode.insertBefore(c,a)}},filterText:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&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]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); -(function(a,d,f,c,i){var j="1.1.3";var h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,h.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(a,d,f,c,j){var k="1.1.3";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-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:"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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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 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2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(j?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(l?"1em":".7em")},".MathJax_MenuLabel":{padding:(l?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(l?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(l?"4px 1px 0px":"4px 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q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var 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o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
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Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(k){if(!k.parentNode){return}if(!this.initialized){this.InitializeMML()}var p=k.previousSibling;if(p&&String(p.className).match(/^MathJax(_MathML|_Display)?$/)){p.parentNode.removeChild(p)}var o=k.MathJax.elementJax.root;var n=(o.Get("display")==="block"?"div":"span");var m=d.Element(n,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),j=m.firstChild;o.toNativeMML(j.firstChild);k.parentNode.insertBefore(m,k);if(h){if(j.addEventListener){j.addEventListener("contextmenu",g.Menu,true);j.addEventListener("mouseover",g.Mouseover,true);j.addEventListener("mouseout",g.Mouseout,true);j.addEventListener("mousedown",g.Mousedown,true);j.addEventListener("mouseup",g.False,true);j.addEventListener("click",g.Click,true);j.addEventListener("dblclick",g.DblClick,true)}else{var l=(this.config.showMathMenuMSIE!=null?this:b).config;if(l.showMathMenuMSIE){this.MSIEoverlay(j)}}}else{j.oncontextmenu=g.Menu;j.onmouseover=g.Mouseover;j.onmouseout=g.Mouseout;j.onmousedown=g.Mousedown;j.onclick=g.Click;j.ondblclick=g.DblClick}},Remove:function(j){var k=j.SourceElement();if(!k){return}k=k.previousSibling;if(!k){return}if(k.className.match(/MathJax_MathML/)){k.parentNode.removeChild(k)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(j){var k=j.firstChild;if(k.nodeName.toLowerCase()==="span"){k=k.firstChild}var l=this.getHoverBBox(null,k,{});d.addElement(j,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-l.w),top:c.Px(-l.h-(l.y||0)-1),width:c.Px(l.w),height:c.Px(l.h+l.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(j,{msieMath:k,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var k=window.event;var j=i.MSIEevents[k.type];if(i[j]&&i[j](k,this)===false){return false}if(MathJax.Extension.MathZoom&&MathJax.Extension.MathZoom.HandleEvent(k,j,this)===false){return false}if(k.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+k.type,k)}return g.False(k)},getJaxFromMath:function(j){if(j.className==="MathJax_MSIE_Overlay"){j=j.parentNode.parentNode}return b.getJaxFor(j.parentNode.nextSibling)},getHoverSpan:function(j,k){if(k.className==="MathJax_MSIE_Overlay"){return k.parentNode}return k.firstChild},getHoverBBox:function(l,n,o){n=n.parentNode;n.appendChild(this.topImg);var m=this.topImg.offsetTop,p=n.offsetHeight-m,k=n.offsetWidth;n.removeChild(this.topImg);var j=(o.className==="MathJax_MSIE_Overlay"?-k:0);return{w:k,h:m,d:p,x:j}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(o){var l=this.NativeMMLelement(this.type);this.NativeMMLattributes(l);for(var n=0,k=this.data.length;n7;i.msieInlineBlockAlignBug=(!l||k);i.msieTopBug=(!j.versionAtLeast("8.0")||document.documentMode===7)},Opera:function(j){i.operaPositionBug=true}});i.topImg=(i.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(i.operaPositionBug||i.msieTopBug){i.topImg.style.border="1px solid"}b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); +(function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+l.type,l)}return g.False(l)},getJaxFromMath:function(k){if(k.className==="MathJax_MSIE_Overlay"){k=k.parentNode.parentNode}return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){if(l.className==="MathJax_MSIE_Overlay"){return l.parentNode}return l.firstChild},getHoverBBox:function(k,l,m){var n=g.getBBox(l.parentNode);n.x=(m.className==="MathJax_MSIE_Overlay"?-n.w:0);return n},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o=0){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(i){return this.Percent(this.length2em(i))},length2em:function(o,l){if(typeof(o)!=="string"){o=o.toString()}if(o===""){return""}if(o===a.SIZE.NORMAL){return 1}if(o===a.SIZE.BIG){return 2}if(o===a.SIZE.SMALL){return 0.71}if(o==="infinity"){return e.BIGDIMEN}var k=this.FONTDATA.TeX_factor;if(o.match(/mathspace$/)){return e.MATHSPACE[o]*k}var j=o.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(j[1]||"1"),n=j[2];if(l==null){l=1}if(n==="em"){return i*k}if(n==="ex"){return i*e.TeX.x_height*k}if(n==="%"){return i/100*l}if(n==="px"){return i/e.em}if(n==="pt"){return i/10*k}if(n==="pc"){return i*1.2*k}if(n==="in"){return i*this.pxPerInch/e.em}if(n==="cm"){return i*this.pxPerInch/e.em/2.54}if(n==="mm"){return i*this.pxPerInch/e.em/25.4}if(n==="mu"){return i/18*k}return i*k*l},thickness2em:function(i){var j=e.TeX.rule_thickness;if(i===a.LINETHICKNESS.MEDIUM){return j}if(i===a.LINETHICKNESS.THIN){return 0.67*j}if(i===a.LINETHICKNESS.THICK){return 1.67*j}return this.length2em(i,j)},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var 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j=this.getValues("scriptlevel","lspace","rspace");if(j.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){j.lspace=Math.max(0,e.length2em(j.lspace));j.rspace=Math.max(0,e.length2em(j.rspace));var i=this,k=this.Parent();while(k&&k.isEmbellished()&&k.Core()===i){i=k;k=k.Parent();l=i.HTMLspanElement()}if(j.lspace){l.style.paddingLeft=e.Em(j.lspace)}if(j.rspace){l.style.paddingRight=e.Em(j.rspace)}}}else{var m=this.texSpacing();if(m!==""){m=e.length2em(m)/(l.scale||1);if(l.style.paddingLeft){m+=parseFloat(l.style.paddingLeft)}l.style.paddingLeft=e.Em(m)}}},HTMLgetScale:function(){var k=1,i=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var k=e.TeX.axis_height,o=l.scale;if(i.symmetric){j=2*Math.max(m-k,p+k)}else{j=m+p}i.maxsize=e.length2em(i.maxsize,l.bbox.h+l.bbox.d);i.minsize=e.length2em(i.minsize,l.bbox.h+l.bbox.d);j=Math.max(i.minsize,Math.min(i.maxsize,j));l=this.HTMLcreateSpan(n);e.createDelimiter(l,this.data.join("").charCodeAt(0),j,o);if(i.symmetric){j=(l.bbox.h+l.bbox.d)/2+k}else{j=(l.bbox.h+l.bbox.d)*m/(m+p)}e.positionDelimiter(l,j);this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:function(l,i){this.HTMLremoveColor();var j=this.getValues("maxsize","minsize","mathvariant","fontweight");if(j.fontweight==="bold"&&!this.mathvariant){j.mathvariant=a.VARIANT.BOLD}var k=this.HTMLspanElement(),m=k.scale;j.maxsize=e.length2em(j.maxsize,k.bbox.w);j.minsize=e.length2em(j.minsize,k.bbox.w);i=Math.max(j.minsize,Math.min(j.maxsize,i));k=this.HTMLcreateSpan(l);e.createDelimiter(k,this.data.join("").charCodeAt(0),i,m,j.mathvariant);this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var 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Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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:(l?"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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 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q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 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Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax 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#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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial 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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.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){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End 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h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var 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");q.document.write("
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");q.document.write("
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Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. 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+(function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+l.type,l)}return g.False(l)},getJaxFromMath:function(k){if(k.className==="MathJax_MSIE_Overlay"){k=k.parentNode.parentNode}return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){if(l.className==="MathJax_MSIE_Overlay"){return l.parentNode}return l.firstChild},getHoverBBox:function(k,l,m){var n=g.getBBox(l.parentNode);n.x=(m.className==="MathJax_MSIE_Overlay"?-n.w:0);return n},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o=0){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(i){return this.Percent(this.length2em(i))},length2em:function(o,l){if(typeof(o)!=="string"){o=o.toString()}if(o===""){return""}if(o===a.SIZE.NORMAL){return 1}if(o===a.SIZE.BIG){return 2}if(o===a.SIZE.SMALL){return 0.71}if(o==="infinity"){return e.BIGDIMEN}var k=this.FONTDATA.TeX_factor;if(o.match(/mathspace$/)){return e.MATHSPACE[o]*k}var j=o.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(j[1]||"1"),n=j[2];if(l==null){l=1}if(n==="em"){return i*k}if(n==="ex"){return i*e.TeX.x_height*k}if(n==="%"){return i/100*l}if(n==="px"){return i/e.em}if(n==="pt"){return i/10*k}if(n==="pc"){return i*1.2*k}if(n==="in"){return i*this.pxPerInch/e.em}if(n==="cm"){return i*this.pxPerInch/e.em/2.54}if(n==="mm"){return i*this.pxPerInch/e.em/25.4}if(n==="mu"){return i/18*k}return i*k*l},thickness2em:function(i){var j=e.TeX.rule_thickness;if(i===a.LINETHICKNESS.MEDIUM){return j}if(i===a.LINETHICKNESS.THIN){return 0.67*j}if(i===a.LINETHICKNESS.THICK){return 1.67*j}return this.length2em(i,j)},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var 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j=this.getValues("scriptlevel","lspace","rspace");if(j.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){j.lspace=Math.max(0,e.length2em(j.lspace));j.rspace=Math.max(0,e.length2em(j.rspace));var i=this,k=this.Parent();while(k&&k.isEmbellished()&&k.Core()===i){i=k;k=k.Parent();l=i.HTMLspanElement()}if(j.lspace){l.style.paddingLeft=e.Em(j.lspace)}if(j.rspace){l.style.paddingRight=e.Em(j.rspace)}}}else{var m=this.texSpacing();if(m!==""){m=e.length2em(m)/(l.scale||1);if(l.style.paddingLeft){m+=parseFloat(l.style.paddingLeft)}l.style.paddingLeft=e.Em(m)}}},HTMLgetScale:function(){var k=1,i=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var k=e.TeX.axis_height,o=l.scale;if(i.symmetric){j=2*Math.max(m-k,p+k)}else{j=m+p}i.maxsize=e.length2em(i.maxsize,l.bbox.h+l.bbox.d);i.minsize=e.length2em(i.minsize,l.bbox.h+l.bbox.d);j=Math.max(i.minsize,Math.min(i.maxsize,j));l=this.HTMLcreateSpan(n);e.createDelimiter(l,this.data.join("").charCodeAt(0),j,o);if(i.symmetric){j=(l.bbox.h+l.bbox.d)/2+k}else{j=(l.bbox.h+l.bbox.d)*m/(m+p)}e.positionDelimiter(l,j);this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:function(l,i){this.HTMLremoveColor();var j=this.getValues("maxsize","minsize","mathvariant","fontweight");if(j.fontweight==="bold"&&!this.mathvariant){j.mathvariant=a.VARIANT.BOLD}var k=this.HTMLspanElement(),m=k.scale;j.maxsize=e.length2em(j.maxsize,k.bbox.w);j.minsize=e.length2em(j.minsize,k.bbox.w);i=Math.max(j.minsize,Math.min(j.maxsize,i));k=this.HTMLcreateSpan(l);e.createDelimiter(k,this.data.join("").charCodeAt(0),i,m,j.mathvariant);this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var 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Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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:(l?"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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 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q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 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Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax 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#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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial 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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.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){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End 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h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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:(l?"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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 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q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 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Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax 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#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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial 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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End 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Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(k){if(!k.parentNode){return}if(!this.initialized){this.InitializeMML()}var p=k.previousSibling;if(p&&String(p.className).match(/^MathJax(_MathML|_Display)?$/)){p.parentNode.removeChild(p)}var o=k.MathJax.elementJax.root;var n=(o.Get("display")==="block"?"div":"span");var m=d.Element(n,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),j=m.firstChild;o.toNativeMML(j.firstChild);k.parentNode.insertBefore(m,k);if(h){if(j.addEventListener){j.addEventListener("contextmenu",g.Menu,true);j.addEventListener("mouseover",g.Mouseover,true);j.addEventListener("mouseout",g.Mouseout,true);j.addEventListener("mousedown",g.Mousedown,true);j.addEventListener("mouseup",g.False,true);j.addEventListener("click",g.Click,true);j.addEventListener("dblclick",g.DblClick,true)}else{var l=(this.config.showMathMenuMSIE!=null?this:b).config;if(l.showMathMenuMSIE){this.MSIEoverlay(j)}}}else{j.oncontextmenu=g.Menu;j.onmouseover=g.Mouseover;j.onmouseout=g.Mouseout;j.onmousedown=g.Mousedown;j.onclick=g.Click;j.ondblclick=g.DblClick}},Remove:function(j){var k=j.SourceElement();if(!k){return}k=k.previousSibling;if(!k){return}if(k.className.match(/MathJax_MathML/)){k.parentNode.removeChild(k)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(j){var k=j.firstChild;if(k.nodeName.toLowerCase()==="span"){k=k.firstChild}var l=this.getHoverBBox(null,k,{});d.addElement(j,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-l.w),top:c.Px(-l.h-(l.y||0)-1),width:c.Px(l.w),height:c.Px(l.h+l.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(j,{msieMath:k,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var k=window.event;var j=i.MSIEevents[k.type];if(i[j]&&i[j](k,this)===false){return false}if(MathJax.Extension.MathZoom&&MathJax.Extension.MathZoom.HandleEvent(k,j,this)===false){return false}if(k.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+k.type,k)}return g.False(k)},getJaxFromMath:function(j){if(j.className==="MathJax_MSIE_Overlay"){j=j.parentNode.parentNode}return b.getJaxFor(j.parentNode.nextSibling)},getHoverSpan:function(j,k){if(k.className==="MathJax_MSIE_Overlay"){return k.parentNode}return k.firstChild},getHoverBBox:function(l,n,o){n=n.parentNode;n.appendChild(this.topImg);var m=this.topImg.offsetTop,p=n.offsetHeight-m,k=n.offsetWidth;n.removeChild(this.topImg);var j=(o.className==="MathJax_MSIE_Overlay"?-k:0);return{w:k,h:m,d:p,x:j}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(o){var l=this.NativeMMLelement(this.type);this.NativeMMLattributes(l);for(var n=0,k=this.data.length;n7;i.msieInlineBlockAlignBug=(!l||k);i.msieTopBug=(!j.versionAtLeast("8.0")||document.documentMode===7)},Opera:function(j){i.operaPositionBug=true}});i.topImg=(i.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(i.operaPositionBug||i.msieTopBug){i.topImg.style.border="1px solid"}b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); +(function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+l.type,l)}return g.False(l)},getJaxFromMath:function(k){if(k.className==="MathJax_MSIE_Overlay"){k=k.parentNode.parentNode}return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){if(l.className==="MathJax_MSIE_Overlay"){return l.parentNode}return l.firstChild},getHoverBBox:function(k,l,m){var n=g.getBBox(l.parentNode);n.x=(m.className==="MathJax_MSIE_Overlay"?-n.w:0);return n},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o=0){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return k},Remeasured:function(j,i){i.bbox=this.Measured(j,i).bbox},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(i){return this.Percent(this.length2em(i))},length2em:function(o,l){if(typeof(o)!=="string"){o=o.toString()}if(o===""){return""}if(o===a.SIZE.NORMAL){return 1}if(o===a.SIZE.BIG){return 2}if(o===a.SIZE.SMALL){return 0.71}if(o==="infinity"){return e.BIGDIMEN}var k=this.FONTDATA.TeX_factor;if(o.match(/mathspace$/)){return e.MATHSPACE[o]*k}var j=o.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(j[1]||"1"),n=j[2];if(l==null){l=1}if(n==="em"){return i*k}if(n==="ex"){return i*e.TeX.x_height*k}if(n==="%"){return i/100*l}if(n==="px"){return i/e.em}if(n==="pt"){return i/10*k}if(n==="pc"){return i*1.2*k}if(n==="in"){return i*this.pxPerInch/e.em}if(n==="cm"){return i*this.pxPerInch/e.em/2.54}if(n==="mm"){return i*this.pxPerInch/e.em/25.4}if(n==="mu"){return i/18*k}return i*k*l},thickness2em:function(i){var j=e.TeX.rule_thickness;if(i===a.LINETHICKNESS.MEDIUM){return j}if(i===a.LINETHICKNESS.THIN){return 0.67*j}if(i===a.LINETHICKNESS.THICK){return 1.67*j}return this.length2em(i,j)},createStrut:function(k,j,l){var i=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:j+"px",width:"1px",marginRight:"-1px"}});if(l){k.insertBefore(i,k.firstChild)}else{k.appendChild(i)}return i},createBlank:function(j,i,k){var l=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(i)}});if(k){j.insertBefore(l,j.firstChild)}else{j.appendChild(l)}return l},createShift:function(j,i,l){var k=this.Element("span",{style:{marginLeft:this.Em(i)},isMathJax:true});if(l){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}return k},createSpace:function(m,l,o,i,j){var k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" "+this.Em(k)+")"}}if(A&&v){if(A.H!=null&&(v.H==null||A.H+o>v.H)){v.H=A.H+o}if(A.D!=null&&(v.D==null||A.D-o>v.D)){v.D=A.D-o}if(A.h+o>v.h){v.h=A.h+o}if(A.d-o>v.d){v.d=A.d-o}if(v.H!=null&&v.H<=v.h){delete v.H}if(v.D!=null&&v.D<=v.d){delete v.D}if(A.w+p>v.w){v.w=A.w+p;if(v.width==null){s.style.width=this.Em(v.w)}}if(A.rw+p>v.rw){v.rw=A.rw+p}if(A.lw+p=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(x,r,C,D,u){var l=this.createStack(x,true);var t=this.createBox(l),s=this.createBox(l);this.createChar(t,(C.top||C.ext),D,u);this.createChar(s,(C.bot||C.ext),D,u);var j={bbox:{w:0,lw:0,rw:0}},B=j,m;var z=t.bbox.h+t.bbox.d+s.bbox.h+s.bbox.d;var p=-t.bbox.h;this.placeBox(t,0,p,true);p-=t.bbox.d;if(C.mid){B=this.createBox(l);this.createChar(B,C.mid,D,u);z+=B.bbox.h+B.bbox.d}if(r>z){j=this.Element("span");this.createChar(j,C.ext,D,u);var A=j.bbox.h+j.bbox.d,i=A-0.05,v,o,w=(C.mid?2:1);o=v=Math.ceil((r-z)/(w*i));if(!C.fullExtenders){i=(r-z)/(w*v)}var 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j=this.getValues("scriptlevel","lspace","rspace");if(j.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){j.lspace=Math.max(0,e.length2em(j.lspace));j.rspace=Math.max(0,e.length2em(j.rspace));var i=this,k=this.Parent();while(k&&k.isEmbellished()&&k.Core()===i){i=k;k=k.Parent();l=i.HTMLspanElement()}if(j.lspace){l.style.paddingLeft=e.Em(j.lspace)}if(j.rspace){l.style.paddingRight=e.Em(j.rspace)}}}else{var m=this.texSpacing();if(m!==""){m=e.length2em(m)/(l.scale||1);if(l.style.paddingLeft){m+=parseFloat(l.style.paddingLeft)}l.style.paddingLeft=e.Em(m)}}},HTMLgetScale:function(){var k=1,i=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var k=e.TeX.axis_height,o=l.scale;if(i.symmetric){j=2*Math.max(m-k,p+k)}else{j=m+p}i.maxsize=e.length2em(i.maxsize,l.bbox.h+l.bbox.d);i.minsize=e.length2em(i.minsize,l.bbox.h+l.bbox.d);j=Math.max(i.minsize,Math.min(i.maxsize,j));l=this.HTMLcreateSpan(n);e.createDelimiter(l,this.data.join("").charCodeAt(0),j,o);if(i.symmetric){j=(l.bbox.h+l.bbox.d)/2+k}else{j=(l.bbox.h+l.bbox.d)*m/(m+p)}e.positionDelimiter(l,j);this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:function(l,i){this.HTMLremoveColor();var j=this.getValues("maxsize","minsize","mathvariant","fontweight");if(j.fontweight==="bold"&&!this.mathvariant){j.mathvariant=a.VARIANT.BOLD}var k=this.HTMLspanElement(),m=k.scale;j.maxsize=e.length2em(j.maxsize,k.bbox.w);j.minsize=e.length2em(j.minsize,k.bbox.w);i=Math.max(j.minsize,Math.min(j.maxsize,i));k=this.HTMLcreateSpan(l);e.createDelimiter(k,this.data.join("").charCodeAt(0),i,m,j.mathvariant);this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var 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Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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:(l?"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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 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q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 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Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax 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#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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial 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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.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){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End 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k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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 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3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(l?"Highlight":"#606872"),color:(l?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"},}});var g,d;c.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.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){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End 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j=this.getValues("scriptlevel","lspace","rspace");if(j.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){j.lspace=Math.max(0,e.length2em(j.lspace));j.rspace=Math.max(0,e.length2em(j.rspace));var i=this,k=this.Parent();while(k&&k.isEmbellished()&&k.Core()===i){i=k;k=k.Parent();l=i.HTMLspanElement()}if(j.lspace){l.style.paddingLeft=e.Em(j.lspace)}if(j.rspace){l.style.paddingRight=e.Em(j.rspace)}}}else{var m=this.texSpacing();if(m!==""){m=e.length2em(m)/(l.scale||1);if(l.style.paddingLeft){m+=parseFloat(l.style.paddingLeft)}l.style.paddingLeft=e.Em(m)}}},HTMLgetScale:function(){var k=1,i=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var k=e.TeX.axis_height,o=l.scale;if(i.symmetric){j=2*Math.max(m-k,p+k)}else{j=m+p}i.maxsize=e.length2em(i.maxsize,l.bbox.h+l.bbox.d);i.minsize=e.length2em(i.minsize,l.bbox.h+l.bbox.d);j=Math.max(i.minsize,Math.min(i.maxsize,j));l=this.HTMLcreateSpan(n);e.createDelimiter(l,this.data.join("").charCodeAt(0),j,o);if(i.symmetric){j=(l.bbox.h+l.bbox.d)/2+k}else{j=(l.bbox.h+l.bbox.d)*m/(m+p)}e.positionDelimiter(l,j);this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:function(l,i){this.HTMLremoveColor();var j=this.getValues("maxsize","minsize","mathvariant","fontweight");if(j.fontweight==="bold"&&!this.mathvariant){j.mathvariant=a.VARIANT.BOLD}var k=this.HTMLspanElement(),m=k.scale;j.maxsize=e.length2em(j.maxsize,k.bbox.w);j.minsize=e.length2em(j.minsize,k.bbox.w);i=Math.max(j.minsize,Math.min(j.maxsize,i));k=this.HTMLcreateSpan(l);e.createDelimiter(k,this.data.join("").charCodeAt(0),i,m,j.mathvariant);this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var 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k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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,f,i,e,b){var n="1.1.8";MathJax.Extension.MathMenu={version:n};var l=c.Browser.isPC,j=c.Browser.isMSIE;var h=(l?null:"5px");var m=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:i.fileURL(b.imageDir+"/CloseX-31.png"),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_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:(l?"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":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"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:(l?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(l?"-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":(j?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(j?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(l?"1em":".7em")},".MathJax_MenuLabel":{padding:(l?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(l?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(l?"4px 1px 0px":"4px 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q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" 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o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
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Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax 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a=MathJax.Menu=MathJax.Object.Subclass({version:n,items:[],posted:false,title:null,margin:5,Init:function(o){this.items=[].slice.call(arguments,0)},With:function(o){if(o){c.Insert(this,o)}return this},Post:function(p,z){if(!p){p=window.event}var v=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var o=document.getElementById("MathJax_MenuFrame");if(!o){o=a.Background(this);delete k.lastItem;delete k.lastMenu;delete a.skipUp}var q=f.addElement(o,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},v);for(var s=0,r=this.items.length;sdocument.body.offsetWidth-this.margin){w=document.body.offsetWidth-q.offsetWidth-this.margin}if(a.isMobile){w=Math.max(5,w-Math.floor(q.offsetWidth/2));u-=20}a.skipUp=p.isContextMenu}else{var t="left",A=z.offsetWidth;w=(a.isMobile?30:A-2);u=0;while(z&&z!==o){w+=z.offsetLeft;u+=z.offsetTop;z=z.parentNode}if(w+q.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){t="right";w=Math.max(this.margin,w-A-q.offsetWidth+6)}if(!l){q.style["borderRadiusTop"+t]=0;q.style["WebkitBorderRadiusTop"+t]=0;q.style["MozBorderRadiusTop"+t]=0;q.style["KhtmlBorderRadiusTop"+t]=0}}q.style.left=w+"px";q.style.top=u+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(p)},Remove:function(o,p){var q=document.getElementById("MathJax_MenuFrame");if(q){q.parentNode.removeChild(q);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}},Find:function(p){var r=[].slice.call(arguments,1);for(var q=0,o=this.items.length;q=0&&u.parentNode.menuItem!==t[o].menuItem){t[o].menuItem.posted=false;t[o].parentNode.removeChild(t[o]);o--}if(this.Timer&&!a.isMobile){this.Timer(s,u)}}},Mouseout:function(o,p){if(!this.menu||!this.menu.posted){this.Deactivate(p)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(o,p){return this.Remove(o,p)},Touchstart:function(o,p){return this.TouchEvent(o,p,"Mousedown")},Touchend:function(o,p){return this.TouchEvent(o,p,"Mouseup")},TouchEvent:function(p,q,o){if(this!==k.lastItem){if(k.lastMenu){a.Event(p,k.lastMenu,"Mouseout")}a.Event(p,q,"Mouseover",true);k.lastItem=this;k.lastMenu=q}if(this.nativeTouch){return null}a.Event(p,q,o);return false},Remove:function(o,p){p=p.parentNode.menuItem;return p.Remove(o,p)},Activate:function(o){this.Deactivate(o);o.className+=" MathJax_MenuActive"},Deactivate:function(o){o.className=o.className.replace(/ MathJax_MenuActive/,"")},With:function(o){if(o){c.Insert(this,o)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(o,q,p){this.name=o;this.action=q;this.With(p)},Label:function(o,p){return[this.name]},Mouseup:function(o,p){if(!this.disabled){this.Remove(o,p);this.action.call(this,o)}return g(o)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(l&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(o,q){this.name=o;var p=1;if(!(q instanceof a.ITEM)){this.With(q),p++}this.menu=a.apply(a,[].slice.call(arguments,p))},Label:function(o,p){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(o,p){if(this.timer){clearTimeout(this.timer)}o={clientX:o.clientX,clientY:o.clientY};this.timer=setTimeout(e(["Mouseup",this,o,p]),m.delay)},Touchend:function(p,r){var q=this.menu.posted;var o=this.SUPER(arguments).Touchend.apply(this,arguments);if(q){this.Deactivate(r);delete k.lastItem;delete k.lastMenu}return o},Mouseup:function(p,r){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(p,r)}else{var q=document.getElementById("MathJax_MenuFrame").childNodes,o=q.length-1;while(o>=0){var s=q[o];s.menuItem.posted=false;s.parentNode.removeChild(s);if(s.menuItem===this.menu){break}o--}}}return g(p)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(l?"\u25CF":"\u2713"),Init:function(p,o,q){this.name=p;this.variable=o;this.With(q);if(this.value==null){this.value=this.name}},Label:function(p,q){var o={className:"MathJax_MenuRadioCheck"};if(m.settings[this.variable]!==this.value){o={style:{display:"none"}}}return[["span",o,[this.marker]]," "+this.name]},Mouseup:function(r,s){if(!this.disabled){var t=s.parentNode.childNodes;for(var p=0,o=t.length;p/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("
"+u+"
");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.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){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE(),k.CHECKBOX("Highlight on Hover","discoverable")),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(o){a.cookie.showRenderer=m.showRenderer=o;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!o};a.showFontMenu=function(o){a.cookie.showFontMenu=m.showFontMenu=o;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!o};a.showContext=function(o){a.cookie.showContext=m.showContext=o;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!o};if(a.isMobile){(function(){var p=m.settings;var o=a.menu.Find("Math Settings","Zoom Trigger").menu;o.items[0].disabled=o.items[1].disabled=true;if(p.zoom==="Hover"||p.zoom=="Click"){p.zoom="None"}o.items=o.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",i,m.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",i,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); diff --git a/extensions/MathZoom.js b/extensions/MathZoom.js index b018fe93d..c4f9eed3b 100644 --- a/extensions/MathZoom.js +++ b/extensions/MathZoom.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(a,d,f,c,i){var j="1.1.3";var h=a.CombineConfig("MathZoom",{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)"}}});var e,b;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var g=MathJax.Extension.MathZoom={version:j,settings:a.config.menuSettings,HandleEvent:function(m,k,l){if(g.settings.CTRL&&!m.ctrlKey){return true}if(g.settings.ALT&&!m.altKey){return true}if(g.settings.CMD&&!m.metaKey){return true}if(g.settings.Shift&&!m.shiftKey){return true}if(!g[k]){return true}return g[k](m,l)},Click:function(l,k){if(this.settings.zoom==="Click"){return this.Zoom(k,l)}},DblClick:function(l,k){if(this.settings.zoom==="Double-Click"){return this.Zoom(k,l)}},Hover:function(l,k){if(this.settings.zoom==="Hover"){this.Zoom(k,l);return true}return false},Zoom:function(t,m){this.Remove();b.ClearHoverTimer();var w=t.parentNode;if(w.className==="MathJax_MathContainer"){w=w.parentNode}if(w.parentNode.className==="MathJax_MathContainer"){w=w.parentNode.parentNode}var r=(String(w.className).match(/^MathJax_(MathML|Display)$/)?w:t).nextSibling;var n=a.getJaxFor(r),s=n.root;var p=(c&&n.outputJax.isa(c.constructor)?"HTMLCSS":(i&&n.outputJax.isa(i.constructor)?"MathML":null));if(!p){return}if(n.hover){b.UnHover(n)}var k=Math.floor(0.85*document.body.clientWidth),q=Math.floor(0.85*document.body.clientHeight);var l=d.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":k+"px","max-height":q+"px"}},[["span"]]]]);var y=l.lastChild,v=y.firstChild,o=l.firstChild;t.parentNode.insertBefore(l,t);if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});l.style.position="relative";l.style.zIndex=h.styles["#MathJax_ZoomOverlay"]["z-index"];l=u}var x=(this["Zoom"+p])(s,v,t,k,q);if(this.msiePositionBug){if(this.msieSizeBug){y.style.height=x.zH+"px";y.style.width=x.zW+"px"}if(y.offsetHeight>q){y.style.height=q+"px"}if(y.offsetWidth>k){y.style.width=k+"px"}if(t.nextSibling){t.parentNode.insertBefore(l,t.nextSibling)}else{w.appendChild(l)}}if(this.operaPositionBug){y.style.width=Math.min(k,x.zW)+"px"}if(y.offsetWidth<=k&&y.offsetHeight<=q){y.style.overflow="visible"}this.Position(y,x,(p==="MathML"&&w.nodeName.toLowerCase()==="div"));y.style.visibility="";if(this.settings.zoom==="Hover"){o.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 e(m)},ZoomHTMLCSS:function(q,t,s,k,p){t.className="MathJax";c.idPostfix="-zoom";c.getScales(t,t);q.toHTML(t,t);var u=q.HTMLspanElement().bbox;c.idPostfix="";if(u.width){t.style.width=Math.floor(k-1.5*c.em)+"px";t.style.display="inline-block";var l=(q.id||"MathJax-Span-"+q.spanID)+"-zoom";var m=document.getElementById(l).firstChild;while(m&&m.style.width!==u.width){m=m.nextSibling}if(m){m.style.width="100%"}}t.style.position=s.style.position="absolute";var r=t.offsetWidth,o=t.offsetHeight,v=s.offsetHeight,n=s.offsetWidth;t.style.position=s.style.position="";if(n===0){n=s.offseWidth||s.parentNode.offsetWidth}return{Y:-this.getTop(q,t,s,this.msieTopBug,this.msieBorderBug,false),mW:n,mH:v,zW:r,zH:o}},ZoomMathML:function(k,n,p){k.toNativeMML(n,n);var q=this.getTop(k,n,p,this.msieTopMMLBug,false,this.ffMMLdisplayBug);var r=p.offsetWidth||p.scrollWidth,m=p.offsetHeight||p.scrollHeight;if(this.msieIE8HeightBug){n.style.position="absolute"}var l=n.offsetWidth,o=n.offsetHeight;if(this.msieIE8HeightBug){n.style.position=""}if(this.ffMMLdisplayBug){n.style.display="inline-block";n.style.width=l+"px"}return{Y:-q,mW:r,mH:m,zW:l,zH:o}},getTop:function(q,s,r,t,p,u){s.appendChild(this.topImg);if(u&&r.getAttribute("display")==="block"){r.setAttribute("display","inline");r.MJinline=true;var n=q.NativeMMLelement("mstyle");while(r.firstChild){n.appendChild(r.firstChild)}r.appendChild(n);n.setAttribute("displaystyle","true")}if(r.MJinline){s.insertBefore(this.topImg,s.firstChild);var l=s.childNodes[1],m=q.NativeMMLelement("mstyle");l.setAttribute("display","inline");while(l.firstChild){m.appendChild(l.firstChild)}l.appendChild(m);m.setAttribute("displaystyle","true");m.setAttribute("displaystyle","true")}var o=this.topImg.offsetTop;if(t){var k=r.parentNode.style.whiteSpace;r.parentNode.style.whiteSpace="nowrap";r.parentNode.insertBefore(this.topImg,r);o-=this.topImg.offsetTop-s.parentNode.parentNode.offsetTop;r.parentNode.style.whiteSpace=k}if(p){o+=Math.floor(0.5*c.em)}this.topImg.parentNode.removeChild(this.topImg);return o},Position:function(q,o,s){var l=this.Resize(),n=l.x,m=l.y,k=o.mW;if(this.msieIE8Bug){k=-k}var r=-Math.floor((q.offsetWidth-k)/2),p=o.Y;q.style.left=Math.max(r,10-n)+"px";q.style.top=Math.max(p,10-m)+"px"},Resize:function(m){if(g.onresize){g.onresize(m)}var k=0,p=0,o=document.getElementById("MathJax_ZoomFrame"),n=o,l=document.getElementById("MathJax_ZoomOverlay");if(g.operaPositionBug){o.style.border="1px solid"}if(n.offsetParent){do{k+=n.offsetLeft;p+=n.offsetTop}while(n=n.offsetParent)}if(g.operaPositionBug){o.style.border=""}l.style.left=(-k)+"px";l.style.top=(-p)+"px";if(g.msiePositionBug){setTimeout(g.SetWH,0)}else{g.SetWH()}return{x:k,y:p}},SetWH:function(){var k=document.getElementById("MathJax_ZoomOverlay");k.style.width=k.style.height="1px";k.style.width=document.body.scrollWidth+"px";k.style.height=document.body.scrollHeight+"px"},Remove:function(l){var m=document.getElementById("MathJax_ZoomFrame");if(m){m.parentNode.removeChild(m);m=document.getElementById("MathJax_ZoomTracker");if(m){m.parentNode.removeChild(m)}if(g.operaRefreshBug){var k=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(k)}if(window.removeEventListener){removeEventListener("resize",g.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",g.Resize)}else{window.onresize=g.onresize;delete g.onresize}}}return e(l)}};a.Browser.Select({MSIE:function(k){var l=(document.compatMode==="BackCompat");var n=k.versionAtLeast("8.0")&&document.documentMode>7;var m=document.documentMode>=9;g.msiePositionBug=!m;g.msieSizeBug=k.versionAtLeast("7.0")&&(!document.documentMode||document.documentMode===7||document.documentMode===8);g.msieIE8Bug=n&&(document.documentMode===8);g.msieIE8HeightBug=(document.documentMode===8);g.msieZIndexBug=!n;g.msieTopBug=(!k.versionAtLeast("8.0")||document.documentMode===7);g.msieTopMMLBug=g.msieTopBug||(!n||document.documentMode>=9);g.msieBorderBug=l&&k.versionAtLeast("8.0");g.msieInlineBlockAlignBug=(!n||l);if(document.documentMode>=9){delete h.styles["#MathJax_Zoom"].filter}},Opera:function(k){g.operaPositionBug=true;g.operaRefreshBug=true},Firefox:function(k){g.ffMMLdisplayBug=true}});g.topImg=(g.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(g.operaPositionBug||g.msieTopBug){g.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,h.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(a,d,f,c,j){var k="1.1.3";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-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:"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)"}}});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,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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,t){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[t.jaxID];var o=q.getJaxFromMath(t),s=o.root;if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*document.body.clientHeight);var m=d.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":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,v=x.firstChild,p=m.firstChild;t.parentNode.insertBefore(m,t);if(v.addEventListener){v.addEventListener("mousedown",this.Remove,true)}if(this.msieZIndexBug){var u=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=u}var w=q.Zoom(s,v,t,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=w.zH+"px";x.style.width=w.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";v.style.marginRight="16px"}if(x.offsetWidth>l){x.style.width=l+"px";v.style.marginBottom="16px"}}if(this.operaPositionBug){x.style.width=Math.min(l,w.zW)+"px"}if(x.offsetWidth=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);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); diff --git a/jax/output/HTML-CSS/config.js b/jax/output/HTML-CSS/config.js index 3c7957ea3..b01cbcdc2 100644 --- a/jax/output/HTML-CSS/config.js +++ b/jax/output/HTML-CSS/config.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.12",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=0){if(this.negativeSkipBug){var i=l.style.position;l.style.position="absolute";m=this.startMarker;if(l.firstChild){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}m=this.startMarker}l.appendChild(this.endMarker);j=this.endMarker.offsetLeft-m.offsetLeft;l.removeChild(this.endMarker);if(this.negativeSkipBug){l.removeChild(m);l.style.position=i}}return j/this.em},Measured:function(k,j){if(k.bbox.width==null&&k.bbox.w&&!k.bbox.isMultiline){var i=this.getW(k);k.bbox.rw+=i-k.bbox.w;k.bbox.w=i}if(!j){j=k.parentNode}if(!j.bbox){j.bbox=k.bbox}return 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k=this.Em(Math.max(0,l+o)),n=this.Em(-o);if(this.msieInlineBlockAlignBug){n=this.Em(e.getHD(m.parentNode).d-o)}if(m.isBox||m.className=="mspace"){m.bbox={h:l*m.scale,d:o*m.scale,w:i*m.scale,rw:i*m.scale,lw:0};m.style.height=k;m.style.verticalAlign=n}else{m=this.addElement(m,"span",{style:{height:k,verticalAlign:n},isMathJax:true})}if(i>=0){m.style.width=this.Em(i);m.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){m.style.height=""}m.style.marginLeft=this.Em(i);if(e.safariNegativeSpaceBug&&m.parentNode.firstChild==m){this.createBlank(m,0,true)}}if(j&&j!==a.COLOR.TRANSPARENT){m.style.backgroundColor=j}return m},createRule:function(p,l,n,q,j){var k=e.TeX.min_rule_thickness;if(q>0&&q*this.em0&&(l+n)*this.em0&&o.offsetWidth==0){o.style.width=this.Em(q)}if(p.isBox||p.className=="mspace"){p.bbox=o.bbox}return o},createFrame:function(q,o,p,r,u,j){var n=(this.msieBorderWidthBug?0:2*u);var s=this.Em(o+p-n),i=this.Em(-p-u),m=this.Em(r-n);var k=this.Em(u)+" "+j;var 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s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" 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Array)){q=[q]}if(o.fonts!=q){o.fonts=q}o.FONTS=[];for(l=0,j=q.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(j){var i=MathJax.Callback.Queue();i.Push(["Require",c,this.fontDir+"/"+j]);if(this.imgFonts){if(!MathJax.isPacked){j=j.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}i.Push(["Require",c,this.webfontDir+"/png/"+j])}d.RestartAfter(i.Push({}))},loadWebFont:function(i){i.available=i.isWebFont=true;if(e.FontFaceBug){i.family=i.name;if(e.msieFontCSSBug){i.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(i))},loadWebFontError:function(j,i){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");j.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax 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l=this.addElement(q,"span",{style:{border:k,display:"inline-block",overflow:"hidden",width:m,height:s},bbox:{h:o,d:p,w:r,rw:r,lw:0},noAdjust:true,isMathJax:true});if(i){l.style.verticalAlign=i}return l},createStack:function(k,m,j){if(this.msiePaddingWidthBug){this.createStrut(k,0)}var l=String(j).match(/%$/);var i=(!l&&j!=null?j:0);k=this.addElement(k,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(l?"100%":this.Em(i)),height:0}});if(!m){k.parentNode.bbox=k.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:i,lw:this.BIGDIMEN,rw:(!l&&j!=null?j:-this.BIGDIMEN)};if(l){k.bbox.width=j}}return k},createBox:function(j,i){var k=this.addElement(j,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(i!=null){k.style.width=i}return k},addBox:function(i,j){j.style.position="absolute";j.isBox=true;return i.appendChild(j)},placeBox:function(q,p,o,m){q.isMathJax=true;var s=q.parentNode,A=q.bbox,v=s.bbox;if(this.msiePlaceBoxBug){this.addText(q,this.NBSP)}if(this.imgSpaceBug){this.addText(q,this.imgSpace)}var u=q.offsetHeight/this.em+1,C=0;if(q.noAdjust){u-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(q,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(u)}})}else{this.addElement(q,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(u)}})}}q.style.top=this.Em(-o-u);q.style.left=this.Em(p+C);if(A){if(this.negativeSkipBug){if(A.lw<0){C=A.lw;e.createBlank(q,-C,true);k=0}if(A.rw>A.w){e.createBlank(q,A.rw-A.w+0.1)}}if(!this.msieClipRectBug&&!A.noclip&&!m){var z=3/this.em;var w=(A.H==null?A.h:A.H),j=(A.D==null?A.d:A.D);var B=u-w-z,n=u+j+z,k=A.lw-3*z,i=1000;if(A.isFixed){i=A.width-k}q.style.clip="rect("+this.Em(B)+" "+this.Em(i)+" "+this.Em(n)+" 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B={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},j;this.placeBox(m,-m.bbox.lw,0,true);var s=(m.bbox.rw-m.bbox.lw)+(A.bbox.rw-A.bbox.lw)-0.05,r=m.bbox.rw-m.bbox.lw-0.025,t;if(C.mid){B=this.createBox(p);this.createChar(B,C.mid,E,u);s+=B.bbox.w}if(l>s){var 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p=this.getValues("mathcolor","color");if(this.mathbackground){p.mathbackground=this.mathbackground}if(this.background){p.background=this.background}if(this.style&&n.style.backgroundColor){p.mathbackground=n.style.backgroundColor;n.style.backgroundColor="transparent"}if(p.color&&!this.mathcolor){p.mathcolor=p.color}if(p.background&&!this.mathbackground){p.mathbackground=p.background}if(p.mathcolor){n.style.color=p.mathcolor}if(p.mathbackground&&p.mathbackground!==a.COLOR.TRANSPARENT){var q=1/e.em,m=0,l=0;if(this.isToken){m=n.bbox.lw;l=n.bbox.rw-n.bbox.w}if(n.style.paddingLeft!==""){m+=parseFloat(n.style.paddingLeft)*(n.scale||1)}if(n.style.paddingRight!==""){l-=parseFloat(n.style.paddingRight)*(n.scale||1)}var k=Math.max(0,e.getW(n)+(e.PaddingWidthBug?0:l-m));if(e.msieCharPaddingWidthBug&&n.style.paddingLeft!==""){k+=parseFloat(n.style.paddingLeft)*(n.scale||1)}var o=n.bbox.h+n.bbox.d,i=-n.bbox.d;if(k>0){k+=2*q;m-=q}if(o>0){o+=2*q;i-=q}l=-k-m;var j=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:p.mathbackground,width:e.Em(k),height:e.Em(o),verticalAlign:e.Em(i),marginLeft:e.Em(m),marginRight:e.Em(l)}});if(e.msieInlineBlockAlignBug){j.style.position="relative";j.style.width=j.style.height=0;j.style.verticalAlign=j.style.marginLeft=j.style.marginRight="";e.placeBox(e.addElement(j,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",width:e.Em(k),height:e.Em(o),background:p.mathbackground}}),m,n.bbox.h+q)}n.parentNode.insertBefore(j,n);if(e.msieColorPositionBug){n.style.position="relative"}return j}return null},HTMLremoveColor:function(){var i=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(i){i.parentNode.removeChild(i)}},HTMLhandleSpace:function(l){if(this.useMMLspacing){if(this.type!=="mo"){return}var j=this.getValues("scriptlevel","lspace","rspace");if(j.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){j.lspace=Math.max(0,e.length2em(j.lspace));j.rspace=Math.max(0,e.length2em(j.rspace));var i=this,k=this.Parent();while(k&&k.isEmbellished()&&k.Core()===i){i=k;k=k.Parent();l=i.HTMLspanElement()}if(j.lspace){l.style.paddingLeft=e.Em(j.lspace)}if(j.rspace){l.style.paddingRight=e.Em(j.rspace)}}}else{var m=this.texSpacing();if(m!==""){m=e.length2em(m)/(l.scale||1);if(l.style.paddingLeft){m+=parseFloat(l.style.paddingLeft)}l.style.paddingLeft=e.Em(m)}}},HTMLgetScale:function(){var k=1,i=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var j=this.HTMLspanElement();if(j.style.fontSize!=""){i.fontsize=j.style.fontSize}}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=e.length2em(i.scriptminsize);if(ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;e.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(i){if(!this.Get("stretchy")){return false}var j=this.data.join("");if(j.length>1){return false}j=e.FONTDATA.DELIMITERS[j.charCodeAt(0)];return(j&&j.dir==i.substr(0,1))},HTMLstretchV:function(n,m,p){this.HTMLremoveColor();var i=this.getValues("symmetric","maxsize","minsize");var l=this.HTMLspanElement(),j;var k=e.TeX.axis_height,o=l.scale;if(i.symmetric){j=2*Math.max(m-k,p+k)}else{j=m+p}i.maxsize=e.length2em(i.maxsize,l.bbox.h+l.bbox.d);i.minsize=e.length2em(i.minsize,l.bbox.h+l.bbox.d);j=Math.max(i.minsize,Math.min(i.maxsize,j));l=this.HTMLcreateSpan(n);e.createDelimiter(l,this.data.join("").charCodeAt(0),j,o);if(i.symmetric){j=(l.bbox.h+l.bbox.d)/2+k}else{j=(l.bbox.h+l.bbox.d)*m/(m+p)}e.positionDelimiter(l,j);this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:function(l,i){this.HTMLremoveColor();var j=this.getValues("maxsize","minsize","mathvariant","fontweight");if(j.fontweight==="bold"&&!this.mathvariant){j.mathvariant=a.VARIANT.BOLD}var k=this.HTMLspanElement(),m=k.scale;j.maxsize=e.length2em(j.maxsize,k.bbox.w);j.minsize=e.length2em(j.minsize,k.bbox.w);i=Math.max(j.minsize,Math.min(j.maxsize,i));k=this.HTMLcreateSpan(l);e.createDelimiter(k,this.data.join("").charCodeAt(0),i,m,j.mathvariant);this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});a.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;if(this.Parent().type==="merror"){e.addText(o,this.data.join(""));var p=e.getHD(o),k=e.getW(o);o.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k}}else{var n=this.HTMLgetVariant();for(var l=0,j=this.data.length;lu){i=((n.bbox.h+n.bbox.d)-(u-w))/2}var y=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!y||lI){I=u.bbox.w}if(!L[K]&&I>l){l=I}}}if(C==null&&F!=null){l=F}else{if(l==-e.BIGDIMEN){l=I}}for(K=I=0,G=this.data.length;KI){I=u.bbox.w}}}var B=e.TeX.rule_thickness,E=e.FONTDATA.TeX_factor;var n=p[this.base]||{bbox:this.HTMLzeroBBox()},M=(n.bbox.ic||0);var s,q,w,v,r,A,H;for(K=0,G=this.data.length;K0){w+=B;o-=B}}e.placeBox(i,l.bbox.w+y,Math.max(w,F.superscriptshift));e.placeBox(n,l.bbox.w+y-I,-Math.max(o,F.subscriptshift))}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(p,i){var m=this.Get("alttext");if(m){i.setAttribute("aria-label",m)}var j=e.addElement(p,"nobr",{isMathJax:true});p=this.HTMLcreateSpan(j);var n=e.createStack(p),k=e.createBox(n),o;n.style.fontSize=j.parentNode.style.fontSize;j.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;o=e.Measured(this.data[0].toHTML(k),k)}e.placeBox(k,0,0);var l=e.em/e.outerEm;e.em/=l;p.bbox.h*=l;p.bbox.d*=l;p.bbox.w*=l;p.bbox.lw*=l;p.bbox.rw*=l;if(o&&o.bbox.width!=null){n.style.width=o.bbox.width;k.style.width="100%"}this.HTMLhandleColor(p);if(o){e.createRule(p,o.bbox.h*l,o.bbox.d*l,0)}if(!this.isMultiline&&this.Get("display")==="block"&&p.bbox.width==null){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}i.style.textAlign=q.indentalign;if(q.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){q.indentshift=q.indentshiftfirst}if(q.indentshift==="auto"){q.indentshift=this.displayIndent}if(q.indentshift&&q.indentalign!==a.INDENTALIGN.CENTER){p.style[{left:"marginLeft",right:"marginRight"}[q.indentalign]]=e.Em(e.length2em(q.indentshift))}}return p},HTMLspanElement:a.mbase.prototype.HTMLspanElement});a.TeXAtom.Augment({toHTML:function(j){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var i=e.createStack(j);var k=e.createBox(i);e.Measured(this.data[0].toHTML(k),k);e.placeBox(k,0,e.TeX.axis_height-(k.bbox.h+k.bbox.d)/2+k.bbox.d)}else{j.bbox=this.data[0].toHTML(j).bbox}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(i){var l=i.versionAtLeast("7.0");var k=i.versionAtLeast("8.0")&&document.documentMode>7;var j=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax 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i=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var n=(j&&m.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!m.versionAtLeast("5.0"))||(i!=null&&(i[1]<2||(i[1]==2&&i[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!j,safariTextNodeBug:!k,safariWebFontSerif:["serif"],allowWebFonts:(j&&!n?"otf":false)});if(n){var l=d.config["HTML-CSS"];if(l){l.availableFonts=[];l.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(i){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(i.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(i){i.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:i.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(i.versionAtLeast("10.0")&&!i.isMini?"otf":false),adjustAvailableFonts:function(l){for(var k=0,j=l.length;k span":{"text-align":l+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var j=document.createElement("object");j.id="mathplayer";j.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(j);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(k){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(k){if(!k.parentNode){return}if(!this.initialized){this.InitializeMML()}var p=k.previousSibling;if(p&&String(p.className).match(/^MathJax(_MathML|_Display)?$/)){p.parentNode.removeChild(p)}var o=k.MathJax.elementJax.root;var n=(o.Get("display")==="block"?"div":"span");var m=d.Element(n,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),j=m.firstChild;o.toNativeMML(j.firstChild);k.parentNode.insertBefore(m,k);if(h){if(j.addEventListener){j.addEventListener("contextmenu",g.Menu,true);j.addEventListener("mouseover",g.Mouseover,true);j.addEventListener("mouseout",g.Mouseout,true);j.addEventListener("mousedown",g.Mousedown,true);j.addEventListener("mouseup",g.False,true);j.addEventListener("click",g.Click,true);j.addEventListener("dblclick",g.DblClick,true)}else{var l=(this.config.showMathMenuMSIE!=null?this:b).config;if(l.showMathMenuMSIE){this.MSIEoverlay(j)}}}else{j.oncontextmenu=g.Menu;j.onmouseover=g.Mouseover;j.onmouseout=g.Mouseout;j.onmousedown=g.Mousedown;j.onclick=g.Click;j.ondblclick=g.DblClick}},Remove:function(j){var k=j.SourceElement();if(!k){return}k=k.previousSibling;if(!k){return}if(k.className.match(/MathJax_MathML/)){k.parentNode.removeChild(k)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(j){var k=j.firstChild;if(k.nodeName.toLowerCase()==="span"){k=k.firstChild}var l=this.getHoverBBox(null,k,{});d.addElement(j,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-l.w),top:c.Px(-l.h-(l.y||0)-1),width:c.Px(l.w),height:c.Px(l.h+l.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(j,{msieMath:k,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var k=window.event;var j=i.MSIEevents[k.type];if(i[j]&&i[j](k,this)===false){return false}if(MathJax.Extension.MathZoom&&MathJax.Extension.MathZoom.HandleEvent(k,j,this)===false){return false}if(k.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+k.type,k)}return g.False(k)},getJaxFromMath:function(j){if(j.className==="MathJax_MSIE_Overlay"){j=j.parentNode.parentNode}return b.getJaxFor(j.parentNode.nextSibling)},getHoverSpan:function(j,k){if(k.className==="MathJax_MSIE_Overlay"){return k.parentNode}return k.firstChild},getHoverBBox:function(l,n,o){n=n.parentNode;n.appendChild(this.topImg);var m=this.topImg.offsetTop,p=n.offsetHeight-m,k=n.offsetWidth;n.removeChild(this.topImg);var j=(o.className==="MathJax_MSIE_Overlay"?-k:0);return{w:k,h:m,d:p,x:j}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(o){var l=this.NativeMMLelement(this.type);this.NativeMMLattributes(l);for(var n=0,k=this.data.length;n7;i.msieInlineBlockAlignBug=(!l||k);i.msieTopBug=(!j.versionAtLeast("8.0")||document.documentMode===7)},Opera:function(j){i.operaPositionBug=true}});i.topImg=(i.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(i.operaPositionBug||i.msieTopBug){i.topImg.style.border="1px solid"}b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML); +(function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{}},settings:b.config.menuSettings,Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;return f.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},InitializeMML:function(){this.initialized=true;if(b.Browser.isMSIE){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}},Translate:function(l){if(!l.parentNode){return}if(!this.initialized){this.InitializeMML()}var q=l.previousSibling;if(q&&String(q.className).match(/^MathJax(_MathML|_Display)?$/)){q.parentNode.removeChild(q)}var p=l.MathJax.elementJax.root;var o=(p.Get("display")==="block"?"div":"span");var n=d.Element(o,{className:"MathJax_MathML",style:{"font-size":this.config.scale+"%"}},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]),k=n.firstChild;p.toNativeMML(k.firstChild);l.parentNode.insertBefore(n,l);if(h){if(k.addEventListener){k.addEventListener("contextmenu",g.Menu,true);k.addEventListener("mouseover",g.Mouseover,true);k.addEventListener("mouseout",g.Mouseout,true);k.addEventListener("mousedown",g.Mousedown,true);k.addEventListener("mouseup",g.False,true);k.addEventListener("click",g.Click,true);k.addEventListener("dblclick",g.DblClick,true)}else{var m=(this.config.showMathMenuMSIE!=null?this:b).config;if(m.showMathMenuMSIE){this.MSIEoverlay(k)}}}else{k.oncontextmenu=g.Menu;k.onmouseover=g.Mouseover;k.onmouseout=g.Mouseout;k.onmousedown=g.Mousedown;k.onclick=g.Click;k.ondblclick=g.DblClick}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){this.msieMath.fireEvent("on"+l.type,l)}return g.False(l)},getJaxFromMath:function(k){if(k.className==="MathJax_MSIE_Overlay"){k=k.parentNode.parentNode}return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){if(l.className==="MathJax_MSIE_Overlay"){return l.parentNode}return l.firstChild},getHoverBBox:function(k,l,m){var n=g.getBBox(l.parentNode);n.x=(m.className==="MathJax_MSIE_Overlay"?-n.w:0);return n},Zoom:function(o,r,p,k,n){o.toNativeMML(r,r);if(this.msieIE8HeightBug){r.style.position="absolute"}var l=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,m=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:l,mH:s,zW:q,zH:m}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o Mh) {zoom.style.height = Mh+"px"} // IE doesn't do max-height? - if (zoom.offsetWidth > Mw) {zoom.style.width = Mw+"px"} - if (math.nextSibling) {math.parentNode.insertBefore(div,math.nextSibling)} - else {parent.appendChild(div)} // needs to be after to be above? + if (zoom.offsetHeight > Mh) {zoom.style.height = Mh+"px"; span.style.marginRight = "16px"} // IE doesn't do max-height? + if (zoom.offsetWidth > Mw) {zoom.style.width = Mw+"px"; span.style.marginBottom = "16px"} } if (this.operaPositionBug) {zoom.style.width = Math.min(Mw,bbox.zW)+"px"} // Opera gets width as 0? - if (zoom.offsetWidth <= Mw && zoom.offsetHeight <= Mh) {zoom.style.overflow = "visible"} - this.Position(zoom,bbox,(JAX.id === "MathML" && parent.nodeName.toLowerCase() === "div")); + if (zoom.offsetWidth < Mw && zoom.offsetHeight < Mh) {zoom.style.overflow = "visible"} + this.Position(zoom,bbox); zoom.style.visibility = ""; // @@ -192,31 +188,11 @@ return FALSE(event); }, - // - // Get top offset from baseline - // - getTop: function (root,span,math,topBug,borderBug) { - span.appendChild(this.topImg); - var top = this.topImg.offsetTop; - if (topBug) { - // For IE, frame is not at the baseline, so remove extra height - var wrap = math.parentNode.style.whiteSpace; - math.parentNode.style.whiteSpace = "nowrap"; - math.parentNode.insertBefore(this.topImg,math); - top -= this.topImg.offsetTop - span.parentNode.parentNode.offsetTop; - math.parentNode.style.whiteSpace = wrap; - } - if (borderBug) {top += Math.floor(.5*HTMLCSS.em)} // adjust for zoom box padding - this.topImg.parentNode.removeChild(this.topImg); - return top; - }, - // // Set the position of the zoom box and overlay // - Position: function (zoom,bbox,MMLdisplay) { + Position: function (zoom,bbox) { var XY = this.Resize(), x = XY.x, y = XY.y, W = bbox.mW; - if (this.msieIE8Bug) {W = -W} var dx = -Math.floor((zoom.offsetWidth-W)/2), dy = bbox.Y; zoom.style.left = Math.max(dx,10-x)+"px"; zoom.style.top = Math.max(dy,10-y)+"px"; }, @@ -278,16 +254,14 @@ HUB.Browser.Select({ MSIE: function (browser) { - var quirks = (document.compatMode === "BackCompat"); - var isIE8 = browser.versionAtLeast("8.0") && document.documentMode > 7; - var isIE9 = document.documentMode >= 9; + var mode = (document.documentMode || 0); + var isIE9 = (mode >= 9); ZOOM.msiePositionBug = !isIE9; ZOOM.msieSizeBug = browser.versionAtLeast("7.0") && - (!document.documentMode || document.documentMode === 7 || document.documentMode === 8); - ZOOM.msieIE8Bug = isIE8 && (document.documentMode === 8); - ZOOM.msieZIndexBug = !isIE8; - ZOOM.msieInlineBlockAlignBug = (!isIE8 || quirks); - if (document.documentMode >= 9) {delete CONFIG.styles["#MathJax_Zoom"].filter} + (!document.documentMode || mode === 7 || mode === 8); + ZOOM.msieZIndexBug = (mode <= 7); + ZOOM.msieInlineBlockAlignBug = (mode <= 7); + if (isIE9) {delete CONFIG.styles["#MathJax_Zoom"].filter} }, Opera: function (browser) { diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js index ae74e8c24..63869bedd 100644 --- a/unpacked/jax/output/HTML-CSS/jax.js +++ b/unpacked/jax/output/HTML-CSS/jax.js @@ -443,19 +443,16 @@ // // Re-render at larger size // - span.className = "MathJax"; - this.idPostfix = "-zoom"; - this.getScales(span,span); - root.toHTML(span,span); - var bbox = root.HTMLspanElement().bbox; - this.idPostfix = ""; - if (bbox.width) { + span.className = "MathJax"; this.getScales(span,span); + this.idPostfix = "-zoom"; root.toHTML(span,span); this.idPostfix = ""; + var width = root.HTMLspanElement().bbox.width; + if (width) { // Handle full-width displayed equations // FIXME: this is a hack for now span.style.width = Math.floor(Mw-1.5*HTMLCSS.em)+"px"; span.style.display="inline-block"; var id = (root.id||"MathJax-Span-"+root.spanID)+"-zoom"; var child = document.getElementById(id).firstChild; - while (child && child.style.width !== bbox.width) {child = child.nextSibling} + while (child && child.style.width !== width) {child = child.nextSibling} if (child) {child.style.width = "100%"} } // @@ -467,9 +464,7 @@ if (mW === 0) {mW = math.parentNode.offsetWidth}; // IE7 gets mW == 0? span.style.position = math.style.position = ""; // - var ZOOM = MathJax.Extension.MathZoom; - return {Y:-ZOOM.getTop(root,span,math,ZOOM.msieTopBug,ZOOM.msieBorderBug), - mW:mW, mH:mH, zW:zW, zH:zH}; + return {Y:-EVENT.getBBox(span).h, mW:mW, mH:mH, zW:zW, zH:zH}; }, initImg: function (span) {}, @@ -2205,8 +2200,6 @@ msieClipRectBug: !isIE8, msieNegativeSpaceBug: quirks, msieCloneNodeBug: (isIE8 && browser.version === "8.0"), - msieTopBug: (!browser.versionAtLeast("8.0") || document.documentMode === 7), - msieBorderBug: (quirks && browser.versionAtLeast("8.0")), negativeSkipBug: true, msieIE6: !isIE7, msieItalicWidthBug: true, diff --git a/unpacked/jax/output/NativeMML/jax.js b/unpacked/jax/output/NativeMML/jax.js index f8909a067..e3fe7dd23 100644 --- a/unpacked/jax/output/NativeMML/jax.js +++ b/unpacked/jax/output/NativeMML/jax.js @@ -205,23 +205,19 @@ return math.firstChild; }, getHoverBBox: function (jax,span,math) { - span = span.parentNode; - span.appendChild(this.topImg); - var h = this.topImg.offsetTop, d = span.offsetHeight-h, w = span.offsetWidth; - span.removeChild(this.topImg); - var x = (math.className === "MathJax_MSIE_Overlay" ? -w : 0); - return {w:w, h:h, d:d, x:x} + var bbox = EVENT.getBBox(span.parentNode); + bbox.x = (math.className === "MathJax_MSIE_Overlay" ? -bbox.w : 0); + return bbox; }, - Zoom: function (root,span,math) { + Zoom: function (root,span,math,Mw,Mh) { root.toNativeMML(span,span); - var top = ZOOM.getTop(root,span.parentNode,math,this.msieTopBug,false); if (this.msieIE8HeightBug) {span.style.position = "absolute"} var mW = math.offsetWidth || math.scrollWidth, mH = math.offsetHeight || math.scrollHeight; var zW = span.offsetWidth, zH = span.offsetHeight; if (this.msieIE8HeightBug) {span.style.position = ""} - return {Y:-top, mW:mW, mH:mH, zW:zW, zH:zH} + return {Y:-EVENT.getBBox(span.parentNode).h, mW:mW, mH:mH, zW:zW, zH:zH} }, NAMEDSPACE: { @@ -492,30 +488,14 @@ // HUB.Browser.Select({ MSIE: function (browser) { - var quirks = (document.compatMode === "BackCompat"); var mode = (document.documentMode || 0); - var isIE8 = browser.versionAtLeast("8.0"); - nMML.Augment({ - msieInlineBlockAlignBug: (!isIE8 || mode < 8 || quirks), - msieTopBug: (!isIE8 || mode === 7), - msieIE8HeightBug: (mode === 8), - msieTopBug: (!isIE8 || mode !== 8) - }); + nMML.msieIE8HeightBug = (mode === 8); }, Opera: function (browser) { nMML.operaPositionBug = true; } }); - // - // Used in measuring zoom and hover positions - // - nMML.topImg = (nMML.msieInlineBlockAlignBug ? - HTML.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}) : - HTML.Element("span",{style:{width:0,height:0,display:"inline-block"}}) - ); - if (nMML.operaPositionBug || nMML.msieTopBug) {nMML.topImg.style.border="1px solid"} - HUB.Register.StartupHook("End Cookie",function () { if (HUB.config.menuSettings.zoom !== "None")