diff --git a/config/Accessible-full.js b/config/Accessible-full.js index 49ba92dd8..c3456fcda 100644 --- a/config/Accessible-full.js +++ b/config/Accessible-full.js @@ -56,7 +56,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",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:"1.1.9",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); @@ -88,7 +88,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a= (function(b,e,d){var a,c=e.Browser.isMSIE;b.Augment({LEFTBUTTON:(c?1:0),MENUKEY:"altKey",noContextMenuBug:e.Browser.isKonequeror,msieQuirks:(c&&!(document.compatMode==="BackCompat")),msieEventBug:e.Browser.isIE9,config:{styles:{}},settings:e.config.menuSettings,Startup:function(){return MathJax.Ajax.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(e.config.displayAlign!=="center"){var h=e.config.displayAlign,f=e.config.displayIndent;var g={"text-align":h+"!important"};g["margin-"+h]=f+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":g,"div.MathJax_MathML math":{"text-align":h},"div.MathJax_MathContainer > span":{"text-align":h+"!important"}})}},InitializeMML:function(){this.initialized=true;if(MathJax.Hub.Browser.isMSIE){try{var f=document.createElement("object");f.id="mathplayer";f.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(f);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(g){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(g){if(!g.parentNode){return}if(!this.initialized){this.InitializeMML()}var k=g.previousSibling;if(k&&String(k.className).match(/^MathJax(_MathML|_Display)?$/)){k.parentNode.removeChild(k)}var j=g.MathJax.elementJax.root;var i=(j.Get("display")==="block"?"div":"span");var h=document.createElement(i),f=h;h.className="MathJax_MathML";h.style.fontSize=this.config.scale+"%";if(c&&this.config.showMathMenuMSIE){f=MathJax.HTML.addElement(h,"span",{className:"MathJax_MathContainer",style:{display:"inline-block",position:"relative"}})}j.toNativeMML(f);g.parentNode.insertBefore(h,g);if(c){if(this.config.showMathMenuMSIE){this.MSIEoverlay(h)}}else{j=h.firstChild;j.oncontextmenu=this.ContextMenu;j.onmouseover=this.Mouseover;j.onmousedown=this.Mousedown;j.onclick=this.Click;j.ondblclick=this.DblClick}},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/MathJax_MathML/)){g.parentNode.removeChild(g)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(m){var l=m.firstChild;m.style.position="absolute";var n=m.scrollHeight,h=m.offsetWidth;var j=MathJax.HTML.addElement(m,"img",{src:"about:blank",style:{width:0,height:n+"px"}});var f=m.scrollHeight-n;m.removeChild(j);m.style.position="";var k,i,g=(m.parentNode.nodeName.toLowerCase()==="div");if(g&&this.quirks){k=-n;i=Math.floor(-h/2)}else{k=f-n,i=-h}MathJax.HTML.addElement(m,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{style:{display:"inline-block",position:"absolute",left:i+"px",top:k+"px",width:l.offsetWidth+"px",height:n+"px",cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"},onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent}]])},MSIEmath:function(f){var g=f.parentNode.previousSibling.firstChild;return(g.nodeName.toLowerCase()==="span"?g.firstChild:g)},MSIEevent:function(){var g=b.MSIEmath(this);var f=window.event;var h=b["MSIE"+f.type];if(h&&h.call(b,f,g,this)){return false}g.fireEvent("on"+f.type,f);return false},MSIEmousedown:function(h,g,f){if(h[this.MENUKEY]&&h.button===this.LEFTBUTTON&&this.settings.context!=="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}if(this.MSIEzoomKeys&&this.MSIEzoomKeys(h)){this.trapUp=true;return true}return false},MSIEcontextmenu:function(h,g,f){if(this.settings.context==="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}return false},ContextMenu:function(i,j){if(b.config.showMathMenu&&(b.settings.context==="MathJax"||j)){if(b.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||b.msieEventBug){i=window.event}var g=MathJax.Menu;if(g){if(document.selection){setTimeout("document.selection.empty()",0)}var f=(c?this.parentNode.parentNode.nextSibling:this.parentNode.nextSibling);g.jax=e.getJaxFor(f);g.menu.items[1].menu.items[1].name=(g.jax.inputJax==="MathML"?"Original":g.jax.inputJax);delete b.trapClick;delete b.trapUp;return g.menu.Post(i)}else{if(!d.loadingMathMenu){d.loadingMathMenu=true;var h={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(d.Require("[MathJax]/extensions/MathMenu.js"),function(){delete d.loadingMathMenu},[this,arguments.callee,h,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(b.config.showMathMenu){if(!f){f=window.event}if(b.settings.context==="MathJax"){if(!b.noContextMenuBug||f.button!==2){return}}else{if(!f[b.MENUKEY]||f.button!==b.LEFTBUTTON){return}}return b.ContextMenu.call(this,f,true)}},Mouseover:function(f){b.HandleEvent(f,"Mouseover",this)},Click:function(f){b.HandleEvent(f,"Click",this)},DblClick:function(f){b.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});e.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toNativeMML:function(k){var h=this.NativeMMLelement(this.type);this.NativeMMLattributes(h);for(var j=0,g=this.data.length;j=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;ho){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;he.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(ro){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var aL=b.FONTDATA.baselineskip*am*aJ.useHeight,Z=b.FONTDATA.lineH*am,af=b.FONTDATA.lineD*am;for(aF=0,aC=this.data.length;aFv){v=aE}K[aE]=b.createStack(b.createBox(ag));l[aE]=-b.BIGDIMEN}O[aF][aE]=b.createBox(K[aE]);b.Measured(R.data[aE-ay].toHTML(O[aF][aE]),O[aF][aE]);if(R.data[aE-ay].isMultiline){O[aF][aE].style.width="100%"}if(O[aF][aE].bbox.h>w[aF]){w[aF]=O[aF][aE].bbox.h}if(O[aF][aE].bbox.d>I[aF]){I[aF]=O[aF][aE].bbox.d}if(O[aF][aE].bbox.w>l[aE]){l[aE]=O[aF][aE].bbox.w}}}if(w[0]+I[0]){w[0]=Math.max(w[0],Z)}if(w[O.length-1]+I[O.length-1]){I[O.length-1]=Math.max(I[O.length-1],af)}var al=aJ.columnspacing.split(/ /),S=aJ.rowspacing.split(/ /),ah=aJ.columnalign.split(/ /),L=aJ.rowalign.split(/ /),N=aJ.columnlines.split(/ /),k=aJ.rowlines.split(/ /),ap=aJ.columnwidth.split(/ /),au=[];for(aF=0,aC=al.length;aF0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); diff --git a/config/MML_HTMLorMML-full.js b/config/MML_HTMLorMML-full.js index 403079c54..9465ee01f 100644 --- a/config/MML_HTMLorMML-full.js +++ b/config/MML_HTMLorMML-full.js @@ -34,7 +34,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",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:"1.1.9",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); @@ -54,7 +54,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var (function(b,e,d){var a,c=e.Browser.isMSIE;b.Augment({LEFTBUTTON:(c?1:0),MENUKEY:"altKey",noContextMenuBug:e.Browser.isKonequeror,msieQuirks:(c&&!(document.compatMode==="BackCompat")),msieEventBug:e.Browser.isIE9,config:{styles:{}},settings:e.config.menuSettings,Startup:function(){return MathJax.Ajax.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(e.config.displayAlign!=="center"){var h=e.config.displayAlign,f=e.config.displayIndent;var g={"text-align":h+"!important"};g["margin-"+h]=f+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":g,"div.MathJax_MathML math":{"text-align":h},"div.MathJax_MathContainer > span":{"text-align":h+"!important"}})}},InitializeMML:function(){this.initialized=true;if(MathJax.Hub.Browser.isMSIE){try{var f=document.createElement("object");f.id="mathplayer";f.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(f);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(g){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(g){if(!g.parentNode){return}if(!this.initialized){this.InitializeMML()}var k=g.previousSibling;if(k&&String(k.className).match(/^MathJax(_MathML|_Display)?$/)){k.parentNode.removeChild(k)}var j=g.MathJax.elementJax.root;var i=(j.Get("display")==="block"?"div":"span");var h=document.createElement(i),f=h;h.className="MathJax_MathML";h.style.fontSize=this.config.scale+"%";if(c&&this.config.showMathMenuMSIE){f=MathJax.HTML.addElement(h,"span",{className:"MathJax_MathContainer",style:{display:"inline-block",position:"relative"}})}j.toNativeMML(f);g.parentNode.insertBefore(h,g);if(c){if(this.config.showMathMenuMSIE){this.MSIEoverlay(h)}}else{j=h.firstChild;j.oncontextmenu=this.ContextMenu;j.onmouseover=this.Mouseover;j.onmousedown=this.Mousedown;j.onclick=this.Click;j.ondblclick=this.DblClick}},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/MathJax_MathML/)){g.parentNode.removeChild(g)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(m){var l=m.firstChild;m.style.position="absolute";var n=m.scrollHeight,h=m.offsetWidth;var j=MathJax.HTML.addElement(m,"img",{src:"about:blank",style:{width:0,height:n+"px"}});var f=m.scrollHeight-n;m.removeChild(j);m.style.position="";var k,i,g=(m.parentNode.nodeName.toLowerCase()==="div");if(g&&this.quirks){k=-n;i=Math.floor(-h/2)}else{k=f-n,i=-h}MathJax.HTML.addElement(m,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{style:{display:"inline-block",position:"absolute",left:i+"px",top:k+"px",width:l.offsetWidth+"px",height:n+"px",cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"},onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent}]])},MSIEmath:function(f){var g=f.parentNode.previousSibling.firstChild;return(g.nodeName.toLowerCase()==="span"?g.firstChild:g)},MSIEevent:function(){var g=b.MSIEmath(this);var f=window.event;var h=b["MSIE"+f.type];if(h&&h.call(b,f,g,this)){return false}g.fireEvent("on"+f.type,f);return false},MSIEmousedown:function(h,g,f){if(h[this.MENUKEY]&&h.button===this.LEFTBUTTON&&this.settings.context!=="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}if(this.MSIEzoomKeys&&this.MSIEzoomKeys(h)){this.trapUp=true;return true}return false},MSIEcontextmenu:function(h,g,f){if(this.settings.context==="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}return false},ContextMenu:function(i,j){if(b.config.showMathMenu&&(b.settings.context==="MathJax"||j)){if(b.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||b.msieEventBug){i=window.event}var g=MathJax.Menu;if(g){if(document.selection){setTimeout("document.selection.empty()",0)}var f=(c?this.parentNode.parentNode.nextSibling:this.parentNode.nextSibling);g.jax=e.getJaxFor(f);g.menu.items[1].menu.items[1].name=(g.jax.inputJax==="MathML"?"Original":g.jax.inputJax);delete b.trapClick;delete b.trapUp;return g.menu.Post(i)}else{if(!d.loadingMathMenu){d.loadingMathMenu=true;var h={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(d.Require("[MathJax]/extensions/MathMenu.js"),function(){delete d.loadingMathMenu},[this,arguments.callee,h,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(b.config.showMathMenu){if(!f){f=window.event}if(b.settings.context==="MathJax"){if(!b.noContextMenuBug||f.button!==2){return}}else{if(!f[b.MENUKEY]||f.button!==b.LEFTBUTTON){return}}return b.ContextMenu.call(this,f,true)}},Mouseover:function(f){b.HandleEvent(f,"Mouseover",this)},Click:function(f){b.HandleEvent(f,"Click",this)},DblClick:function(f){b.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});e.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toNativeMML:function(k){var h=this.NativeMMLelement(this.type);this.NativeMMLattributes(h);for(var j=0,g=this.data.length;j=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;ho){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;he.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(ro){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var aL=b.FONTDATA.baselineskip*am*aJ.useHeight,Z=b.FONTDATA.lineH*am,af=b.FONTDATA.lineD*am;for(aF=0,aC=this.data.length;aFv){v=aE}K[aE]=b.createStack(b.createBox(ag));l[aE]=-b.BIGDIMEN}O[aF][aE]=b.createBox(K[aE]);b.Measured(R.data[aE-ay].toHTML(O[aF][aE]),O[aF][aE]);if(R.data[aE-ay].isMultiline){O[aF][aE].style.width="100%"}if(O[aF][aE].bbox.h>w[aF]){w[aF]=O[aF][aE].bbox.h}if(O[aF][aE].bbox.d>I[aF]){I[aF]=O[aF][aE].bbox.d}if(O[aF][aE].bbox.w>l[aE]){l[aE]=O[aF][aE].bbox.w}}}if(w[0]+I[0]){w[0]=Math.max(w[0],Z)}if(w[O.length-1]+I[O.length-1]){I[O.length-1]=Math.max(I[O.length-1],af)}var al=aJ.columnspacing.split(/ /),S=aJ.rowspacing.split(/ /),ah=aJ.columnalign.split(/ /),L=aJ.rowalign.split(/ /),N=aJ.columnlines.split(/ /),k=aJ.rowlines.split(/ /),ap=aJ.columnwidth.split(/ /),au=[];for(aF=0,aC=al.length;aF0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); diff --git a/config/TeX-AMS-MML_HTMLorMML-full.js b/config/TeX-AMS-MML_HTMLorMML-full.js index fc8b957e9..b3cf89cf3 100644 --- a/config/TeX-AMS-MML_HTMLorMML-full.js +++ b/config/TeX-AMS-MML_HTMLorMML-full.js @@ -43,7 +43,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",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:"1.1.9",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); @@ -75,7 +75,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a= (function(b,e,d){var a,c=e.Browser.isMSIE;b.Augment({LEFTBUTTON:(c?1:0),MENUKEY:"altKey",noContextMenuBug:e.Browser.isKonequeror,msieQuirks:(c&&!(document.compatMode==="BackCompat")),msieEventBug:e.Browser.isIE9,config:{styles:{}},settings:e.config.menuSettings,Startup:function(){return MathJax.Ajax.Styles(this.config.styles)},Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(e.config.displayAlign!=="center"){var h=e.config.displayAlign,f=e.config.displayIndent;var g={"text-align":h+"!important"};g["margin-"+h]=f+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":g,"div.MathJax_MathML math":{"text-align":h},"div.MathJax_MathContainer > span":{"text-align":h+"!important"}})}},InitializeMML:function(){this.initialized=true;if(MathJax.Hub.Browser.isMSIE){try{var f=document.createElement("object");f.id="mathplayer";f.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(f);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(g){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(g){if(!g.parentNode){return}if(!this.initialized){this.InitializeMML()}var k=g.previousSibling;if(k&&String(k.className).match(/^MathJax(_MathML|_Display)?$/)){k.parentNode.removeChild(k)}var j=g.MathJax.elementJax.root;var i=(j.Get("display")==="block"?"div":"span");var h=document.createElement(i),f=h;h.className="MathJax_MathML";h.style.fontSize=this.config.scale+"%";if(c&&this.config.showMathMenuMSIE){f=MathJax.HTML.addElement(h,"span",{className:"MathJax_MathContainer",style:{display:"inline-block",position:"relative"}})}j.toNativeMML(f);g.parentNode.insertBefore(h,g);if(c){if(this.config.showMathMenuMSIE){this.MSIEoverlay(h)}}else{j=h.firstChild;j.oncontextmenu=this.ContextMenu;j.onmouseover=this.Mouseover;j.onmousedown=this.Mousedown;j.onclick=this.Click;j.ondblclick=this.DblClick}},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/MathJax_MathML/)){g.parentNode.removeChild(g)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(m){var l=m.firstChild;m.style.position="absolute";var n=m.scrollHeight,h=m.offsetWidth;var j=MathJax.HTML.addElement(m,"img",{src:"about:blank",style:{width:0,height:n+"px"}});var f=m.scrollHeight-n;m.removeChild(j);m.style.position="";var k,i,g=(m.parentNode.nodeName.toLowerCase()==="div");if(g&&this.quirks){k=-n;i=Math.floor(-h/2)}else{k=f-n,i=-h}MathJax.HTML.addElement(m,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{style:{display:"inline-block",position:"absolute",left:i+"px",top:k+"px",width:l.offsetWidth+"px",height:n+"px",cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"},onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent}]])},MSIEmath:function(f){var g=f.parentNode.previousSibling.firstChild;return(g.nodeName.toLowerCase()==="span"?g.firstChild:g)},MSIEevent:function(){var g=b.MSIEmath(this);var f=window.event;var h=b["MSIE"+f.type];if(h&&h.call(b,f,g,this)){return false}g.fireEvent("on"+f.type,f);return false},MSIEmousedown:function(h,g,f){if(h[this.MENUKEY]&&h.button===this.LEFTBUTTON&&this.settings.context!=="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}if(this.MSIEzoomKeys&&this.MSIEzoomKeys(h)){this.trapUp=true;return true}return false},MSIEcontextmenu:function(h,g,f){if(this.settings.context==="MathJax"){this.trapUp=this.trapClick=true;this.ContextMenu.call(f,h,true);return true}return false},ContextMenu:function(i,j){if(b.config.showMathMenu&&(b.settings.context==="MathJax"||j)){if(b.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||b.msieEventBug){i=window.event}var g=MathJax.Menu;if(g){if(document.selection){setTimeout("document.selection.empty()",0)}var f=(c?this.parentNode.parentNode.nextSibling:this.parentNode.nextSibling);g.jax=e.getJaxFor(f);g.menu.items[1].menu.items[1].name=(g.jax.inputJax==="MathML"?"Original":g.jax.inputJax);delete b.trapClick;delete b.trapUp;return g.menu.Post(i)}else{if(!d.loadingMathMenu){d.loadingMathMenu=true;var h={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(d.Require("[MathJax]/extensions/MathMenu.js"),function(){delete d.loadingMathMenu},[this,arguments.callee,h,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(b.config.showMathMenu){if(!f){f=window.event}if(b.settings.context==="MathJax"){if(!b.noContextMenuBug||f.button!==2){return}}else{if(!f[b.MENUKEY]||f.button!==b.LEFTBUTTON){return}}return b.ContextMenu.call(this,f,true)}},Mouseover:function(f){b.HandleEvent(f,"Mouseover",this)},Click:function(f){b.HandleEvent(f,"Click",this)},DblClick:function(f){b.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});e.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toNativeMML:function(k){var h=this.NativeMMLelement(this.type);this.NativeMMLattributes(h);for(var j=0,g=this.data.length;j=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;ho){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;he.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(ro){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var aL=b.FONTDATA.baselineskip*am*aJ.useHeight,Z=b.FONTDATA.lineH*am,af=b.FONTDATA.lineD*am;for(aF=0,aC=this.data.length;aFv){v=aE}K[aE]=b.createStack(b.createBox(ag));l[aE]=-b.BIGDIMEN}O[aF][aE]=b.createBox(K[aE]);b.Measured(R.data[aE-ay].toHTML(O[aF][aE]),O[aF][aE]);if(R.data[aE-ay].isMultiline){O[aF][aE].style.width="100%"}if(O[aF][aE].bbox.h>w[aF]){w[aF]=O[aF][aE].bbox.h}if(O[aF][aE].bbox.d>I[aF]){I[aF]=O[aF][aE].bbox.d}if(O[aF][aE].bbox.w>l[aE]){l[aE]=O[aF][aE].bbox.w}}}if(w[0]+I[0]){w[0]=Math.max(w[0],Z)}if(w[O.length-1]+I[O.length-1]){I[O.length-1]=Math.max(I[O.length-1],af)}var al=aJ.columnspacing.split(/ /),S=aJ.rowspacing.split(/ /),ah=aJ.columnalign.split(/ /),L=aJ.rowalign.split(/ /),N=aJ.columnlines.split(/ /),k=aJ.rowlines.split(/ /),ap=aJ.columnwidth.split(/ /),au=[];for(aF=0,aC=al.length;aF0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); diff --git a/config/TeX-AMS_HTML-full.js b/config/TeX-AMS_HTML-full.js index 1fef9fc0b..1cd34d372 100644 --- a/config/TeX-AMS_HTML-full.js +++ b/config/TeX-AMS_HTML-full.js @@ -33,7 +33,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+a},formatURL:function(a){return"#mjx-eqn-"+escape(a)}}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.9",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); @@ -55,7 +55,7 @@ MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels: MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); -(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;ho){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;he.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(ro){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var aL=b.FONTDATA.baselineskip*am*aJ.useHeight,Z=b.FONTDATA.lineH*am,af=b.FONTDATA.lineD*am;for(aF=0,aC=this.data.length;aFv){v=aE}K[aE]=b.createStack(b.createBox(ag));l[aE]=-b.BIGDIMEN}O[aF][aE]=b.createBox(K[aE]);b.Measured(R.data[aE-ay].toHTML(O[aF][aE]),O[aF][aE]);if(R.data[aE-ay].isMultiline){O[aF][aE].style.width="100%"}if(O[aF][aE].bbox.h>w[aF]){w[aF]=O[aF][aE].bbox.h}if(O[aF][aE].bbox.d>I[aF]){I[aF]=O[aF][aE].bbox.d}if(O[aF][aE].bbox.w>l[aE]){l[aE]=O[aF][aE].bbox.w}}}if(w[0]+I[0]){w[0]=Math.max(w[0],Z)}if(w[O.length-1]+I[O.length-1]){I[O.length-1]=Math.max(I[O.length-1],af)}var al=aJ.columnspacing.split(/ /),S=aJ.rowspacing.split(/ /),ah=aJ.columnalign.split(/ /),L=aJ.rowalign.split(/ /),N=aJ.columnlines.split(/ /),k=aJ.rowlines.split(/ /),ap=aJ.columnwidth.split(/ /),au=[];for(aF=0,aC=al.length;aF0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;gdocument.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n/g,">");n.document.open();n.document.write("MathJax Equation Source");n.document.write("
"+r+"
");n.document.write("");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); diff --git a/config/default.js b/config/default.js index c4e35c262..b69353d0e 100644 --- a/config/default.js +++ b/config/default.js @@ -472,6 +472,42 @@ MathJax.Hub.Config({ // if it doesn't contain the needed character), so order these carefully. // undefinedFamily: "STIXGeneral,'Arial Unicode MS',serif", + + // + // These settings control automatic line breaking. It is off by + // default, so only explicit line breaks are performed (via + // linebreak="newline" attributes on and elements). To + // perform automatic line breaking on line expressions, set + // 'automatic' to 'true' below. The line breaks will be applied via a + // penalty-based heuristic, which does well, but isn't perfect. You + // might need to use linebreak="goodbreak" or linebreak="badbreak" by + // hand in order to get better effects. It is also possible to modify + // the penalty values; contact the MathJax user's forum for details. + // + linebreaks: { + + // + // This controls the automatic breaking of expressions: + // when false, only process linebreak="newline", + // when true, line breaks are inserted automatically in long expressions. + // + automatic: false, + + // + // This controls how wide the lines of mathematics can be + // + // Use an explicit with like "30em" for a fixed width. + // Use "container" to compute size from containing element. + // Use "nn% container" for a portion of the container. + // Use "nn%" for a portion of the window size. + // + // The container-based widths may be slower, and may not produce the + // expected results if the layout width changes due to the removal + // of previews or inclusion of mathematics during typesetting. + // + width: "container" + }, + // // This controls whether the MathJax contextual menu will be available diff --git a/jax/element/mml/jax.js b/jax/element/mml/jax.js index 70ac14144..63c7de8c7 100644 --- a/jax/element/mml/jax.js +++ b/jax/element/mml/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},linebreakContainer:d,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return d}for(var g=0,f=this.data.length;g=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:b,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,linebreakContainer:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},linebreakContainer:b,Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,"^":e.ORD11,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2111":e.ORD,"\u2113":e.ORD,"\u2118":e.ORD,"\u211C":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u2500":e.ORD,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); diff --git a/jax/output/HTML-CSS/autoload/maction.js b/jax/output/HTML-CSS/autoload/maction.js index 91ca12306..4c7c6e526 100644 --- a/jax/output/HTML-CSS/autoload/maction.js +++ b/jax/output/HTML-CSS/autoload/maction.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var g="1.1.2";var c=MathJax.ElementJax.mml,e=MathJax.OutputJax["HTML-CSS"];var d,f,b;var a=e.config.tooltip=MathJax.Hub.Insert({delayPost:600,delayClear:600,offsetX:10,offsetY:5},e.config.tooltip||{});c.maction.Augment({HTMLtooltip:e.addElement(document.body,"div",{id:"MathJax_Tooltip"}),toHTML:function(k,h,m){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;var i=this.getValues("actiontype","selection"),n;var j=this.data[i.selection-1];if(j){e.Measured(j.toHTML(k),k);if(m!=null){e.Remeasured(j.HTMLstretchV(k,h,m),k)}else{if(h!=null){e.Remeasured(j.HTMLstretchH(k,h),k)}}if(e.msieHitBoxBug){var l=e.addElement(k,"span");n=e.createFrame(l,k.bbox.h,k.bbox.d,k.bbox.w,0,"none");k.insertBefore(l,k.firstChild);l.style.marginRight=e.Em(-k.bbox.w);if(e.msieInlineBlockAlignBug){n.style.verticalAlign=e.Em(e.getHD(k).d-k.bbox.d)}}else{n=e.createFrame(k,k.bbox.h,k.bbox.d,k.bbox.w,0,"none");k.insertBefore(n,k.firstChild);n.style.marginRight=e.Em(-k.bbox.w)}n.className="MathJax_HitBox";n.id="MathJax-HitBox-"+this.spanID;if(this.HTMLaction[i.actiontype]){this.HTMLaction[i.actiontype].call(this,k,n,i.selection)}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:c.mbase.HTMLstretchH,HTMLstretchV:c.mbase.HTMLstretchV,HTMLaction:{toggle:function(i,j,h){this.selection=h;j.onclick=i.childNodes[1].onclick=MathJax.Callback(["HTMLclick",this]);j.style.cursor=i.childNodes[1].style.cursor="pointer"},statusline:function(i,j,h){j.onmouseover=i.childNodes[1].onmouseover=MathJax.Callback(["HTMLsetStatus",this]);j.onmouseout=i.childNodes[1].onmouseout=MathJax.Callback(["HTMLclearStatus",this]);j.onmouseover.autoReset=j.onmouseout.autoReset=true},tooltip:function(i,j,h){if(this.data[1]&&this.data[1].isToken){j.title=j.alt=i.childNodes[1].title=i.childNodes[1].alt=this.data[1].data.join("")}else{j.onmouseover=i.childNodes[1].onmouseover=MathJax.Callback(["HTMLtooltipOver",this]);j.onmouseout=i.childNodes[1].onmouseout=MathJax.Callback(["HTMLtooltipOut",this]);j.onmouseover.autoReset=j.onmouseout.autoReset=true}}},HTMLclick:function(i){this.selection++;if(this.selection>this.data.length){this.selection=1}var h=this;while(h.type!=="math"){h=h.inherit}MathJax.Hub.getJaxFor(h.inputID).Update();if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false},HTMLsetStatus:function(h){window.status=((this.data[1]&&this.data[1].isToken)?this.data[1].data.join(""):this.data[1].toString())},HTMLclearStatus:function(h){window.status=""},HTMLtooltipOver:function(i){if(!i){i=window.event}if(b){clearTimeout(b);b=null}if(f){clearTimeout(f)}var h=i.pageX;var k=i.pageY;if(h==null){h=i.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;k=i.clientY+document.body.scrollTop+document.documentElement.scrollTop}var j=MathJax.Callback(["HTMLtooltipPost",this,h+a.offsetX,k+a.offsetY]);f=setTimeout(j,a.delayPost)},HTMLtooltipOut:function(h){if(f){clearTimeout(f);f=null}if(b){clearTimeout(b)}var i=MathJax.Callback(["HTMLtooltipClear",this,80]);b=setTimeout(i,a.delayClear)},HTMLtooltipPost:function(i,m){f=null;if(b){clearTimeout(b);b=null}var l=this.HTMLtooltip;l.style.display="block";l.style.opacity="";l.style.filter=e.config.styles["#MathJax_Tooltip"].filter;if(this===d){return}l.style.left=i+"px";l.style.top=m+"px";l.innerHTML='';e.getScales(l.firstChild,l.firstChild);var h=e.createStack(l.firstChild.firstChild);var k=e.createBox(h);try{e.Measured(this.data[1].toHTML(k),k)}catch(j){if(!j.restart){throw j}l.style.display="none";MathJax.Callback.After(["HTMLtooltipPost",this,i,m],j.restart)}e.placeBox(k,0,0);e.createRule(l.firstChild.firstChild,k.bbox.h,k.bbox.d,0);d=this},HTMLtooltipClear:function(i){var h=this.HTMLtooltip;if(i<=0){h.style.display="none";h.style.opacity=h.style.filter="";b=null}else{h.style.opacity=i/100;h.style.filter="alpha(opacity="+i+")";b=setTimeout(MathJax.Callback(["HTMLtooltipClear",this,i-20]),50)}}});MathJax.Hub.Browser.Select({MSIE:function(h){e.msieHitBoxBug=true}});MathJax.Hub.Startup.signal.Post("HTML-CSS maction Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/maction.js")}); +MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var g="1.1.2";var c=MathJax.ElementJax.mml,e=MathJax.OutputJax["HTML-CSS"];var d,f,b;var a=e.config.tooltip=MathJax.Hub.Insert({delayPost:600,delayClear:600,offsetX:10,offsetY:5},e.config.tooltip||{});c.maction.Augment({HTMLtooltip:e.addElement(document.body,"div",{id:"MathJax_Tooltip"}),toHTML:function(j,h,k){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));j.bbox=null;var i=this.selected();if(i){e.Measured(i.toHTML(j),j);if(k!=null){e.Remeasured(i.HTMLstretchV(j,h,k),j)}else{if(h!=null){e.Remeasured(i.HTMLstretchH(j,h),j)}}this.HTMLhandleHitBox(j)}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLhandleHitBox:function(i,l){var k;if(e.msieHitBoxBug){var j=e.addElement(i,"span");k=e.createFrame(j,i.bbox.h,i.bbox.d,i.bbox.w,0,"none");i.insertBefore(j,i.firstChild);j.style.marginRight=e.Em(-i.bbox.w);if(e.msieInlineBlockAlignBug){k.style.verticalAlign=e.Em(e.getHD(i).d-i.bbox.d)}}else{k=e.createFrame(i,i.bbox.h,i.bbox.d,i.bbox.w,0,"none");i.insertBefore(k,i.firstChild);k.style.marginRight=e.Em(-i.bbox.w)}k.className="MathJax_HitBox";k.id="MathJax-HitBox-"+this.spanID+(l||"")+e.idPostfix;var h=this.Get("actiontype");if(this.HTMLaction[h]){this.HTMLaction[h].call(this,i,k,this.Get("selection"))}},HTMLstretchH:c.mbase.HTMLstretchH,HTMLstretchV:c.mbase.HTMLstretchV,HTMLaction:{toggle:function(i,j,h){this.selection=h;j.onclick=i.childNodes[1].onclick=MathJax.Callback(["HTMLclick",this]);j.style.cursor=i.childNodes[1].style.cursor="pointer"},statusline:function(i,j,h){j.onmouseover=i.childNodes[1].onmouseover=MathJax.Callback(["HTMLsetStatus",this]);j.onmouseout=i.childNodes[1].onmouseout=MathJax.Callback(["HTMLclearStatus",this]);j.onmouseover.autoReset=j.onmouseout.autoReset=true},tooltip:function(i,j,h){if(this.data[1]&&this.data[1].isToken){j.title=j.alt=i.childNodes[1].title=i.childNodes[1].alt=this.data[1].data.join("")}else{j.onmouseover=i.childNodes[1].onmouseover=MathJax.Callback(["HTMLtooltipOver",this]);j.onmouseout=i.childNodes[1].onmouseout=MathJax.Callback(["HTMLtooltipOut",this]);j.onmouseover.autoReset=j.onmouseout.autoReset=true}}},HTMLclick:function(i){this.selection++;if(this.selection>this.data.length){this.selection=1}var h=this;while(h.type!=="math"){h=h.inherit}MathJax.Hub.getJaxFor(h.inputID).Update();if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false},HTMLsetStatus:function(h){window.status=((this.data[1]&&this.data[1].isToken)?this.data[1].data.join(""):this.data[1].toString())},HTMLclearStatus:function(h){window.status=""},HTMLtooltipOver:function(i){if(!i){i=window.event}if(b){clearTimeout(b);b=null}if(f){clearTimeout(f)}var h=i.pageX;var k=i.pageY;if(h==null){h=i.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;k=i.clientY+document.body.scrollTop+document.documentElement.scrollTop}var j=MathJax.Callback(["HTMLtooltipPost",this,h+a.offsetX,k+a.offsetY]);f=setTimeout(j,a.delayPost)},HTMLtooltipOut:function(h){if(f){clearTimeout(f);f=null}if(b){clearTimeout(b)}var i=MathJax.Callback(["HTMLtooltipClear",this,80]);b=setTimeout(i,a.delayClear)},HTMLtooltipPost:function(i,m){f=null;if(b){clearTimeout(b);b=null}var l=this.HTMLtooltip;l.style.display="block";l.style.opacity="";l.style.filter=e.config.styles["#MathJax_Tooltip"].filter;if(this===d){return}l.style.left=i+"px";l.style.top=m+"px";l.innerHTML='';e.getScales(l.firstChild,l.firstChild);var h=e.createStack(l.firstChild.firstChild);var k=e.createBox(h);try{e.Measured(this.data[1].toHTML(k),k)}catch(j){if(!j.restart){throw j}l.style.display="none";MathJax.Callback.After(["HTMLtooltipPost",this,i,m],j.restart)}e.placeBox(k,0,0);e.createRule(l.firstChild.firstChild,k.bbox.h,k.bbox.d,0);d=this},HTMLtooltipClear:function(i){var h=this.HTMLtooltip;if(i<=0){h.style.display="none";h.style.opacity=h.style.filter="";b=null}else{h.style.opacity=i/100;h.style.filter="alpha(opacity="+i+")";b=setTimeout(MathJax.Callback(["HTMLtooltipClear",this,i-20]),50)}}});MathJax.Hub.Browser.Select({MSIE:function(h){e.msieHitBoxBug=true}});MathJax.Hub.Startup.signal.Post("HTML-CSS maction Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/maction.js")}); diff --git a/jax/output/HTML-CSS/autoload/multiline.js b/jax/output/HTML-CSS/autoload/multiline.js index 7ffcfd938..305a04909 100644 --- a/jax/output/HTML-CSS/autoload/multiline.js +++ b/jax/output/HTML-CSS/autoload/multiline.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mbase.Augment({toHTMLmultiline:function(u,r){u=this.HTMLcreateSpan(u);if(!this.type!=="mrow"){u=this.HTMLhandleSize(u)}var g=b.createStack(u);var o=[],f=[],p=-b.BIGDIMEN,q=-b.BIGDIMEN,v,t,s,k;for(t=0,k=r.length-1;tp){p=o[t].bbox.h}if(o[t].bbox.d>q){q=o[t].bbox.d}}var n=0,x=this.HTMLgetScale(),e=b.FONTDATA.baselineskip*x;var l=this,h;while(l.inferred||(l.parent&&l.parent.type==="mrow"&&l.parent.data.length===1)){l=l.parent}var w=(l.type==="math"||l.type==="mtd");l.isMultiline=true;for(t=0,k=r.length-1;t=b.linebreakWidth||i.penalty==e.newline)){this.HTMLaddLine(m,g,i.index,f,i.values,j);g=i.index.slice(0);j=true;k=this.HTMLgetAlign(f,i.values);h=this.HTMLgetShift(f,i.values,k);if(k===a.INDENTALIGN.CENTER){h=0}i.W=i.shift=i.scanW=h;i.penalty=e.nobreak}f.isLast=true;this.HTMLaddLine(m,g,[],f,c,j);if(l){m.style.width="100%";if(o.type==="math"){n.bbox.width="100%"}}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);n.bbox.isMultiline=true;return n},HTMLbetterBreak:function(h,f){if(this.isToken){return false}if(this.isEmbellished()){h.embellished=this;return this.CoreMO().HTMLbetterBreak(h,f)}if(this.linebreakContainer){return false}var p=h.index.slice(0),n=h.index.shift(),l=this.data.length,k,j=h.W,o=(h.index.length>0),g=false;if(n==null){n=-1}if(!o){n++;h.W+=h.w}h.w=0;h.nest++;while(n0){var k=b.FONTDATA.baselineskip*f.scale;var i=(f.values.lineleading==null?f.VALUES:f.values).lineleading;f.Y-=Math.max(k,f.d+line.bbox.h+i)}b.alignBox(line,m,f.Y);f.d=line.bbox.d;f.values=o;f.n++},HTMLgetAlign:function(i,f){var j=f,g=i.values,h=i.VALUES,k;if(i.n===0){k=j.indentalignfirst||g.indentalignfirst||h.indentalignfirst}else{if(i.isLast){k=g.indentalignlast||h.indentalignlast}else{k=g.indentalign||h.indentalign}}if(k===a.INDENTALIGN.INDENTALIGN){k=g.indentalign||h.indentalign}if(k===a.INDENTALIGN.AUTO){k=(i.isTop?this.displayAlign:a.INDENTALIGN.LEFT)}return k},HTMLgetShift:function(j,g,l){if(l===a.INDENTALIGN.CENTER){return 0}var k=g,h=j.values,i=j.VALUES,f;if(j.n===0){f=k.indentshiftfirst||h.indentshiftfirst||i.indentshiftfirst}else{if(j.isLast){f=h.indentshiftlast||i.indentshiftlast}else{f=h.indentshift||i.indentshift}}if(f===a.INDENTSHIFT.INDENTSHIFT){f=h.indentshift||i.indentshift}if(f==="auto"||f===""){f=(j.isTSop?this.displayIndent:"0")}return b.length2em(f,0)},HTMLmoveLine:function(o,f,l,n,g){var k=o[0],h=f[0];if(k==null){k=-1}if(h==null){h=this.data.length-1}if(k===h&&o.length>1){this.data[k].HTMLmoveSlice(o.slice(1),f.slice(1),l,n,g,"paddingLeft")}else{var m=n.last;n.last=false;while(k=0){m=q*h.nest}}else{m=Math.max(1,m+q[0]*h.nest)}if(m>=h.penalty){return false}h.penalty=m;h.values=p;h.W=i;h.w=o;p.lineleading=b.length2em(p.lineleading,f.VALUES.lineleading);return true}});a.mspace.Augment({HTMLbetterBreak:function(g,f){var m=this.getValues("linebreak");var h=g.W,k=this.HTMLspanElement(),l=k.bbox.w;if(k.style.paddingLeft){l+=parseFloat(k.style.paddingLeft)}if(m.linebreakstyle===a.LINEBREAKSTYLE.AFTER){h+=l;l=0}if(h-g.shift===0){return false}var i=b.linebreakWidth-h;var j=Math.floor(i/b.linebreakWidth*1000);if(j<0){j=e.toobig-3*j}j+=g.nest*e.nestfactor;var n=e[m.linebreak||a.LINEBREAK.AUTO];if(!(n instanceof Array)){if(i>=0){j=n*g.nest}}else{j=Math.max(1,j+n[0]*g.nest)}if(j>=g.penalty){return false}g.penalty=j;g.values=m;g.W=h;g.w=l;m.lineleading=f.VALUES.lineleading;m.linebreakstyle="before";return true}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({HTMLbetterBreak:function(g,f){return this.Core().HTMLbetterBreak(g,f)},HTMLmoveLine:function(j,f,h,i,g){return this.Core().HTMLmoveSlice(j,f,h,i,g)}})});a.maction.Augment({HTMLbetterBreak:function(g,f){return this.Core().HTMLbetterBreak(g,f)},HTMLmoveLine:function(j,f,h,i,g){return this.Core().HTMLmoveSlice(j,f,h,i,g)},HTMLmoveSlice:function(g,i,l,f,m,j){var o=document.getElementById("MathJax-HitBox-"+this.spanID+b.idPostfix);if(o){o.parentNode.removeChild(o)}var k=this.SUPER(arguments).HTMLmoveSlice.apply(this,arguments);if(i.length===0){l=this.HTMLspanElement();var h=0;while(l){o=this.HTMLhandleHitBox(l,"-Continue-"+h);l=l.nextMathJaxSpan;h++}}return k}});a.semantics.Augment({HTMLbetterBreak:function(g,f){return(this.data[0]?this.data[0].HTMLbetterBreak(g,f):false)},HTMLmoveLine:function(j,f,h,i,g){return(this.data[0]?this.data[0].HTMLmoveSlice(j,f,h,i,g):null)}});MathJax.Hub.Startup.signal.Post("HTML-CSS multiline Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/multiline.js")}); diff --git a/jax/output/HTML-CSS/config.js b/jax/output/HTML-CSS/config.js index d5e03f160..ff1abefef 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:"1.1.9",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(l){var j=this.HTMLlineBreaks();if(j.length>2){return this.toHTMLmultiline(l,j)}l=this.HTMLcreateSpan(l);if(this.type!="mrow"){l=this.HTMLhandleSize(l)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;ho){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em0&&(k+m)*this.em0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;gg.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lwg.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(hk.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;he.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(ro){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||iF){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;HF){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); diff --git a/unpacked/config/default.js b/unpacked/config/default.js index c4e35c262..b69353d0e 100644 --- a/unpacked/config/default.js +++ b/unpacked/config/default.js @@ -472,6 +472,42 @@ MathJax.Hub.Config({ // if it doesn't contain the needed character), so order these carefully. // undefinedFamily: "STIXGeneral,'Arial Unicode MS',serif", + + // + // These settings control automatic line breaking. It is off by + // default, so only explicit line breaks are performed (via + // linebreak="newline" attributes on and elements). To + // perform automatic line breaking on line expressions, set + // 'automatic' to 'true' below. The line breaks will be applied via a + // penalty-based heuristic, which does well, but isn't perfect. You + // might need to use linebreak="goodbreak" or linebreak="badbreak" by + // hand in order to get better effects. It is also possible to modify + // the penalty values; contact the MathJax user's forum for details. + // + linebreaks: { + + // + // This controls the automatic breaking of expressions: + // when false, only process linebreak="newline", + // when true, line breaks are inserted automatically in long expressions. + // + automatic: false, + + // + // This controls how wide the lines of mathematics can be + // + // Use an explicit with like "30em" for a fixed width. + // Use "container" to compute size from containing element. + // Use "nn% container" for a portion of the container. + // Use "nn%" for a portion of the window size. + // + // The container-based widths may be slower, and may not produce the + // expected results if the layout width changes due to the removal + // of previews or inclusion of mathematics during typesetting. + // + width: "container" + }, + // // This controls whether the MathJax contextual menu will be available diff --git a/unpacked/jax/element/mml/jax.js b/unpacked/jax/element/mml/jax.js index 73034ca51..fe199d73b 100644 --- a/unpacked/jax/element/mml/jax.js +++ b/unpacked/jax/element/mml/jax.js @@ -27,7 +27,7 @@ MathJax.ElementJax.mml = MathJax.ElementJax({ mimeType: "jax/mml" },{ id: "mml", - version: "1.1.1", + version: "1.1.2", directory: MathJax.ElementJax.directory + "/mml", extensionDir: MathJax.ElementJax.extensionDir + "/mml", optableDir: MathJax.ElementJax.directory + "/mml/optable" @@ -215,6 +215,7 @@ MathJax.ElementJax.mml.Augment({ mathcolor: MML.INHERIT }, noInherit: {}, + linebreakContainer: FALSE, Init: function () { this.data = []; @@ -343,16 +344,23 @@ MathJax.ElementJax.mml.Augment({ isEmbellished: function () {return FALSE}, Core: function () {return this}, CoreMO: function () {return this}, - lineBreak: function () { + lineBreak: function () { // FIXME: should be removed (and from elements below) when SVG is converted to new linebreak style if (this.isEmbellished()) {return this.CoreMO().lineBreak()} else {return "none"} }, + hasNewline: function () { + if (this.isEmbellished()) {return this.CoreMO().hasNewline()} + if (this.isToken || this.linebreakContainer) {return FALSE} + for (var i = 0, m = this.data.length; i < m; i++) { + if (this.data[i] && this.data[i].hasNewline()) {return TRUE} + } + return FALSE; + }, array: function () {if (this.inferred) {return this.data} else {return [this]}}, toString: function () {return this.type+"("+this.data.join(",")+")"} },{ childrenSpacelike: function () { - for (var i = 0; i < this.data.length; i++) { - if (!this.data[i].isSpacelike()) {return FALSE} - } + for (var i = 0, m = this.data.length; i < m; i++) + {if (!this.data[i].isSpacelike()) {return FALSE}} return TRUE; }, childEmbellished: function () { @@ -533,6 +541,7 @@ MathJax.ElementJax.mml.Augment({ return MML.FORM.INFIX; }, isEmbellished: function () {return TRUE}, + hasNewline: function () {return (this.Get("linebreak") === MML.LINEBREAK.NEWLINE)}, lineBreak: function () { var values = this.getValues("linebreak","linebreakstyle"); if (values.linebreak === MML.LINEBREAK.NEWLINE) { @@ -589,6 +598,7 @@ MathJax.ElementJax.mml.Augment({ depth: "0ex", linebreak: MML.LINEBREAK.AUTO }, + hasNewline: function () {return (this.Get("linebreak") === MML.LINEBREAK.NEWLINE)}, lineBreak: function () { return (this.Get("linebreak") === MML.LINEBREAK.NEWLINE ? MML.LINEBREAKSTYLE.AFTER : "none"); @@ -675,6 +685,7 @@ MathJax.ElementJax.mml.Augment({ MML.mfrac = MML.mbase.Subclass({ type: "mfrac", num: 0, den: 1, + linebreakContainer: TRUE, texClass: MML.TEXCLASS.INNER, isEmbellished: MML.mbase.childEmbellished, Core: MML.mbase.childCore, @@ -703,6 +714,7 @@ MathJax.ElementJax.mml.Augment({ MML.msqrt = MML.mbase.Subclass({ type: "msqrt", inferRow: TRUE, + linebreakContainer: TRUE, texClass: MML.TEXCLASS.ORD, setTeXclass: MML.mbase.setSeparateTeXclasses, adjustChild_texprimestyle: function (n) {return TRUE} @@ -710,6 +722,7 @@ MathJax.ElementJax.mml.Augment({ MML.mroot = MML.mbase.Subclass({ type: "mroot", + linebreakContainer: TRUE, texClass: MML.TEXCLASS.ORD, adjustChild_displaystyle: function (n) { if (n === 1) {return FALSE} @@ -767,6 +780,7 @@ MathJax.ElementJax.mml.Augment({ MML.merror = MML.mbase.Subclass({ type: "merror", inferRow: TRUE, + linebreakContainer: TRUE, texClass: MML.TEXCLASS.ORD }); @@ -852,6 +866,7 @@ MathJax.ElementJax.mml.Augment({ MML.menclose = MML.mbase.Subclass({ type: "menclose", inferRow: TRUE, + linebreakContainer: TRUE, defaults: { mathbackground: MML.INHERIT, mathcolor: MML.INHERIT, @@ -863,6 +878,7 @@ MathJax.ElementJax.mml.Augment({ MML.msubsup = MML.mbase.Subclass({ type: "msubsup", base: 0, sub: 1, sup: 2, + linebreakContainer: TRUE, isEmbellished: MML.mbase.childEmbellished, Core: MML.mbase.childCore, CoreMO: MML.mbase.childCoreMO, @@ -910,6 +926,7 @@ MathJax.ElementJax.mml.Augment({ type: "munderover", base: 0, under: 1, over: 2, sub: 1, sup: 2, ACCENTS: ["", "accentunder", "accent"], + linebreakContainer: TRUE, isEmbellished: MML.mbase.childEmbellished, Core: MML.mbase.childCore, CoreMO: MML.mbase.childCoreMO, @@ -989,6 +1006,7 @@ MathJax.ElementJax.mml.Augment({ side: TRUE, minlabelspacing: TRUE, texClass: TRUE, useHeight: 1 } }, + linebreakContainer: TRUE, Append: function () { for (var i = 0, m = arguments.length; i < m; i++) { if (!((arguments[i] instanceof MML.mtr) || @@ -1013,6 +1031,7 @@ MathJax.ElementJax.mml.Augment({ mrow: {rowalign: TRUE, columnalign: TRUE, groupalign: TRUE}, mtable: {rowalign: TRUE, columnalign: TRUE, groupalign: TRUE} }, + linebreakContainer: TRUE, Append: function () { for (var i = 0, m = arguments.length; i < m; i++) { if (!(arguments[i] instanceof MML.mtd)) {arguments[i] = MML.mtd(arguments[i])} @@ -1025,6 +1044,7 @@ MathJax.ElementJax.mml.Augment({ MML.mtd = MML.mbase.Subclass({ type: "mtd", inferRow: TRUE, + linebreakContainer: TRUE, isEmbellished: MML.mbase.childEmbellished, Core: MML.mbase.childCore, CoreMO: MML.mbase.childCoreMO, @@ -1098,6 +1118,7 @@ MathJax.ElementJax.mml.Augment({ }); MML.annotation = MML.mbase.Subclass({ type: "annotation", isToken: TRUE, + linebreakContainer: TRUE, defaults: { definitionURL: null, encoding: null, @@ -1143,6 +1164,8 @@ MathJax.ElementJax.mml.Augment({ indentalign: MML.INDENTALIGN.AUTO, indentalignfirst: MML.INDENTALIGN.INDENTALIGN, indentshiftfirst: MML.INDENTSHIFT.INDENTSHIFT, + indentalignlast: MML.INDENTALIGN.INDENTALIGN, + indentshiftlast: MML.INDENTSHIFT.INDENTSHIFT, decimalseparator: ".", texprimestyle: FALSE // is it in TeX's C' style? }, @@ -1150,6 +1173,7 @@ MathJax.ElementJax.mml.Augment({ if (name === "displaystyle") {return this.Get("display") === "block"} return ""; }, + linebreakContainer: TRUE, setTeXclass: MML.mbase.setChildTeXclass }); @@ -1374,6 +1398,7 @@ MathJax.ElementJax.mml.Augment({ '~': MO.WIDEACCENT // tilde }, infix: { + '': MO.ORD, // empty '%': [3,3,TEXCLASS.ORD], // percent sign '\u2022': MO.BIN4, // bullet '\u2026': MO.INNER, // horizontal ellipsis diff --git a/unpacked/jax/output/HTML-CSS/autoload/maction.js b/unpacked/jax/output/HTML-CSS/autoload/maction.js index b33be10b7..4b350dd1b 100644 --- a/unpacked/jax/output/HTML-CSS/autoload/maction.js +++ b/unpacked/jax/output/HTML-CSS/autoload/maction.js @@ -42,35 +42,38 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { toHTML: function (span,HW,D) { span = this.HTMLhandleSize(this.HTMLcreateSpan(span)); span.bbox = null; - var values = this.getValues("actiontype","selection"), frame; - var selected = this.data[values.selection-1]; + var selected = this.selected(); if (selected) { HTMLCSS.Measured(selected.toHTML(span),span); if (D != null) {HTMLCSS.Remeasured(selected.HTMLstretchV(span,HW,D),span)} else if (HW != null) {HTMLCSS.Remeasured(selected.HTMLstretchH(span,HW),span)} - if (HTMLCSS.msieHitBoxBug) { - // margin-left doesn't work on inline-block elements in IE, so put it in a SPAN - var box = HTMLCSS.addElement(span,"span"); - frame = HTMLCSS.createFrame(box,span.bbox.h,span.bbox.d,span.bbox.w,0,"none"); - span.insertBefore(box,span.firstChild); // move below the content - box.style.marginRight = HTMLCSS.Em(-span.bbox.w); - if (HTMLCSS.msieInlineBlockAlignBug) - {frame.style.verticalAlign = HTMLCSS.Em(HTMLCSS.getHD(span).d-span.bbox.d)} - } else { - frame = HTMLCSS.createFrame(span,span.bbox.h,span.bbox.d,span.bbox.w,0,"none"); - span.insertBefore(frame,span.firstChild); // move below the content - frame.style.marginRight = HTMLCSS.Em(-span.bbox.w); - } - frame.className = "MathJax_HitBox"; - frame.id = "MathJax-HitBox-"+this.spanID; - - if (this.HTMLaction[values.actiontype]) - {this.HTMLaction[values.actiontype].call(this,span,frame,values.selection)} + this.HTMLhandleHitBox(span); } this.HTMLhandleSpace(span); this.HTMLhandleColor(span); return span; }, + HTMLhandleHitBox: function (span,postfix) { + var frame; + if (HTMLCSS.msieHitBoxBug) { + // margin-left doesn't work on inline-block elements in IE, so put it in a SPAN + var box = HTMLCSS.addElement(span,"span"); + frame = HTMLCSS.createFrame(box,span.bbox.h,span.bbox.d,span.bbox.w,0,"none"); + span.insertBefore(box,span.firstChild); // move below the content + box.style.marginRight = HTMLCSS.Em(-span.bbox.w); + if (HTMLCSS.msieInlineBlockAlignBug) + {frame.style.verticalAlign = HTMLCSS.Em(HTMLCSS.getHD(span).d-span.bbox.d)} + } else { + frame = HTMLCSS.createFrame(span,span.bbox.h,span.bbox.d,span.bbox.w,0,"none"); + span.insertBefore(frame,span.firstChild); // move below the content + frame.style.marginRight = HTMLCSS.Em(-span.bbox.w); + } + frame.className = "MathJax_HitBox"; + frame.id = "MathJax-HitBox-" + this.spanID + (postfix||"") + HTMLCSS.idPostfix; + + var type = this.Get("actiontype"); + if (this.HTMLaction[type]) {this.HTMLaction[type].call(this,span,frame,this.Get("selection"))} + }, HTMLstretchH: MML.mbase.HTMLstretchH, HTMLstretchV: MML.mbase.HTMLstretchV, diff --git a/unpacked/jax/output/HTML-CSS/autoload/multiline.js b/unpacked/jax/output/HTML-CSS/autoload/multiline.js index 96fa6253c..3676ccec4 100644 --- a/unpacked/jax/output/HTML-CSS/autoload/multiline.js +++ b/unpacked/jax/output/HTML-CSS/autoload/multiline.js @@ -2,7 +2,7 @@ * * MathJax/jax/output/HTML-CSS/autoload/multiline.js * - * Implements the HTML-CSS output 's that contain line breaks. + * Implements the HTML-CSS output for 's that contain line breaks. * * --------------------------------------------------------------------- * @@ -25,59 +25,97 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { var VERSION = "1.1"; var MML = MathJax.ElementJax.mml, HTMLCSS = MathJax.OutputJax["HTML-CSS"]; + + // + // Penalties for the various line breaks + // + var PENALTY = { + newline: 0, + nobreak: 1000000, + goodbreak: [-200], + badbreak: [+200], + auto: [0], + + toobig: 500, + nestfactor: 400, + fence: 500 + }; + + var ENDVALUES = {linebreakstyle: "after"}; + + + /**************************************************************************/ MML.mbase.Augment({ - toHTMLmultiline: function (span,split) { - span = this.HTMLcreateSpan(span); if (!this.type !== "mrow") {span = this.HTMLhandleSize(span)} - var stack = HTMLCSS.createStack(span); - var box = [], stretchy = [], H = -HTMLCSS.BIGDIMEN, D = -HTMLCSS.BIGDIMEN, i, j, m, M; - for (j = 0, M = split.length-1; j < M; j++) { - box[j] = HTMLCSS.createBox(stack); - for (i = split[j][0], m = split[j+1][0]; i < m; i++) - {if (this.data[i]) {this.data[i].toHTML(box[j])}} - // remove inter-object spacing - if (this.data[split[j][0]]) {this.data[split[j][0]].HTMLspanElement().style.paddingLeft = ""} - if (this.data[split[j][m-1]]) {this.data[split[j][m-1]].HTMLspanElement().style.paddingRight = ""} - // - stretchy[j] = this.HTMLcomputeBBox(box[j],null,split[j][0],split[j+1][0]); - if (box[j].bbox.h > H) {H = box[j].bbox.h} - if (box[j].bbox.d > D) {D = box[j].bbox.d} - } - var y = 0, scale = this.HTMLgetScale(), LHD = HTMLCSS.FONTDATA.baselineskip * scale; - var parent = this, first; + HTMLlinebreakPenalty: PENALTY, + + /****************************************************************/ + // + // Handle breaking an mrow into separate lines + // + HTMLmultiline: function (span) { + + // + // Find the parent element and mark it as multiline + // + var parent = this; while (parent.inferred || (parent.parent && parent.parent.type === "mrow" && parent.parent.data.length === 1)) {parent = parent.parent} - var isTop = (parent.type === "math" || parent.type === "mtd"); parent.isMultiline = true; - for (j = 0, M = split.length-1; j < M; j++) { - for (i = 0, m = stretchy[j].length; i < m; i++) {stretchy[j][i].HTMLstretchV(box[j],H,D)} - if (stretchy[j].length) {this.HTMLcomputeBBox(box[j],true,split[j][0],split[j+1][0])} - var values = split[j][1].getValues("indentalign","indentshift"); - values.lineleading = HTMLCSS.length2em(split[j+1][1].Get("lineleading"),.5); - // handle first/last special cases - if (j === 0) { - first = split[j+1][1].getValues("indentalignfirst","indentshiftfirst"); - values.ALIGN = first.indentalignfirst; values.SHIFT = first.indentshiftfirst; - } else if (j === M-1) { - first = split[j][1].getValues("indentalignlast","indentshiftlast"); - values.ALIGN = first.indentalignlast; values.SHIFT = first.indentshiftlast; - } - if (values.ALIGN && values.ALIGN !== MML.INDENTALIGN.INDENTALIGN) - {values.indentalign = values.ALIGN} - if (values.SHIFT && values.SHIFT !== MML.INDENTSHIFT.INDENTSHIFT) - {values.indentshift = values.SHIFT} - // - if (values.indentalign == MML.INDENTALIGN.AUTO) - {values.indentalign = (isTop ? this.displayAlign : MML.INDENTALIGN.LEFT)} - if (values.indentshift === "auto" || values.indentshift === "") - {values.indentshift = (isTop ? this.displayIndent : "0")} - values.indentshift = HTMLCSS.length2em(values.indentshift,0); - if (values.indentshift && values.indentalign !== MML.INDENTALIGN.CENTER) { - HTMLCSS.createBlank(box[j],values.indentshift,(values.indentalign !== MML.INDENTALIGN.RIGHT)); - box[j].bbox.w += values.indentshift; box[j].bbox.rw += values.indentshift; - } - HTMLCSS.alignBox(box[j],values.indentalign,y); - if (j < M-1) {y -= Math.max(LHD,box[j].bbox.d + box[j+1].bbox.h + values.lineleading)} + var isTop = ((parent.type === "math" && parent.Get("display") === "block") || + parent.type === "mtd"); + parent.isMultiline = true; + + // + // Default values for the line-breaking parameters + // + var VALUES = this.getValues( + "linebreak","linebreakstyle","lineleading","linebreakmultchar", + "indentalign","indentshift", + "indentalignfirst","indentshiftfirst", + "indentalignlast","indentshiftlast" + ); + if (VALUES.linebreakstyle === MML.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE) + {VALUES.linebreakstyle = this.Get("infixlinebreakstyle")} + VALUES.lineleading = HTMLCSS.length2em(VALUES.lineleading,0.5); + + // + // Remove old color and break the span at its best line breaks + // + this.HTMLremoveColor(span); + var stack = HTMLCSS.createStack(span); + var state = { + n: 0, Y: 0, + scale: this.HTMLgetScale(), + isTop: isTop, + values: {}, + VALUES: VALUES + }, + align = this.HTMLgetAlign(state,{}), + shift = this.HTMLgetShift(state,{},align), + start = [], + end = { + index:[], penalty:PENALTY.nobreak, + w:0, W:shift, shift:shift, scanW:shift, + nest: 0 + }, + broken = false; + + while (this.HTMLbetterBreak(end,state) && + (end.scanW >= HTMLCSS.linebreakWidth || end.penalty == PENALTY.newline)) { + this.HTMLaddLine(stack,start,end.index,state,end.values,broken); + start = end.index.slice(0); broken = true; + align = this.HTMLgetAlign(state,end.values); + shift = this.HTMLgetShift(state,end.values,align); + if (align === MML.INDENTALIGN.CENTER) {shift = 0} + end.W = end.shift = end.scanW = shift; end.penalty = PENALTY.nobreak; } + state.isLast = true; + this.HTMLaddLine(stack,start,[],state,ENDVALUES,broken); + + // + // Make top-level spans 100% wide. + // Finish up the space and add the color again + // if (isTop) { stack.style.width = "100%"; if (parent.type === "math") {span.bbox.width = "100%"} @@ -85,10 +123,399 @@ MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () { this.HTMLhandleSpace(span); this.HTMLhandleColor(span); span.bbox.isMultiline = true; + return span; + }, + + /****************************************************************/ + // + // Locate the next linebreak that is better than the current one + // + HTMLbetterBreak: function (info,state) { + if (this.isToken) {return false} // FIXME: handle breaking of token elements + if (this.isEmbellished()) { + info.embellished = this; + return this.CoreMO().HTMLbetterBreak(info,state); + } + if (this.linebreakContainer) {return false} + // + // Get the current breakpoint position and other data + // + var index = info.index.slice(0), i = info.index.shift(), + m = this.data.length, W, scanW = info.W, + broken = (info.index.length > 0), better = false; + if (i == null) {i = -1}; if (!broken) {i++; info.W += info.w}; + info.w = 0; info.nest++; + // + // Look through the line for breakpoints, + // (as long as we are not too far past the breaking width) + // + while (i < m && info.W < 1.33*HTMLCSS.linebreakWidth) { + if (this.data[i]) { + if (this.data[i].HTMLbetterBreak(info,state)) { + better = true; index = [i].concat(info.index); W = info.W; + if (info.penalty === PENALTY.newline) {info.index = index; info.nest--; return true} + } + if (!broken) { + var span = this.data[i].HTMLspanElement(); + scanW += span.bbox.w; + if (span.style.paddingLeft) {scanW += parseFloat(span.style.paddingLeft)} + if (span.style.paddingRight) {scanW += parseFloat(span.style.paddingRight)} + info.W = info.scanW = scanW; + } + } + info.index = []; i++; broken = false; + } + info.nest--; info.index = index; + if (better) {info.W = W} + return better; + }, + + /****************************************************************/ + // + // Create a new line and move the required elements into it + // Position it using proper alignment and indenting + // + HTMLaddLine: function (stack,start,end,state,values,broken) { + // + // Create a box for the line, with empty BBox + // fill it with the proper elements, + // and clean up the bbox + // + line = HTMLCSS.createBox(stack); + line.bbox = this.HTMLemptyBBox({}); + state.first = broken; state.last = true; + this.HTMLmoveLine(start,end,line,state,values); + this.HTMLcleanBBox(line.bbox); + // + // Get the alignment and shift values + // + var align = this.HTMLgetAlign(state,values), + shift = this.HTMLgetShift(state,values,align); + // + // Add in space for the shift + // + if (shift) { + HTMLCSS.createBlank(line,shift,(align !== MML.INDENTALIGN.RIGHT)); + line.bbox.w += shift; line.bbox.rw += shift; + } + // + // Set the Y offset based on previous depth, leading, and current height + // + if (state.n > 0) { + var LHD = HTMLCSS.FONTDATA.baselineskip * state.scale; + var leading = (state.values.lineleading == null ? state.VALUES : state.values).lineleading; + state.Y -= Math.max(LHD,state.d + line.bbox.h + leading); + } + // + // Place the new line + // + HTMLCSS.alignBox(line,align,state.Y); + // + // Save the values needed for the future + // + state.d = line.bbox.d; state.values = values; state.n++; + }, + + /****************************************************************/ + // + // Get alignment and shift values from the given data + // + HTMLgetAlign: function (state,values) { + var cur = values, prev = state.values, def = state.VALUES, align; + if (state.n === 0) {align = cur.indentalignfirst || prev.indentalignfirst || def.indentalignfirst} + else if (state.isLast) {align = prev.indentalignlast || def.indentalignlast} + else {align = prev.indentalign || def.indentalign} + if (align === MML.INDENTALIGN.INDENTALIGN) {align = prev.indentalign || def.indentalign} + if (align === MML.INDENTALIGN.AUTO) {align = (state.isTop ? this.displayAlign : MML.INDENTALIGN.LEFT)} + return align; + }, + HTMLgetShift: function (state,values,align) { + if (align === MML.INDENTALIGN.CENTER) {return 0} + var cur = values, prev = state.values, def = state.VALUES, shift; + if (state.n === 0) {shift = cur.indentshiftfirst || prev.indentshiftfirst || def.indentshiftfirst} + else if (state.isLast) {shift = prev.indentshiftlast || def.indentshiftlast} + else {shift = prev.indentshift || def.indentshift} + if (shift === MML.INDENTSHIFT.INDENTSHIFT) {shift = prev.indentshift || def.indentshift} + if (shift === "auto" || shift === "") {shift = (state.isTSop ? this.displayIndent : "0")} + return HTMLCSS.length2em(shift,0); + }, + + /****************************************************************/ + // + // Move the selected elements into the new line's span, + // moving whole items when possible, and parts of ones + // that are split by a line break. + // + HTMLmoveLine: function (start,end,span,state,values) { + var i = start[0], j = end[0]; + if (i == null) {i = -1}; if (j == null) {j = this.data.length-1} + if (i === j && start.length > 1) { + // + // If starting and ending in the same element move the subpiece to the new line + // + this.data[i].HTMLmoveSlice(start.slice(1),end.slice(1),span,state,values,"paddingLeft"); + } else { + // + // Otherwise, move the remainder of the initial item + // and any others up tp the last one + // + var last = state.last; state.last = false; + while (i < j) { + if (this.data[i]) { + if (start.length <= 1) {this.data[i].HTMLmoveSpan(span,state,values)} + else {this.data[i].HTMLmoveSlice(start.slice(1),[],span,state,values,"paddingLeft")} + } + i++; state.first = false; start = []; + } + // + // If the last item is complete, move it, + // otherwise move the first part of it up to the split + // + state.last = last; + if (this.data[i]) { + if (end.length <= 1) {this.data[i].HTMLmoveSpan(span,state,values)} + else {this.data[i].HTMLmoveSlice([],end.slice(1),span,state,values,"paddingRight")} + } + } + }, + + /****************************************************************/ + // + // Split an element and copy the selected items into the new part + // + HTMLmoveSlice: function (start,end,span,state,values,padding) { + // + // Get rid of color, if any (added back in later) + // Create a new span for the slice of the element + // Move the selected portion into the slice + // If it is the last slice + // Remove the original (now empty) span + // Rename the Continue-0 span with the original name (for HTMLspanElement) + // Add back the color + // + this.HTMLremoveColor(); + var slice = this.HTMLcreateSliceSpan(span); + this.HTMLmoveLine(start,end,slice,state,values); + slice.style[padding] = ""; + this.HTMLcombineBBoxes(slice,span.bbox); + this.HTMLcleanBBox(slice.bbox); + if (end.length === 0) { + span = this.HTMLspanElement(); + span.parentNode.removeChild(span); + span.nextMathJaxSpan.id = span.id; var n = 0; + while (span = span.nextMathJaxSpan) { + var color = this.HTMLhandleColor(span); + if (color) {color.id += "-MathJax-Continue-"+n; n++} + } + } + return slice; + }, + + /****************************************************************/ + // + // Create a new span for an element that is split in two + // Clone the original and update its ID. + // Link the old span to the new one so we can find it later + // + HTMLcreateSliceSpan: function (span) { + var SPAN = this.HTMLspanElement(), n = 0; + var LAST = SPAN; while (LAST.nextMathJaxSpan) {LAST = LAST.nextMathJaxSpan; n++} + var SLICE = SPAN.cloneNode(false); LAST.nextMathJaxSpan = SLICE; + SLICE.id += "-MathJax-Continue-"+n; + SLICE.bbox = this.HTMLemptyBBox({}); + return span.appendChild(SLICE); + }, + + /****************************************************************/ + // + // Move an element from its original span to its new location in + // a split element or the new line's span + // + HTMLmoveSpan: function (line,state,values) { + // FIXME: handle linebreakstyle === "duplicate" + // FIXME: handle linebreakmultchar + if (!(state.first || state.last) || + (state.first && state.values.linebreakstyle === MML.LINEBREAKSTYLE.BEFORE) || + (state.last && values.linebreakstyle === MML.LINEBREAKSTYLE.AFTER)) { + // + // Move color and span + // + var color = document.getElementById("MathJax-Color-"+this.spanID+HTMLCSS.idPostfix); + if (color) {line.appendChild(color)} + var span = this.HTMLspanElement(); + line.appendChild(span); + // + // If it is last, remove right padding + // If it is first, remove left padding and recolor + // + if (state.last) {span.style.paddingRight = ""} + if (state.first || state.nextIsFirst) { + delete state.nextIsFirst; + span.style.paddingLeft = ""; + if (color) {this.HTMLremoveColor(span); this.HTMLhandleColor(span)} + } + // + // Update bounding box + // + this.HTMLcombineBBoxes(this,line.bbox); + } else if (state.first) {state.nextIsFirst = true} else {delete state.nextIsFirst} + } + }); + + /**************************************************************************/ + + MML.mo.Augment({ + // + // Override the method for checking line breaks to properly handle + // + HTMLbetterBreak: function (info,state) { + var values = this.getValues( + "linebreak","linebreakstyle","lineleading","linebreakmultchar", + "indentalign","indentshift", + "indentalignfirst","indentshiftfirst", + "indentalignlast","indentshiftlast" + ); + if (values.linebreakstyle === MML.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE) + {values.linebreakstyle = this.Get("infixlinebreakstyle")} + // + // Get the default penalty for this location + // + var W = info.W, mo = (info.embellished||this); delete info.embellished; + var span = mo.HTMLspanElement(), w = span.bbox.w; + if (span.style.paddingLeft) {w += parseFloat(span.style.paddingLeft)} + if (values.linebreakstyle === MML.LINEBREAKSTYLE.AFTER) {W += w; w = 0} + if (W - info.shift === 0) {return false} // don't break at zero width (FIXME?) + var offset = HTMLCSS.linebreakWidth - W; + // adjust offest for explicit first-line indent and align + if (state.n === 0 && (values.indentshiftfirst !== state.VALUES.indentshiftfirst || + values.indentalignfirst !== state.VALUES.indentalignfirst)) { + var align = this.HTMLgetAlign(state,values), + shift = this.HTMLgetShift(state,values,align); + offset += (info.shift - shift); + } + // + var penalty = Math.floor(offset / HTMLCSS.linebreakWidth * 1000); + if (penalty < 0) {penalty = PENALTY.toobig - 3*penalty} + if (this.Get("fence")) {penalty += PENALTY.fence} + penalty += info.nest * PENALTY.nestfactor; + // + // Get the penalty for this type of break and + // use it to modify the default penalty + // + var linebreak = PENALTY[values.linebreak||MML.LINEBREAK.AUTO]; + if (!(linebreak instanceof Array)) { + // for breaks past the width, don't modify penalty + if (offset >= 0) {penalty = linebreak * info.nest} + } else {penalty = Math.max(1,penalty + linebreak[0] * info.nest)} + // + // If the penalty is no better than the current one, return false + // Otherwise save the data for this breakpoint and return true + // + if (penalty >= info.penalty) {return false} + info.penalty = penalty; info.values = values; info.W = W; info.w = w; + values.lineleading = HTMLCSS.length2em(values.lineleading,state.VALUES.lineleading); + return true; } }); + /**************************************************************************/ + + MML.mspace.Augment({ + // + // Override the method for checking line breaks to properly handle + // + HTMLbetterBreak: function (info,state) { + var values = this.getValues("linebreak"); + // + // Get the default penalty for this location + // + var W = info.W, span = this.HTMLspanElement(), w = span.bbox.w; + if (span.style.paddingLeft) {w += parseFloat(span.style.paddingLeft)} + if (values.linebreakstyle === MML.LINEBREAKSTYLE.AFTER) {W += w; w = 0} + if (W - info.shift === 0) {return false} // don't break at zero width (FIXME?) + var offset = HTMLCSS.linebreakWidth - W; + // + var penalty = Math.floor(offset / HTMLCSS.linebreakWidth * 1000); + if (penalty < 0) {penalty = PENALTY.toobig - 3*penalty} + penalty += info.nest * PENALTY.nestfactor; + // + // Get the penalty for this type of break and + // use it to modify the default penalty + // + var linebreak = PENALTY[values.linebreak||MML.LINEBREAK.AUTO]; + if (!(linebreak instanceof Array)) { + // for breaks past the width, don't modify penalty + if (offset >= 0) {penalty = linebreak * info.nest} + } else {penalty = Math.max(1,penalty + linebreak[0] * info.nest)} + // + // If the penalty is no better than the current one, return false + // Otherwise save the data for this breakpoint and return true + // + if (penalty >= info.penalty) {return false} + info.penalty = penalty; info.values = values; info.W = W; info.w = w; + values.lineleading = state.VALUES.lineleading; values.linebreakstyle = "before"; + return true; + } + }); + + // + // Hook into the mathchoice extension + // + MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function () { + MML.TeXmathchoice.Augment({ + HTMLbetterBreak: function (info,state) { + return this.Core().HTMLbetterBreak(info,state); + }, + HTMLmoveLine: function (start,end,span,state,values) { + return this.Core().HTMLmoveSlice(start,end,span,state,values); + } + }); + }); + + // + // Have maction process only the selected item + // + MML.maction.Augment({ + HTMLbetterBreak: function (info,state) { + return this.Core().HTMLbetterBreak(info,state); + }, + HTMLmoveLine: function (start,end,span,state,values) { + return this.Core().HTMLmoveSlice(start,end,span,state,values); + }, + // + // Split and move the hit boxes as well + // + HTMLmoveSlice: function (start,end,span,state,values,padding) { + var hitbox = document.getElementById("MathJax-HitBox-"+this.spanID+HTMLCSS.idPostfix); + if (hitbox) {hitbox.parentNode.removeChild(hitbox)} + var slice = this.SUPER(arguments).HTMLmoveSlice.apply(this,arguments); + if (end.length === 0) { + span = this.HTMLspanElement(); var n = 0; + while (span) { + hitbox = this.HTMLhandleHitBox(span,"-Continue-"+n); + span = span.nextMathJaxSpan; n++; + } + } + return slice; + } + }); + + // + // Have semantics only do the first element + // (FIXME: do we need to do anything special about annotation-xml?) + // + MML.semantics.Augment({ + HTMLbetterBreak: function (info,state) { + return (this.data[0] ? this.data[0].HTMLbetterBreak(info,state) : false); + }, + HTMLmoveLine: function (start,end,span,state,values) { + return (this.data[0] ? this.data[0].HTMLmoveSlice(start,end,span,state,values) : null); + } + }); + + /**************************************************************************/ + MathJax.Hub.Startup.signal.Post("HTML-CSS multiline Ready"); MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/multiline.js"); diff --git a/unpacked/jax/output/HTML-CSS/config.js b/unpacked/jax/output/HTML-CSS/config.js index e184fa72c..a4211cf8b 100644 --- a/unpacked/jax/output/HTML-CSS/config.js +++ b/unpacked/jax/output/HTML-CSS/config.js @@ -24,7 +24,7 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ id: "HTML-CSS", - version: "1.1.9", + version: "1.1.10", directory: MathJax.OutputJax.directory + "/HTML-CSS", extensionDir: MathJax.OutputJax.extensionDir + "/HTML-CSS", autoloadDir: MathJax.OutputJax.directory + "/HTML-CSS/autoload", @@ -39,6 +39,16 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ imageFont: "TeX", undefinedFamily: "STIXGeneral,'Arial Unicode MS',serif", + linebreaks: { + automatic: false, // when false, only process linebreak="newline", + // when true, insert line breaks automatically in long expressions. + + width: "container" // maximum width of a line for automatic line breaks (e.g. "30em"). + // use "container" to compute size from containing element, + // use "nn% container" for a portion of the container, + // use "nn%" for a portion of the window size + }, + showMathMenu: true, styles: { @@ -58,7 +68,7 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ }, ".MathJax_Preview": {color: "#888888"}, - + "#MathJax_Tooltip": { "background-color": "InfoBackground", color: "InfoText", border: "1px solid black", diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js index 374f99235..bcbc34b96 100644 --- a/unpacked/jax/output/HTML-CSS/jax.js +++ b/unpacked/jax/output/HTML-CSS/jax.js @@ -242,7 +242,12 @@ }, ".MathJax .MathJax_HitBox": { - cursor: "text" + cursor: "text", + background: "white", + opacity:0, filter:"alpha(opacity=0)" + }, + ".MathJax .MathJax_HitBox *": { + filter: "none", opacity:1, background:"transparent" // for IE }, "#MathJax_Tooltip": { @@ -251,7 +256,7 @@ display: "none" }, "#MathJax_Tooltip *": { - filter: "none", background:"transparent" // for IE + filter: "none", opacity:1, background:"transparent" // for IE } } @@ -362,6 +367,10 @@ [["span",{style: {display:"inline-block", width:"5em"}}]]); this.marginMove = HTMLCSS.addElement(this.marginCheck,"span", {style: {display:"inline-block", width:"5em", marginLeft:"-5em"}}); + + // Used in getLinebreakWidth + this.linebreakSpan = HTMLCSS.Element("span",null, + [["hr",{style: {width:"100%", size:1, padding:0, border:0, margin:0}}]]); // Set up styles and preload web fonts return AJAX.Styles(this.config.styles,["PreloadWebFonts",this]); @@ -410,6 +419,7 @@ script.parentNode.insertBefore(frame,script); var isHidden; try {this.getScales(span); isHidden = (this.em === 0 || String(this.em) === "NaN")} catch (err) {isHidden = true} if (isHidden) {this.hiddenDiv.appendChild(frame); this.getScales(span)} + this.getLinebreakWidth(frame); this.initImg(span); this.initHTML(math,span); math.setTeXclass(); @@ -493,6 +503,21 @@ span = span.previousSibling; if (!span) return; if (span.className.match(/^MathJax/)) {span.parentNode.removeChild(span)} }, + + getLinebreakWidth: function (div) { + if (this.config.linebreaks.automatic) { + var width = this.config.linebreaks.width, maxwidth; + if (width.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)) { + div.parentNode.insertBefore(this.linebreakSpan,div); + maxwidth = this.linebreakSpan.firstChild.offsetWidth / this.em; + this.linebreakSpan.parentNode.removeChild(this.linebreakSpan); + width = width.replace(/\s*container\s*/,""); + } else {maxwidth = document.body.offsetWidth / this.em} + this.linebreakWidth = (width === "" ? maxwidth : this.length2em(width,maxwidth)); + } else { + this.linebreakWidth = 100000; // a big width, so no implicit line breaks + } + }, getScales: function (span) { span.parentNode.insertBefore(this.HDMspan,span); @@ -1238,8 +1263,6 @@ MML.mbase.Augment({ toHTML: function (span) { - var split = this.HTMLlineBreaks(); - if (split.length > 2) {return this.toHTMLmultiline(span,split)} span = this.HTMLcreateSpan(span); if (this.type != "mrow") {span = this.HTMLhandleSize(span)} for (var i = 0, m = this.data.length; i < m; i++) {if (this.data[i]) {this.data[i].toHTML(span)}} @@ -1247,26 +1270,13 @@ var h = span.bbox.h, d = span.bbox.d; for (i = 0, m = stretchy.length; i < m; i++) {stretchy[i].HTMLstretchV(span,h,d)} if (stretchy.length) {this.HTMLcomputeBBox(span,true)} + if (this.HTMLlineBreaks(span)) {span = this.HTMLmultiline(span)} this.HTMLhandleSpace(span); this.HTMLhandleColor(span); return span; }, - HTMLlineBreaks: function () { - var split = [[0,this]]; - for (var i = 0, m = this.data.length; i < m; i++) { - if (this.data[i]) { - var lb = this.data[i].lineBreak(); - if (lb !== "none") { - var j = (lb === "after" ? i+1 : i); - if (split.length === 0 || split[split.length-1] !== j) - {split.push([j,this.data[i]])} else {split[split.length-1] = [j,this.data[i]]} - } - } - } - split.push([this.data.length,split[split.length-1][1]]); - return split; - }, - toHTMLmultiline: function (span) {MML.mbase.HTMLautoloadFile("multiline")}, + HTMLlineBreaks: function () {return false}, + HTMLmultiline: function () {MML.mbase.HTMLautoloadFile("multiline")}, HTMLcomputeBBox: function (span,full,i,m) { if (i == null) {i = 0}; if (m == null) {m = this.data.length} var BBOX = span.bbox = {}, stretchy = []; @@ -1281,7 +1291,8 @@ }, HTMLcombineBBoxes: function (core,BBOX) { if (BBOX.w == null) {this.HTMLemptyBBox(BBOX)} - var child = core.HTMLspanElement(); if (!child || !child.bbox) return; + var child = (core.bbox ? core : core.HTMLspanElement()); + if (!child || !child.bbox) return; var bbox = child.bbox; if (bbox.d > BBOX.d) {BBOX.d = bbox.d} if (bbox.h > BBOX.h) {BBOX.h = bbox.h} @@ -1410,7 +1421,9 @@ marginLeft: HTMLCSS.Em(lW), marginRight: HTMLCSS.Em(rW)} }); HTMLCSS.setBorders(frame,borders); + if (span.bbox.width) {frame.style.width = span.bbox.width; frame.style.marginRight = "-"+span.bbox.width} if (HTMLCSS.msieInlineBlockAlignBug) { + // FIXME: handle variable width background frame.style.position = "relative"; frame.style.width = frame.style.height = 0; frame.style.verticalAlign = frame.style.marginLeft = frame.style.marginRight = ""; frame.style.border = frame.style.padding = ""; @@ -1763,6 +1776,11 @@ }); MML.mrow.Augment({ + HTMLlineBreaks: function (span) { + if (!this.parent.linebreakContainer) {return false} + return (HTMLCSS.config.linebreaks.automatic && + span.bbox.w > HTMLCSS.linebreakWidth) || this.hasNewline(); + }, HTMLstretchH: function (box,w) { this.HTMLremoveColor(); var span = this.HTMLspanElement(); @@ -1782,30 +1800,20 @@ }); MML.mstyle.Augment({ - toHTML: function (span) { + toHTML: function (span,HW,D) { + span = this.HTMLcreateSpan(span); if (this.data[0] != null) { - if (this.style) { - span = this.HTMLcreateSpan(span); - span.bbox = this.data[0].toHTML(span).bbox; - } else { - span = this.data[0].toHTML(span); - this.spanID = this.data[0].spanID; - } - this.HTMLhandleSpace(span); - this.HTMLhandleColor(span); + var SPAN = this.data[0].toHTML(span); + if (D != null) {this.data[0].HTMLstretchV(span,HW,D)} + else if (HW != null) {this.data[0].HTMLstretchH(span,HW)} + span.bbox = SPAN.bbox; } + this.HTMLhandleSpace(span); + this.HTMLhandleColor(span); return span; }, - HTMLspanElement: function () { - if (this.style) {return this.SUPER(arguments).HTMLspanElement.call(this)} - return (this.data[0] != null ? this.data[0].HTMLspanElement() : null); - }, - HTMLstretchH: function (box,w) { - return (this.data[0] != null ? this.data[0].HTMLstretchH(box,w) : box); - }, - HTMLstretchV: function (box,h,d) { - return (this.data[0] != null ? this.data[0].HTMLstretchV(box,h,d) : box); - } + HTMLstretchH: MML.mbase.HTMLstretchH, + HTMLstretchV: MML.mbase.HTMLstretchV }); MML.mfrac.Augment({ @@ -2140,7 +2148,8 @@ MML.math.Augment({ toHTML: function (span,node) { - var alttext = this.Get("alttext"); if (alttext) {node.setAttribute("aria-label",alttext)} + var alttext = this.Get("alttext"); + if (alttext && alttext !== "") {node.setAttribute("aria-label",alttext)} var nobr = HTMLCSS.addElement(span,"nobr"); span = this.HTMLcreateSpan(nobr); var stack = HTMLCSS.createStack(span), box = HTMLCSS.createBox(stack), math;