From bb35eb004cf442a9ddfce353ce2ca3d289e8ee7b Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Fri, 13 Jan 2012 12:29:44 -0500 Subject: [PATCH] Add full support for unicode planes 1 through 10 (both in \unicode{}, as input, and in HTML-CSS and SVG output) --- config/Accessible-full.js | 6 +++--- config/Accessible.js | 4 ++-- config/MML_HTMLorMML-full.js | 4 ++-- config/MML_HTMLorMML.js | 2 +- config/TeX-AMS-MML_HTMLorMML-full.js | 6 +++--- config/TeX-AMS-MML_HTMLorMML.js | 4 ++-- config/TeX-AMS_HTML-full.js | 6 +++--- config/TeX-AMS_HTML.js | 4 ++-- jax/element/mml/jax.js | 2 +- jax/input/TeX/jax.js | 2 +- jax/output/HTML-CSS/jax.js | 2 +- jax/output/SVG/jax.js | 2 +- unpacked/jax/element/mml/jax.js | 14 ++++++++------ unpacked/jax/input/TeX/jax.js | 5 +++-- unpacked/jax/output/HTML-CSS/jax.js | 12 +++++++----- unpacked/jax/output/SVG/jax.js | 16 ++++++++++------ 16 files changed, 50 insertions(+), 41 deletions(-) diff --git a/config/Accessible-full.js b/config/Accessible-full.js index fcde61223..02a751ebf 100644 --- a/config/Accessible-full.js +++ b/config/Accessible-full.js @@ -71,7 +71,7 @@ MathJax.Extension.mml2jax={version:"1.1.2",config:{preview:"alttext"},MMLnamespa (function(c,f,j,e,b){var o="1.1.9";var i=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:o,signal:i};var m=c.Browser.isPC,k=c.Browser.isMSIE;var h=(m?null:"5px");var n=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:j.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(m?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(m?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(m?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(k?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(k?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(m?"1em":".7em")},".MathJax_MenuLabel":{padding:(m?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(m?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(m?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(m?"Highlight":"#606872"),color:(m?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var g,d;c.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:o,items:[],posted:false,title:null,margin:5,Init:function(p){this.items=[].slice.call(arguments,0)},With:function(p){if(p){c.Insert(this,p)}return this},Post:function(q,A){if(!q){q=window.event}var w=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var p=document.getElementById("MathJax_MenuFrame");if(!p){p=a.Background(this);delete l.lastItem;delete l.lastMenu;delete a.skipUp;i.Post(["post",a.jax])}var r=f.addElement(p,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},w);for(var t=0,s=this.items.length;tdocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -79,7 +79,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,q,p,o){var m=q[5];if(m.img){return this.handleImg(k,j,q,p,o)}if(m.isUnknown&&this.FONTDATA.DELIMITERS[p]){if(o.length){this.addText(k,o)}var l=k.scale;d.createDelimiter(k,p,0,1,j);k.scale=l;q[0]=k.bbox.h*1000;q[1]=k.bbox.d*1000;q[2]=k.bbox.w*1000;q[3]=k.bbox.lw*1000;q[4]=k.bbox.rw*1000;return""}if(m.c==null){if(p<=65535){m.c=String.fromCharCode(p)}else{m.c=this.PLANE1+String.fromCharCode(p-119808+56320)}}if(m.rfix){this.addText(k,m.c);d.createShift(k,m.rfix/1000);return""}if(q[2]||!this.msieAccentBug||o.length){return o+m.c}d.createShift(k,q[3]/1000);d.createShift(k,(q[4]-q[3])/1000);this.addText(k,m.c);d.createShift(k,-q[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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:"\uD835",NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=55296&&v<56319){z++;v=(((v-55296)<<10)+(r.charCodeAt(z)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var l=q-65536;o.c=String.fromCharCode((l>>10)+55296)+String.fromCharCode((l&1023)+56320)}}if(o.rfix){this.addText(k,o.c);d.createShift(k,o.rfix/1000);return""}if(r[2]||!this.msieAccentBug||p.length){return p+o.c}d.createShift(k,r[3]/1000);d.createShift(k,(r[4]-r[3])/1000);this.addText(k,o.c);d.createShift(k,-r[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var G=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aF=G.width.match(/%$/);var av=b.createStack(r);var aC=this.HTMLgetScale(),ax=this.HTMLgetMu(r),ay=-1;var ao=[],ar=[],ai=[],au=[],at=[],ad,ac,an=-1,ab,am,V,aB,aJ=[];var aj=b.FONTDATA.baselineskip*aC*G.useHeight,E=b.FONTDATA.lineH*aC,L=b.FONTDATA.lineD*aC;for(ad=0,ab=this.data.length;adan){an=ac}at[ac]=b.createStack(b.createBox(av));ai[ac]=-b.BIGDIMEN}au[ad][ac]=b.createBox(at[ac]);aJ.push(aB.data[ac-V].toHTML(au[ad][ac]))}}b.MeasureSpans(aJ);for(ad=0,ab=this.data.length;adao[ad]){ao[ad]=au[ad][ac].bbox.h}if(au[ad][ac].bbox.d>ar[ad]){ar[ad]=au[ad][ac].bbox.d}if(au[ad][ac].bbox.w>ai[ac]){ai[ac]=au[ad][ac].bbox.w}}}if(ao[0]+ar[0]){ao[0]=Math.max(ao[0],E)}if(ao[au.length-1]+ar[au.length-1]){ar[au.length-1]=Math.max(ar[au.length-1],L)}var aw=G.columnspacing.split(/ /),aL=G.rowspacing.split(/ /),e=G.columnalign.split(/ /),z=G.rowalign.split(/ /),d=G.columnlines.split(/ /),v=G.rowlines.split(/ /),aH=G.columnwidth.split(/ /),T=[];for(ad=0,ab=aw.length;adau.length){Z=au.length}}ah=0;aO=-(aN+aD)+ao[0];for(ad=0,ab=Z-1;ad0.98){Q=0.98/ae;ae=0.98}}else{if(G.width==="auto"){if(ae>0.98){Q=I/(w+I);aa=w+I}else{aa=w/(1-ae)}}else{aa=b.length2em(G.width,ax);for(ad=0,ab=Math.min(an+1,aw.length);ad0.01){if(af&&aa>w){aa=(aa-w)/af;for(ad=0,ab=aq.length;addocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -76,7 +76,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;ldocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -57,7 +57,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var (function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{".MathJax_mmlExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex",padding:0,border:0,margin:0}}},settings:b.config.menuSettings,Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,q,p,o){var m=q[5];if(m.img){return this.handleImg(k,j,q,p,o)}if(m.isUnknown&&this.FONTDATA.DELIMITERS[p]){if(o.length){this.addText(k,o)}var l=k.scale;d.createDelimiter(k,p,0,1,j);k.scale=l;q[0]=k.bbox.h*1000;q[1]=k.bbox.d*1000;q[2]=k.bbox.w*1000;q[3]=k.bbox.lw*1000;q[4]=k.bbox.rw*1000;return""}if(m.c==null){if(p<=65535){m.c=String.fromCharCode(p)}else{m.c=this.PLANE1+String.fromCharCode(p-119808+56320)}}if(m.rfix){this.addText(k,m.c);d.createShift(k,m.rfix/1000);return""}if(q[2]||!this.msieAccentBug||o.length){return o+m.c}d.createShift(k,q[3]/1000);d.createShift(k,(q[4]-q[3])/1000);this.addText(k,m.c);d.createShift(k,-q[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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:"\uD835",NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=55296&&v<56319){z++;v=(((v-55296)<<10)+(r.charCodeAt(z)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var l=q-65536;o.c=String.fromCharCode((l>>10)+55296)+String.fromCharCode((l&1023)+56320)}}if(o.rfix){this.addText(k,o.c);d.createShift(k,o.rfix/1000);return""}if(r[2]||!this.msieAccentBug||p.length){return p+o.c}d.createShift(k,r[3]/1000);d.createShift(k,(r[4]-r[3])/1000);this.addText(k,o.c);d.createShift(k,-r[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var G=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aF=G.width.match(/%$/);var av=b.createStack(r);var aC=this.HTMLgetScale(),ax=this.HTMLgetMu(r),ay=-1;var ao=[],ar=[],ai=[],au=[],at=[],ad,ac,an=-1,ab,am,V,aB,aJ=[];var aj=b.FONTDATA.baselineskip*aC*G.useHeight,E=b.FONTDATA.lineH*aC,L=b.FONTDATA.lineD*aC;for(ad=0,ab=this.data.length;adan){an=ac}at[ac]=b.createStack(b.createBox(av));ai[ac]=-b.BIGDIMEN}au[ad][ac]=b.createBox(at[ac]);aJ.push(aB.data[ac-V].toHTML(au[ad][ac]))}}b.MeasureSpans(aJ);for(ad=0,ab=this.data.length;adao[ad]){ao[ad]=au[ad][ac].bbox.h}if(au[ad][ac].bbox.d>ar[ad]){ar[ad]=au[ad][ac].bbox.d}if(au[ad][ac].bbox.w>ai[ac]){ai[ac]=au[ad][ac].bbox.w}}}if(ao[0]+ar[0]){ao[0]=Math.max(ao[0],E)}if(ao[au.length-1]+ar[au.length-1]){ar[au.length-1]=Math.max(ar[au.length-1],L)}var aw=G.columnspacing.split(/ /),aL=G.rowspacing.split(/ /),e=G.columnalign.split(/ /),z=G.rowalign.split(/ /),d=G.columnlines.split(/ /),v=G.rowlines.split(/ /),aH=G.columnwidth.split(/ /),T=[];for(ad=0,ab=aw.length;adau.length){Z=au.length}}ah=0;aO=-(aN+aD)+ao[0];for(ad=0,ab=Z-1;ad0.98){Q=0.98/ae;ae=0.98}}else{if(G.width==="auto"){if(ae>0.98){Q=I/(w+I);aa=w+I}else{aa=w/(1-ae)}}else{aa=b.length2em(G.width,ax);for(ad=0,ab=Math.min(an+1,aw.length);ad0.01){if(af&&aa>w){aa=(aa-w)/af;for(ad=0,ab=aq.length;addocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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 b075c3a32..6c0965881 100644 --- a/config/TeX-AMS-MML_HTMLorMML-full.js +++ b/config/TeX-AMS-MML_HTMLorMML-full.js @@ -60,7 +60,7 @@ MathJax.Extension.mml2jax={version:"1.1.2",config:{preview:"alttext"},MMLnamespa (function(c,f,j,e,b){var o="1.1.9";var i=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:o,signal:i};var m=c.Browser.isPC,k=c.Browser.isMSIE;var h=(m?null:"5px");var n=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",closeImg:j.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(m?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":h,"-webkit-border-radius":h,"-moz-border-radius":h,"-khtml-border-radius":h,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(m?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(m?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(k?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(k?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(m?"1em":".7em")},".MathJax_MenuLabel":{padding:(m?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(m?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(m?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(m?"Highlight":"#606872"),color:(m?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var g,d;c.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:o,items:[],posted:false,title:null,margin:5,Init:function(p){this.items=[].slice.call(arguments,0)},With:function(p){if(p){c.Insert(this,p)}return this},Post:function(q,A){if(!q){q=window.event}var w=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var p=document.getElementById("MathJax_MenuFrame");if(!p){p=a.Background(this);delete l.lastItem;delete l.lastMenu;delete a.skipUp;i.Post(["post",a.jax])}var r=f.addElement(p,"div",{onmouseup:a.Mouseup,ondblclick:g,ondragstart:g,onselectstart:g,oncontextmenu:g,menuItem:this,className:"MathJax_Menu"},w);for(var t=0,s=this.items.length;tdocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -68,7 +68,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l span":{"text-align":m+"!important"}})}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("mjx","http://www.w3.org/1998/Math/MathML");document.namespaces.mjx.doImport("#mathplayer")}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,q,p,o){var m=q[5];if(m.img){return this.handleImg(k,j,q,p,o)}if(m.isUnknown&&this.FONTDATA.DELIMITERS[p]){if(o.length){this.addText(k,o)}var l=k.scale;d.createDelimiter(k,p,0,1,j);k.scale=l;q[0]=k.bbox.h*1000;q[1]=k.bbox.d*1000;q[2]=k.bbox.w*1000;q[3]=k.bbox.lw*1000;q[4]=k.bbox.rw*1000;return""}if(m.c==null){if(p<=65535){m.c=String.fromCharCode(p)}else{m.c=this.PLANE1+String.fromCharCode(p-119808+56320)}}if(m.rfix){this.addText(k,m.c);d.createShift(k,m.rfix/1000);return""}if(q[2]||!this.msieAccentBug||o.length){return o+m.c}d.createShift(k,q[3]/1000);d.createShift(k,(q[4]-q[3])/1000);this.addText(k,m.c);d.createShift(k,-q[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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:"\uD835",NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=55296&&v<56319){z++;v=(((v-55296)<<10)+(r.charCodeAt(z)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var l=q-65536;o.c=String.fromCharCode((l>>10)+55296)+String.fromCharCode((l&1023)+56320)}}if(o.rfix){this.addText(k,o.c);d.createShift(k,o.rfix/1000);return""}if(r[2]||!this.msieAccentBug||p.length){return p+o.c}d.createShift(k,r[3]/1000);d.createShift(k,(r[4]-r[3])/1000);this.addText(k,o.c);d.createShift(k,-r[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var G=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aF=G.width.match(/%$/);var av=b.createStack(r);var aC=this.HTMLgetScale(),ax=this.HTMLgetMu(r),ay=-1;var ao=[],ar=[],ai=[],au=[],at=[],ad,ac,an=-1,ab,am,V,aB,aJ=[];var aj=b.FONTDATA.baselineskip*aC*G.useHeight,E=b.FONTDATA.lineH*aC,L=b.FONTDATA.lineD*aC;for(ad=0,ab=this.data.length;adan){an=ac}at[ac]=b.createStack(b.createBox(av));ai[ac]=-b.BIGDIMEN}au[ad][ac]=b.createBox(at[ac]);aJ.push(aB.data[ac-V].toHTML(au[ad][ac]))}}b.MeasureSpans(aJ);for(ad=0,ab=this.data.length;adao[ad]){ao[ad]=au[ad][ac].bbox.h}if(au[ad][ac].bbox.d>ar[ad]){ar[ad]=au[ad][ac].bbox.d}if(au[ad][ac].bbox.w>ai[ac]){ai[ac]=au[ad][ac].bbox.w}}}if(ao[0]+ar[0]){ao[0]=Math.max(ao[0],E)}if(ao[au.length-1]+ar[au.length-1]){ar[au.length-1]=Math.max(ar[au.length-1],L)}var aw=G.columnspacing.split(/ /),aL=G.rowspacing.split(/ /),e=G.columnalign.split(/ /),z=G.rowalign.split(/ /),d=G.columnlines.split(/ /),v=G.rowlines.split(/ /),aH=G.columnwidth.split(/ /),T=[];for(ad=0,ab=aw.length;adau.length){Z=au.length}}ah=0;aO=-(aN+aD)+ao[0];for(ad=0,ab=Z-1;ad0.98){Q=0.98/ae;ae=0.98}}else{if(G.width==="auto"){if(ae>0.98){Q=I/(w+I);aa=w+I}else{aa=w/(1-ae)}}else{aa=b.length2em(G.width,ax);for(ad=0,ab=Math.min(an+1,aw.length);ad0.01){if(af&&aa>w){aa=(aa-w)/af;for(ad=0,ab=aq.length;addocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -65,7 +65,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;ldocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -52,13 +52,13 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,q,p,o){var m=q[5];if(m.img){return this.handleImg(k,j,q,p,o)}if(m.isUnknown&&this.FONTDATA.DELIMITERS[p]){if(o.length){this.addText(k,o)}var l=k.scale;d.createDelimiter(k,p,0,1,j);k.scale=l;q[0]=k.bbox.h*1000;q[1]=k.bbox.d*1000;q[2]=k.bbox.w*1000;q[3]=k.bbox.lw*1000;q[4]=k.bbox.rw*1000;return""}if(m.c==null){if(p<=65535){m.c=String.fromCharCode(p)}else{m.c=this.PLANE1+String.fromCharCode(p-119808+56320)}}if(m.rfix){this.addText(k,m.c);d.createShift(k,m.rfix/1000);return""}if(q[2]||!this.msieAccentBug||o.length){return o+m.c}d.createShift(k,q[3]/1000);d.createShift(k,(q[4]-q[3])/1000);this.addText(k,m.c);d.createShift(k,-q[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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:"\uD835",NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=55296&&v<56319){z++;v=(((v-55296)<<10)+(r.charCodeAt(z)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var l=q-65536;o.c=String.fromCharCode((l>>10)+55296)+String.fromCharCode((l&1023)+56320)}}if(o.rfix){this.addText(k,o.c);d.createShift(k,o.rfix/1000);return""}if(r[2]||!this.msieAccentBug||p.length){return p+o.c}d.createShift(k,r[3]/1000);d.createShift(k,(r[4]-r[3])/1000);this.addText(k,o.c);d.createShift(k,-r[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var G=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aF=G.width.match(/%$/);var av=b.createStack(r);var aC=this.HTMLgetScale(),ax=this.HTMLgetMu(r),ay=-1;var ao=[],ar=[],ai=[],au=[],at=[],ad,ac,an=-1,ab,am,V,aB,aJ=[];var aj=b.FONTDATA.baselineskip*aC*G.useHeight,E=b.FONTDATA.lineH*aC,L=b.FONTDATA.lineD*aC;for(ad=0,ab=this.data.length;adan){an=ac}at[ac]=b.createStack(b.createBox(av));ai[ac]=-b.BIGDIMEN}au[ad][ac]=b.createBox(at[ac]);aJ.push(aB.data[ac-V].toHTML(au[ad][ac]))}}b.MeasureSpans(aJ);for(ad=0,ab=this.data.length;adao[ad]){ao[ad]=au[ad][ac].bbox.h}if(au[ad][ac].bbox.d>ar[ad]){ar[ad]=au[ad][ac].bbox.d}if(au[ad][ac].bbox.w>ai[ac]){ai[ac]=au[ad][ac].bbox.w}}}if(ao[0]+ar[0]){ao[0]=Math.max(ao[0],E)}if(ao[au.length-1]+ar[au.length-1]){ar[au.length-1]=Math.max(ar[au.length-1],L)}var aw=G.columnspacing.split(/ /),aL=G.rowspacing.split(/ /),e=G.columnalign.split(/ /),z=G.rowalign.split(/ /),d=G.columnlines.split(/ /),v=G.rowlines.split(/ /),aH=G.columnwidth.split(/ /),T=[];for(ad=0,ab=aw.length;adau.length){Z=au.length}}ah=0;aO=-(aN+aD)+ao[0];for(ad=0,ab=Z-1;ad0.98){Q=0.98/ae;ae=0.98}}else{if(G.width==="auto"){if(ae>0.98){Q=I/(w+I);aa=w+I}else{aa=w/(1-ae)}}else{aa=b.length2em(G.width,ax);for(ad=0,ab=Math.min(an+1,aw.length);ad0.01){if(af&&aa>w){aa=(aa-w)/af;for(ad=0,ab=aq.length;addocument.body.offsetWidth-this.margin){z=document.body.offsetWidth-r.offsetWidth-this.margin}if(a.isMobile){z=Math.max(5,z-Math.floor(r.offsetWidth/2));v-=20}a.skipUp=q.isContextMenu}else{var u="left",B=A.offsetWidth;z=(a.isMobile?30:B-2);v=0;while(A&&A!==p){z+=A.offsetLeft;v+=A.offsetTop;A=A.parentNode}if(z+r.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){u="right";z=Math.max(this.margin,z-B-r.offsetWidth+6)}if(!m){r.style["borderRadiusTop"+u]=0;r.style["WebkitBorderRadiusTop"+u]=0;r.style["MozBorderRadiusTop"+u]=0;r.style["KhtmlBorderRadiusTop"+u]=0}}r.style.left=z+"px";r.style.top=v+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return g(q)},Remove:function(p,q){i.Post(["unpost",a.jax]);var r=document.getElementById("MathJax_MenuFrame");if(r){r.parentNode.removeChild(r);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return g(p)},Find:function(q){var s=[].slice.call(arguments,1);for(var r=0,p=this.items.length;r=0&&v.parentNode.menuItem!==u[p].menuItem){u[p].menuItem.posted=false;u[p].parentNode.removeChild(u[p]);p--}if(this.Timer&&!a.isMobile){this.Timer(t,v)}}},Mouseout:function(p,q){if(!this.menu||!this.menu.posted){this.Deactivate(q)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(p,q){return this.Remove(p,q)},Touchstart:function(p,q){return this.TouchEvent(p,q,"Mousedown")},Touchend:function(p,q){return this.TouchEvent(p,q,"Mouseup")},TouchEvent:function(q,r,p){if(this!==l.lastItem){if(l.lastMenu){a.Event(q,l.lastMenu,"Mouseout")}a.Event(q,r,"Mouseover",true);l.lastItem=this;l.lastMenu=r}if(this.nativeTouch){return null}a.Event(q,r,p);return false},Remove:function(p,q){q=q.parentNode.menuItem;return q.Remove(p,q)},Activate:function(p){this.Deactivate(p);p.className+=" MathJax_MenuActive"},Deactivate:function(p){p.className=p.className.replace(/ MathJax_MenuActive/,"")},With:function(p){if(p){c.Insert(this,p)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(p,r,q){this.name=p;this.action=r;this.With(q)},Label:function(p,q){return[this.name]},Mouseup:function(p,q){if(!this.disabled){this.Remove(p,q);i.Post(["command",this]);this.action.call(this,p)}return g(p)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(m&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(p,r){this.name=p;var q=1;if(!(r instanceof a.ITEM)){this.With(r),q++}this.menu=a.apply(a,[].slice.call(arguments,q))},Label:function(p,q){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(p,q){if(this.timer){clearTimeout(this.timer)}p={clientX:p.clientX,clientY:p.clientY};this.timer=setTimeout(e(["Mouseup",this,p,q]),n.delay)},Touchend:function(q,s){var r=this.menu.posted;var p=this.SUPER(arguments).Touchend.apply(this,arguments);if(r){this.Deactivate(s);delete l.lastItem;delete l.lastMenu}return p},Mouseup:function(q,s){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(q,s)}else{var r=document.getElementById("MathJax_MenuFrame").childNodes,p=r.length-1;while(p>=0){var t=r[p];t.menuItem.posted=false;t.parentNode.removeChild(t);if(t.menuItem===this.menu){break}p--}}}return g(q)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(m?"\u25CF":"\u2713"),Init:function(q,p,r){this.name=q;this.variable=p;this.With(r);if(this.value==null){this.value=this.name}},Label:function(q,r){var p={className:"MathJax_MenuRadioCheck"};if(n.settings[this.variable]!==this.value){p={style:{display:"none"}}}return[["span",p,[this.marker]]," "+this.name]},Mouseup:function(s,t){if(!this.disabled){var u=t.parentNode.childNodes;for(var q=0,p=u.length;q/g,">");if(a.isMobile){r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("
");r.document.write("");r.document.close()}else{r.document.open();r.document.write("MathJax Equation Source");r.document.write("
"+v+"
");r.document.write("");r.document.close();var t=r.document.body.firstChild;var s=(r.outerHeight-r.innerHeight)||30,q=(r.outerWidth-r.innerWidth)||30;q=Math.min(Math.floor(0.5*screen.width),t.offsetWidth+q+25);s=Math.min(Math.floor(0.5*screen.height),t.offsetHeight+s+25);r.resizeTo(q,s);if(u&&u.screenX!=null){var p=Math.max(0,Math.min(u.screenX-Math.floor(q/2),screen.width-q-20)),z=Math.max(0,Math.min(u.screenY-Math.floor(s/2),screen.height-s-20));r.moveTo(p,z)}}delete a.ShowSource.w};a.Scale=function(){var q=b["HTML-CSS"],p=b.NativeMML;var s=(q?q.config.scale:p.config.scale);var r=prompt("Scale all mathematics (compared to surrounding text) by",s+"%");if(r){if(r.match(/^\s*\d+\s*%?\s*$/)){r=parseInt(r);if(r){if(r!==s){if(q){q.config.scale=r}if(p){p.config.scale=r}a.cookie.scale=r;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){j.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var p=c.outputJax["jax/mml"];if(p[0]!==n.settings.renderer){c.Queue(["setRenderer",c,n.settings.renderer,"jax/mml"],["Rerender",c])}};a.Font=function(){var p=b["HTML-CSS"];if(!p){return}document.location.reload()};c.Browser.Select({MSIE:function(p){var q=(document.compatMode==="BackCompat");var r=p.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(q||!r),msieAboutBug:q});if(document.documentMode>=9){delete n.styles["#MathJax_About"].filter;delete n.styles[".MathJax_Menu"].filter}},Firefox:function(p){a.skipMouseover=p.isMobile&&p.versionAtLeast("6.0");a.skipMousedown=p.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){n.settings=c.config.menuSettings;if(typeof(n.settings.showRenderer)!=="undefined"){n.showRenderer=n.settings.showRenderer}if(typeof(n.settings.showFontMenu)!=="undefined"){n.showFontMenu=n.settings.showFontMenu}if(typeof(n.settings.showContext)!=="undefined"){n.showContext=n.settings.showContext}a.getCookie();a.menu=a(l.SUBMENU("Show Math As",l.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),l.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),l.RULE(),l.SUBMENU("Math Settings",l.SUBMENU("Zoom Trigger",l.RADIO("Hover","zoom",{action:a.Zoom}),l.RADIO("Click","zoom",{action:a.Zoom}),l.RADIO("Double-Click","zoom",{action:a.Zoom}),l.RADIO("No Zoom","zoom",{value:"None"}),l.RULE(),l.LABEL("Trigger Requires:"),l.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),l.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),l.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),l.CHECKBOX("Shift","Shift")),l.SUBMENU("Zoom Factor",l.RADIO("125%","zscale"),l.RADIO("133%","zscale"),l.RADIO("150%","zscale"),l.RADIO("175%","zscale"),l.RADIO("200%","zscale"),l.RADIO("250%","zscale"),l.RADIO("300%","zscale"),l.RADIO("400%","zscale")),l.RULE(),l.SUBMENU("Math Renderer",{hidden:!n.showRenderer},l.RADIO("HTML-CSS","renderer",{action:a.Renderer}),l.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),l.RADIO("SVG","renderer",{action:a.Renderer})),l.SUBMENU("Font Preference",{hidden:!n.showFontMenu},l.LABEL("For HTML-CSS:"),l.RADIO("Auto","font",{action:a.Font}),l.RULE(),l.RADIO("TeX (local)","font",{action:a.Font}),l.RADIO("TeX (web)","font",{action:a.Font}),l.RADIO("TeX (image)","font",{action:a.Font}),l.RULE(),l.RADIO("STIX (local)","font",{action:a.Font})),l.SUBMENU("Contextual Menu",{hidden:!n.showContext},l.RADIO("MathJax","context"),l.RADIO("Browser","context")),l.COMMAND("Scale All Math ...",a.Scale),l.RULE().With({hidden:n.showDiscoverable,name:"discover_rule"}),l.CHECKBOX("Highlight on Hover","discoverable",{hidden:n.showDiscoverable})),l.RULE(),l.COMMAND("About MathJax",a.About),l.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(p){a.cookie.showRenderer=n.showRenderer=p;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!p};a.showFontMenu=function(p){a.cookie.showFontMenu=n.showFontMenu=p;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!p};a.showContext=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!p};a.showDiscoverable=function(p){a.cookie.showContext=n.showContext=p;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!p;a.menu.Find("Math Settings","discover_rule").hidden=!p};if(a.isMobile){(function(){var q=n.settings;var p=a.menu.Find("Math Settings","Zoom Trigger").menu;p.items[0].disabled=p.items[1].disabled=true;if(q.zoom==="Hover"||q.zoom=="Click"){q.zoom="None"}p.items=p.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",j,n.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",j,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax); -MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],PLANE1:"\uD835"});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.3";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.toMathMLattributes();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+""},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){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.toMathMLattribute(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.toMathMLattributes();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.toMathMLattributes();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(d){var c=this.toMathMLattributes();return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(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"); @@ -50,7 +50,7 @@ MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error("Erroneous nesting of equation structures")}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.4",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},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}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:true,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(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,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:true,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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}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(d){if(d%2===1){return true}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:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}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:true,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:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); diff --git a/jax/input/TeX/jax.js b/jax/input/TeX/jax.js index c8ec213ea..587ffc696 100644 --- a/jax/input/TeX/jax.js +++ b/jax/input/TeX/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(d,c,i){var h,g="\u00A0";var e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true,variantForm:d.isSTIX}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(od.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){if(c.Browser.isKonqueror){l=l.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,q,p,o){var m=q[5];if(m.img){return this.handleImg(k,j,q,p,o)}if(m.isUnknown&&this.FONTDATA.DELIMITERS[p]){if(o.length){this.addText(k,o)}var l=k.scale;d.createDelimiter(k,p,0,1,j);k.scale=l;q[0]=k.bbox.h*1000;q[1]=k.bbox.d*1000;q[2]=k.bbox.w*1000;q[3]=k.bbox.lw*1000;q[4]=k.bbox.rw*1000;return""}if(m.c==null){if(p<=65535){m.c=String.fromCharCode(p)}else{m.c=this.PLANE1+String.fromCharCode(p-119808+56320)}}if(m.rfix){this.addText(k,m.c);d.createShift(k,m.rfix/1000);return""}if(q[2]||!this.msieAccentBug||o.length){return o+m.c}d.createShift(k,q[3]/1000);d.createShift(k,(q[4]-q[3])/1000);this.addText(k,m.c);d.createShift(k,-q[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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:"\uD835",NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*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",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,"white-space":"nowrap",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(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-q[p][1].offsetLeft}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p=0){n.style.width=this.Em(j);n.style.display="inline-block";n.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){n.style.height=""}n.style.marginLeft=this.Em(j);if(d.safariNegativeSpaceBug&&n.parentNode.firstChild==n){this.createBlank(n,0,true)}}if(k&&k!==f.COLOR.TRANSPARENT){n.style.backgroundColor=k;n.style.position="relative"}return n},createRule:function(q,m,o,r,k){var l=d.TeX.min_rule_thickness,n=1;if(r>0&&r*this.em0&&(m+o)*this.em0&&p.offsetWidth==0){p.style.width=this.Em(r)}if(q.isBox||q.className=="mspace"){q.bbox=p.bbox,q.HH=m+o}return p},createFrame:function(r,p,q,s,v,k){var o=(this.msieBorderWidthBug?0:2*v);var u=this.Em(p+q-o),j=this.Em(-q-v),n=this.Em(s-o);var l=this.Em(v)+" "+k;var m=this.addElement(r,"span",{style:{border:l,display:"inline-block",overflow:"hidden",width:n,height:u},bbox:{h:p,d:q,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:p+q,isMathJax:true});if(j){m.style.verticalAlign=j}return m},createStack:function(l,n,k){if(this.msiePaddingWidthBug){this.createStrut(l,0)}var m=String(k).match(/%$/);var j=(!m&&k!=null?k:0);l=this.addElement(l,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(m?"100%":this.Em(j)),height:0}});if(!n){l.parentNode.bbox=l.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:j,lw:this.BIGDIMEN,rw:(!m&&k!=null?k:-this.BIGDIMEN)};if(m){l.bbox.width=k}}return l},createBox:function(k,j){var l=this.addElement(k,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(j!=null){l.style.width=j}return l},addBox:function(j,k){k.style.position="absolute";k.isBox=true;return j.appendChild(k)},placeBox:function(s,q,p,n){s.isMathJax=true;var u=s.parentNode,B=s.bbox,w=u.bbox;if(this.msiePlaceBoxBug){this.addText(s,this.NBSP)}if(this.imgSpaceBug){this.addText(s,this.imgSpace)}var v,E=0;if(s.HH!=null){v=s.HH}else{if(B){v=Math.max(3,B.h+B.d)}else{v=s.offsetHeight/this.em}}if(!s.noAdjust){v+=1;if(this.msieInlineBlockAlignBug){this.addElement(s,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(v)}})}else{this.addElement(s,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(v)}})}}s.style.top=this.Em(-p-v);s.style.left=this.Em(q+E);if(B){if(this.initialSkipBug){if(B.lw<0){E=B.lw;d.createBlank(s,-E,true);m=0}if(B.rw>B.w){d.createBlank(s,B.rw-B.w+0.1)}}if(!this.msieClipRectBug&&!B.noclip&&!n){var A=3/this.em;var z=(B.H==null?B.h:B.H),k=(B.D==null?B.d:B.D);var C=v-z-A,o=v+k+A,m=B.lw-3*A,j=1000;if(B.isFixed){j=B.width-m}s.style.clip="rect("+this.Em(C)+" "+this.Em(j)+" "+this.Em(o)+" "+this.Em(m)+")"}}if(B&&w){if(B.H!=null&&(w.H==null||B.H+p>w.H)){w.H=B.H+p}if(B.D!=null&&(w.D==null||B.D-p>w.D)){w.D=B.D-p}if(B.h+p>w.h){w.h=B.h+p}if(B.d-p>w.d){w.d=B.d-p}if(w.H!=null&&w.H<=w.h){delete w.H}if(w.D!=null&&w.D<=w.d){delete w.D}if(B.w+q>w.w){w.w=B.w+q;if(w.width==null){u.style.width=this.Em(w.w)}}if(B.rw+q>w.rw){w.rw=B.rw+q}if(B.lw+q=l-0.01||(r==o-1&&!k.stretch)){if(k.HW[r][2]){p*=k.HW[r][2]}if(k.HW[r][3]){j=k.HW[r][3]}var q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var r=(w/(w+1))*(B-j);j=B-r;q+=r+j-l.bbox.h;while(x-->0){while(w-->0){if(!this.msieCloneNodeBug){o=l.cloneNode(true)}else{o=this.Element("span");this.createChar(o,D.ext,E,v)}q-=j;this.placeBox(this.addBox(m,o),0,q,true)}q+=r-l.bbox.d;if(D.mid&&x){this.placeBox(C,0,q-C.bbox.h,true);w=p;q+=-(C.bbox.h+C.bbox.d)+r+j-l.bbox.h}}}else{q+=(A-s)/2;if(D.mid){this.placeBox(C,0,q-C.bbox.h,true);q+=-(C.bbox.h+C.bbox.d)}q+=(A-s)/2}this.placeBox(t,0,q-t.bbox.h,true);q-=t.bbox.h+t.bbox.d;z.bbox={w:Math.max(u.bbox.w,l.bbox.w,t.bbox.w,C.bbox.w),lw:Math.min(u.bbox.lw,l.bbox.lw,t.bbox.lw,C.bbox.lw),rw:Math.max(u.bbox.rw,l.bbox.rw,t.bbox.rw,C.bbox.rw),h:0,d:-q,exactW:true};z.scale=E;z.offset=0.55*z.bbox.w;z.isMultiChar=true;this.setStackWidth(m,z.bbox.w)},extendDelimiterH:function(A,m,D,F,v){var q=this.createStack(A,true);var o=this.createBox(q),B=this.createBox(q);this.createChar(o,(D.left||D.rep),F,v);this.createChar(B,(D.right||D.rep),F,v);var j=this.Element("span");this.createChar(j,D.rep,F,v);var C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var p=0,k=o[0].length;p=55296&&v<56319){z++;v=(((v-55296)<<10)+(r.charCodeAt(z)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(v,o);v=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&v<=u[t].high){if(u[t].remap&&u[t].remap[v]){v=p+u[t].remap[v]}else{v=v-u[t].low+p;if(u[t].add){v+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[v]){if(o.remap[v] instanceof Array){var l=o.remap[v];v=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{v=o.remap[v];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}if(this.FONTDATA.REMAP[v]&&!o.noRemap){v=this.FONTDATA.REMAP[v]}s=this.lookupChar(o,v);B=s[v];if(o!==A&&!B[5].img){if(x.length){this.addText(j,x);x=""}j=y;A=k;if(o!==A){if(A){j=this.addElement(y,"span",{isMathJax:true})}else{k=o}}this.handleFont(j,s,j!==y);A=o}x=this.handleChar(j,s,B,v,x);if(B[0]/1000>y.bbox.h){y.bbox.h=B[0]/1000}if(B[1]/1000>y.bbox.d){y.bbox.d=B[1]/1000}if(y.bbox.w+B[3]/1000y.bbox.rw){y.bbox.rw=y.bbox.w+B[4]/1000}y.bbox.w+=B[2]/1000}if(x.length){this.addText(j,x)}if(y.scale&&y.scale!==1){y.bbox.h*=y.scale;y.bbox.d*=y.scale;y.bbox.w*=y.scale;y.bbox.lw*=y.scale;y.bbox.rw*=y.scale}if(r.length==1&&s.skew&&s.skew[v]){y.bbox.skew=s.skew[v]}},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var l=q-65536;o.c=String.fromCharCode((l>>10)+55296)+String.fromCharCode((l&1023)+56320)}}if(o.rfix){this.addText(k,o.c);d.createShift(k,o.rfix/1000);return""}if(r[2]||!this.msieAccentBug||p.length){return p+o.c}d.createShift(k,r[3]/1000);d.createShift(k,(r[4]-r[3])/1000);this.addText(k,o.c);d.createShift(k,-r[4]/1000);return""},handleImg:function(k,j,o,m,l){return l},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){var j=MathJax.Callback.Queue();j.Push(["Require",g,this.fontDir+"/"+k]);if(this.imgFonts){if(!MathJax.isPacked){k=k.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}j.Push(["Require",g,this.webfontDir+"/png/"+k])}b.RestartAfter(j.Push({}))},loadWebFont:function(j){j.available=j.isWebFont=true;if(d.FontFaceBug){j.family=j.name;if(d.msieFontCSSBug){j.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(j))},loadWebFontError:function(k,j){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");k.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);g.Require(this.directory+"/imageFonts.js",j)}else{this.allowWebFonts=false;j()}},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},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.type!="mrow"){n=this.HTMLhandleSize(n)}for(var k=0,j=this.data.length;kk.d){k.d=l.d}if(l.h>k.h){k.h=l.h}if(l.D!=null&&l.D>k.D){k.D=l.D}if(l.H!=null&&l.H>k.H){k.H=l.H}if(m.style.paddingLeft){k.w+=parseFloat(m.style.paddingLeft)*(m.scale||1)}if(k.w+l.lwk.rw){k.rw=k.w+l.rw}k.w+=l.w;if(m.style.paddingRight){k.w+=parseFloat(m.style.paddingRight)*(m.scale||1)}if(l.width){k.width=l.width}if(l.ic){k.ic=l.ic}else{delete k.ic}if(k.exactW&&!l.exactW){delete k.exactW}},HTMLemptyBBox:function(j){j.h=j.d=j.H=j.D=j.rw=-d.BIGDIMEN;j.w=0;j.lw=d.BIGDIMEN;return j},HTMLcleanBBox:function(j){if(j.h===this.BIGDIMEN){j.h=j.d=j.H=j.D=j.w=j.rw=j.lw=0}if(j.D<=j.d){delete j.D}if(j.H<=j.h){delete j.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(j){if(this.isEmbellished()){return this.Core().HTMLcanStretch(j)}return false},HTMLstretchH:function(k,j){return this.HTMLspanElement()},HTMLstretchV:function(k,j,l){return this.HTMLspanElement()},HTMLnotEmpty:function(j){while(j){if((j.type!=="mrow"&&j.type!=="texatom")||j.data.length>1){return true}j=j.data[0]}return false},HTMLmeasureChild:function(k,j){if(this.data[k]){d.Measured(this.data[k].toHTML(j),j)}else{j.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(k,j){if(this.data[k]){return this.data[k].toHTML(j)}return null},HTMLcreateSpan:function(j){if(this.spanID){var k=this.HTMLspanElement();if(k){while(k.firstChild){k.removeChild(k.firstChild)}k.bbox={w:0,h:0,d:0,lw:0,rw:0};k.scale=1;k.isMultChar=null;k.style.cssText="";return k}}if(this.href){j=d.addElement(j,"a",{href:this.href,isMathJax:true})}j=d.addElement(j,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){j.style.display="inline-block"}if(this["class"]!=null){j.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}j.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;j.bbox={w:0,h:0,d:0,lw:0,rw:0};this.styles={};if(this.style){j.style.cssText=this.style;if(j.style.fontSize){this.mathsize=j.style.fontSize;j.style.fontSize=""}this.styles={border:d.getBorders(j),padding:d.getPadding(j)};if(this.styles.border){j.style.border=""}if(this.styles.padding){j.style.padding=""}}if(this.href){j.parentNode.bbox=j.bbox}return j},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(k,j,l){d.handleVariant(k,j,l)},HTMLhandleSize:function(j){if(!j.scale){j.scale=this.HTMLgetScale();if(j.scale!==1){j.style.fontSize=d.Percent(j.scale)}}return j},HTMLhandleColor:function(u){var w=this.getValues("mathcolor","color");if(this.mathbackground){w.mathbackground=this.mathbackground}if(this.background){w.background=this.background}if(this.style&&u.style.backgroundColor){w.mathbackground=u.style.backgroundColor;u.style.backgroundColor="transparent"}var r=(this.styles||{}).border,t=(this.styles||{}).padding;if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.background&&!this.mathbackground){w.mathbackground=w.background}if(w.mathcolor){u.style.color=w.mathcolor}if((w.mathbackground&&w.mathbackground!==f.COLOR.TRANSPARENT)||r||t){var x=(u.bbox.exact?0:1/d.em),s=0,q=0,k=u.style.paddingLeft,o=u.style.paddingRight;if(this.isToken){s=u.bbox.lw;q=u.bbox.rw-u.bbox.w}if(k!==""){s+=parseFloat(k)*(u.scale||1)}if(o!==""){q-=parseFloat(o)*(u.scale||1)}var m=Math.max(0,d.getW(u)+(d.PaddingWidthBug||u.bbox.keepPadding?0:q-s));var v=u.bbox.h+u.bbox.d,j=-u.bbox.d,p=0,n=0;if(m>0){m+=2*x;s-=x}if(v>0){v+=2*x;j-=x}q=-m-s;if(r){q-=r.right;j-=r.bottom;p+=r.left;n+=r.right;u.bbox.h+=r.top;u.bbox.d+=r.bottom;u.bbox.w+=r.left+r.right;u.bbox.lw-=r.left;u.bbox.rw+=r.right}if(t){v+=t.top+t.bottom;m+=t.left+t.right;q-=t.right;j-=t.bottom;p+=t.left;n+=t.right;u.bbox.h+=t.top;u.bbox.d+=t.bottom;u.bbox.w+=t.left+t.right;u.bbox.lw-=t.left;u.bbox.rw+=t.right}if(n){u.style.paddingRight=d.Em(n)}var l=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:w.mathbackground,width:d.Em(m),height:d.Em(v),verticalAlign:d.Em(j),marginLeft:d.Em(s),marginRight:d.Em(q)}});d.setBorders(l,r);if(u.bbox.width){l.style.width=u.bbox.width;l.style.marginRight="-"+u.bbox.width}if(d.msieInlineBlockAlignBug){l.style.position="relative";l.style.width=l.style.height=0;l.style.verticalAlign=l.style.marginLeft=l.style.marginRight="";l.style.border=l.style.padding="";if(r&&d.msieBorderWidthBug){v+=r.top+r.bottom;m+=r.left+r.right}l.style.width=d.Em(p+x);d.placeBox(d.addElement(l,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(w.mathbackground||"transparent"),width:d.Em(m),height:d.Em(v)}}),s,u.bbox.h+x);d.setBorders(l.firstChild,r)}u.parentNode.insertBefore(l,u);if(d.msieColorPositionBug){u.style.position="relative"}return l}return null},HTMLremoveColor:function(){var j=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(j){j.parentNode.removeChild(j)}},HTMLhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var l=this.getValues("scriptlevel","lspace","rspace");if(l.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var k=this.HTMLgetMu(n);l.lspace=Math.max(0,d.length2em(l.lspace,k));l.rspace=Math.max(0,d.length2em(l.rspace,k));var j=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===j){j=m;m=m.Parent();n=j.HTMLspanElement()}if(l.lspace){n.style.paddingLeft=d.Em(l.lspace)}if(l.rspace){n.style.paddingRight=d.Em(l.rspace)}}}else{var o=this.texSpacing();if(o!==""){o=d.length2em(o,this.HTMLgetScale())/(n.scale||1);if(n.style.paddingLeft){o+=parseFloat(n.style.paddingLeft)}n.style.paddingLeft=d.Em(o)}}},HTMLgetScale:function(){var l=1,j=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var k=this.HTMLspanElement();if(k.style.fontSize!=""){j.fontsize=k.style.fontSize}}if(j.fontsize&&!this.mathsize){j.mathsize=j.fontsize}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),j.scriptlevel);j.scriptminsize=d.length2em(this.Get("scriptminsize"));if(l2){k.scriptlevel=2}j=Math.sqrt(Math.pow(k.scriptsizemultiplier,k.scriptlevel))}return j},HTMLgetVariant:function(){var j=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var l=this.HTMLspanElement();if(l.style.fontFamily){j.fontfamily=l.style.fontFamily}if(l.style.fontWeight){j.fontweight=l.style.fontWeight}if(l.style.fontStyle){j.fontStyle=l.style.fontStyle}}var k=j.mathvariant;if(this.variantForm){k="-"+d.fontInUse+"-variant"}if(j.fontfamily&&!this.mathvariant){if(!j.fontweight&&j.mathvariant.match(/bold/)){j.fontweight="bold"}if(!j.fontstyle&&j.mathvariant.match(/italic/)){j.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:j.fontfamily,style:j.fontstyle,weight:j.fontweight}}}if(!this.mathvariant){if(j.fontweight==="bold"){k={normal:f.VARIANT.BOLD,italic:f.VARIANT.BOLDITALIC,fraktur:f.VARIANT.BOLDFRAKTUR,script:f.VARIANT.BOLDSCRIPT,"sans-serif":f.VARIANT.BOLDSANSSERIF,"sans-serif-italic":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontweight==="normal"){k={bold:f.VARIANT.normal,"bold-italic":f.VARIANT.ITALIC,"bold-fraktur":f.VARIANT.FRAKTUR,"bold-script":f.VARIANT.SCRIPT,"bold-sans-serif":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.SANSSERIFITALIC}[k]||k}}if(j.fontstyle==="italic"){k={normal:f.VARIANT.ITALIC,bold:f.VARIANT.BOLDITALIC,"sans-serif":f.VARIANT.SANSSERIFITALIC,"bold-sans-serif":f.VARIANT.SANSSERIFBOLDITALIC}[k]||k}else{if(j.fontstyle==="normal"){k={italic:f.VARIANT.NORMAL,"bold-italic":f.VARIANT.BOLD,"sans-serif-italic":f.VARIANT.SANSSERIF,"sans-serif-bold-italic":f.VARIANT.BOLDSANSSERIF}[k]||k}}}return d.FONTDATA.VARIANT[k]}},{HTMLautoload:function(){var j=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(g.Require(j))},HTMLautoloadFile:function(j){var k=d.autoloadDir+"/"+j+".js";b.RestartAfter(g.Require(k))},HTMLstretchH:function(k,j){this.HTMLremoveColor();return this.toHTML(k,j)},HTMLstretchV:function(k,j,l){this.HTMLremoveColor();return this.toHTML(k,j,l)}});f.chars.Augment({toHTML:function(l,k){var o=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.entity.Augment({toHTML:function(l,k){var o=this.toString().replace(/[\u2061-\u2064]/g,"");if(!k){var n=Math.floor(100/d.scale+0.5)+"%";d.addElement(l,"span",{style:{"font-size":n}},[o]);var m=d.getHD(l),j=d.getW(l);l.bbox={h:m.h,d:m.d,w:j,lw:0,rw:j,exactW:true}}else{this.HTMLhandleVariant(l,k,o)}}});f.mi.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.w&&p.length===1&&!l.noIC){o.ic=o.rw-o.w;d.createBlank(n,o.ic);o.w=o.rw}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.mn.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));n.bbox=null;var l=this.HTMLgetVariant();for(var k=0,j=this.data.length;ko.bbox.w){o.bbox.ic=o.bbox.rw-o.bbox.w;d.createBlank(o,o.bbox.ic);o.bbox.w=o.bbox.rw}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcanStretch:function(j){if(!this.Get("stretchy")){return false}var k=this.data.join("");if(k.length>1){return false}k=d.FONTDATA.DELIMITERS[k.charCodeAt(0)];return(k&&k.dir==j.substr(0,1))},HTMLstretchV:function(l,m,n){this.HTMLremoveColor();var q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if(l.fontweight==="bold"&&!this.mathvariant){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;kd.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(l,j){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchH(k,j);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();var j=this.HTMLspanElement();this.data[this.core].HTMLstretchV(j,k,m);this.HTMLcomputeBBox(j,true);this.HTMLhandleColor(j);return j}});f.mstyle.Augment({toHTML:function(k,j,l){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){var m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(yw){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||nJ){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;LJ){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.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}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:k,msieDisappearingBug:(n>=8),msieMarginScaleBug:(n<8),msiePaddingWidthBug:true,msieBorderWidthBug:k,msieInlineBlockAlignBug:(!l||k),msiePlaceBoxBug:(l&&!k),msieClipRectBug:!l,msieNegativeSpaceBug:k,msieCloneNodeBug:(l&&j.version==="8.0"),initialSkipBug:(n<8),msieNegativeBBoxBug:(n>=8),msieIE6:!m,msieItalicWidthBug:true,zeroWidthBug:(n<8),FontFaceBug:true,msieFontCSSBug:j.isIE9,allowWebFonts:"eot"})},Firefox:function(k){var l=false;if(k.versionAtLeast("3.5")){var j=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,j.length)===j){l="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:l})},Safari:function(n){var l=n.versionAtLeast("3.0");var k=n.versionAtLeast("3.1");var j=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var o=(k&&n.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!n.versionAtLeast("5.0"))||(j!=null&&(j[1]<2||(j[1]==2&&j[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!k,safariTextNodeBug:!l,safariWebFontSerif:["serif"],forceReflow:true,allowWebFonts:(k&&!o?"otf":false)});if(n.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts})}if(o){var m=b.config["HTML-CSS"];if(m){m.availableFonts=[];m.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(j){d.Augment({rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(j.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(j){j.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:j.versionAtLeast("10.61"),initialSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(j.versionAtLeast("10.0")&&!j.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(j){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); diff --git a/jax/output/SVG/jax.js b/jax/output/SVG/jax.js index af232e59f..c78feaf1a 100644 --- a/jax/output/SVG/jax.js +++ b/jax/output/SVG/jax.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -(function(h,c,e,a){var g;var b="http://www.w3.org/2000/svg";var j="http://www.w3.org/1999/xlink";a.Augment({config:{styles:{".MathJax_SVG":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_SVG_Display":{position:"relative",display:"block",width:"100%"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,Config:function(){var k=c.config.menuSettings;if(k.scale){this.config.scale=k.scale}this.SUPER(arguments).Config.apply(this,arguments);this.fontInUse=this.config.font;this.fontDir+="/"+this.config.font;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){EVENT=MathJax.Extension.MathEvents.Event;TOUCH=MathJax.Extension.MathEvents.Touch;HOVER=MathJax.Extension.MathEvents.Hover;this.ContextMenu=EVENT.ContextMenu;this.Mousedown=EVENT.AltContextMenu;this.Mouseover=HOVER.Mouseover;this.Mouseout=HOVER.Mouseout;this.Mousemove=HOVER.Mousemove;this.hiddenDiv=e.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=e.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var k=e.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.textSVG=this.Element("svg");d=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});f={};this.ExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_SVG_ExBox"}]]);this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"auto",size:1,padding:0,border:0,margin:0}}]]);return h.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){document.body.appendChild(this.ExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.ExSpan.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.ExSpan)},preTranslate:function(o){var t=o.jax[this.id],u,r=t.length,z,s,A,n,y,l,x,q,k,w=false,v,B=this.config.linebreaks.automatic,p=this.config.linebreaks.width;if(B){w=(p.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(w){p=p.replace(/\s*container\s*/,"")}else{k=this.defaultWidth}if(p===""){p="100%"}}else{k=100000}for(u=0;u=p.SVGlast+p.SVGchunk){this.postTranslate(p);p.SVGchunk=Math.floor(p.SVGchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var l=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.SVGlast,k=q.SVGeqn;o=k[l].low&&o<=k[l].high){if(k[l].remap&&k[l].remap[o]){o=v+k[l].remap[o]}else{o=o-k[l].low+v;if(k[l].add){o+=k[l].add}}if(s["variant"+k[l].offset]){s=this.FONTDATA.VARIANT[s["variant"+k[l].offset]]}break}}}if(s.remap&&s.remap[o]){if(s.remap[o] instanceof Array){var A=s.remap[o];o=A[0];s=this.FONTDATA.VARIANT[A[1]]}else{o=s.remap[o];if(s.remap.variant){s=this.FONTDATA.VARIANT[s.remap.variant]}}}if(this.FONTDATA.REMAP[o]&&!s.noRemap){o=this.FONTDATA.REMAP[o]}p=this.lookupChar(s,o);y=p[o];if(y){y=[r,p.id+"-"+o.toString(16).toUpperCase()].concat(y);u.Add(i.GLYPH.apply(i,y),u.w,0)}else{if(this.FONTDATA.DELIMITERS[o]){u.Add(this.createDelimiter(o,0,1,p),u.w,0)}else{B=i.TEXT(r,String.fromCharCode(o),{"font-family":s.defaultFamily||a.config.MISSINGFONT,"font-style":(s.italic?"italic":""),"font-weight":(s.bold?"bold":"")});if(s.h!=null){B.h=s.h}if(s.d!=null){B.d=s.d}y=i.G();y.Add(B);u.Add(y,u.w,0);B="";c.signal.Post(["SVG Jax - unknown char",o,s])}}}if(B.length==1&&p.skew&&p.skew[o]){u.skew=p.skew[o]*1000}if(u.element.childNodes.length===1){u.element=u.element.firstChild;u.removeable=false;u.scale=r}return u},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){c.RestartAfter(h.Require(this.fontDir+"/"+k))},createDelimiter:function(k,n,q,o){if(!q){q=1}var s=i.G();if(!k){s.Clean();delete s.element;s.w=s.r=this.TeX.nulldelimiterspace*q;return s}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){c.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var r=0,p=l.HW.length;r=n-10||(r==p-1&&!l.stretch)){if(l.HW[r][2]){q*=l.HW[r][2]}if(l.HW[r][3]){k=l.HW[r][3]}return this.createChar(q,[k,l.HW[r][1]],o).With({stretched:true})}}if(l.stretch){this["extendDelimiter"+l.dir](s,t,l.stretch,q,o)}return s},createChar:function(s,q,n){var r="",p={fonts:[q[1]],noRemap:true};if(n&&n===g.VARIANT.BOLD){p.fonts=[q[1]+"-bold",q[1]]}if(typeof(q[1])!=="string"){p=q[1]}if(q[0] instanceof Array){for(var o=0,k=q[0].length;oq){var l=this.createChar(o,m.ext,n);var p=(m.mid?2:1),v=(A-q)/p,B=(v+100)/(l.h+l.d);while(p-->0){var t=a.Element("g",{transform:"translate(0,"+(w-B*l.h+50)+") scale(1,"+B+")"});t.appendChild(l.element.cloneNode(false));r.element.appendChild(t);w-=v;if(m.mid&&p){r.Add(z,0,w-z.h);w-=(z.h+z.d)}}}else{if(m.mid){w+=(q-A)/2;r.Add(z,0,w-z.h);w+=-(z.h+z.d)+(q-A)/2}else{w+=(q-A)}}r.Add(u,0,w-u.h);r.Clean();r.scale=o;r.isMultiChar=true},extendDelimiterH:function(t,o,m,q,n){var p=this.createChar(q,(m.left||m.rep),n);var C=this.createChar(q,(m.right||m.rep),n);t.Add(p,-p.l,0);var B=(p.r-p.l)+(C.r-C.l),z=p.r-p.l;if(m.mid){var A=this.createChar(q,m.mid,n);B+=A.w}if(o>B){var y=this.createChar(q,m.rep,n),l=m.fuzz||0;var r=(m.mid?2:1),v=(o-B)/r,E=(v+l)/(y.r-y.l);while(r-->0){var u=a.Element("g",{transform:"translate("+(z-l/2-E*y.l)+",0) scale("+E+",1)"});u.appendChild(y.element.cloneNode(false));t.element.appendChild(u);z+=v;if(m.mid&&r){t.Add(A,z,0);z+=A.w}}}else{if(m.mid){var D=Math.min(B-o,p.w/2);z-=D/2;t.Add(A,z,0);z+=A.w-D/2}else{z-=(B-o)}}t.Add(C,z-C.l,0);t.Clean();t.scale=q;t.isMultiChar=true},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:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:100,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,PLANE1:"\uD835",NBSP:"\u00A0"});var i=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(k){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,k)}},With:function(k){return c.Insert(this,k)},Add:function(n,m,l,p,o){if(m){n.x+=m}if(l){n.y+=l}if(n.element){if(n.removeable&&n.element.childNodes.length===1&&n.n===1){var r=n.element.firstChild;if(r.nodeName==="use"||r.nodeName==="rect"){n.element=r;n.scale=n.childScale;var k=parseFloat(n.element.getAttribute("x")||"0")*n.scale,q=parseFloat(n.element.getAttribute("y")||"0")*n.scale;n.x+=k;n.y+=q;n.h+=q;n.d+=q;n.H+=q;n.D+=q;n.w-=k;n.r-=k;n.l+=k;n.removeable=false}}if(Math.abs(n.x)<1&&Math.abs(n.y)<1){n.remove=n.removeable}else{if(n.element.nodeName==="g"){if(!n.element.firstChild){n.remove=n.removeable}else{n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}}else{if(n.element.nodeName==="line"||n.element.nodeName==="polygon"||n.element.nodeName==="path"||n.element.nodeName==="a"){n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}else{n.element.setAttribute("x",Math.floor(n.x/n.scale));n.element.setAttribute("y",Math.floor(n.y/n.scale))}}}if(n.remove){this.n+=n.n;while(n.element.firstChild){if(o&&this.element.firstChild){this.element.insertBefore(n.element.firstChild,this.element.firstChild)}else{this.element.appendChild(n.element.firstChild)}}}else{if(o){this.element.insertBefore(n.element,this.element.firstChild)}else{this.element.appendChild(n.element)}}delete n.element}if(n.d-n.y>this.d){this.d=n.d-n.y;if(this.d>this.D){this.D=this.d}}if(n.y+n.h>this.h){this.h=n.y+n.h;if(this.h>this.H){this.H=this.h}}if(n.D-n.y>this.D){this.D=n.D-n.y}if(n.y+n.H>this.H){this.H=n.y+n.H}if(n.x+n.lthis.r){this.r=n.x+n.r}if(p||n.x+n.w+(n.X||0)>this.w){this.w=n.x+n.w+(n.X||0)}this.childScale=n.scale;this.n++;return n},Align:function(m,n,l,k){l=({left:l,center:(this.w-m.w)/2,right:this.w-m.w-l})[n]||0;this.Add(m,l,k)},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});i.ROW=i.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(l){var k=l.toSVG();this.svg.push(k);if(l.SVGcanStretch("Vertical")){k.mml=l}if(k.h>this.sh){this.sh=k.h}if(k.d>this.sd){this.sd=k.d}},Stretch:function(){for(var n=0,k=this.svg.length;nl.w&&p.length===1&&!o.noIC){l.ic=l.r-l.w;l.w=l.r}this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGdataStretched:function(l,k,m){this.SVGdata={HW:k,D:m};if(m!=null){return this.data[l].SVGstretchV(k,m)}if(k!=null){return this.data[l].SVGstretchH(k)}return this.data[l].toSVG()},SVGsaveData:function(l){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=l.w,this.SVGdata.x=l.x;if(l.X!=null){this.SVGdata.X=l.X}if(this["class"]){l.removeable=false;a.Element(l.element,{"class":this["class"]})}if(this.id){l.removeable=false;a.Element(l.element,{id:this.id})}if(this.href){var k=a.Element("a");k.setAttributeNS(j,"href",this.href);a.addElement(k,"rect",{width:l.w,height:l.h+l.d,y:-l.d,fill:"none",stroke:"none","pointer-events":"all"});if(l.type==="svg"){var n=l.element.firstChild;while(n.firstChild){k.appendChild(n.firstChild)}n.appendChild(k)}else{if(l.removeable&&l.element.nodeName==="g"){while(l.element.firstChild){k.appendChild(l.element.firstChild)}}else{k.appendChild(l.element)}l.element=k}l.removeable=false}if(a.config.addMMLclasses){l.removeable=false;l.element.setAttribute("className","mjx-svg-"+this.type)}var m=this.Get("style");if(m){l.element.style.cssText=m;l.element.style.border=l.element.style.padding="";if(l.removeable){l.removeable=l.element.style.cssText===""}}},SVGgetStyles:function(){var l=this.Get("style");if(l){var k=e.Element("span");k.style.cssText=l;this.styles={border:a.getBorders(k),padding:a.getPadding(k)};if(k.style.fontSize){this.styles.fontSize=k.style.fontSize}if(k.style.color){this.styles.color=k.style.color}if(k.style.backgroundColor){this.styles.background=k.style.backgroundColor}if(k.style.fontStyle){this.styles.fontStyle=k.style.fontStyle}if(k.style.fontWeight){this.styles.fontWeight=k.style.fontWeight}if(k.style.fontFamily){this.styles.fontFamily=k.style.fontFamily}}},SVGhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.SVGgetMu(n);m.lspace=Math.max(0,a.length2em(m.lspace,l));m.rspace=Math.max(0,a.length2em(m.rspace,l));var k=this,o=this.Parent();while(o&&o.isEmbellished()&&o.Core()===k){k=o;o=o.Parent()}if(m.lspace){n.x+=m.lspace}if(m.rspace){n.X=m.rspace}}}else{var p=this.texSpacing();if(p!==""){n.x+=a.length2em(p,this.SVGgetScale())/n.scale}}},SVGhandleColor:function(o){var w=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!w.color){w.color=this.styles.color}if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.mathcolor){a.Element(o.element,{fill:w.mathcolor,stroke:w.mathcolor});o.removeable=false}var s=(this.styles||{}).border,u=(this.styles||{}).padding,t=((s||{}).left||0),q=((u||{}).left||0),k;w.background=(this.mathbackground||this.background||(this.styles||{}).background||g.COLOR.TRANSPARENT);if(t+q){var l=i();for(k in o){if(o.hasOwnProperty(k)){l[k]=o[k]}}l.x=0;l.y=0;o.element=a.Element("g");o.removeable=true;o.Add(l,t+q,0)}if(u){o.w+=u.right;o.h+=u.top;o.d+=u.bottom}if(s){o.w+=s.right;o.h+=s.top;o.d+=s.bottom}if(w.background!==g.COLOR.TRANSPARENT){if(o.element.nodeName!=="g"&&o.element.nodeName!=="svg"){var p=a.Element("g");p.appendChild(o.element);o.element=p;o.removable=true}o.Add(i.RECT(o.h,o.d,o.w,{fill:w.background}),0,0,false,true)}if(s){var v=5;var m={left:["V",o.h+o.d,-v,-o.d],right:["V",o.h+o.d,o.w-s.right+v,-o.d],top:["H",o.w,0,o.h-s.top+v],bottom:["H",o.w,0,-o.d-v]};for(k in m){if(m.hasOwnProperty(k)){if(s[k]){var r=m[k],n=i[r[0]+"LINE"];o.Add(n(r[1],s[k],s[k+"Style"],s[k+"Color"]),r[2],r[3])}}}}},SVGhandleVariant:function(k,m,l){return a.HandleVariant(k,m,l)},SVGgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var l=k.mathvariant;if(this.variantForm){l="-TeX-variant"}if(this.styles){if(!k.fontstyle&&this.styles.fontStyle){k.fontstyle=this.styles.fontStyle}if(!k.fontweight&&this.styles.fontWeight){k.fontweight=this.styles.fontWeight}if(!k.fontfamily&&this.styles.fontFamily){k.fontfamily=this.styles.fontFamily}}if(k.fontfamily&&!this.mathvariant){if(!k.fontweight&&k.mathvariant.match(/bold/)){k.fontweight="bold"}if(!k.fontstyle&&k.mathvariant.match(/italic/)){k.fontstyle="italic"}l={forceFamily:true,font:{"font-family":k.fontfamily}};if(k.fontstyle){l.font["font-style"]=k.fontstyle}if(k.fontweight){l.font["font-weight"]=k.fontweight}return l}if(!this.mathvariant){if(k.fontweight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.fontweight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.fontstyle==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.fontstyle==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}}return a.FONTDATA.VARIANT[l]},SVGgetScale:function(){var l=1,k=this.getValues("mathsize","scriptlevel","fontsize");if((this.styles||{}).fontSize&&!k.fontsize){k.fontsize=this.styles.fontSize}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(l2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},SVGnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},SVGcanStretch:function(k){if(this.isEmbellished()){return this.Core().SVGcanStretch(k)}return false},SVGstretchV:function(k,l){return this.toSVG(k,l)},SVGstretchH:function(k){return this.toSVG(k)},SVGlineBreaks:function(){return false}},{SVGautoload:function(){var k=a.autoloadDir+"/"+this.type+".js";c.RestartAfter(h.Require(k))},SVGautoloadFile:function(k){var l=a.autoloadDir+"/"+k+".js";c.RestartAfter(h.Require(l))}});g.chars.Augment({toSVG:function(k,l){return this.SVGhandleVariant(k,l,this.data.join("").replace(/[\u2061-\u2064]/g,""))}});g.entity.Augment({toSVG:function(k,l){return this.SVGhandleVariant(k,l,this.toString().replace(/[\u2061-\u2064]/g,""))}});g.mo.Augment({toSVG:function(){this.SVGgetStyles();var o=this.svg=this.SVG();this.SVGhandleSpace(o);if(this.data.length==0){o.Clean();this.SVGsaveData(o);return o}var s=this.SVGgetScale(),q=this.SVGgetVariant();var n=this.getValues("largeop","displaystyle");if(n.largeop){q=a.FONTDATA.VARIANT[n.displaystyle?"-largeOp":"-smallOp"]}for(var p=0,l=this.data.length;p10*r.w){k+=-r.l}o.Add(r,k,0,true);if(r.skew){o.skew=r.skew}}}o.Clean();if(this.data.join("").length!==1){delete o.skew}if(n.largeop){o.y=(o.h-o.d)/2/s-a.TeX.axis_height;if(o.r>o.w){o.ic=o.r-o.w;o.w=o.r}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGcanStretch:function(l){if(!this.Get("stretchy")){return false}var m=this.data.join("");if(m.length>1){return false}m=a.FONTDATA.DELIMITERS[m.charCodeAt(0)];var k=(m&&m.dir==l.substr(0,1));if(!k){delete this.svg}return k},SVGstretchV:function(p,q){var m=this.svg||this.toSVG();var l=this.getValues("symmetric","maxsize","minsize");var o=a.TeX.axis_height,k=this.SVGgetMu(m),n;if(l.symmetric){n=2*Math.max(p-o,q+o)}else{n=p+q}l.maxsize=a.length2em(l.maxsize,k,m.h+m.d);l.minsize=a.length2em(l.minsize,k,m.h+m.d);n=Math.max(l.minsize,Math.min(l.maxsize,n));m=a.createDelimiter(this.data.join("").charCodeAt(0),n,m.scale);if(l.symmetric){n=(m.h+m.d)/2+o}else{n=(m.h+m.d)*p/(p+q)}m.y=n-m.h;this.SVGhandleSpace(m);this.SVGhandleColor(m);delete this.svg;this.SVGsaveData(m);return m},SVGstretchH:function(l){var n=this.svg||this.toSVG(),k=this.SVGgetMu(n);var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if(m.fontweight==="bold"&&!this.mathvariant){m.mathvariant=g.VARIANT.BOLD}m.maxsize=a.length2em(m.maxsize,k,n.w);m.minsize=a.length2em(m.minsize,k,n.w);l=Math.max(m.minsize,Math.min(m.maxsize,l));n=a.createDelimiter(this.data.join("").charCodeAt(0),l,n.scale,m.mathvariant);this.SVGhandleSpace(n);this.SVGhandleColor(n);delete this.svg;this.SVGsaveData(n);return n}});g.mtext.Augment({toSVG:function(){this.SVGgetStyles();var k,m,l=this.SVGgetScale();if(this.Parent().type==="merror"){k=this.SVG();this.SVGhandleSpace(k);m=i.G();m.Add(i.TEXT(0.9*l,this.data.join(""),{fill:"#C00"}));k.Add(i.RECT(m.h+100,m.d+100,m.w+200,{fill:"#FF8",stroke:"#C00","stroke-width":50}),0,0);k.Add(m,150,0);k.H+=150;k.D+=50;k.Clean();this.SVGsaveData(k);return k}else{if(a.config.mtextFontInherit){k=this.SVG();this.SVGhandleSpace(k);k.Add(i.TEXT(l,this.data.join("")));k.Clean();this.SVGhandleColor(k);this.SVGsaveData(k);return k}else{return this.SUPER(arguments).toSVG.call(this)}}}});g.ms.Augment({toSVG:g.mbase.SVGautoload});g.mglyph.Augment({toSVG:g.mbase.SVGautoload});g.mspace.Augment({toSVG:function(){this.SVGgetStyles();var m=this.getValues("height","depth","width");m.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){m.mathbackground=this.background}var l=this.SVG(),k=this.SVGgetMu(l);l.h=a.length2em(m.height,k)/l.scale;l.d=a.length2em(m.depth,k)/l.scale;l.w=l.r=a.length2em(m.width,k)/l.scale;if(l.w<0){l.x=l.w;l.w=l.r=0}l.l=0;l.Clean();this.SVGhandleColor(l);this.SVGsaveData(l);return l}});g.mphantom.Augment({toSVG:function(k,m){this.SVGgetStyles();var l=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(l);l.Add(this.SVGdataStretched(0,k,m));l.Clean();while(l.element.firstChild){l.element.removeChild(l.element.firstChild)}}this.SVGhandleColor(l);if(!l.element.firstChild){delete l.element}this.SVGsaveData(l);return l}});g.mpadded.Augment({toSVG:function(m,q){this.SVGgetStyles();var o=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(o);var p=this.SVGdataStretched(0,m,q),l=this.SVGgetMu(o);var n=this.getValues("height","depth","width","lspace","voffset"),k=0,r=0;if(n.lspace){k=this.SVGlength2em(p,n.lspace,l)}if(n.voffset){r=this.SVGlength2em(p,n.voffset,l)}o.Add(p,k,r);o.Clean();o.h=p.h;o.d=p.d;o.w=p.w;if(n.height!==""){o.h=this.SVGlength2em(o,n.height,l,"h",0)}if(n.depth!==""){o.d=this.SVGlength2em(o,n.depth,l,"d",0)}if(n.width!==""){o.w=this.SVGlength2em(o,n.width,l,"w",0)}if(o.h>o.H){o.H=o.h}if(o.d>o.D){o.D=o.d}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGlength2em:function(o,r,l,s,k){if(k==null){k=-a.BIGDIMEN}var p=String(r).match(/width|height|depth/);var q=(p?o[p[0].charAt(0)]:(s?o[s]:null));var n=a.length2em(r,l,q);if(s&&String(r).match(/^\s*[-+]/)){return Math.max(k,o[s]+n)}else{return n}}});g.mrow.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);for(var n=0,k=this.data.length;na.linebreakWidth)||this.hasNewline()},SVGmultiline:function(k){g.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(k){var l=this.data[this.core].SVGstretchH(k);this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGstretchV:function(l,m){var k=this.data[this.core].SVGstretchV(l,m);this.SVGhandleColor(k);this.SVGsaveData(k);return k}});g.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(k);var l=k.Add(this.data[0].toSVG());k.Clean();if(l.ic){k.ic=l.ic}this.SVGhandleColor(k)}this.SVGsaveData(k);return k},SVGstretchH:function(k){return(this.data[0]!=null?this.data[0].SVGstretchH(k):i.NULL())},SVGstretchV:function(k,l){return(this.data[0]!=null?this.data[0].SVGstretchV(k,l):i.NULL())}});g.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var w=this.SVG();this.SVGhandleSpace(w);var s=this.data[0].toSVG(),y=this.data[1].toSVG();var C=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var r=w.scale=this.SVGgetScale(),n=C.displaystyle;var x=a.TeX.axis_height*r;if(C.bevelled){var B=(n?400:150);var A=Math.max(s.h+s.d,y.h+y.d)+2*B;var F=a.createDelimiter(47,A);w.Add(s,0,(s.d-s.h)/2+x+B);w.Add(F,s.w-B/2,(F.d-F.h)/2+x);w.Add(y,s.w+F.w-B,(y.d-y.h)/2+x-B)}else{var o=Math.max(s.w,y.w);var E=a.thickness2em(C.linethickness,r),m,l,D,z;var k=a.TeX.min_rule_thickness/a.em*1000;if(n){D=a.TeX.num1;z=a.TeX.denom1}else{D=(E===0?a.TeX.num3:a.TeX.num2);z=a.TeX.denom2}D*=r;z*=r;if(E===0){m=Math.max((n?7:3)*a.TeX.rule_thickness,2*k);l=(D-s.d)-(y.h-z);if(lv){k=((o.h+o.d)-(v-w))/2}s=i.RECT(w,0,m.w);v=m.h+k+w;u=this.SVGaddRoot(r,o,u,o.h+o.d-v,n);r.Add(o,u,v-o.h);r.Add(s,u+o.w,v-s.h);r.Add(m,u+o.w,0);r.Clean();r.h+=w;r.H+=w;this.SVGhandleColor(r);this.SVGsaveData(r);return r},SVGaddRoot:function(l,m,k,o,n){return k}});g.mroot.Augment({toSVG:g.msqrt.prototype.toSVG,SVGaddRoot:function(n,l,q,o,k){var s=(l.isMultiChar?0.55:0.65)*l.w;if(this.data[1]){var p=this.data[1].toSVG();p.x=0;var m=this.SVGrootHeight(l.h+l.d,k,p)-o;var r=Math.min(p.w,p.r);q=Math.max(r,s);n.Add(p,q-r,m)}return q-s},SVGrootHeight:function(m,l,k){return 0.45*(m-900*l)+600*l+Math.max(0,k.d-75)}});g.mfenced.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);if(this.data.open){l.Check(this.data.open)}if(this.data[0]!=null){l.Check(this.data[0])}for(var n=1,k=this.data.length;nI){I=p[J].w}if(!K[J]&&I>n){n=I}}}if(C==null&&F!=null){n=F}else{if(n==-a.BIGDIMEN){n=I}}for(J=I=0,G=this.data.length;JI){I=p[J].w}}}var B=a.TeX.rule_thickness;var o=p[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,scale:M};var s,q,w,v,r,A,H,L=0;if(o.ic){L=1.3*o.ic+0.05}for(J=0,G=this.data.length;Ju.H){u.H=u.h}}else{if(J==this.under){if(z){H=3*B*M;r=0}else{w=a.TeX.big_op_spacing2*M;v=a.TeX.big_op_spacing4*M;H=Math.max(w,v-u.h)}H=Math.max(H,1500/a.em);s-=L/2;q=-(o.d+u.h+H);u.d+=r;if(u.d>u.D){u.D=u.d}}}E.Add(u,s,q)}}E.Clean();this.SVGhandleColor(E);this.SVGsaveData(E);return E}});g.msubsup.Augment({toSVG:function(G,z){this.SVGgetStyles();var B=this.SVG();this.SVGhandleSpace(B);var K=B.scale=this.SVGgetScale(),E=this.SVGgetMu(B);var m=B.Add(this.SVGdataStretched(this.base,G,z));var l=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var I=a.TeX.x_height*K,y=a.TeX.scriptspace*K;var k,n;if(this.SVGnotEmpty(this.data[this.sup])){k=this.data[this.sup].toSVG();k.w+=y;k.r=Math.max(k.w,k.r)}if(this.SVGnotEmpty(this.data[this.sub])){n=this.data[this.sub].toSVG();n.w+=y;n.r=Math.max(n.w,n.r)}var C=a.TeX.sup_drop*l,A=a.TeX.sub_drop*l;var w=m.h-C,o=m.d+A,J=0,F;if(m.ic){m.w-=m.ic;J=1.3*m.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&m.scale===1&&!m.stretched&&!this.data[this.base].Get("largeop")){w=o=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:a.length2em(H.subscriptshift,E));H.superscriptshift=(H.superscriptshift===""?0:a.length2em(H.superscriptshift,E));if(!k){if(n){o=Math.max(o,a.TeX.sub1*K,n.h-(4/5)*I,H.subscriptshift);B.Add(n,m.w,-o)}}else{if(!n){values=this.getValues("displaystyle","texprimestyle");F=a.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];w=Math.max(w,F*K,k.d+(1/4)*I,H.superscriptshift);B.Add(k,m.w+J,w)}else{o=Math.max(o,a.TeX.sub2*K);var x=a.TeX.rule_thickness*K;if((w-k.d)-(n.h-o)<3*x){o=3*x-w+k.d+n.h;C=(4/5)*I-(w-k.d);if(C>0){w+=C;o-=C}}B.Add(k,m.w+J,Math.max(w,H.superscriptshift));B.Add(n,m.w,-Math.max(o,H.subscriptshift))}}B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B}});g.mmultiscripts.Augment({toSVG:g.mbase.SVGautoload});g.mtable.Augment({toSVG:g.mbase.SVGautoload});g["annotation-xml"].Augment({toSVG:g.mbase.SVGautoload});g.math.Augment({SVG:i.Subclass({type:"svg",removeable:false}),toSVG:function(t,m){if(this.data[0]){this.SVGgetStyles();g.mbase.prototype.displayAlign=c.config.displayAlign;g.mbase.prototype.displayIndent=c.config.displayIndent;var q=i.G({stroke:"black",fill:"black","stroke-thickness":0,transform:"matrix(1 0 0 -1 0 0)"}).With({removeable:false});q.Add(this.data[0].toSVG(),0,0,true);q.Clean();this.SVGhandleColor(q);var s=this.SVG();s.element.setAttribute("xmlns:xlink",j);s.Add(q);s.Clean();this.SVGsaveData(s);var p=Math.max(-s.l,0),k=Math.max(s.r-s.w,0);var n=s.element.style;n.width=a.Ex(p+s.w+k);n.height=a.Ex(s.H+s.D);n.verticalAlign=a.Ex(-s.D);n.marginLeft=a.Ex(-p);n.marginRight=a.Ex(-k);s.element.setAttribute("viewBox",(-p)+" "+(-s.H)+" "+(p+s.w+k)+" "+(s.H+s.D));t.style.padding="1px 0";if(s.H>s.h||s.D>s.d){var o=e.Element("span",{style:{display:"inline-block","white-space":"nowrap"},isMathJax:true},[["span",{style:{display:"inline-block",position:"relative",isMathJax:true,width:a.Ex(s.w),height:a.Ex(s.h+s.d),"vertical-align":a.Ex(-s.d)}}]]);o.firstChild.appendChild(s.element);s.element=o;n.verticalAlign="";n.position="absolute";n.bottom=a.Ex(s.d-s.D);n.left=0}t.appendChild(s.element);s.element=null;if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===g.INDENTALIGN.AUTO){u.indentalign=this.displayAlign}m.style.textAlign=u.indentalign;if(u.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift=this.displayIndent}if(u.indentshift&&u.indentalign!==g.INDENTALIGN.CENTER){t.style[{left:"marginLeft",right:"marginRight"}[u.indentalign]]=a.Ex(a.length2em(u.indentshift))}}}return t}});g.TeXAtom.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(this.data[0]!=null){var l=this.data[0].toSVG(),m=0;if(this.texClass===g.TEXCLASS.VCENTER){m=a.TeX.axis_height-(l.h+l.d)/2+l.d}k.Add(l,0,m);k.ic=l.ic}this.SVGhandleColor(k);this.SVGsaveData(k);return k}});c.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +(function(h,c,e,a){var g;var b="http://www.w3.org/2000/svg";var j="http://www.w3.org/1999/xlink";a.Augment({config:{styles:{".MathJax_SVG":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_SVG_Display":{position:"relative",display:"block",width:"100%"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,Config:function(){var k=c.config.menuSettings;if(k.scale){this.config.scale=k.scale}this.SUPER(arguments).Config.apply(this,arguments);this.fontInUse=this.config.font;this.fontDir+="/"+this.config.font;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){EVENT=MathJax.Extension.MathEvents.Event;TOUCH=MathJax.Extension.MathEvents.Touch;HOVER=MathJax.Extension.MathEvents.Hover;this.ContextMenu=EVENT.ContextMenu;this.Mousedown=EVENT.AltContextMenu;this.Mouseover=HOVER.Mouseover;this.Mouseout=HOVER.Mouseout;this.Mousemove=HOVER.Mousemove;this.hiddenDiv=e.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=e.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var k=e.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.textSVG=this.Element("svg");d=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});f={};this.ExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_SVG_ExBox"}]]);this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"auto",size:1,padding:0,border:0,margin:0}}]]);return h.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){document.body.appendChild(this.ExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.ExSpan.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.ExSpan)},preTranslate:function(o){var t=o.jax[this.id],u,r=t.length,z,s,A,n,y,l,x,q,k,w=false,v,B=this.config.linebreaks.automatic,p=this.config.linebreaks.width;if(B){w=(p.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(w){p=p.replace(/\s*container\s*/,"")}else{k=this.defaultWidth}if(p===""){p="100%"}}else{k=100000}for(u=0;u=p.SVGlast+p.SVGchunk){this.postTranslate(p);p.SVGchunk=Math.floor(p.SVGchunk*this.config.EqnChunkFactor)}}},postTranslate:function(q){var l=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.SVGlast,k=q.SVGeqn;o=55296&&o<56319){t++;o=(((o-55296)<<10)+(B.charCodeAt(t)-56320))+65536;if(this.FONTDATA.RemapPlane1){var v=this.FONTDATA.RemapPlane1(o,s);o=v.n;s=v.variant}}else{k=this.FONTDATA.RANGES;for(l=0,x=k.length;l=k[l].low&&o<=k[l].high){if(k[l].remap&&k[l].remap[o]){o=w+k[l].remap[o]}else{o=o-k[l].low+w;if(k[l].add){o+=k[l].add}}if(s["variant"+k[l].offset]){s=this.FONTDATA.VARIANT[s["variant"+k[l].offset]]}break}}}if(s.remap&&s.remap[o]){if(s.remap[o] instanceof Array){var A=s.remap[o];o=A[0];s=this.FONTDATA.VARIANT[A[1]]}else{o=s.remap[o];if(s.remap.variant){s=this.FONTDATA.VARIANT[s.remap.variant]}}}if(this.FONTDATA.REMAP[o]&&!s.noRemap){o=this.FONTDATA.REMAP[o]}p=this.lookupChar(s,o);y=p[o];if(y){y=[r,p.id+"-"+o.toString(16).toUpperCase()].concat(y);u.Add(i.GLYPH.apply(i,y),u.w,0)}else{if(this.FONTDATA.DELIMITERS[o]){u.Add(this.createDelimiter(o,0,1,p),u.w,0)}else{if(o<=65535){y=String.fromCharCode(o)}else{w=o-65536;y=String.fromCharCode((w>>10)+55296)+String.fromCharCode((w&1023)+56320)}B=i.TEXT(r,y,{"font-family":s.defaultFamily||a.config.MISSINGFONT,"font-style":(s.italic?"italic":""),"font-weight":(s.bold?"bold":"")});if(s.h!=null){B.h=s.h}if(s.d!=null){B.d=s.d}y=i.G();y.Add(B);u.Add(y,u.w,0);B="";c.signal.Post(["SVG Jax - unknown char",o,s])}}}if(B.length==1&&p.skew&&p.skew[o]){u.skew=p.skew[o]*1000}if(u.element.childNodes.length===1){u.element=u.element.firstChild;u.removeable=false;u.scale=r}return u},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(k){c.RestartAfter(h.Require(this.fontDir+"/"+k))},createDelimiter:function(k,n,q,o){if(!q){q=1}var s=i.G();if(!k){s.Clean();delete s.element;s.w=s.r=this.TeX.nulldelimiterspace*q;return s}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){c.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var r=0,p=l.HW.length;r=n-10||(r==p-1&&!l.stretch)){if(l.HW[r][2]){q*=l.HW[r][2]}if(l.HW[r][3]){k=l.HW[r][3]}return this.createChar(q,[k,l.HW[r][1]],o).With({stretched:true})}}if(l.stretch){this["extendDelimiter"+l.dir](s,t,l.stretch,q,o)}return s},createChar:function(s,q,n){var r="",p={fonts:[q[1]],noRemap:true};if(n&&n===g.VARIANT.BOLD){p.fonts=[q[1]+"-bold",q[1]]}if(typeof(q[1])!=="string"){p=q[1]}if(q[0] instanceof Array){for(var o=0,k=q[0].length;oq){var l=this.createChar(o,m.ext,n);var p=(m.mid?2:1),v=(A-q)/p,B=(v+100)/(l.h+l.d);while(p-->0){var t=a.Element("g",{transform:"translate(0,"+(w-B*l.h+50)+") scale(1,"+B+")"});t.appendChild(l.element.cloneNode(false));r.element.appendChild(t);w-=v;if(m.mid&&p){r.Add(z,0,w-z.h);w-=(z.h+z.d)}}}else{if(m.mid){w+=(q-A)/2;r.Add(z,0,w-z.h);w+=-(z.h+z.d)+(q-A)/2}else{w+=(q-A)}}r.Add(u,0,w-u.h);r.Clean();r.scale=o;r.isMultiChar=true},extendDelimiterH:function(t,o,m,q,n){var p=this.createChar(q,(m.left||m.rep),n);var C=this.createChar(q,(m.right||m.rep),n);t.Add(p,-p.l,0);var B=(p.r-p.l)+(C.r-C.l),z=p.r-p.l;if(m.mid){var A=this.createChar(q,m.mid,n);B+=A.w}if(o>B){var y=this.createChar(q,m.rep,n),l=m.fuzz||0;var r=(m.mid?2:1),v=(o-B)/r,E=(v+l)/(y.r-y.l);while(r-->0){var u=a.Element("g",{transform:"translate("+(z-l/2-E*y.l)+",0) scale("+E+",1)"});u.appendChild(y.element.cloneNode(false));t.element.appendChild(u);z+=v;if(m.mid&&r){t.Add(A,z,0);z+=A.w}}}else{if(m.mid){var D=Math.min(B-o,p.w/2);z-=D/2;t.Add(A,z,0);z+=A.w-D/2}else{z-=(B-o)}}t.Add(C,z-C.l,0);t.Clean();t.scale=q;t.isMultiChar=true},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:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:100,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var i=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(k){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,k)}},With:function(k){return c.Insert(this,k)},Add:function(n,m,l,p,o){if(m){n.x+=m}if(l){n.y+=l}if(n.element){if(n.removeable&&n.element.childNodes.length===1&&n.n===1){var r=n.element.firstChild;if(r.nodeName==="use"||r.nodeName==="rect"){n.element=r;n.scale=n.childScale;var k=parseFloat(n.element.getAttribute("x")||"0")*n.scale,q=parseFloat(n.element.getAttribute("y")||"0")*n.scale;n.x+=k;n.y+=q;n.h+=q;n.d+=q;n.H+=q;n.D+=q;n.w-=k;n.r-=k;n.l+=k;n.removeable=false}}if(Math.abs(n.x)<1&&Math.abs(n.y)<1){n.remove=n.removeable}else{if(n.element.nodeName==="g"){if(!n.element.firstChild){n.remove=n.removeable}else{n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}}else{if(n.element.nodeName==="line"||n.element.nodeName==="polygon"||n.element.nodeName==="path"||n.element.nodeName==="a"){n.element.setAttribute("transform","translate("+Math.floor(n.x)+","+Math.floor(n.y)+")")}else{n.element.setAttribute("x",Math.floor(n.x/n.scale));n.element.setAttribute("y",Math.floor(n.y/n.scale))}}}if(n.remove){this.n+=n.n;while(n.element.firstChild){if(o&&this.element.firstChild){this.element.insertBefore(n.element.firstChild,this.element.firstChild)}else{this.element.appendChild(n.element.firstChild)}}}else{if(o){this.element.insertBefore(n.element,this.element.firstChild)}else{this.element.appendChild(n.element)}}delete n.element}if(n.d-n.y>this.d){this.d=n.d-n.y;if(this.d>this.D){this.D=this.d}}if(n.y+n.h>this.h){this.h=n.y+n.h;if(this.h>this.H){this.H=this.h}}if(n.D-n.y>this.D){this.D=n.D-n.y}if(n.y+n.H>this.H){this.H=n.y+n.H}if(n.x+n.lthis.r){this.r=n.x+n.r}if(p||n.x+n.w+(n.X||0)>this.w){this.w=n.x+n.w+(n.X||0)}this.childScale=n.scale;this.n++;return n},Align:function(m,n,l,k){l=({left:l,center:(this.w-m.w)/2,right:this.w-m.w-l})[n]||0;this.Add(m,l,k)},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});i.ROW=i.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(l){var k=l.toSVG();this.svg.push(k);if(l.SVGcanStretch("Vertical")){k.mml=l}if(k.h>this.sh){this.sh=k.h}if(k.d>this.sd){this.sd=k.d}},Stretch:function(){for(var n=0,k=this.svg.length;nl.w&&p.length===1&&!o.noIC){l.ic=l.r-l.w;l.w=l.r}this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGdataStretched:function(l,k,m){this.SVGdata={HW:k,D:m};if(m!=null){return this.data[l].SVGstretchV(k,m)}if(k!=null){return this.data[l].SVGstretchH(k)}return this.data[l].toSVG()},SVGsaveData:function(l){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=l.w,this.SVGdata.x=l.x;if(l.X!=null){this.SVGdata.X=l.X}if(this["class"]){l.removeable=false;a.Element(l.element,{"class":this["class"]})}if(this.id){l.removeable=false;a.Element(l.element,{id:this.id})}if(this.href){var k=a.Element("a");k.setAttributeNS(j,"href",this.href);a.addElement(k,"rect",{width:l.w,height:l.h+l.d,y:-l.d,fill:"none",stroke:"none","pointer-events":"all"});if(l.type==="svg"){var n=l.element.firstChild;while(n.firstChild){k.appendChild(n.firstChild)}n.appendChild(k)}else{if(l.removeable&&l.element.nodeName==="g"){while(l.element.firstChild){k.appendChild(l.element.firstChild)}}else{k.appendChild(l.element)}l.element=k}l.removeable=false}if(a.config.addMMLclasses){l.removeable=false;l.element.setAttribute("className","mjx-svg-"+this.type)}var m=this.Get("style");if(m){l.element.style.cssText=m;l.element.style.border=l.element.style.padding="";if(l.removeable){l.removeable=l.element.style.cssText===""}}},SVGgetStyles:function(){var l=this.Get("style");if(l){var k=e.Element("span");k.style.cssText=l;this.styles={border:a.getBorders(k),padding:a.getPadding(k)};if(k.style.fontSize){this.styles.fontSize=k.style.fontSize}if(k.style.color){this.styles.color=k.style.color}if(k.style.backgroundColor){this.styles.background=k.style.backgroundColor}if(k.style.fontStyle){this.styles.fontStyle=k.style.fontStyle}if(k.style.fontWeight){this.styles.fontWeight=k.style.fontWeight}if(k.style.fontFamily){this.styles.fontFamily=k.style.fontFamily}}},SVGhandleSpace:function(n){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.SVGgetMu(n);m.lspace=Math.max(0,a.length2em(m.lspace,l));m.rspace=Math.max(0,a.length2em(m.rspace,l));var k=this,o=this.Parent();while(o&&o.isEmbellished()&&o.Core()===k){k=o;o=o.Parent()}if(m.lspace){n.x+=m.lspace}if(m.rspace){n.X=m.rspace}}}else{var p=this.texSpacing();if(p!==""){n.x+=a.length2em(p,this.SVGgetScale())/n.scale}}},SVGhandleColor:function(o){var w=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!w.color){w.color=this.styles.color}if(w.color&&!this.mathcolor){w.mathcolor=w.color}if(w.mathcolor){a.Element(o.element,{fill:w.mathcolor,stroke:w.mathcolor});o.removeable=false}var s=(this.styles||{}).border,u=(this.styles||{}).padding,t=((s||{}).left||0),q=((u||{}).left||0),k;w.background=(this.mathbackground||this.background||(this.styles||{}).background||g.COLOR.TRANSPARENT);if(t+q){var l=i();for(k in o){if(o.hasOwnProperty(k)){l[k]=o[k]}}l.x=0;l.y=0;o.element=a.Element("g");o.removeable=true;o.Add(l,t+q,0)}if(u){o.w+=u.right;o.h+=u.top;o.d+=u.bottom}if(s){o.w+=s.right;o.h+=s.top;o.d+=s.bottom}if(w.background!==g.COLOR.TRANSPARENT){if(o.element.nodeName!=="g"&&o.element.nodeName!=="svg"){var p=a.Element("g");p.appendChild(o.element);o.element=p;o.removable=true}o.Add(i.RECT(o.h,o.d,o.w,{fill:w.background}),0,0,false,true)}if(s){var v=5;var m={left:["V",o.h+o.d,-v,-o.d],right:["V",o.h+o.d,o.w-s.right+v,-o.d],top:["H",o.w,0,o.h-s.top+v],bottom:["H",o.w,0,-o.d-v]};for(k in m){if(m.hasOwnProperty(k)){if(s[k]){var r=m[k],n=i[r[0]+"LINE"];o.Add(n(r[1],s[k],s[k+"Style"],s[k+"Color"]),r[2],r[3])}}}}},SVGhandleVariant:function(k,m,l){return a.HandleVariant(k,m,l)},SVGgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var l=k.mathvariant;if(this.variantForm){l="-TeX-variant"}if(this.styles){if(!k.fontstyle&&this.styles.fontStyle){k.fontstyle=this.styles.fontStyle}if(!k.fontweight&&this.styles.fontWeight){k.fontweight=this.styles.fontWeight}if(!k.fontfamily&&this.styles.fontFamily){k.fontfamily=this.styles.fontFamily}}if(k.fontfamily&&!this.mathvariant){if(!k.fontweight&&k.mathvariant.match(/bold/)){k.fontweight="bold"}if(!k.fontstyle&&k.mathvariant.match(/italic/)){k.fontstyle="italic"}l={forceFamily:true,font:{"font-family":k.fontfamily}};if(k.fontstyle){l.font["font-style"]=k.fontstyle}if(k.fontweight){l.font["font-weight"]=k.fontweight}return l}if(!this.mathvariant){if(k.fontweight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.fontweight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.fontstyle==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.fontstyle==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}}return a.FONTDATA.VARIANT[l]},SVGgetScale:function(){var l=1,k=this.getValues("mathsize","scriptlevel","fontsize");if((this.styles||{}).fontSize&&!k.fontsize){k.fontsize=this.styles.fontSize}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}l=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(l2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},SVGnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},SVGcanStretch:function(k){if(this.isEmbellished()){return this.Core().SVGcanStretch(k)}return false},SVGstretchV:function(k,l){return this.toSVG(k,l)},SVGstretchH:function(k){return this.toSVG(k)},SVGlineBreaks:function(){return false}},{SVGautoload:function(){var k=a.autoloadDir+"/"+this.type+".js";c.RestartAfter(h.Require(k))},SVGautoloadFile:function(k){var l=a.autoloadDir+"/"+k+".js";c.RestartAfter(h.Require(l))}});g.chars.Augment({toSVG:function(k,l){return this.SVGhandleVariant(k,l,this.data.join("").replace(/[\u2061-\u2064]/g,""))}});g.entity.Augment({toSVG:function(k,l){return this.SVGhandleVariant(k,l,this.toString().replace(/[\u2061-\u2064]/g,""))}});g.mo.Augment({toSVG:function(){this.SVGgetStyles();var o=this.svg=this.SVG();this.SVGhandleSpace(o);if(this.data.length==0){o.Clean();this.SVGsaveData(o);return o}var s=this.SVGgetScale(),q=this.SVGgetVariant();var n=this.getValues("largeop","displaystyle");if(n.largeop){q=a.FONTDATA.VARIANT[n.displaystyle?"-largeOp":"-smallOp"]}for(var p=0,l=this.data.length;p10*r.w){k+=-r.l}o.Add(r,k,0,true);if(r.skew){o.skew=r.skew}}}o.Clean();if(this.data.join("").length!==1){delete o.skew}if(n.largeop){o.y=(o.h-o.d)/2/s-a.TeX.axis_height;if(o.r>o.w){o.ic=o.r-o.w;o.w=o.r}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGcanStretch:function(l){if(!this.Get("stretchy")){return false}var m=this.data.join("");if(m.length>1){return false}m=a.FONTDATA.DELIMITERS[m.charCodeAt(0)];var k=(m&&m.dir==l.substr(0,1));if(!k){delete this.svg}return k},SVGstretchV:function(p,q){var m=this.svg||this.toSVG();var l=this.getValues("symmetric","maxsize","minsize");var o=a.TeX.axis_height,k=this.SVGgetMu(m),n;if(l.symmetric){n=2*Math.max(p-o,q+o)}else{n=p+q}l.maxsize=a.length2em(l.maxsize,k,m.h+m.d);l.minsize=a.length2em(l.minsize,k,m.h+m.d);n=Math.max(l.minsize,Math.min(l.maxsize,n));m=a.createDelimiter(this.data.join("").charCodeAt(0),n,m.scale);if(l.symmetric){n=(m.h+m.d)/2+o}else{n=(m.h+m.d)*p/(p+q)}m.y=n-m.h;this.SVGhandleSpace(m);this.SVGhandleColor(m);delete this.svg;this.SVGsaveData(m);return m},SVGstretchH:function(l){var n=this.svg||this.toSVG(),k=this.SVGgetMu(n);var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if(m.fontweight==="bold"&&!this.mathvariant){m.mathvariant=g.VARIANT.BOLD}m.maxsize=a.length2em(m.maxsize,k,n.w);m.minsize=a.length2em(m.minsize,k,n.w);l=Math.max(m.minsize,Math.min(m.maxsize,l));n=a.createDelimiter(this.data.join("").charCodeAt(0),l,n.scale,m.mathvariant);this.SVGhandleSpace(n);this.SVGhandleColor(n);delete this.svg;this.SVGsaveData(n);return n}});g.mtext.Augment({toSVG:function(){this.SVGgetStyles();var k,m,l=this.SVGgetScale();if(this.Parent().type==="merror"){k=this.SVG();this.SVGhandleSpace(k);m=i.G();m.Add(i.TEXT(0.9*l,this.data.join(""),{fill:"#C00"}));k.Add(i.RECT(m.h+100,m.d+100,m.w+200,{fill:"#FF8",stroke:"#C00","stroke-width":50}),0,0);k.Add(m,150,0);k.H+=150;k.D+=50;k.Clean();this.SVGsaveData(k);return k}else{if(a.config.mtextFontInherit){k=this.SVG();this.SVGhandleSpace(k);k.Add(i.TEXT(l,this.data.join("")));k.Clean();this.SVGhandleColor(k);this.SVGsaveData(k);return k}else{return this.SUPER(arguments).toSVG.call(this)}}}});g.ms.Augment({toSVG:g.mbase.SVGautoload});g.mglyph.Augment({toSVG:g.mbase.SVGautoload});g.mspace.Augment({toSVG:function(){this.SVGgetStyles();var m=this.getValues("height","depth","width");m.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){m.mathbackground=this.background}var l=this.SVG(),k=this.SVGgetMu(l);l.h=a.length2em(m.height,k)/l.scale;l.d=a.length2em(m.depth,k)/l.scale;l.w=l.r=a.length2em(m.width,k)/l.scale;if(l.w<0){l.x=l.w;l.w=l.r=0}l.l=0;l.Clean();this.SVGhandleColor(l);this.SVGsaveData(l);return l}});g.mphantom.Augment({toSVG:function(k,m){this.SVGgetStyles();var l=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(l);l.Add(this.SVGdataStretched(0,k,m));l.Clean();while(l.element.firstChild){l.element.removeChild(l.element.firstChild)}}this.SVGhandleColor(l);if(!l.element.firstChild){delete l.element}this.SVGsaveData(l);return l}});g.mpadded.Augment({toSVG:function(m,q){this.SVGgetStyles();var o=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(o);var p=this.SVGdataStretched(0,m,q),l=this.SVGgetMu(o);var n=this.getValues("height","depth","width","lspace","voffset"),k=0,r=0;if(n.lspace){k=this.SVGlength2em(p,n.lspace,l)}if(n.voffset){r=this.SVGlength2em(p,n.voffset,l)}o.Add(p,k,r);o.Clean();o.h=p.h;o.d=p.d;o.w=p.w;if(n.height!==""){o.h=this.SVGlength2em(o,n.height,l,"h",0)}if(n.depth!==""){o.d=this.SVGlength2em(o,n.depth,l,"d",0)}if(n.width!==""){o.w=this.SVGlength2em(o,n.width,l,"w",0)}if(o.h>o.H){o.H=o.h}if(o.d>o.D){o.D=o.d}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGlength2em:function(o,r,l,s,k){if(k==null){k=-a.BIGDIMEN}var p=String(r).match(/width|height|depth/);var q=(p?o[p[0].charAt(0)]:(s?o[s]:null));var n=a.length2em(r,l,q);if(s&&String(r).match(/^\s*[-+]/)){return Math.max(k,o[s]+n)}else{return n}}});g.mrow.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);for(var n=0,k=this.data.length;na.linebreakWidth)||this.hasNewline()},SVGmultiline:function(k){g.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(k){var l=this.data[this.core].SVGstretchH(k);this.SVGhandleColor(l);this.SVGsaveData(l);return l},SVGstretchV:function(l,m){var k=this.data[this.core].SVGstretchV(l,m);this.SVGhandleColor(k);this.SVGsaveData(k);return k}});g.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(k);var l=k.Add(this.data[0].toSVG());k.Clean();if(l.ic){k.ic=l.ic}this.SVGhandleColor(k)}this.SVGsaveData(k);return k},SVGstretchH:function(k){return(this.data[0]!=null?this.data[0].SVGstretchH(k):i.NULL())},SVGstretchV:function(k,l){return(this.data[0]!=null?this.data[0].SVGstretchV(k,l):i.NULL())}});g.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var w=this.SVG();this.SVGhandleSpace(w);var s=this.data[0].toSVG(),y=this.data[1].toSVG();var C=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var r=w.scale=this.SVGgetScale(),n=C.displaystyle;var x=a.TeX.axis_height*r;if(C.bevelled){var B=(n?400:150);var A=Math.max(s.h+s.d,y.h+y.d)+2*B;var F=a.createDelimiter(47,A);w.Add(s,0,(s.d-s.h)/2+x+B);w.Add(F,s.w-B/2,(F.d-F.h)/2+x);w.Add(y,s.w+F.w-B,(y.d-y.h)/2+x-B)}else{var o=Math.max(s.w,y.w);var E=a.thickness2em(C.linethickness,r),m,l,D,z;var k=a.TeX.min_rule_thickness/a.em*1000;if(n){D=a.TeX.num1;z=a.TeX.denom1}else{D=(E===0?a.TeX.num3:a.TeX.num2);z=a.TeX.denom2}D*=r;z*=r;if(E===0){m=Math.max((n?7:3)*a.TeX.rule_thickness,2*k);l=(D-s.d)-(y.h-z);if(lv){k=((o.h+o.d)-(v-w))/2}s=i.RECT(w,0,m.w);v=m.h+k+w;u=this.SVGaddRoot(r,o,u,o.h+o.d-v,n);r.Add(o,u,v-o.h);r.Add(s,u+o.w,v-s.h);r.Add(m,u+o.w,0);r.Clean();r.h+=w;r.H+=w;this.SVGhandleColor(r);this.SVGsaveData(r);return r},SVGaddRoot:function(l,m,k,o,n){return k}});g.mroot.Augment({toSVG:g.msqrt.prototype.toSVG,SVGaddRoot:function(n,l,q,o,k){var s=(l.isMultiChar?0.55:0.65)*l.w;if(this.data[1]){var p=this.data[1].toSVG();p.x=0;var m=this.SVGrootHeight(l.h+l.d,k,p)-o;var r=Math.min(p.w,p.r);q=Math.max(r,s);n.Add(p,q-r,m)}return q-s},SVGrootHeight:function(m,l,k){return 0.45*(m-900*l)+600*l+Math.max(0,k.d-75)}});g.mfenced.Augment({SVG:i.ROW,toSVG:function(){this.SVGgetStyles();var l=this.SVG();this.SVGhandleSpace(l);if(this.data.open){l.Check(this.data.open)}if(this.data[0]!=null){l.Check(this.data[0])}for(var n=1,k=this.data.length;nI){I=p[J].w}if(!K[J]&&I>n){n=I}}}if(C==null&&F!=null){n=F}else{if(n==-a.BIGDIMEN){n=I}}for(J=I=0,G=this.data.length;JI){I=p[J].w}}}var B=a.TeX.rule_thickness;var o=p[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,scale:M};var s,q,w,v,r,A,H,L=0;if(o.ic){L=1.3*o.ic+0.05}for(J=0,G=this.data.length;Ju.H){u.H=u.h}}else{if(J==this.under){if(z){H=3*B*M;r=0}else{w=a.TeX.big_op_spacing2*M;v=a.TeX.big_op_spacing4*M;H=Math.max(w,v-u.h)}H=Math.max(H,1500/a.em);s-=L/2;q=-(o.d+u.h+H);u.d+=r;if(u.d>u.D){u.D=u.d}}}E.Add(u,s,q)}}E.Clean();this.SVGhandleColor(E);this.SVGsaveData(E);return E}});g.msubsup.Augment({toSVG:function(G,z){this.SVGgetStyles();var B=this.SVG();this.SVGhandleSpace(B);var K=B.scale=this.SVGgetScale(),E=this.SVGgetMu(B);var m=B.Add(this.SVGdataStretched(this.base,G,z));var l=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var I=a.TeX.x_height*K,y=a.TeX.scriptspace*K;var k,n;if(this.SVGnotEmpty(this.data[this.sup])){k=this.data[this.sup].toSVG();k.w+=y;k.r=Math.max(k.w,k.r)}if(this.SVGnotEmpty(this.data[this.sub])){n=this.data[this.sub].toSVG();n.w+=y;n.r=Math.max(n.w,n.r)}var C=a.TeX.sup_drop*l,A=a.TeX.sub_drop*l;var w=m.h-C,o=m.d+A,J=0,F;if(m.ic){m.w-=m.ic;J=1.3*m.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&m.scale===1&&!m.stretched&&!this.data[this.base].Get("largeop")){w=o=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:a.length2em(H.subscriptshift,E));H.superscriptshift=(H.superscriptshift===""?0:a.length2em(H.superscriptshift,E));if(!k){if(n){o=Math.max(o,a.TeX.sub1*K,n.h-(4/5)*I,H.subscriptshift);B.Add(n,m.w,-o)}}else{if(!n){values=this.getValues("displaystyle","texprimestyle");F=a.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];w=Math.max(w,F*K,k.d+(1/4)*I,H.superscriptshift);B.Add(k,m.w+J,w)}else{o=Math.max(o,a.TeX.sub2*K);var x=a.TeX.rule_thickness*K;if((w-k.d)-(n.h-o)<3*x){o=3*x-w+k.d+n.h;C=(4/5)*I-(w-k.d);if(C>0){w+=C;o-=C}}B.Add(k,m.w+J,Math.max(w,H.superscriptshift));B.Add(n,m.w,-Math.max(o,H.subscriptshift))}}B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B}});g.mmultiscripts.Augment({toSVG:g.mbase.SVGautoload});g.mtable.Augment({toSVG:g.mbase.SVGautoload});g["annotation-xml"].Augment({toSVG:g.mbase.SVGautoload});g.math.Augment({SVG:i.Subclass({type:"svg",removeable:false}),toSVG:function(t,m){if(this.data[0]){this.SVGgetStyles();g.mbase.prototype.displayAlign=c.config.displayAlign;g.mbase.prototype.displayIndent=c.config.displayIndent;var q=i.G({stroke:"black",fill:"black","stroke-thickness":0,transform:"matrix(1 0 0 -1 0 0)"}).With({removeable:false});q.Add(this.data[0].toSVG(),0,0,true);q.Clean();this.SVGhandleColor(q);var s=this.SVG();s.element.setAttribute("xmlns:xlink",j);s.Add(q);s.Clean();this.SVGsaveData(s);var p=Math.max(-s.l,0),k=Math.max(s.r-s.w,0);var n=s.element.style;n.width=a.Ex(p+s.w+k);n.height=a.Ex(s.H+s.D);n.verticalAlign=a.Ex(-s.D);n.marginLeft=a.Ex(-p);n.marginRight=a.Ex(-k);s.element.setAttribute("viewBox",(-p)+" "+(-s.H)+" "+(p+s.w+k)+" "+(s.H+s.D));t.style.padding="1px 0";if(s.H>s.h||s.D>s.d){var o=e.Element("span",{style:{display:"inline-block","white-space":"nowrap"},isMathJax:true},[["span",{style:{display:"inline-block",position:"relative",isMathJax:true,width:a.Ex(s.w),height:a.Ex(s.h+s.d),"vertical-align":a.Ex(-s.d)}}]]);o.firstChild.appendChild(s.element);s.element=o;n.verticalAlign="";n.position="absolute";n.bottom=a.Ex(s.d-s.D);n.left=0}t.appendChild(s.element);s.element=null;if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===g.INDENTALIGN.AUTO){u.indentalign=this.displayAlign}m.style.textAlign=u.indentalign;if(u.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift=this.displayIndent}if(u.indentshift&&u.indentalign!==g.INDENTALIGN.CENTER){t.style[{left:"marginLeft",right:"marginRight"}[u.indentalign]]=a.Ex(a.length2em(u.indentshift))}}}return t}});g.TeXAtom.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(this.data[0]!=null){var l=this.data[0].toSVG(),m=0;if(this.texClass===g.TEXCLASS.VCENTER){m=a.TeX.axis_height-(l.h+l.d)/2+l.d}k.Add(l,0,m);k.ic=l.ic}this.SVGhandleColor(k);this.SVGsaveData(k);return k}});c.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); diff --git a/unpacked/jax/element/mml/jax.js b/unpacked/jax/element/mml/jax.js index 0150b238f..3024941f2 100644 --- a/unpacked/jax/element/mml/jax.js +++ b/unpacked/jax/element/mml/jax.js @@ -213,8 +213,7 @@ MathJax.ElementJax.mml.Augment({ "fontfamily", "fontsize", "fontweight", "fontstyle", "color", "background", "id", "class", "href", "style" - ], - PLANE1: "\uD835" + ] }); (function (MML) { @@ -419,7 +418,8 @@ MathJax.ElementJax.mml.Augment({ autoDefault: function (name) { if (name === "mathvariant") { var mi = (this.data[0]||"").toString(); - return (mi.length === 1 || (mi.length === 2 && mi.charCodeAt(0) === this.PLANE1) ? + return (mi.length === 1 || + (mi.length === 2 && mi.charCodeAt(0) >= 0xD800 && mi.charCodeAt(0) < 0xDC00) ? MML.VARIANT.ITALIC : MML.VARIANT.NORMAL); } return ""; @@ -520,7 +520,7 @@ MathJax.ElementJax.mml.Augment({ }, CheckRange: function (mo) { var n = mo.charCodeAt(0); - if (mo.charAt(0) === MML.PLANE1) {n = mo.charCodeAt(1) + 0x1D400 - 0xDC00} + if (n >= 0xD800 && n < 0xDC00) {n = (((n-0xD800)<<10)+(mo.charCodeAt(1)-0xDC00))+0x10000} for (var i = 0, m = this.RANGES.length; i < m && this.RANGES[i][0] <= n; i++) { if (n <= this.RANGES[i][1]) { if (this.RANGES[i][3]) { @@ -528,7 +528,7 @@ MathJax.ElementJax.mml.Augment({ this.RANGES[i][3] = null; MathJax.Hub.RestartAfter(MathJax.Ajax.Require(file)); } - var data = (["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER"])[this.RANGES[i][2]]; + var data = MML.TEXCLASSNAMES[this.RANGES[i][2]]; data = this.OPTABLE.infix[mo] = MML.mo.OPTYPES[data === "BIN" ? "BIN3" : data]; return this.makeDef(data); } @@ -1198,7 +1198,9 @@ MathJax.ElementJax.mml.Augment({ toString: function () { var n = this.value(); if (n <= 0xFFFF) {return String.fromCharCode(n)} - return this.PLANE1 + String.fromCharCode(n-0x1D400+0xDC00); + n -= 0x10000; + return String.fromCharCode((n>>10)+0xD800) + + String.fromCharCode((n&0x3FF)+0xDC00); } }); diff --git a/unpacked/jax/input/TeX/jax.js b/unpacked/jax/input/TeX/jax.js index 20191a2b5..df8dc2524 100644 --- a/unpacked/jax/input/TeX/jax.js +++ b/unpacked/jax/input/TeX/jax.js @@ -966,9 +966,10 @@ this.Parse(); this.Push(STACKITEM.stop()); }, Parse: function () { - var c; + var c, n; while (this.i < this.string.length) { - c = this.string.charAt(this.i++); + c = this.string.charAt(this.i++); n = c.charCodeAt(0); + if (n >= 0xD800 && n < 0xDC00) {c += this.string.charAt(this.i++)} if (TEXDEF.special[c]) {this[TEXDEF.special[c]](c)} else if (TEXDEF.letter.test(c)) {this.Variable(c)} else if (TEXDEF.digit.test(c)) {this.Number(c)} diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js index f2d7bace2..27f2ecbae 100644 --- a/unpacked/jax/output/HTML-CSS/jax.js +++ b/unpacked/jax/output/HTML-CSS/jax.js @@ -1214,8 +1214,8 @@ for (var i = 0, m = text.length; i < m; i++) { variant = VARIANT; n = text.charCodeAt(i); c = text.charAt(i); - if (c === this.PLANE1) { - i++; n = text.charCodeAt(i) + 0x1D400 - 0xDC00; + if (n >= 0xD800 && n < 0xDBFF) { + i++; n = (((n-0xD800)<<10)+(text.charCodeAt(i)-0xDC00))+0x10000; if (this.FONTDATA.RemapPlane1) { var nv = this.FONTDATA.RemapPlane1(n,variant); n = nv.n; variant = nv.variant; @@ -1295,8 +1295,11 @@ return ""; } if (C.c == null) { - if (n <= 0xFFFF) {C.c = String.fromCharCode(n)} - else {C.c = this.PLANE1 + String.fromCharCode(n-0x1D400+0xDC00)} + if (n <= 0xFFFF) {C.c = String.fromCharCode(n)} else { + var N = n - 0x10000; + C.c = String.fromCharCode((N>>10)+0xD800) + + String.fromCharCode((N&0x3FF)+0xDC00); + } } if (C.rfix) {this.addText(span,C.c); HTMLCSS.createShift(span,C.rfix/1000); return ""} if (c[2] || !this.msieAccentBug || text.length) {return text + C.c} @@ -1458,7 +1461,6 @@ min_rule_thickness: 1.25 // in pixels }, - PLANE1: "\uD835", NBSP: "\u00A0", rfuzz: 0 // adjustment to rule placements in roots diff --git a/unpacked/jax/output/SVG/jax.js b/unpacked/jax/output/SVG/jax.js index 0a4d5adcc..83fe6010d 100644 --- a/unpacked/jax/output/SVG/jax.js +++ b/unpacked/jax/output/SVG/jax.js @@ -463,7 +463,7 @@ HandleVariant: function (variant,scale,text) { var svg = BBOX.G(); - var n, c, font, VARIANT, i, m, id, M, RANGES; + var n, N, c, font, VARIANT, i, m, id, M, RANGES; if (!variant) {variant = this.FONTDATA.VARIANT[MML.VARIANT.NORMAL]} if (variant.forceFamily) { text = BBOX.TEXT(scale,text,variant.font); @@ -474,8 +474,8 @@ for (i = 0, m = text.length; i < m; i++) { variant = VARIANT; n = text.charCodeAt(i); c = text.charAt(i); - if (c === this.PLANE1) { - i++; n = text.charCodeAt(i) + 0x1D400 - 0xDC00; + if (n >= 0xD800 && n < 0xDBFF) { + i++; n = (((n-0xD800)<<10)+(text.charCodeAt(i)-0xDC00))+0x10000; if (this.FONTDATA.RemapPlane1) { var nv = this.FONTDATA.RemapPlane1(n,variant); n = nv.n; variant = nv.variant; @@ -484,7 +484,7 @@ RANGES = this.FONTDATA.RANGES; for (id = 0, M = RANGES.length; id < M; id++) { if (RANGES[id].name === "alpha" && variant.noLowerCase) continue; - var N = variant["offset"+RANGES[id].offset]; + N = variant["offset"+RANGES[id].offset]; if (N && n >= RANGES[id].low && n <= RANGES[id].high) { if (RANGES[id].remap && RANGES[id].remap[n]) { n = N + RANGES[id].remap[n]; @@ -515,7 +515,12 @@ } else if (this.FONTDATA.DELIMITERS[n]) { svg.Add(this.createDelimiter(n,0,1,font),svg.w,0); } else { - text = BBOX.TEXT(scale,String.fromCharCode(n),{ + if (n <= 0xFFFF) {c = String.fromCharCode(n)} else { + N = n - 0x10000; + c = String.fromCharCode((N>>10)+0xD800) + + String.fromCharCode((N&0x3FF)+0xDC00); + } + text = BBOX.TEXT(scale,c,{ "font-family":variant.defaultFamily||SVG.config.MISSINGFONT, "font-style":(variant.italic?"italic":""), "font-weight":(variant.bold?"bold":"") @@ -714,7 +719,6 @@ }, BIGDIMEN: 10000000, - PLANE1: "\uD835", NBSP: "\u00A0" });