commit 4ff36e714694cf9d3bd1ffa15fd5c2a3bc463106 parent 493781057095f5eca0a1407be31f94cdaa9b67b0 Author: Davide P. Cervone <dpvc@union.edu> Date: Sun, 11 Sep 2011 10:47:14 -0400 Merge branch 'issue128' with new-features (prevents user macros from being overridden by autoloaded extension) Diffstat:
22 files changed, 483 insertions(+), 85 deletions(-)
diff --git a/config/Accessible-full.js b/config/Accessible-full.js @@ -56,7 +56,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -78,11 +78,11 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/( )+$/,"")}else{if(c.isKonqueror){g=g.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClossing:true})}});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/Accessible.js b/config/Accessible.js @@ -53,7 +53,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -75,11 +75,11 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/( )+$/,"")}else{if(c.isKonqueror){g=g.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClossing:true})}});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/MML_HTMLorMML-full.js b/config/MML_HTMLorMML-full.js @@ -34,7 +34,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); diff --git a/config/MML_HTMLorMML.js b/config/MML_HTMLorMML.js @@ -31,7 +31,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); diff --git a/config/TeX-AMS-MML_HTMLorMML-full.js b/config/TeX-AMS-MML_HTMLorMML-full.js @@ -43,7 +43,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -65,11 +65,11 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/( )+$/,"")}else{if(c.isKonqueror){g=g.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClossing:true})}});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/TeX-AMS-MML_HTMLorMML.js b/config/TeX-AMS-MML_HTMLorMML.js @@ -40,7 +40,7 @@ MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJa MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"1.1.5",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js"); @@ -62,11 +62,11 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); (function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/( )+$/,"")}else{if(c.isKonqueror){g=g.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClossing:true})}});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser); diff --git a/config/TeX-AMS_HTML-full.js b/config/TeX-AMS_HTML-full.js @@ -33,7 +33,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+a},formatURL:function(a){return"#mjx-eqn-"+escape(a)}}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.Extension.tex2jax={version:"1.1.4",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":"")+(b.processRefs?"|\\\\(eq)?ref\\{[^}]*\\}":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"); @@ -49,11 +49,11 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); (function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.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")}var g=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]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=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}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=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];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=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]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},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){var i=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){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};this.hiddenDiv=this.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=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["PreloadWebFonts",this])},removeSTIXfonts:function(h){for(var g=0,f=h.length;g<f;g++){if(h[g]==="STIX"){h.splice(g,1);f--;g--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=h[0]}},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.getLinebreakWidth(h);this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax==="MathML"?"Original":f.jax.inputJax);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getLinebreakWidth:function(h){if(this.config.linebreaks.automatic){var g=this.config.linebreaks.width,f;if(g.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)){h.parentNode.insertBefore(this.linebreakSpan,h);f=this.linebreakSpan.firstChild.offsetWidth/this.em;this.linebreakSpan.parentNode.removeChild(this.linebreakSpan);g=g.replace(/\s*container\s*/,"")}else{f=document.body.offsetWidth/this.em}this.linebreakWidth=(g===""?f:this.length2em(g,f))}else{this.linebreakWidth=100000}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=f*this.scale/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=(2*g-f?g/(2*g-f):1);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},getPadding:function(g){var i={top:0,right:0,bottom:0,left:0},f=false;for(var j in i){if(i.hasOwnProperty(j)){var h=g.style["padding"+j.charAt(0).toUpperCase()+j.substr(1)];if(h){i[j]=this.length2em(h);f=true}}}return(f?i:false)},getBorders:function(k){var h={top:0,right:0,bottom:0,left:0},i={},g=false;for(var l in h){if(h.hasOwnProperty(l)){var f="border"+l.charAt(0).toUpperCase()+l.substr(1);var j=k.style[f+"Style"];if(j){g=true;h[l]=this.length2em(k.style[f+"Width"]);i[f]=[k.style[f+"Width"],k.style[f+"Style"],k.style[f+"Color"]].join(" ")}}}h.css=i;return(g?h:false)},setBorders:function(f,g){if(g){for(var h in g.css){if(g.css.hasOwnProperty(h)){f.style[h]=g.css[h]}}}},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(g.load){d.RestartAfter(c.Require(this.fontDir+"/fontdata-"+g.load+".js"))}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));if(!z.fillExtenders){j=(h-p)/(t*s)}q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(k[4]){h*=k[4]}if(h!==1||k[3]){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(k[3]){o.firstChild.style.verticalAlign=this.Em(k[3]);o.bbox.h+=k[3];if(o.bbox.h<0){o.bbox.h=0}}if(k[5]){o.bbox.h+=k[5]}if(k[6]){o.bbox.d+=k[6]}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts instead",null,3000);c.Require(this.directory+"/imageFonts.js",f)}else{this.allowWebFonts=false;f()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.type!="mrow"){k=this.HTMLhandleSize(k)}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(k)}}var n=this.HTMLcomputeBBox(k);var j=k.bbox.h,l=k.bbox.d;for(g=0,f=n.length;g<f;g++){n[g].HTMLstretchV(k,j,l)}if(n.length){this.HTMLcomputeBBox(k,true)}if(this.HTMLlineBreaks(k)){k=this.HTMLmultiline(k)}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLlineBreaks:function(){return false},HTMLmultiline:function(){a.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(l,k,j,f){if(j==null){j=0}if(f==null){f=this.data.length}var h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=(f.bbox?f:f.HTMLspanElement());if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};this.styles={};if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}this.styles={border:e.getBorders(f),padding:e.getPadding(f)};if(this.styles.border){f.style.border=""}if(this.styles.padding){f.style.padding=""}}if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(q){var s=this.getValues("mathcolor","color");if(this.mathbackground){s.mathbackground=this.mathbackground}if(this.background){s.background=this.background}if(this.style&&q.style.backgroundColor){s.mathbackground=q.style.backgroundColor;q.style.backgroundColor="transparent"}var n=(this.styles||{}).border,p=(this.styles||{}).padding;if(s.color&&!this.mathcolor){s.mathcolor=s.color}if(s.background&&!this.mathbackground){s.mathbackground=s.background}if(s.mathcolor){q.style.color=s.mathcolor}if((s.mathbackground&&s.mathbackground!==a.COLOR.TRANSPARENT)||n||p){var t=1/e.em,o=0,m=0,g=q.style.paddingLeft,k=q.style.paddingRight;if(this.isToken){o=q.bbox.lw;m=q.bbox.rw-q.bbox.w}if(g!==""){o+=parseFloat(g)*(q.scale||1)}if(k!==""){m-=parseFloat(k)*(q.scale||1)}var i=Math.max(0,e.getW(q)+(e.PaddingWidthBug?0:m-o));var r=q.bbox.h+q.bbox.d,f=-q.bbox.d,l=0,j=0;if(i>0){i+=2*t;o-=t}if(r>0){r+=2*t;f-=t}m=-i-o;if(n){m-=n.right;f-=n.bottom;l+=n.left;j+=n.right;q.bbox.h+=n.top;q.bbox.d+=n.bottom;q.bbox.w+=n.left+n.right;q.bbox.lw-=n.left;q.bbox.rw+=n.right}if(p){r+=p.top+p.bottom;i+=p.left+p.right;m-=p.right;f-=p.bottom;l+=p.left;j+=p.right;q.bbox.h+=p.top;q.bbox.d+=p.bottom;q.bbox.w+=p.left+p.right;q.bbox.lw-=p.left;q.bbox.rw+=p.right}if(j){q.style.paddingRight=e.Em(j)}var h=e.Element("span",{id:"MathJax-Color-"+this.spanID+e.idPostfix,style:{display:"inline-block",backgroundColor:s.mathbackground,width:e.Em(i),height:e.Em(r),verticalAlign:e.Em(f),marginLeft:e.Em(o),marginRight:e.Em(m)}});e.setBorders(h,n);if(q.bbox.width){h.style.width=q.bbox.width;h.style.marginRight="-"+q.bbox.width}if(e.msieInlineBlockAlignBug){h.style.position="relative";h.style.width=h.style.height=0;h.style.verticalAlign=h.style.marginLeft=h.style.marginRight="";h.style.border=h.style.padding="";if(n&&e.msieBorderWidthBug){r+=n.top+n.bottom;i+=n.left+n.right}h.style.width=e.Em(l+t);e.placeBox(e.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(s.mathbackground||"transparent"),width:e.Em(i),height:e.Em(r)}}),o,q.bbox.h+t);e.setBorders(h.firstChild,n)}q.parentNode.insertBefore(h,q);if(e.msieColorPositionBug){q.style.position="relative"}return h}return null},HTMLremoveColor:function(){var f=document.getElementById("MathJax-Color-"+this.spanID+e.idPostfix);if(f){f.parentNode.removeChild(f)}},HTMLhandleSpace:function(i){if(this.useMMLspacing){if(this.type!=="mo"){return}var g=this.getValues("scriptlevel","lspace","rspace");if(g.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){g.lspace=Math.max(0,e.length2em(g.lspace));g.rspace=Math.max(0,e.length2em(g.rspace));var f=this,h=this.Parent();while(h&&h.isEmbellished()&&h.Core()===f){f=h;h=h.Parent();i=f.HTMLspanElement()}if(g.lspace){i.style.paddingLeft=e.Em(g.lspace)}if(g.rspace){i.style.paddingRight=e.Em(g.rspace)}}}else{var j=this.texSpacing();if(j!==""){j=e.length2em(j)/(i.scale||1);if(i.style.paddingLeft){j+=parseFloat(i.style.paddingLeft)}i.style.paddingLeft=e.Em(j)}}},HTMLgetScale:function(){var h=1,f=this.getValues("mathsize","scriptlevel","fontsize","scriptminsize");if(this.style){var g=this.HTMLspanElement();if(g.style.fontSize!=""){f.fontsize=g.style.fontSize}}if(f.fontsize&&!this.mathsize){f.mathsize=f.fontsize}if(f.scriptlevel!==0){if(f.scriptlevel>2){f.scriptlevel=2}h=Math.pow(this.Get("scriptsizemultiplier"),f.scriptlevel);f.scriptminsize=e.length2em(f.scriptminsize);if(h<f.scriptminsize){h=f.scriptminsize}}h*=e.length2em(f.mathsize);return h},HTMLgetVariant:function(){var f=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(this.style){var h=this.HTMLspanElement();if(h.style.fontFamily){f.fontfamily=h.style.fontFamily}if(h.style.fontWeight){f.fontweight=h.style.fontWeight}if(h.style.fontStyle){f.fontStyle=h.style.fontStyle}}var g=f.mathvariant;if(this.variantForm){g="-"+e.fontInUse+"-variant"}if(f.fontfamily&&!this.mathvariant){if(!f.fontweight&&f.mathvariant.match(/bold/)){f.fontweight="bold"}if(!f.fontstyle&&f.mathvariant.match(/italic/)){f.fontstyle="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:f.fontfamily,style:f.fontstyle,weight:f.fontweight}}}if(f.fontweight==="bold"){g={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontweight==="normal"){g={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[g]||g}}if(f.fontstyle==="italic"){g={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[g]||g}else{if(f.fontstyle==="normal"){g={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[g]||g}}return e.FONTDATA.VARIANT[g]}},{HTMLautoload:function(){var f=e.autoloadDir+"/"+this.type+".js";d.RestartAfter(c.Require(f))},HTMLautoloadFile:function(f){var g=e.autoloadDir+"/"+f+".js";d.RestartAfter(c.Require(g))},HTMLstretchH:function(g,f){this.HTMLremoveColor();return this.toHTML(g,f)},HTMLstretchV:function(g,f,i){this.HTMLremoveColor();return this.toHTML(g,f,i)}});a.chars.Augment({toHTML:function(g,f){this.HTMLhandleVariant(g,f,this.data.join("").replace(/[\u2061-\u2064]/g,""))}});a.entity.Augment({toHTML:function(g,f){this.HTMLhandleVariant(g,f,this.toString().replace(/[\u2061-\u2064]/g,""))}});a.mi.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));j.bbox=null;var h=this.HTMLgetVariant();for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(j,h)}}if(!j.bbox){j.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete j.bbox.skew}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});a.mn.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));j.bbox=null;var h=this.HTMLgetVariant();for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].toHTML(j,h)}}if(!j.bbox){j.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete j.bbox.skew}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j}});a.mo.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));if(this.data.length==0){return k}else{k.bbox=null}var n=this.data.join("");var j=this.HTMLgetVariant();var g=this.getValues("largeop","displaystyle");if(g.largeop){j=e.FONTDATA.VARIANT[g.displaystyle?"-largeOp":"-smallOp"]}for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){this.data[h].toHTML(k,j)}}if(!k.bbox){k.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(n.length!==1){delete k.bbox.skew}if(e.AccentBug&&k.bbox.w===0&&n.length===1&&k.firstChild){k.firstChild.nodeValue+=e.NBSP;e.createSpace(k,0,0,-k.offsetWidth/e.em)}if(g.largeop){var l=(k.bbox.h-k.bbox.d)/2-e.TeX.axis_height*k.scale;if(e.safariVerticalAlignBug&&k.lastChild.nodeName==="IMG"){k.lastChild.style.verticalAlign=e.Em(parseFloat(k.lastChild.style.verticalAlign||0)/e.em-l/k.scale)}else{if(e.konquerorVerticalAlignBug&&k.lastChild.nodeName==="IMG"){k.style.position="relative";k.lastChild.style.position="relative";k.lastChild.style.top=e.Em(l/k.scale)}else{k.style.verticalAlign=e.Em(-l/k.scale)}}k.bbox.h-=l;k.bbox.d+=l;if(k.bbox.rw>k.bbox.w){k.bbox.ic=k.bbox.rw-k.bbox.w;e.createBlank(k,k.bbox.ic);k.bbox.w=k.bbox.rw}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcanStretch:function(f){if(!this.Get("stretchy")){return false}var g=this.data.join("");if(g.length>1){return false}g=e.FONTDATA.DELIMITERS[g.charCodeAt(0)];return(g&&g.dir==f.substr(0,1))},HTMLstretchV:function(l,k,n){this.HTMLremoveColor();var f=this.getValues("symmetric","maxsize","minsize");var j=this.HTMLspanElement(),g;var i=e.TeX.axis_height,m=j.scale;if(f.symmetric){g=2*Math.max(k-i,n+i)}else{g=k+n}f.maxsize=e.length2em(f.maxsize,j.bbox.h+j.bbox.d);f.minsize=e.length2em(f.minsize,j.bbox.h+j.bbox.d);g=Math.max(f.minsize,Math.min(f.maxsize,g));j=this.HTMLcreateSpan(l);e.createDelimiter(j,this.data.join("").charCodeAt(0),g,m);if(f.symmetric){g=(j.bbox.h+j.bbox.d)/2+i}else{g=(j.bbox.h+j.bbox.d)*k/(k+n)}e.positionDelimiter(j,g);this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:function(i,f){this.HTMLremoveColor();var g=this.getValues("maxsize","minsize","mathvariant","fontweight");if(g.fontweight==="bold"&&!this.mathvariant){g.mathvariant=a.VARIANT.BOLD}var h=this.HTMLspanElement(),j=h.scale;g.maxsize=e.length2em(g.maxsize,h.bbox.w);g.minsize=e.length2em(g.minsize,h.bbox.w);f=Math.max(g.minsize,Math.min(g.maxsize,f));h=this.HTMLcreateSpan(i);e.createDelimiter(h,this.data.join("").charCodeAt(0),f,j,g.mathvariant);this.HTMLhandleSpace(h);this.HTMLhandleColor(h);return h}});a.mtext.Augment({toHTML:function(k){k=this.HTMLhandleSize(this.HTMLcreateSpan(k));k.bbox=null;if(this.Parent().type==="merror"){e.addText(k,this.data.join(""));var l=e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j=this.HTMLgetVariant();for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){this.data[h].toHTML(k,j)}}if(!k.bbox){k.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete k.bbox.skew}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});a.ms.Augment({toHTML:a.mbase.HTMLautoload});a.mglyph.Augment({toHTML:a.mbase.HTMLautoload});a.mspace.Augment({toHTML:function(j){j=this.HTMLhandleSize(this.HTMLcreateSpan(j));var g=this.getValues("height","depth","width");g.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){g.mathbackground=this.background}var i=e.length2em(g.height),k=e.length2em(g.depth),f=e.length2em(g.width);e.createSpace(j,i,k,f,g.mathbackground);return j}});a.mphantom.Augment({toHTML:function(j,g,l){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){var k=e.Measured(this.data[0].toHTML(j),j);if(l!=null){e.Remeasured(this.data[0].HTMLstretchV(j,g,l),j)}else{if(g!=null){e.Remeasured(this.data[0].HTMLstretchH(j,g),j)}}j.bbox={w:k.bbox.w,h:k.bbox.h,d:k.bbox.d,lw:0,rw:0};for(var h=0,f=j.childNodes.length;h<f;h++){j.childNodes[h].style.visibility="hidden"}}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mpadded.Augment({toHTML:function(j,h,l){j=this.HTMLcreateSpan(j);if(this.data[0]!=null){var g=e.createStack(j,true);var k=e.createBox(g);e.Measured(this.data[0].toHTML(k),k);if(l!=null){e.Remeasured(this.data[0].HTMLstretchV(k,h,l),k)}else{if(h!=null){e.Remeasured(this.data[0].HTMLstretchH(k,h),k)}}var i=this.getValues("height","depth","width","lspace","voffset"),f=0,m=0;if(i.lspace){f=this.HTMLlength2em(k,i.lspace)}if(i.voffset){m=this.HTMLlength2em(k,i.voffset)}e.placeBox(k,f,m);j.bbox={h:k.bbox.h,d:k.bbox.d,w:k.bbox.w,lw:Math.min(0,k.bbox.lw+f),rw:Math.max(k.bbox.w,k.bbox.rw+f),H:Math.max((k.bbox.H==null?-e.BIGDIMEN:k.bbox.H),k.bbox.h+m),D:Math.max((k.bbox.D==null?-e.BIGDIMEN:k.bbox.D),k.bbox.d-m)};if(i.height!==""){j.bbox.h=this.HTMLlength2em(k,i.height,"h",0)}if(i.depth!==""){j.bbox.d=this.HTMLlength2em(k,i.depth,"d",0)}if(i.width!==""){j.bbox.w=this.HTMLlength2em(k,i.width,"w",0)}if(j.bbox.H<=j.bbox.h){delete j.bbox.H}if(j.bbox.D<=j.bbox.d){delete j.bbox.D}e.setStackWidth(g,j.bbox.w)}this.HTMLhandleSpace(j);this.HTMLhandleColor(j);return j},HTMLlength2em:function(j,k,l,f){if(f==null){f=-e.BIGDIMEN}var h=String(k).match(/width|height|depth/);var i=(h?j.bbox[h[0].charAt(0)]:(l?j.bbox[l]:null));var g=e.length2em(k,i);if(l&&String(k).match(/^\s*[-+]/)){return Math.max(f,j.bbox[l]+g)}else{return g}},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mrow.Augment({HTMLlineBreaks:function(f){if(!this.parent.linebreakContainer){return false}return(e.config.linebreaks.automatic&&f.bbox.w>e.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(h,f){this.HTMLremoveColor();var g=this.HTMLspanElement();this.data[this.core].HTMLstretchH(g,f);this.HTMLcomputeBBox(g,true);this.HTMLhandleColor(g);return g},HTMLstretchV:function(i,g,j){this.HTMLremoveColor();var f=this.HTMLspanElement();this.data[this.core].HTMLstretchV(f,g,j);this.HTMLcomputeBBox(f,true);this.HTMLhandleColor(f);return f}});a.mstyle.Augment({toHTML:function(g,f,h){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){var i=this.data[0].toHTML(g);if(h!=null){this.data[0].HTMLstretchV(g,f,h)}else{if(f!=null){this.data[0].HTMLstretchH(g,f)}}g.bbox=i.bbox}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mfrac.Augment({toHTML:function(y){y=this.HTMLcreateSpan(y);var h=e.createStack(y);var k=e.createBox(h),j=e.createBox(h);this.HTMLmeasureChild(0,k);this.HTMLmeasureChild(1,j);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var C=this.HTMLgetScale(),x=f.displaystyle;var B=e.TeX.axis_height*C;if(f.bevelled){var A=(x?0.4:0.15);var l=Math.max(k.bbox.h+k.bbox.d,j.bbox.h+j.bbox.d)+2*A;var z=e.createBox(h);e.createDelimiter(z,47,l);e.placeBox(k,0,(k.bbox.d-k.bbox.h)/2+B+A);e.placeBox(z,k.bbox.w-A/2,(z.bbox.d-z.bbox.h)/2+B);e.placeBox(j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j.bbox.h)/2+B-A)}else{var g=Math.max(k.bbox.w,j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=e.TeX.min_rule_thickness/this.em;if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*e.TeX.rule_thickness,2*w);r=(n-k.bbox.d)-(j.bbox.h-m);if(r<s){n+=(s-r)/2;m+=(s-r)/2}}else{s=Math.max((x?2:0)*w+o,o/2+1.5*w);r=(n-k.bbox.d)-(B+o/2);if(r<s){n+=s-r}r=(B-o/2)-(j.bbox.h-m);if(r<s){m+=s-r}var i=e.createBox(h);e.createRule(i,o,0,g+2*o);e.placeBox(i,0,B-o/2)}e.alignBox(k,f.numalign,n);e.alignBox(j,f.denomalign,-m)}this.HTMLhandleSpace(y);this.HTMLhandleColor(y);return y},HTMLcanStretch:function(f){return false},HTMLhandleSpace:function(f){if(!this.texWithDelims){var g=(this.useMMLspacing?0:e.length2em(this.texSpacing()||0))+0.12;f.style.paddingLeft=e.Em(g);f.style.paddingRight=".12em"}}});a.msqrt.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);var r=e.createStack(n);var h=e.createBox(r),l=e.createBox(r),k=e.createBox(r);this.HTMLmeasureChild(0,h);var j=this.HTMLgetScale();var s=e.TeX.rule_thickness*j,g,f,o,i;if(this.Get("displaystyle")){g=e.TeX.x_height*j}else{g=s}f=Math.max(s+g/4,1.5*e.TeX.min_rule_thickness/this.em);o=h.bbox.h+h.bbox.d+f+s;i=h.bbox.w;e.createDelimiter(k,8730,o,j);e.Measured(k);var m=0;if(k.isMultiChar||(e.AdjustSurd&&e.imgFonts)){k.bbox.w*=0.95}if(k.bbox.h+k.bbox.d>o){f=((k.bbox.h+k.bbox.d)-(o-s))/2}var u=e.FONTDATA.DELIMITERS[e.FONTDATA.RULECHAR];if(!u||i<u.HW[0][0]*j||j<0.75){e.createRule(l,s,0,i)}else{e.createDelimiter(l,e.FONTDATA.RULECHAR,i,j)}o=h.bbox.h+f+s;m=this.HTMLaddRoot(r,k,m,k.bbox.h+k.bbox.d-o,j);e.placeBox(k,m,o-k.bbox.h);e.placeBox(l,m+k.bbox.w,o-l.bbox.h+e.rfuzz);e.placeBox(h,m+k.bbox.w,0);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n},HTMLaddRoot:function(h,g,f,j,i){return f}});a.mroot.Augment({toHTML:a.msqrt.prototype.toHTML,HTMLaddRoot:function(o,g,m,k,f){var i=e.createBox(o);if(this.data[1]){var l=this.data[1].toHTML(i);l.style.paddingRight=l.style.paddingLeft="";e.Measured(l,i)}else{i.bbox=this.HTMLzeroBBox()}var j=this.HTMLrootHeight(g.bbox.h+g.bbox.d,f,i)-k;var n=Math.min(i.bbox.w,i.bbox.rw);m=Math.max(n,g.offset);e.placeBox(i,m-n,j);return m-g.offset},HTMLrootHeight:function(h,g,f){return 0.45*(h-0.9*g)+0.6*g+Math.max(0,f.bbox.d-0.075)}});a.mfenced.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data.open){this.data.open.toHTML(k)}if(this.data[0]!=null){this.data[0].toHTML(k)}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){if(this.data["sep"+g]){this.data["sep"+g].toHTML(k)}this.data[g].toHTML(k)}}if(this.data.close){this.data.close.toHTML(k)}var n=this.HTMLcomputeBBox(k);var j=k.bbox.h,l=k.bbox.d;for(g=0,f=n.length;g<f;g++){n[g].HTMLstretchV(k,j,l)}if(n.length){this.HTMLcomputeBBox(k,true)}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLcomputeBBox:function(k,j){var g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.munderover.Augment({toHTML:function(G,B,z){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,G)}G=this.HTMLcreateSpan(G);var K=this.HTMLgetScale();var j=e.createStack(G);var l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;H<C;H++){if(this.data[H]){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}if(q.bbox.w>F){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];o=e.TeX.big_op_spacing5*K;var u=(H!=this.base&&f[this.ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q.insertBefore(e.createSpace(q.parentNode,0,0,-q.bbox.lw),q.firstChild)}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(F-q.bbox.w)/2,right:F-q.bbox.w}[f.align];p=v;n=0;if(H==this.over){if(u){E=Math.max(w*K*A,2.5/this.em);o=0;if(h.bbox.skew){p+=h.bbox.skew}}else{s=e.TeX.big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E=Math.max(s,r-Math.max(0,q.bbox.d))}E=Math.max(E,1.5/this.em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==this.under){if(u){E=3*w*K*A;o=0}else{s=e.TeX.big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E=Math.max(s,r-q.bbox.h)}E=Math.max(E,1.5/this.em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}e.placeBox(q,p,n)}}this.HTMLhandleSpace(G);this.HTMLhandleColor(G);return G},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.msubsup.Augment({toHTML:function(C,A,w){C=this.HTMLcreateSpan(C);var G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var m=i.bbox.h-y,l=i.bbox.d+x,F=0,z;if(i.bbox.ic){F=i.bbox.ic}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&&i.bbox.scale===1&&!this.data[this.base].Get("largeop")){m=l=0}}var B=this.getValues("subscriptshift","superscriptshift");B.subscriptshift=(B.subscriptshift===""?0:e.length2em(B.subscriptshift));B.superscriptshift=(B.superscriptshift===""?0:e.length2em(B.superscriptshift));if(!f){if(k){l=Math.max(l,e.TeX.sub1*G,k.bbox.h-(4/5)*E,B.subscriptshift);e.placeBox(k,i.bbox.w+o-F,-l,k.bbox)}}else{if(!k){g=this.getValues("displaystyle","texprimestyle");z=e.TeX[(g.displaystyle?"sup1":(g.texprimestyle?"sup3":"sup2"))];m=Math.max(m,z*G,f.bbox.d+(1/4)*E,B.superscriptshift);e.placeBox(f,i.bbox.w+o,m,f.bbox)}else{l=Math.max(l,e.TeX.sub2*G);var n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k&&k!==""){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}a.mbase.prototype.displayAlign=d.config.displayAlign;a.mbase.prototype.displayIndent=d.config.displayIndent;m=e.Measured(this.data[0].toHTML(i),i)}e.placeBox(i,0,0);var j=e.em/e.outerEm;e.em/=j;n.bbox.h*=j;n.bbox.d*=j;n.bbox.w*=j;n.bbox.lw*=j;n.bbox.rw*=j;if(m&&m.bbox.width!=null){l.style.width=m.bbox.width;i.style.width="100%"}this.HTMLhandleColor(n);if(m){e.createRule(n,m.bbox.h*j,m.bbox.d*j,0)}if(!this.isMultiline&&this.Get("display")==="block"&&n.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return g}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",e,"jax.js"]),0)})});d.Register.StartupHook("End Config",function(){d.Browser.Select({MSIE:function(f){var i=f.versionAtLeast("7.0");var h=f.versionAtLeast("8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");e.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";e.config.styles[".MathJax .MathJax_HitBox"].opacity=0;e.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)";e.Augment({getMarginScale:e.getMSIEmarginScale,PaddingWidthBug:true,msieEventBug:f.isIE9,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,msieBorderWidthBug:g,msieInlineBlockAlignBug:(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,msieCloneNodeBug:(h&&f.version==="8.0"),negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug:true,zeroWidthBug:true,FontFaceBug:true,msieFontCSSBug:f.isIE9,allowWebFonts:"eot"})},Firefox:function(g){var h=false;if(g.versionAtLeast("3.5")){var f=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||(d.config.root+"/").substr(0,f.length)===f){h="otf"}}e.Augment({useProcessingFrame:true,ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:h})},Safari:function(j){var h=j.versionAtLeast("3.0");var g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(j.isPC){e.Augment({adjustAvailableFonts:e.removeSTIXfonts})}if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.05,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:e.removeSTIXfonts})},Konqueror:function(f){e.Augment({konquerorVerticalAlignBug:true,noContextMenuBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); diff --git a/config/TeX-AMS_HTML.js b/config/TeX-AMS_HTML.js @@ -31,7 +31,7 @@ MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.3",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+a},formatURL:function(a){return"#mjx-eqn-"+escape(a)}}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); MathJax.Extension.tex2jax={version:"1.1.4",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":"")+(b.processRefs?"|\\\\(eq)?ref\\{[^}]*\\}":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"); @@ -47,10 +47,10 @@ 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",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); -(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML.js"); diff --git a/extensions/TeX/AMSmath.js b/extensions/TeX/AMSmath.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Extension["TeX/AMSmath"]={version:"1.1.1",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};MathJax.Hub.Insert(d,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}});g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); +MathJax.Extension["TeX/AMSmath"]={version:"1.1.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.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",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],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",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([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",c([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",c([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,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var i=this.trimSpaces(this.GetArgument(j)),h=i;if(i==="*"){h=i=this.GetArgument(j)}else{i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+j)}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h="";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h="\\nolimits";var j=this.trimSpaces(this.GetArgument(i));if(j=="*"){h="\\limits";j=this.trimSpaces(this.GetArgument(i))}j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(i+" must come at the beginning of the line")}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k)),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error("Illegal alignment specified in "+k)}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+i)}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(j,i,h){var k=this.GetArgument("\\begin{"+j.name+"}");if(k.match(/[^0-9]/)){g.Error("Argument to \\begin{"+j.name+"} must me a positive integer")}align="";spacing=[];while(k>0){align+="rl";spacing.push("0em 0em");k--}spacing=spacing.join(" ");if(h){return this.AMSarray(j,i,h,align,spacing)}return this.Array(j,null,null,align,spacing,".5em","D")},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]){g.Error("Missing or unrecognized delimiter for "+h)}return this.convertDelimiter(i)}});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,k;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}var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.table[0]=[this.getTag()].concat(this.table[0]);h=b.mlabeledtr}this.table[0]=h.apply(b,this.table[0]);for(k=1,j=this.table.length;k<j;k++){this.table[k]=b.mtr.apply(b,this.table[k])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput(f.refs)}return null});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"); diff --git a/extensions/TeX/AMSsymbols.js b/extensions/TeX/AMSsymbols.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.1.3";var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var d=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":d,"\u2323":d,"\u25B3":d,"\uE006":d,"\uE007":d,"\uE00C":d,"\uE00D":d,"\uE00E":d,"\uE00F":d,"\uE010":d,"\uE011":d,"\uE016":d,"\uE017":d,"\uE018":d,"\uE019":d,"\uE01A":d,"\uE01B":d,"\uE04B":d,"\uE04F":d}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"); diff --git a/extensions/TeX/HTML.js b/extensions/TeX/HTML.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1";var c=MathJax.InputJax.TeX;var a=c.Definitions;a.macros.href="HREF_attribute";a.macros["class"]="CLASS_attribute";a.macros.style="STYLE_attribute";a.macros.cssId="ID_attribute";c.Parse.Augment({HREF_attribute:function(f){var e=this.GetArgument(f),d=this.GetArgumentMML(f);this.Push(d.With({href:e}))},CLASS_attribute:function(e){var f=this.GetArgument(e),d=this.GetArgumentMML(e);if(d["class"]!=null){f=d["class"]+" "+f}this.Push(d.With({"class":f}))},STYLE_attribute:function(e){var f=this.GetArgument(e),d=this.GetArgumentMML(e);if(d.style!=null){if(f.charAt(f.length-1)!==";"){f+=";"}f=d.style+" "+f}this.Push(d.With({style:f}))},ID_attribute:function(f){var e=this.GetArgument(f),d=this.GetArgumentMML(f);this.Push(d.With({id:e}))},GetArgumentMML:function(e){var d=this.ParseArg(e);if(d.inferred&&d.data.length==1){d=d.data[0]}else{delete d.inferred}return d}});MathJax.Hub.Startup.signal.Post("TeX HTML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/HTML.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.1";var c=MathJax.InputJax.TeX;var a=c.Definitions;a.Add({macros:{href:"HREF_attribute","class":"CLASS_attribute",style:"STYLE_attribute",cssId:"ID_attribute"}});c.Parse.Augment({HREF_attribute:function(f){var e=this.GetArgument(f),d=this.GetArgumentMML(f);this.Push(d.With({href:e}))},CLASS_attribute:function(e){var f=this.GetArgument(e),d=this.GetArgumentMML(e);if(d["class"]!=null){f=d["class"]+" "+f}this.Push(d.With({"class":f}))},STYLE_attribute:function(e){var f=this.GetArgument(e),d=this.GetArgumentMML(e);if(d.style!=null){if(f.charAt(f.length-1)!==";"){f+=";"}f=d.style+" "+f}this.Push(d.With({style:f}))},ID_attribute:function(f){var e=this.GetArgument(f),d=this.GetArgumentMML(f);this.Push(d.With({id:e}))},GetArgumentMML:function(e){var d=this.ParseArg(e);if(d.inferred&&d.data.length==1){d=d.data[0]}else{delete d.inferred}return d}});MathJax.Hub.Startup.signal.Post("TeX HTML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/HTML.js"); diff --git a/extensions/TeX/begingroup.js b/extensions/TeX/begingroup.js @@ -0,0 +1,16 @@ +/* + * /MathJax/extensions/TeX/begingroup.js + * + * Copyright (c) 2010 Design Science, Inc. + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var d="1.1.1";var e=MathJax.InputJax.TeX,b=e.Definitions;var a=MathJax.Object.Subclass({macros:null,environments:null,Init:function(f,g){this.macros=(f||{});this.environments=(g||{})},Find:function(f,g){if(this[g][f]){return this[g][f]}},Def:function(f,h,g){this[g][f]=h},Undef:function(f,g){delete this[g][f]},Merge:function(f){MathJax.Hub.Insert(this.macros,f.macros);MathJax.Hub.Insert(this.environments,f.environments)},MergeGlobals:function(f){var g=this.macros;for(var h in g){if(g.hasOwnProperty(h)&&g[h].global){f.Def(h,g[h],"macros",true);delete g[h].global;delete g[h]}}},Clear:function(h){this.environments={};if(h){this.macros={}}else{var f=this.macros;for(var g in f){if(f.hasOwnProperty(g)&&!f[g].global){delete f[g]}}}return this}});var c=e.nsStack=MathJax.Object.Subclass({stack:null,top:0,isEqn:false,Init:function(f){this.isEqn=f;this.stack=[];if(!f){this.Push(a(b.macros,b.environments))}else{this.Push(a())}},Def:function(f,i,g,h){var j=this.top-1;if(h){while(j>0){this.stack[j].Undef(f,g);j--}if(!(i instanceof Array)){i=[i]}if(this.isEqn){i.global=true}}this.stack[j].Def(f,i,g)},Push:function(f){this.stack.push(f);this.top=this.stack.length},Pop:function(){var f;if(this.top>1){f=this.stack[--this.top];if(this.isEqn){this.stack.pop()}}else{if(this.isEqn){this.Clear()}}return f},Find:function(f,h){for(var g=this.top-1;g>=0;g--){var j=this.stack[g].Find(f,h);if(j){return j}}return null},Merge:function(f){f.stack[0].MergeGlobals(this);this.stack[this.top-1].Merge(f.stack[0]);var g=[this.top,this.stack.length-this.top].concat(f.stack.slice(1));this.stack.splice.apply(this.stack,g);this.top=this.stack.length},Reset:function(){this.top=this.stack.length},Clear:function(f){this.stack=[this.stack[0].Clear()];this.top=this.stack.length}},{nsFrame:a});b.macros.begingroup="BeginGroup";b.macros.endgroup="EndGroup";b.macros.global=["Extension","newcommand"];b.macros.gdef=["Extension","newcommand"];e.Parse.Augment({BeginGroup:function(f){e.eqnStack.Push(a())},EndGroup:function(f){if(e.eqnStack.top>1){e.eqnStack.Pop()}else{if(e.rootStack.top===1){e.Error("Extra "+f+" or missing \\begingroup")}else{e.eqnStack.Clear();e.rootStack.Pop()}}},csFindMacro:function(f){return(e.eqnStack.Find(f,"macros")||e.rootStack.Find(f,"macros"))},envFindName:function(f){return(e.eqnStack.Find(f,"environments")||e.rootStack.Find(f,"environments"))}});e.rootStack=c();e.eqnStack=c(true);e.prefilterHooks.Add(function(){e.rootStack.Reset();e.eqnStack.Clear(true)});e.postfilterHooks.Add(function(){e.rootStack.Merge(e.eqnStack)});MathJax.Hub.Register.StartupHook("TeX newcommand Ready",function(){b.macros.global="Global";b.macros.gdef=["Macro","\\global\\def"];e.Parse.Augment({setDef:function(f,g){g.isUser=true;e.eqnStack.Def(f,g,"macros",this.stack.env.isGlobal);delete this.stack.env.isGlobal},setEnv:function(f,g){g.isUser=true;e.eqnStack.Def(f,g,"environments")},Global:function(f){var g=this.i;var h=this.GetCSname(f);this.i=g;if(h!=="let"&&h!=="def"&&h!=="newcommand"){e.Error(f+" not followed by \\let, \\def, or \\newcommand")}this.stack.env.isGlobal=true}})});MathJax.Hub.Startup.signal.Post("TeX begingroup Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/begingroup.js"); + diff --git a/extensions/TeX/newcommand.js b/extensions/TeX/newcommand.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1";var c=MathJax.InputJax.TeX;var a=c.Definitions;MathJax.Hub.Insert(a,{macros:{newcommand:"NewCommand",renewcommand:"NewCommand",newenvironment:"NewEnvironment",def:"MacroDef"}});c.Parse.Augment({NewCommand:function(d){var e=this.trimSpaces(this.GetArgument(d)),g=this.trimSpaces(this.GetBrackets(d)),f=this.GetArgument(d);if(g===""){g=null}if(e.charAt(0)==="\\"){e=e.substr(1)}if(!e.match(/^(.|[a-z]+)$/i)){c.Error("Illegal control sequence name for "+d)}if(g!=null&&!g.match(/^[0-9]+$/)){c.Error("Illegal number of parameters specified in "+d)}a.macros[e]=["Macro",f,g]},NewEnvironment:function(e){var f=this.trimSpaces(this.GetArgument(e)),h=this.trimSpaces(this.GetBrackets(e)),g=this.GetArgument(e),d=this.GetArgument(e);if(h===""){h=null}if(h!=null&&!h.match(/^[0-9]+$/)){c.Error("Illegal number of parameters specified in "+e)}a.environment[f]=["BeginEnv","EndEnv",g,d,h]},MacroDef:function(d){var e=this.GetCSname(d),g=this.GetTemplate(d,"\\"+e),f=this.GetArgument(d);if(!(g instanceof Array)){a.macros[e]=["Macro",f,g]}else{a.macros[e]=["MacroWithTemplate",f,g[0],g[1]]}},GetCSname:function(e){var f=this.GetNext();if(f!=="\\"){c.Error("\\ must be followed by a control sequence")}var d=this.trimSpaces(this.GetArgument(e));return d.substr(1)},GetTemplate:function(f,e){var j,g=[],h=0;j=this.GetNext();var d=this.i;while(this.i<this.string.length){j=this.GetNext();if(j==="#"){if(d!==this.i){g[h]=this.string.substr(d,this.i-d)}j=this.string.charAt(++this.i);if(!j.match(/^[1-9]$/)){c.Error("Illegal use of # in template for "+e)}if(parseInt(j)!=++h){c.Error("Parameters for "+e+" must be numbered sequentially")}d=this.i+1}else{if(j==="{"){if(d!==this.i){g[h]=this.string.substr(d,this.i-d)}if(g.length>0){return[h,g]}else{return h}}}this.i++}c.Error("Missing replacement string for definition of "+f)},MacroWithTemplate:function(e,h,j,g){if(j){var d=[];this.GetNext();if(g[0]&&!this.MatchParam(g[0])){c.Error("Use of "+e+" doesn't match its definition")}for(var f=0;f<j;f++){d.push(this.GetParameter(e,g[f+1]))}h=this.SubstituteArgs(d,h)}this.string=this.AddArgs(h,this.string.slice(this.i));this.i=0;if(++this.macroCount>c.config.MAXMACROS){c.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},BeginEnv:function(g,j,d,h){if(h){var e=[];for(var f=0;f<h;f++){e.push(this.GetArgument("\\begin{"+name+"}"))}j=this.SubstituteArgs(e,j);d=this.SubstituteArgs(e,d)}g.edef=d;this.string=this.AddArgs(j,this.string.slice(this.i));this.i=0;return g},EndEnv:function(d,e){this.string=this.AddArgs(d.edef,this.string.slice(this.i));this.i=0;return e},GetParameter:function(e,h){if(h==null){return this.GetArgument(e)}var g=this.i,d=0,f=0;while(this.i<this.string.length){if(this.string.charAt(this.i)==="{"){if(this.i===g){f=1}this.GetArgument(e);d=this.i-g}else{if(this.MatchParam(h)){if(f){g++;d-=2}return this.string.substr(g,d)}else{this.i++;d++;f=0}}}c.Error("Runaway argument for "+e+"?")},MatchParam:function(d){if(this.string.substr(this.i,d.length)!==d){return 0}this.i+=d.length;return 1}});c.Environment=function(d){a.environment[d]=["BeginEnv","EndEnv"].concat([].slice.call(arguments,1))};MathJax.Hub.Startup.signal.Post("TeX newcommand Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/newcommand.js"); +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var c=MathJax.InputJax.TeX;var a=c.Definitions;a.Add({macros:{newcommand:"NewCommand",renewcommand:"NewCommand",newenvironment:"NewEnvironment",renewenvironment:"NewEnvironment",def:"MacroDef",let:"Let"}},null,true);c.Parse.Augment({NewCommand:function(d){var e=this.trimSpaces(this.GetArgument(d)),g=this.trimSpaces(this.GetBrackets(d)),f=this.GetArgument(d);if(g===""){g=null}if(e.charAt(0)==="\\"){e=e.substr(1)}if(!e.match(/^(.|[a-z]+)$/i)){c.Error("Illegal control sequence name for "+d)}if(g!=null&&!g.match(/^[0-9]+$/)){c.Error("Illegal number of parameters specified in "+d)}this.setDef(e,["Macro",f,g])},NewEnvironment:function(e){var f=this.trimSpaces(this.GetArgument(e)),h=this.trimSpaces(this.GetBrackets(e)),g=this.GetArgument(e),d=this.GetArgument(e);if(h===""){h=null}if(h!=null&&!h.match(/^[0-9]+$/)){c.Error("Illegal number of parameters specified in "+e)}this.setEnv(f,["BeginEnv","EndEnv",g,d,h])},MacroDef:function(d){var e=this.GetCSname(d),g=this.GetTemplate(d,"\\"+e),f=this.GetArgument(d);if(!(g instanceof Array)){this.setDef(e,["Macro",f,g])}else{this.setDef(e,["MacroWithTemplate",f].concat(g))}},Let:function(d){var e=this.GetCSname(d),f;var g=this.GetNext();if(g==="="){this.i++;g=this.GetNext()}if(g==="\\"){d=this.GetCSname(d);f=this.csFindMacro(d);if(!f){if(a.mathchar0mi[d]){f=["csMathchar0mi",a.mathchar0mi[d]]}else{if(a.mathchar0mo[d]){f=["csMathchar0mo",a.mathchar0mo[d]]}else{if(a.mathchar7[d]){f=["csMathchar7",a.mathchar7[d]]}else{if(a.delimiter["\\"+d]!=null){f=["csDelimiter",a.delimiter["\\"+d]]}}}}}}else{f=["Macro",g];this.i++}this.setDef(e,f)},setDef:function(d,e){e.isUser=true;a.macros[d]=e},setEnv:function(d,e){e.isUser=true;a.environment[d]=e},GetCSname:function(e){var f=this.GetNext();if(f!=="\\"){c.Error("\\ must be followed by a control sequence")}var d=this.trimSpaces(this.GetArgument(e));return d.substr(1)},GetTemplate:function(f,e){var j,g=[],h=0;j=this.GetNext();var d=this.i;while(this.i<this.string.length){j=this.GetNext();if(j==="#"){if(d!==this.i){g[h]=this.string.substr(d,this.i-d)}j=this.string.charAt(++this.i);if(!j.match(/^[1-9]$/)){c.Error("Illegal use of # in template for "+e)}if(parseInt(j)!=++h){c.Error("Parameters for "+e+" must be numbered sequentially")}d=this.i+1}else{if(j==="{"){if(d!==this.i){g[h]=this.string.substr(d,this.i-d)}if(g.length>0){return[h,g]}else{return h}}}this.i++}c.Error("Missing replacement string for definition of "+f)},MacroWithTemplate:function(e,h,j,g){if(j){var d=[];this.GetNext();if(g[0]&&!this.MatchParam(g[0])){c.Error("Use of "+e+" doesn't match its definition")}for(var f=0;f<j;f++){d.push(this.GetParameter(e,g[f+1]))}h=this.SubstituteArgs(d,h)}this.string=this.AddArgs(h,this.string.slice(this.i));this.i=0;if(++this.macroCount>c.config.MAXMACROS){c.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},BeginEnv:function(g,j,d,h){if(h){var e=[];for(var f=0;f<h;f++){e.push(this.GetArgument("\\begin{"+name+"}"))}j=this.SubstituteArgs(e,j);d=this.SubstituteArgs(e,d)}g.edef=d;this.string=this.AddArgs(j,this.string.slice(this.i));this.i=0;return g},EndEnv:function(d,e){this.string=this.AddArgs(d.edef,this.string.slice(this.i));this.i=0;return e},GetParameter:function(e,h){if(h==null){return this.GetArgument(e)}var g=this.i,d=0,f=0;while(this.i<this.string.length){if(this.string.charAt(this.i)==="{"){if(this.i===g){f=1}this.GetArgument(e);d=this.i-g}else{if(this.MatchParam(h)){if(f){g++;d-=2}return this.string.substr(g,d)}else{this.i++;d++;f=0}}}c.Error("Runaway argument for "+e+"?")},MatchParam:function(d){if(this.string.substr(this.i,d.length)!==d){return 0}this.i+=d.length;return 1}});c.Environment=function(d){a.environment[d]=["BeginEnv","EndEnv"].concat([].slice.call(arguments,1));a.environment[d].isUser=true};MathJax.Hub.Startup.signal.Post("TeX newcommand Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/newcommand.js"); diff --git 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(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],def:["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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(s){var m=this.GetCS(),r,p;if(g.macros[m]){var o=g.macros[m];if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,["\\"+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){r=g.mathchar0mi[m];p={mathvariant:j.VARIANT.ITALIC};if(r instanceof Array){p=r[1];r=r[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.mathchar0mo[m]){r=g.mathchar0mo[m];p={stretchy:h};if(r instanceof Array){p=r[1];p.stretchy=h;r=r[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+r)).With(p)))}else{if(g.mathchar7[m]){r=g.mathchar7[m];p={mathvariant:j.VARIANT.NORMAL};if(r instanceof Array){p=r[1];r=r[0]}if(this.stack.env.font){p.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+r)).With(p)))}else{if(g.delimiter["\\"+m]!=null){var q=g.delimiter["\\"+m];p={};if(q instanceof Array){p=q[1];q=q[0]}if(q.length===4){q=j.entity("#x"+q)}else{q=j.chars(q)}this.Push(this.mmlToken(j.mo(q).With({fence:h,stretchy:h}).With(p)))}else{this.csUndefined("\\"+m)}}}}}},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}if(!g.environment[o]){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var p=g.environment[o];if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); +(function(e,c,k){var d=true,h=false,j,i=String.fromCharCode(160);var f=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(p instanceof j.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):d);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n "+this.data.join("\n ")+"\n]"}});var b=f.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(){return this.data.pop()},mmlData:function(m,n){if(m==null){m=d}if(this.data.length===1&&!n){return this.data[0]}return j.mrow.apply(j,this.data).With((m?{inferred:d}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(h);this.data=[]}if(m.type==="cell"&&this.isOpen){e.Error("Misplaced "+m.name)}if(m.isClose&&this[m.type+"Error"]){e.Error(this[m.type+"Error"])}if(!m.isNotStack){return d}this.Push(m.data[0]);return h},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:d,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:d});b.open=b.Subclass({type:"open",isOpen:d,stopError:"Extra open brace or missing close brace",checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(j.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:d});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(n){var m=["","subscript","superscript"][this.position];if(n.type==="open"||n.type==="left"){return d}if(n.type==="mml"){this.data[0].SetData(this.position,n.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,n)){e.Error("Missing open brace for "+m)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:d,name:"\\over",checkItem:function(o,m){if(o.type==="over"){e.Error("Ambiguous use of "+o.name)}if(o.isClose){var n=j.mfrac(this.num,this.mmlData(h));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texClass=j.TEXCLASS.INNER;n.texWithDelims=d;n=j.mfenced(n).With({open:this.open,close:this.close})}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:d,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(n){if(n.type==="right"){var m=j.mfenced(this.data.length===1?this.data[0]:j.mrow.apply(j,this.data));return b.mml(m.With({open:this.delim,close:n.delim}))}return this.SUPER(arguments).checkItem.call(this,n)}});b.right=b.Subclass({type:"right",isClose:d,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:d,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){e.Error("\\begin{"+this.name+"} ended with \\end{"+m.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){e.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:d});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=j.mstyle.apply(j,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){e.Error("Missing box for "+this.name)}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=j.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:d,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return h}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return h}this.EndTable();this.clearEnv();var m=j.mtable.apply(j,this.table).With(this.arraydef);if(this.open||this.close){m=j.mfenced(m).With({open:this.open,close:this.close})}m=b.mml(m);if(this.requireClose){if(n.type==="close"){return m}e.Error("Missing close brace")}return[m,n]}return this.SUPER(arguments).checkItem.call(this,n)},EndEntry:function(){this.row.push(j.mtd.apply(j,this.data));this.data=[]},EndRow:function(){this.table.push(j.mtr.apply(j,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.arraydef.frame=m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:d});b.mml=b.Subclass({type:"mml",isNotStack:d,Push:function(){for(var o=0,n=arguments.length;o<n;o++){if(arguments[o].type!=="mo"&&arguments[o].isEmbellished()){arguments[o]=j.TeXAtom(arguments[o]).With({isEmbellishedWrapper:d})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={Add:function(m,p,o){if(!p){p=this}for(var n in m){if(m.hasOwnProperty(n)){if(typeof m[n]==="object"&&!(m[n] instanceof Array)&&(typeof p[n]==="object"||typeof p[n]==="function")){this.Add(m[n],p[n],m[n],o)}else{if(!p[n]||!p[n].isUser||!o){p[n]=m[n]}}}}return p}};var l=function(){j=MathJax.ElementJax.mml;c.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:j.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:j.VARIANT.NORMAL}],Re:["211C",{mathvariant:j.VARIANT.NORMAL}],Im:["2111",{mathvariant:j.VARIANT.NORMAL}],partial:["2202",{mathvariant:j.VARIANT.NORMAL}],infty:["221E",{mathvariant:j.VARIANT.NORMAL}],prime:["2032",{mathvariant:j.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:j.VARIANT.NORMAL}],nabla:["2207",{mathvariant:j.VARIANT.NORMAL}],top:["22A4",{mathvariant:j.VARIANT.NORMAL}],bot:["22A5",{mathvariant:j.VARIANT.NORMAL}],angle:["2220",{mathvariant:j.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:j.VARIANT.NORMAL}],backslash:["2216",{mathvariant:j.VARIANT.NORMAL}],forall:["2200",{mathvariant:j.VARIANT.NORMAL}],exists:["2203",{mathvariant:j.VARIANT.NORMAL}],neg:["00AC",{mathvariant:j.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:j.VARIANT.NORMAL}],flat:["266D",{mathvariant:j.VARIANT.NORMAL}],natural:["266E",{mathvariant:j.VARIANT.NORMAL}],sharp:["266F",{mathvariant:j.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:j.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:j.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:j.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:j.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigvee:["22C1",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigwedge:["22C0",{texClass:j.TEXCLASS.OP,movesupsub:d}],biguplus:["2A04",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcap:["22C2",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigcup:["22C3",{texClass:j.TEXCLASS.OP,movesupsub:d}],"int":["222B",{texClass:j.TEXCLASS.OP}],intop:["222B",{texClass:j.TEXCLASS.OP,movesupsub:d,movablelimits:d}],iint:["222C",{texClass:j.TEXCLASS.OP}],iiint:["222D",{texClass:j.TEXCLASS.OP}],prod:["220F",{texClass:j.TEXCLASS.OP,movesupsub:d}],sum:["2211",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigotimes:["2A02",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigoplus:["2A01",{texClass:j.TEXCLASS.OP,movesupsub:d}],bigodot:["2A00",{texClass:j.TEXCLASS.OP,movesupsub:d}],oint:["222E",{texClass:j.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:j.TEXCLASS.OP,movesupsub:d}],smallint:["222B",{largeop:h}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:h}],oslash:["2298",{largeop:h}],otimes:["2297",{largeop:h}],ominus:["2296",{largeop:h}],oplus:["2295",{largeop:h}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:j.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:j.TEXCLASS.PUNCT}],colon:["003A",{texClass:j.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:j.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:j.TEXCLASS.ORD}],"\\|":["2225",{texClass:j.TEXCLASS.ORD}],"\\vert":["|",{texClass:j.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",d,0],textstyle:["SetStyle","T",h,0],scriptstyle:["SetStyle","S",h,1],scriptscriptstyle:["SetStyle","SS",h,2],rm:["SetFont",j.VARIANT.NORMAL],mit:["SetFont",j.VARIANT.ITALIC],oldstyle:["SetFont",j.VARIANT.OLDSTYLE],cal:["SetFont",j.VARIANT.CALIGRAPHIC],it:["SetFont",j.VARIANT.ITALIC],bf:["SetFont",j.VARIANT.BOLD],bbFont:["SetFont",j.VARIANT.DOUBLESTRUCK],scr:["SetFont",j.VARIANT.SCRIPT],frak:["SetFont",j.VARIANT.FRAKTUR],sf:["SetFont",j.VARIANT.SANSSERIF],tt:["SetFont",j.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",j.LENGTH.THINMATHSPACE],":":["Spacer",j.LENGTH.THINMATHSPACE],">":["Spacer",j.LENGTH.MEDIUMMATHSPACE],";":["Spacer",j.LENGTH.THICKMATHSPACE],"!":["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",j.LENGTH.THINMATHSPACE],negthinspace:["Spacer",j.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",j.TEXCLASS.ORD,0.85],Big:["MakeBig",j.TEXCLASS.ORD,1.15],bigg:["MakeBig",j.TEXCLASS.ORD,1.45],Bigg:["MakeBig",j.TEXCLASS.ORD,1.75],bigl:["MakeBig",j.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",j.TEXCLASS.OPEN,1.15],biggl:["MakeBig",j.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",j.TEXCLASS.OPEN,1.75],bigr:["MakeBig",j.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",j.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",j.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",j.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",j.TEXCLASS.REL,0.85],Bigm:["MakeBig",j.TEXCLASS.REL,1.15],biggm:["MakeBig",j.TEXCLASS.REL,1.45],Biggm:["MakeBig",j.TEXCLASS.REL,1.75],mathord:["TeXAtom",j.TEXCLASS.ORD],mathop:["TeXAtom",j.TEXCLASS.OP],mathopen:["TeXAtom",j.TEXCLASS.OPEN],mathclose:["TeXAtom",j.TEXCLASS.CLOSE],mathbin:["TeXAtom",j.TEXCLASS.BIN],mathrel:["TeXAtom",j.TEXCLASS.REL],mathpunct:["TeXAtom",j.TEXCLASS.PUNCT],mathinner:["TeXAtom",j.TEXCLASS.INNER],vcenter:["TeXAtom",j.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",j.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",j.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],require:"Require"},environment:{array:["Array"],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",j.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",j.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 m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=e.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var m;while(this.i<this.string.length){m=this.string.charAt(this.i++);if(g.special[m]){this[g.special[m]](m)}else{if(g.letter.test(m)){this.Variable(m)}else{if(g.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},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(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!(o instanceof Array)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi[m]){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo[m]){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7[m]){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter["\\"+m]!=null){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return g.macros[m]},csMathchar0mi:function(m,o){var n={mathvariant:j.VARIANT.ITALIC};if(o instanceof Array){n=o[1];o=o[0]}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(o instanceof Array){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(j.mo(j.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:j.VARIANT.NORMAL};if(o instanceof Array){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=j.entity("#x"+o)}else{o=j.chars(o)}this.Push(this.mmlToken(j.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){e.Error("Undefined control sequence "+m)},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(j.mi(j.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=j.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=j.mo(j.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(j.mtext(j.chars(i)))},Space:function(m){},Superscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sup]){if(!n.data[n.sup].isPrime){e.Error("Double exponent: use braces to clarify")}n=j.msubsup(n,null,null)}m=n.sup}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.over]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.over}else{n=j.msubsup(n,null,null);m=n.sup}}this.Push(b.subsup(n).With({position:m}))},Subscript:function(o){var m,n=this.stack.Prev();if(!n){n=j.mi("")}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}if(n.type==="msubsup"){if(n.data[n.sub]){e.Error("Double subscripts: use braces to clarify")}m=n.sub}else{if(n.movesupsub){if(n.type!=="munderover"||n.data[n.under]){n=j.munderover(n,null,null).With({movesupsub:d})}m=n.under}else{n=j.msubsup(n,null,null);m=n.sub}}this.Push(b.subsup(n).With({position:m}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(o){var n=this.stack.Prev();if(!n){n=j.mi()}if(n.type==="msubsup"&&n.data[n.sup]){e.Error("Prime causes double exponent: use braces to clarify")}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=this.mmlToken(j.mo(j.chars(m)).With({isPrime:d,variantForm:e.isSTIX}));this.Push(j.msubsup(n,null,m))},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){e.Error("You can't use 'macro parameter character #' in math mode")},Other:function(o){var n={stretchy:false},m;if(this.stack.env.font){n.mathvariant=this.stack.env.font}if(g.remap[o]){o=g.remap[o];if(o instanceof Array){n=o[1];o=o[0]}m=j.mo(j.entity("#x"+o))}else{m=j.mo(o)}if(m.autoDefault("texClass",true)==""){m=j.TeXAtom(m)}this.Push(this.mmlToken(m.With(n)))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(j.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(j.mspace().With({width:n,mathsize:j.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},NamedOp:function(o,n,q){var p=(n!=null&&n===0?h:d);if(!q){q=o.substr(1)}n=((n||n==null)?d:h);q=q.replace(/ /,String.fromCharCode(8198));var m=j.mo(q).With({movablelimits:n,movesupsub:p,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var o=this.stack.Prev("nopop");if(o.texClass!==j.TEXCLASS.OP){e.Error(n+" is allowed only on operators")}o.movesupsub=(m?d:h);o.movablelimits=h},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(j.mfrac(m,o))},Sqrt:function(o){var p=this.GetBrackets(o),m=this.ParseArg(o);if(p==""){m=j.msqrt.apply(j,m.array())}else{m=j.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(j.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=e.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=j.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){e.Error(m+" can appear only within a root")}if(this.stack.global[p]){e.Error("Multiple use of "+m)}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){e.Error("The argument to "+m+" must be an integer")}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,r){var q=this.ParseArg(o);var p={accent:true};if(this.stack.env.font){p.mathvariant=this.stack.env.font}var n=this.mmlToken(j.mo(j.entity("#x"+m)).With(p));n.stretchy=(r?d:h);this.Push(j.munderover(q,null,n).With({accent:d}))},UnderOver:function(o,r,m){var q={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}var n=j.munderover(p,null,null);if(m){n.movesupsub=d}n.data[n[q]]=this.mmlToken(j.mo(j.entity("#x"+r)).With({stretchy:d,accent:(q=="under")}));this.Push(n)},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,null,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);this.Push(j.munderover(n,o,null))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==j.TEXCLASS.OP){q.movesupsub=q.movablelimits=d;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){o=this.mmlToken(j.mo(n[1]).With({movablelimits:d,movesupsub:d,mathvariant:j.VARIANT.NORMAL,form:j.FORM.PREFIX,texClass:j.TEXCLASS.OP}));o.useMMLspacing&=~o.SPACE_ATTR.form}else{o=j.TeXAtom(e.Parse(m,this.stack.env).mml()).With(q)}}else{o=j.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},Strut:function(m){this.Push(j.mpadded(j.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=j.mphantom(this.ParseArg(n));if(m||o){p=j.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(p)},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o));var m=j.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(m)},Lap:function(n){var m=j.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1 width"}this.Push(m)},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:j.mspace().With({width:p,mathsize:j.SIZE.NORMAL,scriptlevel:1}),right:j.mspace().With({width:o,mathsize:j.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(m){this.Push(j.mspace().With({width:this.GetDimen(m),mathsize:j.SIZE.NORMAL,scriptlevel:0}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){n=j.mpadded(j.mrow()).With(r);if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){n=j.mstyle(n).With({mathbackground:(this.stack.env.color||"black")})}}else{n=j.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m);this.Push(j.TeXAtom(j.mo(o).With({minsize:n,maxsize:n,scriptlevel:0,fence:d,stretchy:d,symmetric:d})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(j.TeXAtom(j.munderover(o,null,n)).With({mclass:j.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(j.menclose.apply(j,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Require:function(m){var n=this.GetArgument(m);this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=e.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!k.loaded[k.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(k.Require(n))}},Macro:function(n,q,p){if(p){var m=[];for(var o=0;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(n,p,u,r,t,o,m,v){var s=this.GetNext();if(s===""){e.Error("Missing argument for "+n)}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:d,arraydef:{rowspacing:(o||"4pt"),columnspacing:(t||"1em")}});if(v){q.isCases=d}if(p||u){q.open=p;q.close=u}if(m==="D"){q.arraydef.displaystyle=d}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:d,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){e.Error("Extra alignment tab in \\cases text")}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:d,name:m}))},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(p.type!=="array"||p.data.length){e.Error("Misplaced "+n)}if(p.table.length==0){p.arraydef.frame=o}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},Begin:function(n){var o=this.GetArgument(n);if(o.match(/[^a-z*]/i)){e.Error('Invalid environment name "'+o+'"')}var p=this.envFindName(o);if(!p){e.Error('Unknown environment "'+o+'"')}if(++this.macroCount>e.config.MAXMACROS){e.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(p instanceof Array)){p=[p]}var m=b.begin().With({name:o,end:p[1],parse:this});if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}this.Push(m)},End:function(m){this.Push(b.end().With({name:this.GetArgument(m)}))},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(o,q,v,t,u,p,m,r){if(!t){t=this.GetArgument("\\begin{"+o.name+"}")}var w=("c"+t).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");t=t.replace(/[^clr]/g,"").split("").join(" ");t=t.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var s=b.array().With({arraydef:{columnalign:t,columnspacing:(u||"1em"),rowspacing:(p||"4pt")}});if(w.match(/[|:]/)){var n=(w.charAt(0)+w.charAt(w.length-1)).replace(/[^|:]/g,"");if(n!==""){s.arraydef.frame={"|":"solid",":":"dashed"}[n.charAt(0)];s.arraydef.framespacing=".5em .5ex"}w=w.substr(1,w.length-2);s.arraydef.columnlines=w.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(q){s.open=this.convertDelimiter(q)}if(v){s.close=this.convertDelimiter(v)}if(m==="D"){s.arraydef.displaystyle=d}if(m==="S"){s.arraydef.scriptlevel=1}if(r){s.arraydef.useHeight=h}this.Push(o);return s},convertDelimiter:function(m){if(m){m=g.delimiter[m]}if(m==null){return null}if(m instanceof Array){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(m){if(typeof(m)!="string"){return m}return m.replace(/^\s+|\s+$/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 m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){e.Error("Missing argument for "+n)}return null;case"}":if(!o){e.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":p++;break;case"}":if(p==0){e.Error("Extra close brace")}if(--p==0){return this.string.slice(m,this.i-1)}break}}e.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(n){if(this.GetNext()!="["){return""}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":o++;break;case"\\":this.i++;break;case"}":if(o--<=0){e.Error("Extra close brace while looking for ']'")}break;case"]":if(o==0){return this.string.slice(m,this.i-1)}break}}e.Error("Couldn't find closing ']' for argument to "+n)},GetDelimiter:function(m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(n=="\\"){n+=this.GetCS(m)}if(g.delimiter[n]!=null){return this.convertDelimiter(n)}}e.Error("Missing or unrecognized delimiter for "+m)},GetDimen:function(n){var o;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){o=this.GetArgument(n);if(o.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return o.replace(/ /g,"")}}else{o=this.string.slice(this.i);var m=o.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(m){this.i+=m[0].length;return m[1].replace(/ /g,"")}}e.Error("Missing dimension or its units for "+n)},GetUpTo:function(o,p){while(this.nextIsSpace()){this.i++}var n=this.i,m,r,q=0;while(this.i<this.string.length){m=this.i;r=this.string.charAt(this.i++);switch(r){case"\\":r+=this.GetCS();break;case"{":q++;break;case"}":if(q==0){e.Error("Extra close brace while looking for "+p)}q--;break}if(q==0&&r==p){return this.string.slice(n,m)}}e.Error("Couldn't find "+p+" for "+o)},ParseArg:function(m){return e.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return e.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(r,t){var q={displaystyle:h};if(t!=null){q.scriptlevel=t}if(this.stack.env.font){q.mathvariant=this.stack.env.font}if(!r.match(/\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(r,q)]}var p=0,m=0,s,o="";var n=[];while(p<r.length){s=r.charAt(p++);if(s==="$"){if(o==="$"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-1),{}).mml().With(q)));o="";m=p}else{if(o===""){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="$";m=p}}}else{if(s==="}"&&o==="}"){n.push(j.TeXAtom(e.Parse(r.slice(m,p),{}).mml().With(q)));o="";m=p}else{if(s==="\\"){if(o===""&&r.substr(p).match(/^(eq)?ref\s*\{/)){if(m<p-1){n.push(this.InternalText(r.slice(m,p-1),q))}o="}";m=p-1}else{s=r.charAt(p++);if(s==="("&&o===""){if(m<p-2){n.push(this.InternalText(r.slice(m,p-2),q))}o=")";m=p}else{if(s===")"&&o===")"){n.push(j.TeXAtom(e.Parse(r.slice(m,p-2),{}).mml().With(q)));o="";m=p}}}}}}}if(o!==""){e.Error("Math not terminated in text box")}if(m<r.length){n.push(this.InternalText(r.slice(m),q))}return n},InternalText:function(n,m){n=n.replace(/^\s+/,i).replace(/\s+$/,i);return j.mtext(j.chars(n)).With(m)},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(o<m.length){r=m.charAt(o++);if(r==="\\"){q+=r+m.charAt(o++)}else{if(r==="#"){r=m.charAt(o++);if(r==="#"){q+=r}else{if(!r.match(/[1-9]/)||r>n.length){e.Error("Illegal macro parameter reference")}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>e.config.MAXBUFFER){e.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return n+m}});e.Augment({Stack:f,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=m.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};this.prefilterHooks.Execute(r);q=r.math;try{n=e.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.inferred){n=j.apply(MathJax.ElementJax,n.data)}else{n=j(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;this.postfilterHooks.Execute(r);return r.math},prefilterMath:function(m){if(c.Browser.isKonqueror){m.math=m.math.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}m.math=m.math.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(m){this.combineRelations(m.math.root)},formatError:function(o,n,p,m){return j.merror(o.message.replace(/\n.*/,""))},Error:function(m){throw c.Insert(Error(m),{texError:d})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},combineRelations:function(o){for(var p=0,n=o.data.length;p<n;p++){if(o.data[p]){if(o.isa(j.mrow)){while(p+1<n&&o.data[p+1]&&o.data[p].isa(j.mo)&&o.data[p+1].isa(j.mo)&&o.data[p].Get("texClass")===j.TEXCLASS.REL&&o.data[p+1].Get("texClass")===j.TEXCLASS.REL){o.data[p].Append.apply(o.data[p],o.data[p+1].data);o.data.splice(p+1,1);n--}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});e.prefilterHooks.Add(["prefilterMath",e]);e.postfilterHooks.Add(["postfilterMath",e]);e.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax); diff --git a/jax/output/HTML-CSS/config.js b/jax/output/HTML-CSS/config.js @@ -12,5 +12,5 @@ * http://www.apache.org/licenses/LICENSE-2.0 */ -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.10",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.11",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",linebreaks:{automatic:false,width:"container"},showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"); diff --git a/unpacked/extensions/TeX/AMSmath.js b/unpacked/extensions/TeX/AMSmath.js @@ -22,7 +22,7 @@ */ MathJax.Extension["TeX/AMSmath"] = { - version: "1.1.1", + version: "1.1.2", number: 0, // current equation number startNumber: 0, // current starting equation number (for when equation is restarted) @@ -45,7 +45,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { /******************************************************************************/ - MathJax.Hub.Insert(TEXDEF,{ + TEXDEF.Add({ macros: { mathring: ['Accent','2DA'], // or 0x30A @@ -130,7 +130,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { '\\lVert': ['2225',{texClass:MML.TEXCLASS.OPEN}], '\\rVert': ['2225',{texClass:MML.TEXCLASS.CLOSE}] } - }); + },null,true); /******************************************************************************/ diff --git a/unpacked/extensions/TeX/AMSsymbols.js b/unpacked/extensions/TeX/AMSsymbols.js @@ -22,11 +22,12 @@ */ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { - var VERSION = "1.1.2"; + var VERSION = "1.1.3"; - var MML = MathJax.ElementJax.mml; + var MML = MathJax.ElementJax.mml, + TEXDEF = MathJax.InputJax.TeX.Definitions; - MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{ + TEXDEF.Add({ mathchar0mi: { // Lowercase Greek letters @@ -306,7 +307,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { impliedby: ['Macro','\\;\\Longleftarrow\\;'] } - }); + },null,true); var REL = MML.mo.OPTYPES.REL; diff --git a/unpacked/extensions/TeX/HTML.js b/unpacked/extensions/TeX/HTML.js @@ -22,15 +22,19 @@ */ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { - var VERSION = "1.1"; + var VERSION = "1.1.1"; var TEX = MathJax.InputJax.TeX; var TEXDEF = TEX.Definitions; - TEXDEF.macros.href = 'HREF_attribute'; - TEXDEF.macros["class"] = 'CLASS_attribute'; - TEXDEF.macros.style = 'STYLE_attribute'; - TEXDEF.macros.cssId = 'ID_attribute'; + TEXDEF.Add({ + macros: { + href: 'HREF_attribute', + "class": 'CLASS_attribute', + style: 'STYLE_attribute', + cssId: 'ID_attribute' + } + }); TEX.Parse.Augment({ diff --git a/unpacked/extensions/TeX/begingroup.js b/unpacked/extensions/TeX/begingroup.js @@ -0,0 +1,293 @@ +/************************************************************* + * + * MathJax/extensions/TeX/begingroup.js + * + * Implements \begingroup and \endgroup commands that make local + * definitions possible and are removed when the \endgroup occurs. + * + * --------------------------------------------------------------------- + * + * Copyright (c) 2011 Design Science, Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { + var VERSION = "1.1.1"; + + var TEX = MathJax.InputJax.TeX, + TEXDEF = TEX.Definitions; + + /****************************************************/ + + // + // A namespace for localizing macros and environments + // (\begingroup and \endgroup create and destroy these) + // + var NSFRAME = MathJax.Object.Subclass({ + macros: null, // the local macro definitions + environments: null, // the local environments + Init: function (macros,environments) { + this.macros = (macros || {}); + this.environments = (environments || {}); + }, + // + // Find a macro or environment by name + // + Find: function (name,type) {if (this[type][name]) {return this[type][name]}}, + // + // Define or remove a macro or environment + // + Def: function (name,value,type) {this[type][name] = value}, + Undef: function (name,type) {delete this[type][name]}, + // + // Merge two namespaces (used when the equation namespace is combined with the root one) + // + Merge: function (frame) { + MathJax.Hub.Insert(this.macros,frame.macros); + MathJax.Hub.Insert(this.environments,frame.environments); + }, + // + // Move global macros to the stack (globally) and remove from the frame + // + MergeGlobals: function (stack) { + var macros = this.macros; + for (var cs in macros) {if (macros.hasOwnProperty(cs) && macros[cs].global) { + stack.Def(cs,macros[cs],"macros",true); + delete macros[cs].global; delete macros[cs]; + }} + }, + // + // Clear the macro and environment lists + // (but not global macros unless "all" is true) + // + Clear: function (all) { + this.environments = {}; + if (all) {this.macros = {}} else { + var macros = this.macros; + for (var cs in macros) { + if (macros.hasOwnProperty(cs) && !macros[cs].global) {delete macros[cs]} + } + } + return this; + } + }); + + /****************************************************/ + + // + // A Stack of namespace frames + // + var NSSTACK = TEX.nsStack = MathJax.Object.Subclass({ + stack: null, // the namespace frames + top: 0, // the current top one (we don't pop for real until the equation completes) + isEqn: false, // true if this is the equation stack (not the global one) + // + // Set up the initial stack frame + // + Init: function (eqn) { + this.isEqn = eqn; this.stack = []; + if (!eqn) {this.Push(NSFRAME(TEXDEF.macros,TEXDEF.environments))} + else {this.Push(NSFRAME())} + }, + // + // Define a macro or environment in the top frame + // + Def: function (name,value,type,global) { + var n = this.top-1; + if (global) { + // + // Define global macros in the base frame and remove that cs + // from all other frames. Mark the global ones in equations + // so they can be made global when merged with the root stack. + // + while (n > 0) {this.stack[n].Undef(name,type); n--} + if (!(value instanceof Array)) {value = [value]} + if (this.isEqn) {value.global = true} + } + this.stack[n].Def(name,value,type); + }, + // + // Push a new namespace frame on the stack + // + Push: function (frame) { + this.stack.push(frame); + this.top = this.stack.length; + }, + // + // Pop the top stack frame + // (if it is the root, just keep track of the pop so we can + // reset it if the equation is reprocessed) + // + Pop: function () { + var top; + if (this.top > 1) { + top = this.stack[--this.top]; + if (this.isEqn) {this.stack.pop()} + } else if (this.isEqn) { + this.Clear(); + } + return top; + }, + // + // Search the stack from top to bottom for the first + // definition of the given control sequence in the given type + // + Find: function (name,type) { + for (var i = this.top-1; i >= 0; i--) { + var def = this.stack[i].Find(name,type); + if (def) {return def} + } + return null; + }, + // + // Combine the equation stack with the global one + // (The bottom frame of the equation goes with the top frame of the global one, + // and the remainder are pushed on the global stack, truncated to the + // position where items were poped from it.) + // + Merge: function (stack) { + stack.stack[0].MergeGlobals(this); + this.stack[this.top-1].Merge(stack.stack[0]); + var data = [this.top,this.stack.length-this.top].concat(stack.stack.slice(1)); + this.stack.splice.apply(this.stack,data); + this.top = this.stack.length; + }, + // + // Put back the temporarily poped items + // + Reset: function () {this.top = this.stack.length}, + // + // Clear the stack and start with a blank frame + // + Clear: function (all) { + this.stack = [this.stack[0].Clear()]; + this.top = this.stack.length; + } + },{ + nsFrame: NSFRAME + }); + + /****************************************************/ + + // + // Define the new macros + // + TEXDEF.macros.begingroup = "BeginGroup"; + TEXDEF.macros.endgroup = "EndGroup"; + TEXDEF.macros.global = ["Extension","newcommand"]; + TEXDEF.macros.gdef = ["Extension","newcommand"]; + + TEX.Parse.Augment({ + // + // Implement \begingroup + // + BeginGroup: function (name) { + TEX.eqnStack.Push(NSFRAME()); + }, + // + // Implements \endgroup + // + EndGroup: function (name) { + // + // If the equation has pushed frames, pop one, + // Otherwise clear the equation stack and pop the top global one + // + if (TEX.eqnStack.top > 1) { + TEX.eqnStack.Pop(); + } else if (TEX.rootStack.top === 1) { + TEX.Error("Extra "+name+" or missing \\begingroup"); + } else { + TEX.eqnStack.Clear(); + TEX.rootStack.Pop(); + } + }, + + // + // Replace the original routines with ones that looks through the + // equation and root stacks for the given name + // + csFindMacro: function (name) { + return (TEX.eqnStack.Find(name,"macros") || TEX.rootStack.Find(name,"macros")); + }, + envFindName: function (name) { + return (TEX.eqnStack.Find(name,"environments") || TEX.rootStack.Find(name,"environments")); + } + + }); + + /****************************************************/ + + TEX.rootStack = NSSTACK(); // the global namespace stack + TEX.eqnStack = NSSTACK(true); // the equation stack + + // + // Reset the global stack and clear the equation stack + // (this gets us back to the initial stack state as it was + // before the equation was first processed, in case the equation + // get restarted due to an autoloaded file) + // + TEX.prefilterHooks.Add(function () {TEX.rootStack.Reset(); TEX.eqnStack.Clear(true)}); + + // + // We only get here if there were no errors and the equation is fully + // processed (all restarts are complete). So we merge the equation + // stack into the global stack, thus making the changes from this + // equation permanent. + // + TEX.postfilterHooks.Add(function () {TEX.rootStack.Merge(TEX.eqnStack)}); + + /*********************************************************/ + + MathJax.Hub.Register.StartupHook("TeX newcommand Ready",function () { + + // + // Add the commands that depend on the newcommand code + // + TEXDEF.macros.global = "Global"; + TEXDEF.macros.gdef = ["Macro","\\global\\def"]; + + TEX.Parse.Augment({ + // + // Modify the way macros and environments are defined + // to make them go into the equation namespace stack + // + setDef: function (name,value) { + value.isUser = true; + TEX.eqnStack.Def(name,value,"macros",this.stack.env.isGlobal); + delete this.stack.env.isGlobal; + }, + setEnv: function (name,value) { + value.isUser = true; + TEX.eqnStack.Def(name,value,"environments") + }, + + // + // Implement \global (for \global\let, \global\def and \global\newcommand) + // + Global: function (name) { + var i = this.i; var cs = this.GetCSname(name); this.i = i; + if (cs !== "let" && cs !== "def" && cs !== "newcommand") + {TEX.Error(name+" not followed by \\let, \\def, or \\newcommand")} + this.stack.env.isGlobal = true; + } + + }); + + }); + + MathJax.Hub.Startup.signal.Post("TeX begingroup Ready"); + +}); + +MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/begingroup.js"); diff --git a/unpacked/extensions/TeX/newcommand.js b/unpacked/extensions/TeX/newcommand.js @@ -7,7 +7,7 @@ * * --------------------------------------------------------------------- * - * Copyright (c) 2009 Design Science, Inc. + * Copyright (c) 2009-2011 Design Science, Inc. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. @@ -23,19 +23,21 @@ */ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { - var VERSION = "1.1"; + var VERSION = "1.1.2"; var TEX = MathJax.InputJax.TeX; var TEXDEF = TEX.Definitions; - MathJax.Hub.Insert(TEXDEF,{ + TEXDEF.Add({ macros: { - newcommand: 'NewCommand', - renewcommand: 'NewCommand', - newenvironment: 'NewEnvironment', - def: 'MacroDef' + newcommand: 'NewCommand', + renewcommand: 'NewCommand', + newenvironment: 'NewEnvironment', + renewenvironment: 'NewEnvironment', + def: 'MacroDef', + let: 'Let' } - }) + },null,true); TEX.Parse.Augment({ @@ -50,7 +52,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { if (cs.charAt(0) === "\\") {cs = cs.substr(1)} if (!cs.match(/^(.|[a-z]+)$/i)) {TEX.Error("Illegal control sequence name for "+name)} if (n != null && !n.match(/^[0-9]+$/)) {TEX.Error("Illegal number of parameters specified in "+name)} - TEXDEF.macros[cs] = ['Macro',def,n]; + this.setDef(cs,['Macro',def,n]); }, /* @@ -63,7 +65,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { edef = this.GetArgument(name); if (n === '') {n = null} if (n != null && !n.match(/^[0-9]+$/)) {TEX.Error("Illegal number of parameters specified in "+name)} - TEXDEF.environment[env] = ['BeginEnv','EndEnv',bdef,edef,n]; + this.setEnv(env,['BeginEnv','EndEnv',bdef,edef,n]); }, /* @@ -73,11 +75,47 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { var cs = this.GetCSname(name), params = this.GetTemplate(name,"\\"+cs), def = this.GetArgument(name); - if (!(params instanceof Array)) {TEXDEF.macros[cs] = ['Macro',def,params]} - else {TEXDEF.macros[cs] = ['MacroWithTemplate',def,params[0],params[1]]} + if (!(params instanceof Array)) {this.setDef(cs,['Macro',def,params])} + else {this.setDef(cs,['MacroWithTemplate',def].concat(params))} }, /* + * Implements the \let command + */ + Let: function (name) { + var cs = this.GetCSname(name), macro; + var c = this.GetNext(); if (c === "=") {this.i++; c = this.GetNext()} + // + // All \let commands create entries in the macros array, but we + // have to look in the various mathchar and delimiter arrays if + // the source isn't a macro already, and attach the data to a + // macro with the proper routine to process it. + // + // A command of the form \let\cs=char produces a macro equivalent + // to \def\cs{char}, which is as close as MathJax can get for this. + // So \let\bgroup={ is possible, but doesn't work as it does in TeX. + // + if (c === "\\") { + name = this.GetCSname(name); + macro = this.csFindMacro(name); + if (!macro) { + if (TEXDEF.mathchar0mi[name]) {macro = ["csMathchar0mi",TEXDEF.mathchar0mi[name]]} else + if (TEXDEF.mathchar0mo[name]) {macro = ["csMathchar0mo",TEXDEF.mathchar0mo[name]]} else + if (TEXDEF.mathchar7[name]) {macro = ["csMathchar7",TEXDEF.mathchar7[name]]} else + if (TEXDEF.delimiter["\\"+name] != null) {macro = ["csDelimiter",TEXDEF.delimiter["\\"+name]]} + } + } else {macro = ["Macro",c]; this.i++} + this.setDef(cs,macro); + }, + + /* + * Routines to set the macro and environment definitions + * (overridden by begingroup to make localized versions) + */ + setDef: function (name,value) {value.isUser = true; TEXDEF.macros[name] = value}, + setEnv: function (name,value) {value.isUser = true; TEXDEF.environment[name] = value}, + + /* * Get a CS name or give an error */ GetCSname: function (cmd) { @@ -181,6 +219,7 @@ MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () { TEX.Environment = function (name) { TEXDEF.environment[name] = ['BeginEnv','EndEnv'].concat([].slice.call(arguments,1)); + TEXDEF.environment[name].isUser = true; } MathJax.Hub.Startup.signal.Post("TeX newcommand Ready"); diff --git a/unpacked/jax/input/TeX/jax.js b/unpacked/jax/input/TeX/jax.js @@ -292,7 +292,21 @@ }); - var TEXDEF = {}; + var TEXDEF = { + // + // Add new definitions without overriding user-defined ones + // + Add: function (src,dst,nouser) { + if (!dst) {dst = this} + for (var id in src) {if (src.hasOwnProperty(id)) { + if (typeof src[id] === 'object' && !(src[id] instanceof Array) && + (typeof dst[id] === 'object' || typeof dst[id] === 'function')) + {this.Add(src[id],dst[id],src[id],nouser)} + else if (!dst[id] || !dst[id].isUser || !nouser) {dst[id] = src[id]} + }} + return dst; + } + }; var STARTUP = function () { MML = MathJax.ElementJax.mml; HUB.Insert(TEXDEF,{ @@ -842,7 +856,9 @@ newcommand: ['Extension','newcommand'], renewcommand: ['Extension','newcommand'], newenvironment: ['Extension','newcommand'], + renewenvironment: ['Extension','newcommand'], def: ['Extension','newcommand'], + let: ['Extension','newcommand'], verb: ['Extension','verb'], @@ -910,6 +926,7 @@ for (var id in MACROS) {if (MACROS.hasOwnProperty(id)) { if (typeof(MACROS[id]) === "string") {TEXDEF.macros[id] = ['Macro',MACROS[id]]} else {TEXDEF.macros[id] = ["Macro"].concat(MACROS[id])} + TEXDEF.macros[id].isUser = true; }} } }; @@ -952,34 +969,60 @@ * Lookup a control-sequence and process it */ ControlSequence: function (c) { - var name = this.GetCS(), mchar, def; - if (TEXDEF.macros[name]) { // javascript macro - var macro = TEXDEF.macros[name]; + var name = this.GetCS(), macro = this.csFindMacro(name); + if (macro) { if (!(macro instanceof Array)) {macro = [macro]} var fn = macro[0]; if (!(fn instanceof Function)) {fn = this[fn]} - fn.apply(this,["\\"+name].concat(macro.slice(1))); - } else if (TEXDEF.mathchar0mi[name]) { // normal mathchar (mi) - mchar = TEXDEF.mathchar0mi[name]; def = {mathvariant: MML.VARIANT.ITALIC}; - if (mchar instanceof Array) {def = mchar[1]; mchar = mchar[0]} - this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def))); - } else if (TEXDEF.mathchar0mo[name]) { // normal mathchar (mo) - mchar = TEXDEF.mathchar0mo[name]; def = {stretchy: FALSE}; - if (mchar instanceof Array) {def = mchar[1]; def.stretchy = FALSE; mchar = mchar[0]} - this.Push(this.mmlToken(MML.mo(MML.entity("#x"+mchar)).With(def))); - } else if (TEXDEF.mathchar7[name]) { // mathchar in current family - mchar = TEXDEF.mathchar7[name]; def = {mathvariant: MML.VARIANT.NORMAL}; - if (mchar instanceof Array) {def = mchar[1]; mchar = mchar[0]} - if (this.stack.env.font) {def.mathvariant = this.stack.env.font} - this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def))); - } else if (TEXDEF.delimiter["\\"+name] != null) { // delimiter - var delim = TEXDEF.delimiter["\\"+name]; def = {}; - if (delim instanceof Array) {def = delim[1]; delim = delim[0]} - if (delim.length === 4) {delim = MML.entity('#x'+delim)} else {delim = MML.chars(delim)} - this.Push(this.mmlToken(MML.mo(delim).With({fence: FALSE, stretchy: FALSE}).With(def))); - } else { // error - this.csUndefined("\\"+name); - } + fn.apply(this,[c+name].concat(macro.slice(1))); + } else if (TEXDEF.mathchar0mi[name]) {this.csMathchar0mi(name,TEXDEF.mathchar0mi[name])} + else if (TEXDEF.mathchar0mo[name]) {this.csMathchar0mo(name,TEXDEF.mathchar0mo[name])} + else if (TEXDEF.mathchar7[name]) {this.csMathchar7(name,TEXDEF.mathchar7[name])} + else if (TEXDEF.delimiter["\\"+name] != null) {this.csDelimiter(name,TEXDEF.delimiter["\\"+name])} + else {this.csUndefined(c+name)} }, + // + // Look up a macro in the macros list + // (overridden in begingroup extension) + // + csFindMacro: function (name) {return TEXDEF.macros[name]}, + // + // Handle normal mathchar (as an mi) + // + csMathchar0mi: function (name,mchar) { + var def = {mathvariant: MML.VARIANT.ITALIC}; + if (mchar instanceof Array) {def = mchar[1]; mchar = mchar[0]} + this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def))); + }, + // + // Handle normal mathchar (as an m0) + // + csMathchar0mo: function (name,mchar) { + var def = {stretchy: false}; + if (mchar instanceof Array) {def = mchar[1]; def.stretchy = false; mchar = mchar[0]} + this.Push(this.mmlToken(MML.mo(MML.entity("#x"+mchar)).With(def))); + }, + // + // Handle mathchar in current family + // + csMathchar7: function (name,mchar) { + var def = {mathvariant: MML.VARIANT.NORMAL}; + if (mchar instanceof Array) {def = mchar[1]; mchar = mchar[0]} + if (this.stack.env.font) {def.mathvariant = this.stack.env.font} + this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def))); + }, + // + // Handle delimiter + // + csDelimiter: function (name,delim) { + var def = {}; + if (delim instanceof Array) {def = delim[1]; delim = delim[0]} + if (delim.length === 4) {delim = MML.entity('#x'+delim)} else {delim = MML.chars(delim)} + this.Push(this.mmlToken(MML.mo(delim).With({fence: false, stretchy: false}).With(def))); + }, + // + // Handle undefined control sequence + // (overridden in noUndefined extension) + // csUndefined: function (name) { TEX.Error("Undefined control sequence "+name); }, @@ -1432,10 +1475,10 @@ Begin: function (name) { var env = this.GetArgument(name); if (env.match(/[^a-z*]/i)) {TEX.Error('Invalid environment name "'+env+'"')} - if (!TEXDEF.environment[env]) {TEX.Error('Unknown environment "'+env+'"')} + var cmd = this.envFindName(env); if (!cmd) {TEX.Error('Unknown environment "'+env+'"')} if (++this.macroCount > TEX.config.MAXMACROS) {TEX.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")} - var cmd = TEXDEF.environment[env]; if (!(cmd instanceof Array)) {cmd = [cmd]} + if (!(cmd instanceof Array)) {cmd = [cmd]} var mml = STACKITEM.begin().With({name: env, end: cmd[1], parse:this}); if (cmd[0] && this[cmd[0]]) {mml = this[cmd[0]].apply(this,[mml].concat(cmd.slice(2)))} this.Push(mml); @@ -1443,6 +1486,7 @@ End: function (name) { this.Push(STACKITEM.end().With({name: this.GetArgument(name)})); }, + envFindName: function (name) {return TEXDEF.environment[name]}, Equation: function (begin,row) {return row}, @@ -1796,6 +1840,7 @@ // Macro: function (name,def,argn) { TEXDEF.macros[name] = ['Macro'].concat([].slice.call(arguments,1)); + TEXDEF.macros[name].isUser = true; }, // diff --git a/unpacked/jax/output/HTML-CSS/config.js b/unpacked/jax/output/HTML-CSS/config.js @@ -24,7 +24,7 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ id: "HTML-CSS", - version: "1.1.10", + version: "1.1.11", directory: MathJax.OutputJax.directory + "/HTML-CSS", extensionDir: MathJax.OutputJax.extensionDir + "/HTML-CSS", autoloadDir: MathJax.OutputJax.directory + "/HTML-CSS/autoload",