/*
* /MathJax/config/TeX-MML-AM_HTMLorMML.js * * Copyright (c) 2010-2018 The MathJax Consortium * * 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.Config({delayJaxRegistration: true});
MathJax.Ajax.Preloading(
"[MathJax]/jax/input/TeX/config.js", "[MathJax]/jax/input/MathML/config.js", "[MathJax]/jax/input/AsciiMath/config.js", "[MathJax]/jax/output/HTML-CSS/config.js", "[MathJax]/jax/output/NativeMML/config.js", "[MathJax]/jax/output/PreviewHTML/config.js", "[MathJax]/config/MMLorHTML.js", "[MathJax]/extensions/tex2jax.js", "[MathJax]/extensions/mml2jax.js", "[MathJax]/extensions/asciimath2jax.js", "[MathJax]/extensions/MathEvents.js", "[MathJax]/extensions/MathZoom.js", "[MathJax]/extensions/MathMenu.js", "[MathJax]/jax/element/mml/jax.js", "[MathJax]/extensions/toMathML.js", "[MathJax]/extensions/TeX/noErrors.js", "[MathJax]/extensions/TeX/noUndefined.js", "[MathJax]/jax/input/TeX/jax.js", "[MathJax]/extensions/TeX/AMSmath.js", "[MathJax]/extensions/TeX/AMSsymbols.js", "[MathJax]/jax/input/MathML/jax.js", "[MathJax]/jax/input/AsciiMath/jax.js", "[MathJax]/jax/output/PreviewHTML/jax.js", "[MathJax]/extensions/fast-preview.js", "[MathJax]/extensions/AssistiveMML.js", "[MathJax]/extensions/a11y/accessibility-menu.js"
);
MathJax.Hub.Config({
extensions: ['[a11y]/accessibility-menu.js']
});
MathJax.InputJax.TeX=MathJax.InputJax({id:“TeX”,version:“2.7.5”,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-”+String(a).replace(/s/g,“_”)},formatURL:function(b,a){return a+“#”+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register(“math/tex”);MathJax.InputJax.TeX.loadComplete(“config.js”); MathJax.InputJax.MathML=MathJax.InputJax({id:“MathML”,version:“2.7.5”,directory:MathJax.InputJax.directory+“/MathML”,extensionDir:MathJax.InputJax.extensionDir+“/MathML”,entityDir:MathJax.InputJax.directory+“/MathML/entities”,config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register(“math/mml”);MathJax.InputJax.MathML.loadComplete(“config.js”); MathJax.InputJax.AsciiMath=MathJax.InputJax({id:“AsciiMath”,version:“2.7.5”,directory:MathJax.InputJax.directory+“/AsciiMath”,extensionDir:MathJax.InputJax.extensionDir+“/AsciiMath”,config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:“.”}});MathJax.InputJax.AsciiMath.Register(“math/asciimath”);MathJax.InputJax.AsciiMath.loadComplete(“config.js”); MathJax.OutputJax[“HTML-CSS”]=MathJax.OutputJax({id:“HTML-CSS”,version:“2.7.5”,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:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:[“STIX”,“TeX”],preferredFont:“TeX”,webFont:“TeX”,imageFont:“TeX”,undefinedFamily:“STIXGeneral,‘Arial Unicode MS’,serif”,mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:“container”},styles:{“.MathJax_Display”:{“text-align”:“center”,margin:“1em 0em”},“.MathJax .merror”:{“background-color”:“#FFFF88”,color:“#CC0000”,border:“1px solid #CC0000”,padding:“1px 3px”,“font-style”:“normal”,“font-size”:“90%”},“.MathJax .MJX-monospace”:{“font-family”:“monospace”},“.MathJax .MJX-sans-serif”:{“font-family”:“sans-serif”},“#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”,“z-index”:401}}}});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;gn.name
”}“)}var v=(”c“+s).replace(//g,”“).replace(/([|:])+/g,”$1“);s=s.replace(//g,”“).split(”“).join(” “);s=s.replace(/l/g,”left“).replace(/r/g,”right“).replace(/c/g,”center“);var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||”1em“),rowspacing:(o||”4pt“)}});if(v.match(//)){if(v.charAt(0).match(//)){r.frame.push(”left“);r.frame.dashed=v.charAt(0)===”:“}if(v.charAt(v.length-1).match(//)){r.frame.push(”right“)}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split(”“).join(” “).replace(/[^|: ]/g,”none“).replace(/|/g,”solid“).replace(/:/g,”dashed“)}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m===”D“){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m===”S“){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets(”\begin{“m.name
”}“);return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||”“);if(m===”t“){n.arraydef.align=”baseline 1“}else{if(m===”b“){n.arraydef.align=”baseline -1“}else{if(m===”c“){n.arraydef.align=”center“}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter:null)}if(m==null){return null}if(f(m)){m=m}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!=”string“){return n}var m=n.replace(/^s+|s+$/g,”“);if(m.match(/\$/)&&n.match(/ $/)){m+=” “}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^(+|.) ?/i);if(m){this.i+=m.length;return m}else{this.i++;return” “}},GetArgument:function(n,o){switch(this.GetNext()){case”“:if(!o){d.Error([”MissingArgFor“,”Missing argument for %1“,n])}return null;case”}“:if(!o){d.Error([”ExtraCloseMissingOpen“,”Extra close brace or missing open brace“])}return null;case”\“:this.i++;return”\“+this.GetCS();case”{“:var m=++this.i,p=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case”\“:this.i++;break;case”{“:p++;break;case”}“:if(–p==0){return this.string.slice(m,this.i-1)}break}}d.Error([”MissingCloseBrace“,”Missing close brace“]);break}return this.string.charAt(this.i++)},GetBrackets:function(n,p){if(this.GetNext()!=”[“){return p}var m=++this.i,o=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case”{“:o++;break;case”\“:this.i++;break;case”}“:if(o–<=0){d.Error([”ExtraCloseLooking“,”Extra close brace while looking for %1“,”']'“])}break;case”]“:if(o==0){return this.string.slice(m,this.i-1)}break}}d.Error([”MissingCloseBracket“,”Couldn't find closing ']' for argument to %1“,n])},GetDelimiter:function(m,n){while(this.nextIsSpace()){this.i++}var o=this.string.charAt(this.i);this.i++;if(this.i<=this.string.length){if(o==”\“){o+=this.GetCS(m)}else{if(o===”{“&&n){this.i–;o=this.GetArgument(m).replace(/^s+/,”“).replace(/s+$/,”“)}}if(g.delimiter.hasOwnProperty(o)){return this.convertDelimiter(o)}}d.Error([”MissingOrUnrecognizedDelim“,”Missing or unrecognized delimiter for %1“,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,”“).replace(/,/,”.“)}}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.length;return m.replace(/ /g,”“).replace(/,/,”.“)}}d.Error([”MissingDimOrUnits“,”Missing dimension or its units for %1“,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®{case”\“:r+=this.GetCS();break;case”{“:q++;break;case”}“:if(q==0){d.Error([”ExtraCloseLooking“,”Extra close brace while looking for %1“,p])}q–;break}if(q==0&&r==p){return this.string.slice(n,m)}}d.Error([”TokenNotFoundForCommand“,”Couldn't find %1 for %2“,p,o])},ParseArg:function(m){return d.Parse(this.GetArgument(m),this.stack.env).mml()},ParseUpTo:function(m,n){return d.Parse(this.GetUpTo(m,n),this.stack.env).mml()},InternalMath:function(v,m){var o=(this.stack.env.font?{mathvariant:this.stack.env.font}:{});var n=[],r=0,q=0,u,s=”“,p=0;if(v.match(/\?|\(|\(eq)?refs*{/)){while(r<v.length){u=v.charAt(r++);if(u===”$“){if(s===”$“&&p===0){n.push(i.TeXAtom(d.Parse(v.slice(q,r-1),{}).mml()));s=”“;q=r}else{if(s===”“){if(q<r-1){n.push(this.InternalText(v.slice(q,r-1),o))}s=”$“;q=r}}}else{if(u===”{“&&s!==”“){p++}else{if(u===”}“){if(s===”}“&&p===0){n.push(i.TeXAtom(d.Parse(v.slice(q,r),{}).mml().With(o)));s=”“;q=r}else{if(s!==”“){if(p){p–}}}}else{if(u===”\“){if(s===”“&&v.substr®.match(/^(eq)?refs*{/)){var t=RegExp.length;if(q<r-1){n.push(this.InternalText(v.slice(q,r-1),o))}s=”}“;q=r-1;r+=t}else{u=v.charAt(r++);if(u===”(“&&s===”“){if(q<r-2){n.push(this.InternalText(v.slice(q,r-2),o))}s=”)“;q=r}else{if(u===”)“&&s===”)“&&p===0){n.push(i.TeXAtom(d.Parse(v.slice(q,r-2),{}).mml()));s=”“;q=r}else{if(u.match(//)&&s===”“){r–;v=v.substr(0,r-1)+v.substr®}}}}}}}}}if(s!==”“){d.Error([”MathNotTerminated“,”Math not terminated in text box“])}}if(q<v.length){n.push(this.InternalText(v.slice(q),o))}if(m!=null){n=}else{if(n.length>1){n=}}return n},InternalText:function(n,m){n=n.replace(/^s+/,h).replace(/s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros=n},setEnv:function(m,n){n.isUser=true;g.environment=n},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(//)||r>n.length){d.Error([”IllegalMacroParam“,”Illegal macro parameter reference“])}p=this.AddArgs(this.AddArgs(p,q),n);q=”“}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^/i)&&n.match(/(^|)(\\)*\[a-z]+$/i)){n+=” “}if(n.length+m.length>d.config.MAXBUFFER){d.Error([”MaxBufferSize“,”MathJax internal buffer size exceeded; is there a recursive macro call?“])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:[”TeXCommands“,”TeX Commands“],annotationEncoding:”application/x-tex“,prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!==”none“){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push(”AMSmath.js“)}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/n/g,” “).match(/(;|s|n)modes*=s*display(;|s|n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute®;if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle===”inherit“){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display=”block“}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute®||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/n.*/,”“);c.signal.Post([”TeX Jax - parse error“,n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros=[”Macro“].concat([].slice.call(arguments,1));g.macros.isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type===”mrow“&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,”l“))}if(n.type===”mrow“){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,”r“))}return m},mathPalette:function(p,n){if(p===”{“||p===”}“){p=”\“+p}var o=”{\bigg“n
” “p
”}“,m=”{\big“n
” “p
”}“;return d.Parse(”\mathchoice“+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r<n;r++){if(q.data){if(q.isa(i.mrow)){while(r+1l
”}“+i])},HandleOperatorName:function(j){var i=(this.GetStar()?”“:”\nolimits\SkipLimits“);var k=this.trimSpaces(this.GetArgument(j));k=k.replace(/*/g,”\text{*}“).replace(/-/g,”\text{-}“);this.string=”\mathop{\rm “k
”}“i
” “+this.string.slice(this.i);this.i=0},SkipLimits:function(j){var l=this.GetNext(),k=this.i;if(l===”\“&&++this.i&&this.GetCS()!==”limits“){this.i=k}},HandleShove:function(j,i){var k=this.stack.Top();if(k.type!==”multline“){h.Error([”CommandInMultline“,”%1 can only appear within the multline environment“,j])}if(k.data.length){h.Error([”CommandAtTheBeginingOfLine“,”%1 must come at the beginning of the line“,j])}k.data.shove=i},CFrac:function(l){var i=this.trimSpaces(this.GetBrackets(l,”“)),k=this.GetArgument(l),m=this.GetArgument(l);var j=b.mfrac(h.Parse(”\strut\textstyle{“k
”}“,this.stack.env).mml(),h.Parse(”\strut\textstyle{“m
”}“,this.stack.env).mml());i=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,”“:”“})[i];if(i==null){h.Error([”IllegalAlign“,”Illegal alignment specified in %1“,l])}if(i){j.numalign=j.denomalign=i}this.Push(j)},Genfrac:function(j,l,q,n,i){if(l==null){l=this.GetDelimiterArg(j)}if(q==null){q=this.GetDelimiterArg(j)}if(n==null){n=this.GetArgument(j)}if(i==null){i=this.trimSpaces(this.GetArgument(j))}var m=this.ParseArg(j);var p=this.ParseArg(j);var k=b.mfrac(m,p);if(n!==”“){k.linethickness=n}if(l||q){k=h.fixedFence(l,k.With({texWithDelims:true}),q)}if(i!==”“){var o=()[i];if(o==null){h.Error([”BadMathStyleFor“,”Bad math style for %1“,j])}k=b.mstyle(k);if(o===”D“){k.displaystyle=true;k.scriptlevel=0}else{k.displaystyle=false;k.scriptlevel=i-1}}this.Push(k)},Multline:function(j,i){this.Push(j);this.checkEqnEnv();return f.multline(i,this.stack).With({arraydef:{displaystyle:true,rowspacing:”.5em“,width:h.config.MultLineWidth,columnwidth:”100%“,side:h.config.TagSide,minlabelspacing:h.config.TagIndent}})},AMSarray:function(k,j,i,m,l){this.Push(k);if(i){this.checkEqnEnv()}m=m.replace(//g,”“).split(”“).join(” “);m=m.replace(/l/g,”left“).replace(/r/g,”right“).replace(/c/g,”center“);return f.AMSarray(k.name,j,i,this.stack).With({arraydef:{displaystyle:true,rowspacing:”.5em“,columnalign:m,columnspacing:(l||”1em“),rowspacing:”3pt“,side:h.config.TagSide,minlabelspacing:h.config.TagIndent}})},AlignedAMSArray:function(i){var j=this.GetBrackets(”\begin{“i.name
”}“);return this.setArrayAlign(this.AMSarray.apply(this,arguments),j)},AlignAt:function(l,j,i){var q,k,p=”“,o=[];if(!i){k=this.GetBrackets(”\begin{“l.name
”}“)}q=this.GetArgument(”\begin{“l.name
”}“);if(q.match(//)){h.Error([”PositiveIntegerArg“,”Argument to %1 must me a positive integer“,”\begin{“l.name
”}“])}while(q>0){p+=”rl“;o.push(”0em 0em“);q–}o=o.join(” “);if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!==”none“);return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error([”ErroneousNestingEq“,”Erroneous nesting of equation structures“])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l===”\“){var k=this.i;l=this.GetArgument(j);this.i=k;if(l===”\limits“){if(j===”\idotsint“){m=”\!\!\mathop{\,\,“m
”}“}else{m=”\!\!\!\mathop{\,\,\,“m
”}“}}}this.string=m+” “+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:”+“+(n+i)+”mu“,lspace:n+”mu“};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:”.15em“}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:”-.24em“}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==”“){return null}if(j in d.delimiter){return j}h.Error([”MissingOrUnrecognizedDelim“,”Missing or unrecognized delimiter for %1“,i])},GetStar:function(){var i=(this.GetNext()===”*“);if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse(”\text{“+a.formatTag(j.tagID)+”}“,{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs||g.eqIDs){var l=0,j;do{l++;j=k.id+”_“+l}while(document.getElementById(j)||g.IDs||g.eqIDs);k.id=j;if(m.label){g.eqlabels.id=j}}g.eqIDs=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k<j;k++){if(l&&(l.type!==”mspace“&&(l.type!==”texatom“||(l.data&&l.data.data.length)))){if(l.isEmbellished()){l.unshift(b.mi())}break}}}});f.multline=f.array.Subclass({type:”multline“,Init:function(j,i){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!==”none“);this.save={notag:i.global.notag};i.global.tagged=!j&&!i.global.forcetag},EndEntry:function(){if(this.table.length){this.fixInitialMO(this.data)}var i=b.mtd.apply(b,this.data);if(this.data.shove){i.columnalign=this.data.shove}this.row.push(i);this.data=[]},EndRow:function(){if(this.row.length!=1){h.Error([”MultlineRowsOneCol“,”The rows within the %1 environment must have exactly one column“,”multline“])}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var k=this.table.length-1,n,l=-1;if(!this.table[0].columnalign){this.table[0].columnalign=b.ALIGN.LEFT}if(!this.table[0].columnalign){this.table[0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){l=(this.arraydef.side===”left“?0:this.table.length-1);this.table=[this.getTag()].concat(this.table)}for(n=0,k=this.table.length;n<k;n++){var j=(n===l?b.mlabeledtr:b.mtr);this.table=j.apply(b,this.table)}}this.global.notag=this.save.notag}});f.AMSarray=f.array.Subclass({type:”AMSarray“,Init:function(l,k,j,i){this.SUPER(arguments).Init.apply(this);this.numbered=(k&&a.autoNumber!==”none“);this.save={notags:i.global.notags,notag:i.global.notag};i.global.notags=(j?null:l);i.global.tagged=!k&&!i.global.forcetag},EndEntry:function(){if(this.row.length%2===1){this.fixInitialMO(this.data)}this.row.push(b.mtd.apply(b,this.data));this.data=[]},EndRow:function(){var i=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=.concat(this.row);i=b.mlabeledtr}else{this.clearTag()}if(this.numbered){delete this.global.notag}this.table.push(i.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}});f.start.Augment({oldCheckItem:f.start.prototype.checkItem,checkItem:function(k){if(k.type===”stop“){var i=this.mmlData(),j=this.global;if(g.display&&!j.tag&&!j.tagged&&!j.isInner&&(a.autoNumber===”all“||j.forcetag)){this.autoTag()}if(j.tag){var m=;var l={side:h.config.TagSide,minlabelspacing:h.config.TagIndent,displaystyle:”inherit“};i=b.mtable(b.mlabeledtr.apply(b,m)).With(l)}return f.mml(i)}return this.oldCheckItem.call(this,k)}});h.prefilterHooks.Add(function(i){g.display=i.display;g.number=g.startNumber;g.eqlabels={};g.eqIDs={};g.badref=false;if(g.refUpdate){g.number=i.script.MathJax.startNumber}});h.postfilterHooks.Add(function(i){i.script.MathJax.startNumber=g.startNumber;g.startNumber=g.number;MathJax.Hub.Insert(g.IDs,g.eqIDs);MathJax.Hub.Insert(g.labels,g.eqlabels);if(g.badref&&!i.math.texError){g.refs.push(i.script)}},100);MathJax.Hub.Register.MessageHook(”Begin Math Input“,function(){g.refs=[];g.refUpdate=false});MathJax.Hub.Register.MessageHook(”End Math Input“,function(l){if(g.refs.length){g.refUpdate=true;for(var k=0,j=g.refs.length;k<j;k++){g.refs.MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput({scripts:g.refs,start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]})}return null});h.resetEquationNumbers=function(j,i){g.startNumber=(j||0);if(!i){g.labels={};g.IDs={}}};MathJax.Hub.Startup.signal.Post(”TeX AMSmath Ready“)});MathJax.Ajax.loadComplete(”/extensions/TeX/AMSmath.js“); MathJax.Extension={version:”2.7.5“};MathJax.Hub.Register.StartupHook(”TeX Jax Ready“,function(){var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:”03DD“,varkappa:”03F0“,varGamma:,varDelta:,varTheta:,varLambda:,varXi:,varPi:,varSigma:,varUpsilon:,varPhi:,varPsi:,varOmega:,beth:”2136“,gimel:”2137“,daleth:”2138“,backprime:,hslash:”210F“,varnothing:,blacktriangle:”25B4“,triangledown:,blacktriangledown:”25BE“,square:”25FB“,Box:”25FB“,blacksquare:”25FC“,lozenge:”25CA“,Diamond:”25CA“,blacklozenge:”29EB“,circledS:,bigstar:”2605“,sphericalangle:”2222“,measuredangle:”2221“,nexists:”2204“,complement:”2201“,mho:”2127“,eth:,Finv:”2132“,diagup:”2571“,Game:”2141“,diagdown:”2572“,Bbbk:,yen:”00A5“,circledR:”00AE“,checkmark:”2713“,maltese:”2720“},mathchar0mo:{dotplus:”2214“,ltimes:”22C9“,smallsetminus:”2216“,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“,{variantForm:true}],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“,{variantForm:true}],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“,{variantForm:true}],shortmid:[”2223“,{variantForm:true}],smallfrown:[”2322“,{variantForm:true}],shortparallel:[”2225“,{variantForm:true}],bumpeq:”224F“,between:”226C“,Bumpeq:”224E“,pitchfork:”22D4“,varpropto:”221D“,backepsilon:”220D“,blacktriangleleft:”25C2“,blacktriangleright:”25B8“,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“:”231C“,”\urcorner“:”231D“,”\llcorner“:”231E“,”\lrcorner“:”231F“},macros:{implies:[”Macro“,”\;\Longrightarrow\;“],impliedby:[”Macro“,”\;\Longleftarrow\;“]}},null,true);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.Startup.signal.Post(”TeX AMSsymbols Ready“)});MathJax.Ajax.loadComplete(”/extensions/TeX/AMSsymbols.js“); (function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!==”string“){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error([”ErrorParsingMathML“,”Error parsing MathML“])}}var g=j.getElementsByTagName(”parsererror“);if(g){c.Error([”ParsingError“,”Error parsing MathML: %1“,g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,”“)])}if(j.childNodes.length!==1){c.Error([”MathMLSingleElement“,”MathML must be formed by a single element“])}if(j.firstChild.nodeName.toLowerCase()===”html“){var f=j.getElementsByTagName(”h1“);if(f&&f.textContent===”XML parsing error“&&f.nextSibling){c.Error([”ParsingError“,”Error parsing MathML: %1“,String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,”“)])}}if(j.firstChild.nodeName.toLowerCase().replace(/^+:/,”“)!==”math“){c.Error([”MathMLRootElement“,”MathML must be formed by a <math> element, not %1“,”<“j.firstChild.nodeName
”>“])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute(”class“)||”“);var f,g=h.nodeName.toLowerCase().replace(/^+:/,”“);var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e,e===”OP“&&!i.match(/MJX-fixedlimits/))}else{if(!(a&&a.isa&&a.isa(a.mbase))){MathJax.Hub.signal.Post([”MathML Jax - unknown node type“,g]);return a.Error(b(”UnknownNodeType“,”Unknown node type: %1“,g))}else{f=a()}}this.AddAttributes(f,h);this.CheckClass(f,f);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||”“).split(/ /);var j=[];for(var g=0,e=h.length;g<e;g++){if(h.substr(0,4)===”MJX-“){if(h===”MJX-arrow“){if(!f.notation.match(”/“a.NOTATION.UPDIAGONALARROW
”/“)){f.notation+=” “+a.NOTATION.UPDIAGONALARROW}}else{if(h===”MJX-variant“){f.variantForm=true;if(!MathJax.Extension){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(”/extensions/TeX/AMSsymbols.js“))}}else{if(h.substr(0,11)!==”MJX-TeXAtom“){f.mathvariant=h.substr(3);if(f.mathvariant===”-tex-caligraphic-bold“||f.mathvariant===”-tex-oldstyle-bold“){if(!MathJax.Extension){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(”/extensions/TeX/boldsymbol.js“))}}}}}}else{j.push(h)}}if(j.length){f=j.join(” “)}else{delete f}},AddAttributes:function(g,j){g.attr={};g.attrNames=[];for(var h=0,e=j.attributes.length;h<e;h++){var f=j.attributes.name;if(f==”xhref“){f=”href“}if(f.match(/:/)){continue}if(f.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){continue}var k=j.attributes.value;k=this.filterAttribute(f,k);var l=(g.type===”mstyle“?a.math.prototype.defaults:g.defaults);if(k!=null){var n=k.toLowerCase();if(n===”true“||n===”false“){if(typeof(l)===”boolean“||l===a.INHERIT||g.type===”math“||g.type===”mstyle“||(l===a.AUTO&&(g.defaultDef==null||typeof(g.defaultDef)===”boolean“))){k=(n===”true“)}}if(l!=null||a.copyAttributes){g=k}else{g.attr=k}g.attrNames.push(f)}}},filterAttribute:function(e,f){return f},AddChildren:function(e,g){for(var k=0,j=g.childNodes.length;k<j;k++){var f=g.childNodes;if(f.nodeName===”#comment“){continue}if(f.nodeName===”#text“){if((e.isToken||e.isChars)&&!e.mmlSelfClosing){var o=f.nodeValue;if(e.isToken){o=o.replace(/&([a-z0-9]*);/ig,this.replaceEntity);o=this.trimSpace(o)}e.Append(a.chars(o))}else{if(f.nodeValue.match(/S/)){c.Error([”UnexpectedTextNode“,”Unexpected text node: %1“,”'“f.nodeValue
”'“])}}}else{if(e.type===”annotation-xml“){e.Append(a.xml(f))}else{var h=this.MakeMML(f);e.Append(h);if(h.mmlSelfClosing&&h.data.length){e.Append.apply(e,h.data);h.data=[]}}}}if(e.type===”mrow“&&e.data.length>=2){var l=e.data,n=e.data;if(l.type===”mo“&&l.Get(”fence“)&&n.type===”mo“&&n.Get(”fence“)){if(l.data){e.open=l.data.join(”“)}if(n.data){e.close=n.data.join(”“)}}}},preProcessMath:function(f){if(f.match(/^<+:/f=f.replace(/^<(+)(:math)/i,'<$1$2 xmlns:$1=“www.w3.org/1998/Math/MathML”’)}var e=f.match(/^(<math( ('.*?'|“.*?”|[^>])+)>)/i);if(e&&e.match(/ (?!xmlns=)+="i)){f=e[1].replace(/ (?!xmlns=)(+=(['“]).*?2)/ig,” xmlns:$1 $1“)+f.substr(e.length)}if(f.match(/^<math[ >]/s*$/,”$2“);return”>www.w3.org/1998/Math/MathML“‘)}f=f.replace(/^s*(?://)?s*$/,”$2“);return f.replace(/&([a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(//g,” “).replace(/^ +/,”“).replace(/ +$/,”“).replace(/ +/g,” “)},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity){return c.Parse.Entity}var h=f.charAt(0).toLowerCase();var e=f.match(/^(fr|scr|opf)$/);if(e){h=e}if(!c.Parse.loaded){c.Parse.loaded=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+”/“h
”.js“))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:[”OriginalMathML“,”Original MathML“],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^+:/,”“)===”math“){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,”“)}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/n.*/,”“);MathJax.Hub.signal.Post([”MathML Jax - parse error“,f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,”text/xml“)},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML=”n
“)”;m={“-webkit-transform”:o,“-moz-transform”:o,“-ms-transform”:o,“-o-transform”:o,transform:o}}})();var k=1000000;var c=“V”,l=“H”;g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+“/MathEvents.js”)},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,“div”,{style:{width:“5in”}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,)},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax,t,q=s.length,u,r,v,o,n;for(t=0;t<q;t++){u=s;if(!u.parentNode){continue}r=u.previousSibling;if(r&&String(r.className).match(/^MathJax(_PHTML)?(_Display)?( MathJax_Process(ing|ed))?$/)){r.parentNode.removeChild®}n=u.MathJax.elementJax;if(!n){continue}n.PHTML={display:(n.root.Get(“display”)===“block”)};v=o=e.Element(“span”,{className:“MathJax_PHTML”,id:n.inputID+“-Frame”,isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick,onkeydown:j.Keydown,tabIndex:b.getTabOrder(n)});if(b.Browser.noContextMenu){v.ontouchstart=a.start;v.ontouchend=a.end}if(n.PHTML.display){o=e.Element(“div”,{className:“MathJax_PHTML_Display”});o.appendChild(v)}o.className+=“ MathJax_Processing”;u.parentNode.insertBefore(o,u)}},Translate:function(o,s){if(!o.parentNode){return}var n=o.MathJax.elementJax,r=n.root,p=document.getElementById(n.inputID+“-Frame”),t=(n.PHTML.display?p.parentNode:p);this.initPHTML(r,p);try{r.toPreviewHTML(p)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}throw q}t.className=t.className.split(/ /)[0];if(this.hideProcessedMath){t.className+=“ MathJax_Processed”;if(o.MathJax.preview){n.PHTML.preview=o.MathJax.preview;delete o.MathJax.preview}}},postTranslate:function(s){var o=s.jax;if(!this.hideProcessedMath){return}for(var q=0,n=o.length;q<n;q++){var p=o;if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var r=p.MathJax.elementJax.PHTML;if(r.preview){r.preview.innerHTML=“”;p.MathJax.preview=r.preview;delete r.preview}}}},getJaxFromMath:function(n){if(n.parentNode.className.match(/MathJax_PHTML_Display/)){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!==“script”);return b.getJaxFor(n)},getHoverSpan:function(n,o){return n.root.PHTMLspanElement()},getHoverBBox:function(n,q,r){var s=n.root.PHTML,p=n.PHTML.outerEm;var o={w:s.w*p,h:s.h*p,d:s.d*p};if(s.width){o.width=s.width}return o},Zoom:function(o,u,s,n,r){u.className=“MathJax”;this.idPostfix=“-zoom”;o.root.toPHTML(u,u);this.idPostfix=“”;u.style.position=“absolute”;if(!width){s.style.position=“absolute”}var t=u.offsetWidth,q=u.offsetHeight,v=s.offsetHeight,p=s.offsetWidth;if(p===0){p=s.parentNode.offsetWidth}u.style.position=s.style.position=“”;return{Y:-j.getBBox(u).h,mW:p,mH:v,zW:t,zH:q}},initPHTML:function(o,n){},Remove:function(n){var o=document.getElementById(n.inputID+“-Frame”);if(o){if(n.PHTML.display){o=o.parentNode}o.parentNode.removeChild(o)}delete n.PHTML},ID:0,idPostfix:“”,GetID:function(){this.ID++;return this.ID},VARIANT:{bold:“MJXp-bold”,italic:“MJXp-italic”,“bold-italic”:“MJXp-bold MJXp-italic”,script:“MJXp-scr”,“bold-script”:“MJXp-scr MJXp-bold”,fraktur:“MJXp-frak”,“bold-fraktur”:“MJXp-frak MJXp-bold”,monospace:“MJXp-mono”,“sans-serif”:“MJXp-sf”,“-tex-caligraphic”:“MJXp-cal”},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,thin:0.08,medium:0.1,thick:0.15,infinity:k},TeX:{x_height:0.430554},pxPerInch:72,em:16,DELIMITERS:{“(”:{dir:c},“{”:{dir:c,w:0.58},“[”:{dir:c},“|”:{dir:c,w:0.275},“)”:{dir:c},“}”:{dir:c,w:0.58},“]”:{dir:c},“/”:{dir:c},“\”:{dir:c},“u2223”:{dir:c,w:0.275},“u2225”:{dir:c,w:0.55},“u230A”:{dir:c,w:0.5},“u230B”:{dir:c,w:0.5},“u2308”:{dir:c,w:0.5},“u2309”:{dir:c,w:0.5},“u27E8”:{dir:c,w:0.5},“u27E9”:{dir:c,w:0.5},“u2191”:{dir:c,w:0.65},“u2193”:{dir:c,w:0.65},“u21D1”:{dir:c,w:0.75},“u21D3”:{dir:c,w:0.75},“u2195”:{dir:c,w:0.65},“u21D5”:{dir:c,w:0.75},“u27EE”:{dir:c,w:0.275},“u27EF”:{dir:c,w:0.275},“u23B0”:{dir:c,w:0.6},“u23B1”:{dir:c,w:0.6}},REMAPACCENT:{“u20D7”:“u2192”,“'”:“u02CB”,“`”:“u02CA”,“.”:“u02D9”,“^”:“u02C6”,“-”:“u02C9”,“~”:“u02DC”,“u00AF”:“u02C9”,“u00B0”:“u02DA”,“u00B4”:“u02CA”,“u0300”:“u02CB”,“u0301”:“u02CA”,“u0302”:“u02C6”,“u0303”:“u02DC”,“u0304”:“u02C9”,“u0305”:“u02C9”,“u0306”:“u02D8”,“u0307”:“u02D9”,“u0308”:“u00A8”,“u030C”:“u02C7”},REMAPACCENTUNDER:{},length2em:function(r,p){if(typeof®!==“string”){r=r.toString()}if(r===“”){return“”}if(r===h.SIZE.NORMAL){return 1}if(r===h.SIZE.BIG){return 2}if(r===h.SIZE.SMALL){return 0.71}if(this.MATHSPACE){return this.MATHSPACE}var o=r.match(/^s*(?(?:.d+|d+(?:.d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var n=parseFloat(o||“1”),q=o;if(p==null){p=1}if(q===“em”){return n}if(q===“ex”){return n*this.TeX.x_height}if(q===“%”){return n/100*p}if(q===“px”){return n/this.em}if(q===“pt”){return n/10}if(q===“pc”){return n*1.2}if(q===“in”){return n*this.pxPerInch/this.em}if(q===“cm”){return n*this.pxPerInch/this.em/2.54}if(q===“mm”){return n*this.pxPerInch/this.em/25.4}if(q===“mu”){return n/18}return n*p},Em:function(n){if(Math.abs(n)<0.001){return“0em”}return(n.toFixed(3).replace(/.?0+$/,“”))+“em”},arrayEntry:function(n,o){return n}});MathJax.Hub.Register.StartupHook(“mml Jax Ready”,function(){h=MathJax.ElementJax.mml;h.mbase.Augment({toPreviewHTML:function(o,n){return this.PHTMLdefaultSpan(o,n)},PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q},PHTMLaddChild:function(p,o,n){var q=this.data;if(q){if(n.childSpans){p=e.addElement(p,“span”,{className:n.className})}q.toPreviewHTML(p);if(!n.noBBox){this.PHTML.w+=q.PHTML.w+q.PHTML.l+q.PHTML.r;if(q.PHTML.h>this.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,“span”)}}},PHTMLstretchChild:function(q,p,s){var r=this.data;if(r&&r.PHTMLcanStretch(“Vertical”,p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type===“mo”&&this.data.join(“”)===“u222B”){g.lastIsInt=true}else{if(this.type!==“mspace”||this.width!==“negativethinmathspace”){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||“MJXp-Span-”+this.PHTMLspanID);return e.addElement(n,“span”,{className:“MJXp-”+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||“MJXp-Span-”+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues(“mathvariant”);if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=“ ”+g.VARIANT}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get(“scriptlevel”);if(o){n.className+=“ MJXp-script”}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s<r;s++){p=A.charCodeAt(s);v=A.charAt(s);if(p>=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(//)){u=0}if(v.match(//)){x=0.67}else{if(v.match(//)){x=0.36}}if(v.match(//)){t=0.45}else{if(v.match(//)){t=0.75}}if(v.match(//)){x=0.28}}if(g.DELIMITERS){x=g.DELIMITERS.w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data&&this.data.PHTML){return this.data.PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return“”}if(n.isEmbellished()){return n.CoreMO().data.join(“”)}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data){n=n.data}if(!n.isToken){return“”}else{return n.data.join(“”)}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(//g,“”);this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(//g,“”);this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get(“display”)===“block”){n.className+=“ MJXp-display”}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues(“lspace”,“rspace”,“scriptlevel”,“displaystyle”,“largeop”);if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element(“span”,{className:“MJXp-largeop”});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join(“”)===“u222B”){p.className+=“ MJXp-int”}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data).length===1){var q=o.data,n=o.data;var s=this.data.join(“”),r;if(q&&this===q.CoreMO()&&o.Get(“accent”)){r=g.REMAPACCENT}else{if(n&&this===n.CoreMO()&&o.Get(“accentunder”)){r=g.REMAPACCENTUNDER}}if®{s=p.innerHTML=r}if(s.match(//)){this.PHTML.acc=-0.52}else{if(s===“u2192”){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get(“stretchy”)){return false}var r=this.data.join(“”);if(r.length>1){return false}r=g.DELIMITERS;var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get(“minsize”,true)||this.Get(“maxsize”,true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues(“symmetric”,“maxsize”,“minsize”);if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element(“span”,{style:{“font-size”:g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className=“MJXp-right MJXp-scale”+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues(“height”,“depth”,“width”);var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:“MJXp-box”,forceChild:true});var o=u.firstChild;var v=this.getValues(“width”,“height”,“depth”,“lspace”,“voffset”);var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==“”){s=this.PHTMLdimen(v.width,“w”,0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==“”){s=this.PHTMLdimen(v.height,“h”,0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==“”){s=this.PHTMLdimen(v.depth,“d”,0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==“”){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if®{o.style.marginRight=g.Em®}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o.charAt(0)]:(r?this.PHTML:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^/)}}});h.munderover.Augment({toPreviewHTML:function®{var t=this.getValues(“displaystyle”,“accent”,“accentunder”,“align”);var n=this.data;if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get(“movablelimits”))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,“msubsup”);return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:“”,noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element(“span”,{},[[“span”,{className:“MJXp-over”}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data?1:0)){q.firstChild.appendChild(r.firstChild)}this.data.PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize=“60%”;p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data.PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data){if(q.firstChild){q.insertBefore(e.Element(“span”),q.firstChild)}else{q.appendChild(e.Element(“span”))}}var s=this.data,p=this.data,n=this.data;if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=“.05em”;var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element(“span”,{className:“MJXp-script-box”,style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),“vertical-align”:g.Em(-u-p.PHTML.d*0.8)}},[[“span”,{},[[“span”,{},[[“span”,{style:{“margin-bottom”:g.Em(-(n.PHTML.d-0.05))}}]]]]],[“span”,{},[[“span”,{},[[“span”,{style:{“margin-top”:g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild®;t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function®{r=this.PHTMLdefaultSpan(r,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});var o=this.getValues(“linethickness”,“displaystyle”);if(!o.displaystyle){if(this.data){this.data.PHTMLhandleScriptlevel(r.firstChild)}if(this.data){this.data.PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element(“span”,{className:“MJXp-box”},[[“span”,{className:“MJXp-denom”},[[“span”,{},[[“span”,{className:“MJXp-rule”,style:{height:“1em”}}]]],[“span”]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||“0”,0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=“none”;u.style.borderBottom=(o.linethickness<0.15?“1px”:q)+“ solid”;u.style.margin=q+“ 0”;q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop=“-.7em”}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element(“span”,{className:“MJXp-surd”},[[“span”,{style:{“font-size”:q+“%”,“margin-top”:w}},[“u221A”]]]);var s=e.Element(“span”,{className:“MJXp-root”},[[“span”,{className:“MJXp-rule”,style:{“border-top”:“.08em solid”}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className=“MJXp-right MJXp-scale”+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild®;u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:“MJXp-box”,forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element(“span”),q.firstChild);n.className=“MJXp-script”;var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,“open”,{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,“sep”+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,“close”,{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild(“open”,o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild(“sep”+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild(“close”,o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className=“MJXp-mrow”;return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues(“columnalign”,“rowalign”,“columnspacing”,“rowspacing”,“columnwidth”,“equalcolumns”,“equalrows”,“columnlines”,“rowlines”,“frame”,“framespacing”,“align”,“width”);var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N=g.length2em(N)}for(F=0,A=w.length;F<A;F++){w=g.length2em(w)}var K=e.Element(“span”);while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data;if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.PHTML,q=v.PHTMLspanElement();q.style.verticalAlign=C;var B=(v.type===“mlabeledtr”?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data;if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.PHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data){this.data.toPreviewHTML(n);MathJax.Hub.Insert(this.data.PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h.Augment({toPreviewHTML:function(n){}});MathJax.Hub.Register.StartupHook(“onLoad”,function(){setTimeout(MathJax.Callback(),0)})});MathJax.Hub.Register.StartupHook(“End Cookie”,function(){if(b.config.menuSettings.zoom!==“None”){i.Require(“/extensions/MathZoom.js”)}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.PreviewHTML); (function(b,g,f){var c=b.config.menuSettings;var e=MathJax.OutputJax;var a=f.isMSIE&&(document.documentMode||0)<8;var d=MathJax.Extension={version:“2.7.5”,enabled:true,config:b.CombineConfig(“fast-preview”,{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:“inherit!important”,updateTime:30,updateDelay:6,messageStyle:“none”,disabled:f.isMSIE&&!f.versionAtLeast(“8.0”)}),Config:function(){if(b.config){MathJax.Hub.Config({“fast-preview”:b.config})}var m,j,k,h,l;var i=this.config;if(!i.disabled&&c.FastPreview==null){b.Config({menuSettings:{FastPreview:true}})}if(c.FastPreview){MathJax.Ajax.Styles({“.MathJax_Preview .MJXf-math”:{color:i.color}});b.Config({“HTML-CSS”:i.Chunks,CommonHTML:i.Chunks,SVG:i.Chunks})}b.Register.MessageHook(“Begin Math Output”,function(){if(!h&&d.Active()){m=b.processUpdateTime;j=b.processUpdateDelay;k=b.config.messageStyle;b.processUpdateTime=i.updateTime;b.processUpdateDelay=i.updateDelay;b.Config({messageStyle:i.messageStyle});MathJax.Message.Clear(0,0);l=true}});b.Register.MessageHook(“End Math Output”,function(){if(!h&&l){b.processUpdateTime=m;b.processUpdateDelay=j;b.Config({messageStyle:k});h=true}})},Disable:function(){this.enabled=false},Enable:function(){this.enabled=true},Active:function(){return c.FastPreview&&this.enabled&&!(e||{}).noFastPreview},Preview:function(h){if(!this.Active()||!h.script.parentNode){return}var i=h.script.MathJax.preview||h.script.previousSibling;if(!i||i.className!==MathJax.Hub.config.preRemoveClass){i=g.Element(“span”,{className:MathJax.Hub.config.preRemoveClass});h.script.parentNode.insertBefore(i,h.script);h.script.MathJax.preview=i}i.innerHTML=“”;i.style.color=(a?“black”:“inherit”);return this.postFilter(i,h)},postFilter:function(j,i){if(!i.math.root.toPreviewHTML){var h=MathJax.Callback.Queue();h.Push([“Require”,MathJax.Ajax,“/jax/output/PreviewHTML/config.js”],[“Require”,MathJax.Ajax,“/jax/output/PreviewHTML/jax.js”]);b.RestartAfter(h.Push({}))}i.math.root.toPreviewHTML(j)},Register:function(h){b.Register.StartupHook(h+“ Jax Require”,function(){var i=MathJax.InputJax;i.postfilterHooks.Add([“Preview”,MathJax.Extension],50)})}};d.Register(“TeX”);d.Register(“MathML”);d.Register(“AsciiMath”);b.Register.StartupHook(“End Config”,);b.Startup.signal.Post(“fast-preview Ready”)})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete(“/extensions/fast-preview.js”); (function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:“2.7.5”,config:b.CombineConfig(“AssistiveMML”,{disabled:false,styles:{“.MJX_Assistive_MathML”:{position:“absolute!important”,top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?“rect(1px 1px 1px 1px)”:“rect(1px, 1px, 1px, 1px)”),padding:“1px 0 0 0!important”,border:“0!important”,height:“1px!important”,width:“1px!important”,overflow:“hidden!important”,display:“block!important”,“-webkit-touch-callout”:“none”,“-webkit-user-select”:“none”,“-khtml-user-select”:“none”,“-moz-user-select”:“none”,“-ms-user-select”:“none”,“user-select”:“none”},“.MJX_Assistive_MathML.MJX_Assistive_MathML_Block”:{width:“100%!important”}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook(“End Math”,function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g)}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j<g;j++){l=document.getElementById(h.inputID+“-Frame”);if(l&&l.getAttribute(“data-mathml”)){l.removeAttribute(“data-mathml”);if(l.lastChild&&l.lastChild.className.match(/MJX_Assistive_MathML/)){l.removeChild(l.lastChild)}}}},HandleMML:function(l){var g=l.jax.length,h,i,n,j;while(l.i<g){h=l.jax;n=document.getElementById(h.inputID+“-Frame”);if(h.outputJax!==“NativeMML”&&h.outputJax!==“PlainSource”&&n&&!n.getAttribute(“data-mathml”)){try{i=h.root.toMathML(“”).replace(/n */g,“”).replace(/<!–.*?–>/g,“”)}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(,k.restart)}n.setAttribute(“data-mathml”,i);j=f.addElement(n,“span”,{isMathJax:true,unselectable:“on”,className:“MJX_Assistive_MathML”+(h.root.Get(“display”)===“block”?“ MJX_Assistive_MathML_Block”:“”)});try{j.innerHTML=i}catch(k){}n.style.position=“relative”;n.setAttribute(“role”,“presentation”);n.firstChild.setAttribute(“aria-hidden”,“true”);j.setAttribute(“role”,“presentation”)}l.i++}l.callback()}};b.Startup.signal.Post(“AssistiveMML Ready”)})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue([“Require”,MathJax.Ajax,“/extensions/toMathML.js”],[“loadComplete”,MathJax.Ajax,“/extensions/AssistiveMML.js”],function(){MathJax.Hub.Register.StartupHook(“End Config”,)}); !function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty©&&b.push©;return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+“/extensions/a11y”);var i=b={version:“1.5.0”,prefix:“”,defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b;c++){var d=i.MakeOption(a);void 0===e&&(e=i.defaults)}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules;e++)b=a.placeHolder;var f=d.FindId(“Accessibility”);if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId(“Settings”,“Renderer”)||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift(“Accessibility”);var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId(“Locale”);h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules;b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules;d++)e&&c.push(b.module);return c.length?a.Startup.loadArray©:null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:“”,name:,module:“”,placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,“”),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(,i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND([“OptionsWhenActive”,“(Options when Active)”],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue([“Require”,MathJax.Ajax,this.module,])},Enable:function(a){var b=MathJax.Extension;b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j(“collapsible”,“Collapsible Math”,“/collapsible.js”,“collapsible”)),i.Register(j(“autocollapse”,“Auto Collapse”,“/auto-collapse.js”,“auto-collapse”)),i.Register(j(“explorer”,“Explorer”,“/explorer.js”,“explorer”,!0)),i.AddDefaults(),a.Register.StartupHook(“End Extensions”,function(){a.Register.StartupHook(“MathMenu Ready”,function(){i.Startup(),a.Startup.signal.Post(“Accessibility Menu Ready”)},5)},5),MathJax.Hub.Register.StartupHook(“End Cookie”,function(){MathJax.Callback.Queue(,[“loadComplete”,MathJax.Ajax,“/accessibility-menu.js”])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete(“/config/TeX-MML-AM_HTMLorMML.js”);