(function(d){varc=true,f=false,i,h=String.fromCharCode(160);vare=MathJax.Object.Subclass({Init:function(k){this.global={};this.data=[b.start().With({global:this.global})];if(k){this.data[0].env=k}this.env=this.data[0].env},Push:function(){varl,k,n,o;for(l=0,k=arguments.length;l<k;l++){n=arguments[l];if(ninstanceofi.mbase){n=b.mml(n)}n.global=this.global;o=(this.data.length?this.Top().checkItem(n):c);if(oinstanceofArray){this.Pop();this.Push.apply(this,o)}else{if(oinstanceofb){this.Pop();this.Push(o)}else{if(o){this.data.push(n);if(n.env){for(varpinthis.env){if(this.env.hasOwnProperty(p)){n.env[p]=this.env[p]}}this.env=n.env}else{n.env=this.env}}}}}},Pop:function(){vark=this.data.pop();if(!k.isOpen){deletek.env}this.env=(this.data.length?this.Top().env:{});returnk},Top:function(k){if(k==null){k=1}if(this.data.length<k){returnnull}returnthis.data[this.data.length-k]},Prev:function(k){varl=this.Top();if(k){returnl.data[l.data.length-1]}else{returnl.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});varb=e.Item=MathJax.Object.Subclass({type:"base",closeError:"Extra close brace or missing open brace",rightError:"Missing \\left or extra \\right",Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){returnthis.data.pop()},mmlData:function(k,l){if(k==null){k=c}if(this.data.length===1&&!l){returnthis.data[0]}returni.mrow.apply(i,this.data).With((k?{inferred:c}:{}))},checkItem:function(k){if(k.type==="over"&&this.isOpen){k.num=this.mmlData(f);this.data=[]}if(k.type==="cell"&&this.isOpen){d.Error("Misplaced "+k.name)}if(k.isClose&&this[k.type+"Error"]){d.Error(this[k.type+"Error"])}if(!k.isNotStack){returnc}this.Push(k.data[0]);returnf},With:function(k){for(varlink){if(k.hasOwnProperty(l)){this[l]=k[l]}}returnthis},toString:function(){returnthis.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:c,checkItem:function(k){if(k.type==="stop"){returnb.mml(this.mmlData())}returnthis.SUPER(arguments).checkItem.call(this,k)}});b.stop=b.Subclass({type:"stop",isClose:c});b.open=b.Subclass({type:"open",isOpen:c,stopError:"Extra open brace or missing close brace",checkItem:function(l){if(l.type==="close"){vark=this.mmlData();returnb.mml(i.TeXAtom(k))}returnthis.SUPER(arguments).checkItem.call(this,l)}});b.close=b.Subclass({type:"close",isClose:c});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(l){vark=["","subscript","superscript"][this.position];if(l.type==="open"||l.type==="left"){returnc}if(l.type==="mml"){this.data[0].SetData(this.position,l.data[0]);returnb.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error("Missing open brace for "+k)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:c,name:"\\over",checkItem:function(m,k){if(m.type==="over"){d.Error("Ambiguous use of "+m.name)}if(m.isClose){varl=i.mfrac(this.num,this.mmlData(f));if(this.thickness!=null){l.linethickness=this.thickness}if(this.open||this.close){l.texClass=i.TEXCLASS.INNER;l.texWithDelims=c;l=i.mfenced(l).With({open:this.open,close:this.close})}return[b.mml(l),m]}returnthis.SUPER(arguments).checkItem.call(this,m)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:c,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(l){if(l.type==="right"){vark=i.mfenced(this.data.length===1?this.data[0]:i.mrow.apply(i,this.data));returnb.mml(k.With({open:this.delim,close:l.delim}))}returnthis.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:c,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:c,checkItem:function(k){if(k.type==="end"){if(k.name!==this.name){d.Error("\\begin{"+this.name+"} ended with \\end{"+k.name+"}")}if(!this.end){returnb.mml(this.mmlData())}returnthis.parse[this.end].call(this.parse,this,this.data)}if(k.type==="stop"){d.Error("Missing \\end{"+this.n
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){vare="1.1";vara=MathJax.ElementJax.mml;varf=MathJax.InputJax.TeX;varc=f.Definitions;vard=f.Stack.Item;varb=function(g){returng.join("em ")+"em"};MathJax.Hub.Insert(c,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",a.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",a.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["Macro","\\mathop{\\rm inj\\,lim}"],projlim:["Macro","\\mathop{\\rm proj\\,lim}"],varliminf:["Macro","\\mathop{\\underline{\\rm lim}}"],varlimsup:["Macro","\\mathop{\\overline{\\rm lim}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0em",""],tbinom:["Genfrac","(",")","0em",1],dbinom:["Genfrac","(",")","0em",0],cfrac:"CFrac",shoveleft:["HandleShove",a.ALIGN.LEFT],shoveright:["HandleShove",a.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",b([5/18])],gather:["AMSarray",null,true,true,"c"],"gather*":["AMSarray",null,false,true,"c"],alignat:["AlignAt",null,true,true],"alignat*":["AlignAt",null,false,true],alignedat:["AlignAt",null,false,false],aligned:["Array",null,null,null,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".5em","D"],gathered:["Array",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,b([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",b([1/3]),".2em","S",1]},delimiter:{"\\lvert":["2223",{texClass:a.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:a.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:a.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:a.TEXCLASS.CLOSE}]}});f.Parse.Augment({HandleTag:function(h){varg=this.trimSpaces(this.GetArgument(h));if(g==="*"){g=this.GetArgument(h)}else{g="("+g+")"}if(this.stack.global.notag){f.Error(h+" not allowed in "+this.stack.global.notag+" environment")}if(this.stack.global.tag){f.Error("Multiple "+h)}this.stack.global.tag=a.mtd.apply(a,this.InternalMath(g))},HandleNoTag:function(g){if(this.stack.global.tag){deletethis.stack.global.tag}},HandleDeclareOp:function(h){varg="";vari=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}if(i.charAt(0)=="\\"){i=i.substr(1)}varj=this.GetArgument(h);j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");f.Definitions.macros[i]=["Macro","\\mathop{\\rm "+j+"}"+g]},HandleOperatorName:function(h){varg="\\nolimits";vari=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}i=i.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+i+"}"+g+" "+this.string.slice(this.i);this.i=0},HandleShove:function(h,g){vari=this.stack.Top();if(i.type!=="multline"||i.data.length){f.Error(h+" must come at the beginning of the line")}i.data.shove=g},CFrac:function(j){varg=this.trimSpaces(this.GetBracket
(function(c,d,e){vara;varb=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){returng}for(varh=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){returnj[h]}}returnnull},testCollection:function(f){returnthis.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}varg=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){returnfalse}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){returntrue}for(varj=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){returntrue}}}}returnfalse},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){varm=3+(h.weight?2:0)+(h.style?4:0);varg="",i=0;varl=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}varf=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}vark=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];varg=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(vark=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}returnnull},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);vari=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);varf=MathJax.Callback({});varh=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);returnf},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){vari=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){vari=e.all
