/g,">");if(a.isMobile){q.document.open();q.document.write("MathJax Equation Source");q.document.write(""+u+"
");q.document.write("
");q.document.write("");q.document.close()}else{q.document.open();q.document.write("MathJax Equation Source");q.document.write("");q.document.write("");q.document.close();var s=q.document.body.firstChild;var r=(q.outerHeight-q.innerHeight)||30,p=(q.outerWidth-q.innerWidth)||30;p=Math.min(Math.floor(0.5*screen.width),s.offsetWidth+p+25);r=Math.min(Math.floor(0.5*screen.height),s.offsetHeight+r+25);q.resizeTo(p,r);if(t&&t.screenX!=null){var o=Math.max(0,Math.min(t.screenX-Math.floor(p/2),screen.width-p-20)),v=Math.max(0,Math.min(t.screenY-Math.floor(r/2),screen.height-r-20));q.moveTo(o,v)}}delete a.ShowSource.w};a.Scale=function(){var p=b["HTML-CSS"],o=b.NativeMML;var r=(p?p.config.scale:o.config.scale);var q=prompt("Scale all mathematics (compared to surrounding text) by",r+"%");if(q){if(q.match(/^\s*\d+\s*%?\s*$/)){q=parseInt(q);if(q){if(q!==r){if(p){p.config.scale=q}if(o){o.config.scale=q}a.cookie.scale=q;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){i.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var o=c.config.outputJax["jax/mml"];if(o[0]!==m.settings.renderer){e.Queue(["Require",i,"[MathJax]/jax/output/"+m.settings.renderer+"/config.js"],["Post",c.Startup.signal,m.settings.renderer+" output selected"],[function(){var r=b[m.settings.renderer];for(var q=0,p=o.length;q7;a.Augment({margin:20,msieBackgroundBug:(p||!q),msieAboutBug:p});if(document.documentMode>=9){delete m.styles["#MathJax_About"].filter;delete m.styles[".MathJax_Menu"].filter}},Firefox:function(o){a.skipMouseover=o.isMobile&&o.versionAtLeast("6.0");a.skipMousedown=o.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){m.settings=c.config.menuSettings;if(typeof(m.settings.showRenderer)!=="undefined"){m.showRenderer=m.settings.showRenderer}if(typeof(m.settings.showFontMenu)!=="undefined"){m.showFontMenu=m.settings.showFontMenu}if(typeof(m.settings.showContext)!=="undefined"){m.showContext=m.settings.showContext}a.getCookie();a.menu=a(k.SUBMENU("Show Math As",k.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),k.COMMAND("Original Form",a.ShowSource,{nativeTouch:true})),k.RULE(),k.SUBMENU("Math Settings",k.SUBMENU("Zoom Trigger",k.RADIO("Hover","zoom",{action:a.Zoom}),k.RADIO("Click","zoom",{action:a.Zoom}),k.RADIO("Double-Click","zoom",{action:a.Zoom}),k.RADIO("No Zoom","zoom",{value:"None"}),k.RULE(),k.LABEL("Trigger Requires:"),k.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),k.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),k.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),k.CHECKBOX("Shift","Shift")),k.SUBMENU("Zoom Factor",k.RADIO("125%","zscale"),k.RADIO("133%","zscale"),k.RADIO("150%","zscale"),k.RADIO("175%","zscale"),k.RADIO("200%","zscale"),k.RADIO("250%","zscale"),k.RADIO("300%","zscale"),k.RADIO("400%","zscale")),k.RULE(),k.SUBMENU("Math Renderer",{hidden:!m.showRenderer},k.RADIO("HTML-CSS","renderer",{action:a.Renderer}),k.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),k.SUBMENU("Font Preference",{hidden:!m.showFontMenu},k.LABEL("For HTML-CSS:"),k.RADIO("Auto","font",{action:a.Font}),k.RULE(),k.RADIO("TeX (local)","font",{action:a.Font}),k.RADIO("TeX (web)","font",{action:a.Font}),k.RADIO("TeX (image)","font",{action:a.Font}),k.RULE(),k.RADIO("STIX (local)","font",{action:a.Font})),k.SUBMENU("Contextual Menu",{hidden:!m.showContext},k.RADIO("MathJax","context"),k.RADIO("Browser","context")),k.COMMAND("Scale All Math ...",a.Scale),k.RULE().With({hidden:true}),k.CHECKBOX("Highlight on Hover","discoverable",{hidden:true})),k.RULE(),k.COMMAND("About MathJax",a.About),k.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(o){a.cookie.showRenderer=m.showRenderer=o;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!o};a.showFontMenu=function(o){a.cookie.showFontMenu=m.showFontMenu=o;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!o};a.showContext=function(o){a.cookie.showContext=m.showContext=o;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!o};if(a.isMobile){(function(){var p=m.settings;var o=a.menu.Find("Math Settings","Zoom Trigger").menu;o.items[0].disabled=o.items[1].disabled=true;if(p.zoom==="Hover"||p.zoom=="Click"){p.zoom="None"}o.items=o.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}e.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",i,m.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",i,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax);
MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(h){for(var g=0,f=this.data.length;g0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:b,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u02C9":e.ACCENT,"\u02CA":e.ACCENT,"\u02CB":e.ACCENT,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2118":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u27EE":e.OPEN,"\u27EF":e.CLOSE,"\u27FC":e.REL4,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+""+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""+e+">"},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h126){e[f]=""+h.toString(16).toUpperCase()+";"}else{var g={"&":"&","<":"<",">":">",'"':"""}[e[f]];if(g){e[f]=g}}}return e.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.MathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""+e+">"}});a.TeXAtom.Augment({toMathML:function(c){return c+"\n"+this.data[0].toMathML(c+" ")+"\n"+c+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");
(function(){var c="1.1.1";var a=MathJax.Hub.CombineConfig("TeX.noErrors",{multiLine:true,inlineDelimiters:["",""],style:{"font-family":"serif","font-size":"80%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var b="\u00A0";MathJax.Extension["TeX/noErrors"]={version:c,config:a};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){MathJax.InputJax.TeX.Augment({formatError:function(f,e,g,d){var i=a.inlineDelimiters;var h=(g||a.multiLine);if(!g){e=i[0]+e+i[1]}if(h){e=e.replace(/ /g,b)}else{e=e.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(e).With({isError:true,multiLine:h})}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Config",function(){MathJax.Hub.Config({"HTML-CSS":{styles:{".MathJax .merror":MathJax.Hub.Insert({"font-style":null,"background-color":null,"vertical-align":(MathJax.Hub.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})})})();MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var b=MathJax.OutputJax["HTML-CSS"];var c=a.math.prototype.toHTML;a.math.Augment({toHTML:function(d,e){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toHTML(d)}return c.call(this,d,e)}});a.merror.Augment({toHTML:function(j){if(!this.isError){return a.mbase.prototype.toHTML.call(this,j)}j=this.HTMLcreateSpan(j);if(this.multiLine){j.style.display="inline-block"}var l=this.data[0].data[0].data.join("").split(/\n/);for(var g=0,e=l.length;g1){var k=(n.h+n.d)/2,h=b.TeX.x_height/2;var f=b.config.styles[".MathJax .merror"]["font-size"];if(f&&f.match(/%/)){h*=parseInt(f)/100}j.parentNode.style.verticalAlign=b.Em(n.d+(h-k));n.h=h+k;n.d=k-h}j.bbox={h:n.h,d:n.d,w:d,lw:0,rw:d};return j}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Hub.Register.StartupHook("NativeMML Jax Ready",function(){var b=MathJax.ElementJax.mml;var a=MathJax.Extension["TeX/noErrors"].config;var c=b.math.prototype.toNativeMML;b.math.Augment({toNativeMML:function(d){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toNativeMML(d)}return c.call(this,d)}});b.merror.Augment({toNativeMML:function(g){if(!this.isError){return b.mbase.prototype.toNativeMML.call(this,g)}g=g.appendChild(document.createElement("span"));var h=this.data[0].data[0].data.join("").split(/\n/);for(var f=0,e=h.length;f1){g.style.verticalAlign="middle"}}for(var j in a.style){if(a.style.hasOwnProperty(j)){var d=j.replace(/-./g,function(i){return i.charAt(1).toUpperCase()});g.style[d]=a.style[j]}}return g}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");
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(d){var c=true,f=false,i,h=String.fromCharCode(160);var e=MathJax.Object.Subclass({Init:function(k){this.global={};this.data=[b.start().With({global:this.global})];if(k){this.data[0].env=k}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:i.TEXCLASS.ORD}],"\\|":["2225",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.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",c,0],textstyle:["SetStyle","T",f,0],scriptstyle:["SetStyle","S",f,1],scriptscriptstyle:["SetStyle","SS",f,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont",i.VARIANT.ITALIC],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.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",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.THINMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.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"],eqalign:["Matrix",null,null,"right left",i.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",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",i.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:["Macro","",1],nonumber:["Macro",""],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],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",i.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",i.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){g.macros[l]=["Macro",k[l]]}else{g.macros[l]=["Macro"].concat(k[l])}}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.id.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,q,m,k){var r=this.GetNext();if(r===""){d.Error("Missing argument for "+l)}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:c,arraydef:{rowspacing:(m||"4pt"),columnspacing:(q||"1em")}});if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=c}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(k){this.Push(b.cell().With({isEntry:c,name:k}))},Cr:function(k){this.Push(b.cell().With({isCR:c,name:k}))},HLine:function(l,m){if(m==null){m="solid"}var n=this.stack.Top();if(n.type!=="array"||n.data.length){d.Error("Misplaced "+l)}if(n.table.length==0){n.arraydef.frame=m}else{var k=(n.arraydef.rowlines?n.arraydef.rowlines.split(/ /):[]);while(k.lengthd.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var n=g.environment[m];if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(m,o,t,r,s,n,k,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){var l=(u.charAt(0)+u.charAt(u.length-1)).replace(/[^|:]/g,"");if(l!==""){q.arraydef.frame={"|":"solid",":":"dashed"}[l.charAt(0)];q.arraydef.framespacing=".5em .5ex"}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(k==="D"){q.arraydef.displaystyle=c}if(k==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=f}this.Push(m);return q},convertDelimiter:function(k){if(k){k=g.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.il.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",Translate:function(k){var l,n=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(MathJax.Hub.Browser.isKonqueror){n=n.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}var o=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);n=d.prefilterMath(n,o,k);try{l=d.Parse(n).mml()}catch(m){if(!m.texError){throw m}l=this.formatError(m,n,o,k)}if(l.inferred){l=i.apply(MathJax.ElementJax,l.data)}else{l=i(l)}if(o){l.root.display="block"}return this.postfilterMath(l,o,k)},prefilterMath:function(l,m,k){return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(m,l,n,k){return i.merror(m.message.replace(/\n.*/,""))},Error:function(k){throw MathJax.Hub.Insert(Error(k),{texError:c})},Macro:function(k,l,m){g.macros[k]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(l){for(var n=0,k=l.data.length;n0){align+="rl";spacing.push("0em 0em");j--}spacing=spacing.join(" ");if(g){return this.AMSarray(i,h,g,align,spacing)}return this.Array(i,null,null,align,spacing,".5em","D")},MultiIntegral:function(g,k){var j=this.GetNext();if(j==="\\"){var h=this.i;j=this.GetArgument(g);this.i=h;if(j==="\\limits"){if(g==="\\idotsint"){k="\\!\\!\\mathop{\\,\\,"+k+"}"}else{k="\\!\\!\\!\\mathop{\\,\\,\\,"+k+"}"}}}this.string=k+" "+this.string.slice(this.i);this.i=0},xArrow:function(i,m,k,g){var j={width:"+"+(k+g)+"mu",lspace:k+"mu"};var n=this.GetBrackets(i),o=this.ParseArg(i);var p=a.mo(a.chars(String.fromCharCode(m))).With({stretchy:true,texClass:a.TEXCLASS.REL});var h=a.munderover(p);h.SetData(h.over,a.mpadded(o).With(j).With({voffset:".15em"}));if(n){n=f.Parse(n,this.stack.env).mml();h.SetData(h.under,a.mpadded(n).With(j).With({voffset:"-.24em"}))}this.Push(h)},GetDelimiterArg:function(g){var h=this.trimSpaces(this.GetArgument(g));if(h==""){return null}if(!c.delimiter[h]){f.Error("Missing or unrecognized delimiter for "+g)}return this.convertDelimiter(h)}});d.multline=d.array.Subclass({type:"multline",EndEntry:function(){var g=a.mtd.apply(a,this.data);if(this.data.shove){g.columnalign=this.data.shove}this.row.push(g);this.data=[]},EndRow:function(){if(this.row.length!=1){f.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 h=this.table.length-1,j;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=a.ALIGN.LEFT}if(!this.table[h][0].columnalign){this.table[h][0].columnalign=a.ALIGN.RIGHT}var g=a.mtr;if(this.global.tag){this.table[0]=[this.global.tag].concat(this.table[0]);delete this.global.tag;g=a.mlabeledtr}this.table[0]=g.apply(a,this.table[0]);for(j=1,h=this.table.length;j]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?\s*$/,"$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